Emergence of Functional Circuits in the Early Visual Pathway (KAIST Research Series) 9811900302, 9789811900303

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KAIST Research Series

Jaeson Jang Se-Bum Paik

Emergence of Functional Circuits in the Early Visual Pathway

KAIST Research Series Series Editors Byung Kwan Cho, Department of Biological Sciences, KAIST, Daejeon, Taejon-jikhalsi, Korea (Republic of) Han Lim Choi, Department of Aerospace Engineering, KAIST, Daejeon, Taejon-jikhalsi, Korea (Republic of) Insung S. Choi, Department of Chemistry, KAIST, Daejeon, Korea (Republic of) Sung Yoon Chung, Graduate School of EEWS, KAIST, Daejeon, Korea (Republic of) Jae Seung Jeong, Department of Bio and Brain Engineering, KAIST, Daejeon, Korea (Republic of) Ki Jun Jeong, Department of Chemical and Biomolecular Engineering, KAIST, Daejeon, Korea (Republic of) Sang Ouk Kim, Department of Materials Science and Engineering, KAIST, Daejeon, Korea (Republic of) Chongmin Kyung, School of Electrical Engineering, KAIST, Daejeon, Korea (Republic of) Sung Ju Lee, School of Computing, KAIST, Daejeon, Korea (Republic of) Bumki Min, Department of Mechanical Engineering, KAIST, Daejeon, Korea (Republic of)

More information about this series at https://link.springer.com/bookseries/11753

Jaeson Jang · Se-Bum Paik

Emergence of Functional Circuits in the Early Visual Pathway

Jaeson Jang Department of Bio and Brain Engineering Korea Advanced Institute of Science and Technology Daejeon, Korea (Republic of)

Se-Bum Paik Department of Bio and Brain Engineering Program of Brain and Cognitive Engineering Korea Advanced Institute of Science and Technology Daejeon, Korea (Republic of)

ISSN 2214-2541 ISSN 2214-255X (electronic) KAIST Research Series ISBN 978-981-19-0030-3 ISBN 978-981-19-0031-0 (eBook) https://doi.org/10.1007/978-981-19-0031-0 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

To our families

Preface

In South Korea, young males are obliged to perform military service for around two years, unless their services are exempted for a reasonable reason or substituted by other services considering their expertise. One of the ways to be substituted is being selected by the government to work on a doctoral program for science or engineering. Although it was available to be selected for this exemption with my undergraduate major, I did not consider entering graduate school until the beginning of my senior year of the undergraduate course. My rough plan was to join the military service after the spring semester of the year and then look for a job after completing the military service. However, from that spring semester, professor Se-Bum Paik joined our department and opened the course entitled “Computational Neuroscience.” Truly, it was my first time to enjoy doing homework or assignment until the late-night. Therefore, I canceled my previous plan to join the military service and applied for a doctoral program in Prof. Paik’s Laboratory. Fortunately, Prof. Paik welcomed three other students and me, and I stayed for six and a half years as a graduate student. This book was written to summarize and introduce several results I have obtained during my doctoral program. Introducing every face of computational neuroscience, which should include the early works developing the integrate and fire model [1, 2] or the early definition of computational neuroscience [3], is certainly beyond my ability and the given space. Instead, I hope to compile my previous results and to suggest an example of the role of computational neuroscience that might provide new insight into the advancement of artificial intelligence. When I introduced myself as a neuroscientist to normal people, one of the common first questions that I got from them was whether I have experience dissecting mice. As people are reminded, most neuroscience studies are performed by experiments using various animal models, including fruit flies, mice, cats, monkeys, and humans. Showing results of the well-controlled experiments is a very powerful methodology to validate the own hypothesis about the neural system. However, for some assumptions, it is not easy to examine using animal experiments, considering the amount of resources that have to be devoted to experiments. For example, animals obtain intelligence as they develop into adulthood. Thus, “How vii

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neural circuits initiate the intelligence” has been one of the central questions in neurobiology, as well as in machine learning. As artificial neural networks can obtain intelligence with a well-designed training process, it has been commonly believed that learning or training processes refine the neural connections, resulting in the emergence of cognitive functions. However, several cognitive functions such as the orientation tuning or the number sense are already observed in newborn animals, suggesting the role of another developmental mechanism of functions that can apply without the sufficient refinement of recurrent cortical circuits. Regarding this issue, my team and I demonstrated model simulations that functional organizations in the visual cortex [4–6] and the number sense in deep neural networks [7] could be solely and spontaneously initiated by the untrained feedforward projections, without any visual experience or learning process. These findings suggest that cognitive functions can emerge spontaneously from the statistical properties of bottom-up projections in hierarchical neural networks. In this book, my earlier works related to the visual cortex will be introduced. I hope this book could arouse your interest in computational neuroscience, as I was intrigued by Prof. Paik’s course seven years ago. In Autumn of 2021 when the end of the coronavirus outbreak is nearly seen, Daejeon, Korea (Republic of)

Jaeson Jang

Mencius said, “A wise man has three delights … That he can get the most talented individuals, and teach and nourish them; this is the third delight.” Se-Bum Paik

References 1. 2.

3. 4.

5. 6.

7.

Lapique L (1907) Recherches quantitatives sur l’excitation electrique des nerfs traitee comme une polarization. J Physiol Pathololgy 9:620–635 Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544. https://doi.org/ 10.1113/jphysiol.1952.sp004764 Schwartz EL (1993) Computational neuroscience. Mit Press Jang J, Paik S-B (2017) Interlayer repulsion of retinal ganglion cell mosaics regulates spatial organization of functional maps in the visual cortex. J Neurosci 37:12141–12152. https://doi. org/10.1523/JNEUROSCI.1873-17.2017 Song M, Jang J, Kim G, Paik S-B (2021) Projection of orthogonal tiling from the retina to the visual cortex. Cell Rep 34:108581. https://doi.org/10.1016/j.celrep.2020.108581 Jang J, Song M, Paik S-B (2020) Retino-cortical mapping ratio predicts columnar and saltand-pepper organization in mammalian visual cortex. Cell Rep 30:3270-3279.e3. https://doi. org/10.1016/j.celrep.2020.02.038 Kim G, Jang J, Baek S, Song M, Paik S-B (2021) Visual number sense in untrained deep neural networks. Sci Adv 7:1–10. https://doi.org/10.1126/sciadv.abd6127

Acknowledgements

The biggest lesson from these research experiences was that “repeatedly insisting” is not recommended attitude of a researcher, but “proposing the logic that could not be denied” is required. Through an intense reviewing process for publications, I could learn how to persuade the hostile opponent. Most of our reviewers were already familiar with the previous models about the role of recurrent cortical circuits, so they initially hesitated to accept our model focusing on feedforward afferents. After several rejections and the final acceptance, I realized that just repeatedly explaining the same idea in different ways could not derive persuasion, but multiple steps of a small advance of logic with supports—that even the critical opponent could not deny—should be presented one by one. Probably, I expect that this realization would help me more than neurological knowledge. Doctoral training was SLIGHTLY more difficult than I had previously expected. Therefore, I would not have overcome such a difficult time if there was no help and encouragement from many people. To express an immeasurable debt of gratitude as much as I want, numerous pages that could be made into another book will be required. Because of the limitation in the number of pages, I summarized and summarized in a few pages to thank my colleagues. First of all, I would like to thank Prof. Se-Bum Paik for his endless encouragement, even though I had continuously disappointed him as a researcher. Thanks to his advice, I could expand the boundary of the knowledge of human society a bit. Not only the scientific knowledge but also the lesson about the responsibility as an expert made a deep impression and will be remembered for the rest of my life. Although much of my ability as a researcher was still insufficient, Dr. Min Whan Jung, Dr. Seung-Hee Lee, Dr. Yong Jeong, and Dr. Jaeseung Jeong in my committee have added a lot of meaning to my research. I will do my best to be a researcher who deserves their valuable lessons. I also went through ups and downs with Pachaya Sailamul, Min Song, and Gwangsu Kim, who were the co-first authors of my papers. I learned a lot of skills and lessons from them and am hoping that they also learned something from me. Soyoung An led my early steps in the laboratory in a number of aspects. Dr. Woochul Choi and I have followed a similar process in the doctoral program for a long time, ix

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and he has continuously reminded me of the beauty of science. I was an ineffectual senior in the laboratory, so I have felt sorry for Changju Lee, Hyeonsu Lee, Youngjin Park, Chaeyoon Jung, and Seungdae Baek. Jun Ho Song opened my eyes to a world outside of Daejeon. The administrative support of Jinhee Kim was much more careful than my research. Most of all, I would like to thank my parents for their endless encouragement. I will do my best to be a proud son who will sometimes be in a newspaper, definitely with good news. Latin Pub CUBA Gangnam

Jaeson Jang

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Opening Remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Neuronal Tuning in Visual Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Early Visual Pathway—Feedforward Circuits . . . . . . . . . . . . 1.2.2 Cortical Organization of Orientation Selectivity . . . . . . . . . . 1.2.3 Previous Developmental Models . . . . . . . . . . . . . . . . . . . . . . . 1.3 Functional Architectures of Visual Cortex . . . . . . . . . . . . . . . . . . . . . . 1.3.1 Periodicity of Visual Tuning Maps . . . . . . . . . . . . . . . . . . . . . . 1.3.2 Orthogonal Organization of Visual Tuning Maps . . . . . . . . . 1.3.3 Salt-And-Pepper Organization in Rodents . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 2 4 7 11 11 15 17 20

2 Topographical Consistency of Cortical Maps . . . . . . . . . . . . . . . . . . . . . . 2.1 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 Development of Hexagonal RGC Mosaics . . . . . . . . . . . . . . . 2.2.2 ON and OFF RGC Mosaics Alignment . . . . . . . . . . . . . . . . . . 2.2.3 Repulsive Energy Between RGC Mosaics . . . . . . . . . . . . . . . 2.3 Homotypic Repulsive Interaction for Hexagonal RGC Mosaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Heterotypic Interaction for Aligned RGC Mosaics . . . . . . . . . . . . . . . 2.5 Heterotypic Interaction in RGC Mosaics Data . . . . . . . . . . . . . . . . . . 2.6 Robustness of Model Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Limitation of Model Validation from Available RGC Data . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25 25 26 26 29 29 30 32 36 38 41 47

3 Orthogonal Organization of Visual Cortex . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Analysis of RGC Mosaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Analysis of Multi-electrode Recordings . . . . . . . . . . . . . . . . . 3.2.3 Autocorrelation of Cortical Functional Maps . . . . . . . . . . . . .

51 51 55 55 56 56 xi

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3.3 Orthogonal Organization of ON and OFF RGC Mosaics . . . . . . . . . 3.4 Topographic Correlation of ON/OFF Feedforward Projections . . . . 3.5 Retinal Origin of Orthogonal Organization . . . . . . . . . . . . . . . . . . . . . 3.6 Hexagonal Topography of Cortical Tuning Maps . . . . . . . . . . . . . . . . 3.7 Development of Quasi-Periodic Maps in Realistic Conditions . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57 58 64 66 68 71

4 Parametric Classifications of Cortical Organization . . . . . . . . . . . . . . . 4.1 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Analysis of Anatomical Data of Diverse Mammalian Species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Connectivity and Receptive Field Models . . . . . . . . . . . . . . . . 4.3 Failure of Prediction from Single Anatomical Parameters . . . . . . . . . 4.4 Prediction from Retino-Cortical Mapping Ratio . . . . . . . . . . . . . . . . . 4.5 Model Simulation for Parametric Division of V1 Organization . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75 75 79

5 Discussion: Biological Plausibility of the Model . . . . . . . . . . . . . . . . . . . 5.1 Local Repulsion for Development of Hexagonal Mosaics . . . . . . . . . 5.2 Initialization of V1 Tunings from Magnocellular and Contralateral Pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Functional Implication of Disparate V1 Organizations . . . . . . . . . . . 5.4 Emergence of Visual Tunings in Untrained Artificial Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Concluding Remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79 80 81 82 86 90 95 95 100 105 108 110 110

Curriculum Vitae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

Abbreviations and Symbols

cpd DNN IPL LGN OI OSI PIPP PN RF RGC V1 α θ Φ

Cycle per degree Deep neural network Inner plexiform layer Lateral geniculate nucleus Orthogonality index Orientation selectivity index Pairwise interaction point process Preferred numerosity Receptive field Retinal ganglion cell Primary visual cortex Lattice distance ratio Alignment angle Retino-cortical mapping ratio

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List of Figures

Fig. 1.1 Fig. 1.2 Fig. 1.3 Fig. 1.4 Fig. 1.5 Fig. 1.6 Fig. 1.7 Fig. 1.8 Fig. 1.9 Fig. 1.10 Fig. 1.11 Fig. 1.12 Fig. 1.13 Fig. 1.14 Fig. 2.1 Fig. 2.2 Fig. 2.3 Fig. 2.4 Fig. 2.5 Fig. 2.6 Fig. 2.7

Structure of the retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structure of the early visual pathway . . . . . . . . . . . . . . . . . . . . . . . Response dynamics of center-surround ON and OFF RGCs . . . . Orientation selectivity of response of V1 neurons . . . . . . . . . . . . Orientation maps in V1 of diverse mammalian species . . . . . . . . Bandpass-filtered model for development of orientation map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clustered ON/OFF retinotopy of neighboring V1 neurons . . . . . Statistical wiring model for development of orientation selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neurons in the LGN relay the receptive field of a few RGCs . . . Paik-Ringach model for development of orientation map . . . . . . Consistency of orientation map periods in a same species . . . . . . Retinal origin of cortical orientation map and its variation of spatial organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthogonal organization among diverse functional maps in V1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Columnar orientation map and salt-and-pepper organization of orientation tuning . . . . . . . . . . . . . . . . . . . . . . . . . Model of local repulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeled process of mosaic development modulated by local repulsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tiling in a mosaic initiated by a local repulsion . . . . . . . . . . . . . . Local repulsive interaction can develop hexagonal patterns in a monotypic cell mosaic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heterotypic interaction can align both ON and OFF RGCs in a similar alignment angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Searching the amount of rotation and linear expansion in ON and OFF mosaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heterotypic interaction can restrict the angle alignment (θ ) between ON and OFF mosaics . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 4 5 6 8 9 10 11 12 13 14 17 18 19 27 28 31 32 33 34 35 xv

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Fig. 2.8 Fig. 2.9 Fig. 2.10 Fig. 2.11 Fig. 2.12 Fig. 2.13 Fig. 2.14 Fig. 2.15 Fig. 2.16 Fig. 2.17 Fig. 3.1 Fig. 3.2 Fig. 3.3

Fig. 3.4 Fig. 3.5 Fig. 3.6 Fig. 3.7 Fig. 3.8 Fig. 3.9 Fig. 3.10 Fig. 3.11 Fig. 3.12 Fig. 3.13 Fig. 3.14 Fig. 4.1

List of Figures

Restricted mosaics alignment with the heterotypic interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Repulsive energy map devised to investigate the existence of heterotypic interactions in mosaic data . . . . . . . . . . . . . . . . . . . Sample ON and OFF mosaics and their energy map . . . . . . . . . . Observed evidence of heterotypic interactions in animal data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Repulsive interaction function defined by the different forms of decaying functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Consistency of results with different forms of repulsive function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sample mosaics developed by the original interaction form for different interaction ranges, R . . . . . . . . . . . . . . . . . . . . . . . . . Consistency of results with spatial noise in mosaics . . . . . . . . . . Level of long-range hexagonal periodicity similar to that of the measured mosaics . . . . . . . . . . . . . . . . . . . . . . . . . . . Observed RGC mosaics can develop interference patterns, depending on the size of the mosaics . . . . . . . . . . . . . . . . . . . . . . . Orthogonal organization of cortical functional maps . . . . . . . . . . Efficient tiling of diverse tuning in V1 . . . . . . . . . . . . . . . . . . . . . Spatial organization of ON and OFF RGCs might be mirrored to V1 and induces orthogonal tiling of a neural tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Obtaining autocorrelation of measured functional map data . . . . Orthogonal organization between ON–OFF angle and distance in measured RGC mosaic data . . . . . . . . . . . . . . . . . Orthogonal organization between ON–OFF angle and distance in multiple RGC mosaic data . . . . . . . . . . . . . . . . . . Orthogonal tiling of neural tunings in V1 that is mirrored from the orthogonal organization in the retina . . . . . . . . . . . . . . . Receptive fields and functional tunings recorded across the cortical surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Topographic correlation between ON–OFF angle/distance and diverse cortical tunings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthogonal organization in moiré interference pattern of ON and OFF RGC mosaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthogonal organization under realistic conditions of model RGC mosaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hexagonal periodicity of functional maps . . . . . . . . . . . . . . . . . . . Quasi-periodic orientation map seeded by a continuous distribution of local retinal patches . . . . . . . . . . . . . . . . . . . . . . . . Variation of alignment axis in measured orientation maps . . . . . . Columnar orientation map and salt-and-pepper organization observed in mammalian species . . . . . . . . . . . . . . . .

36 37 39 40 41 42 43 44 45 46 52 53

54 57 59 60 61 62 63 64 65 67 69 70 76

List of Figures

Fig. 4.2 Fig. 4.3 Fig. 4.4 Fig. 4.5 Fig. 4.6 Fig. 4.7 Fig. 4.8 Fig. 4.9 Fig. 5.1 Fig. 5.2 Fig. 5.3 Fig. 5.4 Fig. 5.5 Fig. 5.6

Failure of predicting V1 organization from single anatomical parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Revisiting the spectrum of single anatomical parameters . . . . . . . Parametric division of species based on retino-cortical size ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parametric division of species based on retino-cortical cell number ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeled retino-cortical pathways for different mapping conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Variation of V1 organizations with retino-cortical mapping conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Difference between the preferred orientation of neighboring V1 neurons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A single biological factor predicts distinct cortical organizations across mammalian species . . . . . . . . . . . . . . . . . . . Hexagonal patterns observed in the density map of RGC mosaics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Density recovery profiles of RGC mosaic data . . . . . . . . . . . . . . . Flip of preferred direction at the center of iso-orientation domains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Direction preference aligned with ON-to-OFF or OFF-to-ON directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Weak inter-map relationships between the luminance map and other maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two different definitions of visual acuity that have been interchangeably used in previous studies . . . . . . . . . . . . . . . . . . . .

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77 83 84 85 87 88 89 90 97 98 102 103 104 106

List of Tables

Table 1.1 Table 4.1

Table 4.2

Table 4.3

Table 4.4

Orientation map periods are consistent across animals of a same species . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Retino-cortical size ratio and related experimental data on the retina and V1 anatomy in species having columnar orientation maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Retino-cortical size ratio and related experimental data on the retina and V1 anatomy in species having salt-and-pepper organizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . Retino-cortical cell number ratio and related experimental data on the retina and V1 anatomy in species having columnar orientation maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Retino-cortical cell number ratio and related experimental data on the retina and V1 anatomy in species having salt-and-pepper organizations . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

78

78

79

79

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“The pathway between the eye to the cortex” (© 2021. Jaeson Jang all rights reserved.)

Chapter 1

Introduction

Understanding the developmental mechanism of functional organizations in the visual pathway has provided insight into the emergence of intelligence in the brain. For example, as the functional unit encoding the elementary visual cue, neurons in the primary visual cortex (V1) are tuned to the orientation of visual stimuli. The preferred orientation of these neurons is arranged quasi-periodically across the cortical surface, termed an orientation map. Previously, most studies on the developmental mechanism of these functional organizations have focused on the intra-cortical developmental mechanism modulated by the visual experience. However, several functional organizations have been observed in early developmental stages even before the visual experience, implying that the emergence of these organizations may be initiated by another fundamental mechanism that can operate without any visual experience. Using a computer simulation of the neural network, we show that the emergence of functional organizations could be spontaneously initiated by the haphazard wiring of feedforward projections, even in the absence of any further refinement of neural circuits. In this chapter, the background and related questions examined in our studies will be introduced.

1.1 Opening Remark How do functional organizations arise in the visual pathway of the brain? Understanding the developmental mechanism of these functional organizations has provided insight into the emergence of intelligence in the brain. Regarding this issue, most previous studies have focused on the intra-cortical developmental mechanism modulated by the postnatal cortical activity triggered by visual experience. However, several functional organizations have been observed in early developmental stages even before the visual experience, implying that the emergence of these circuits may be initiated by a more fundamental mechanism that can operate without any visual experience. Inspired by previous studies of the retinal origin of orientation selectivity in the primary visual cortex (V1) [1–4], the purpose of this book is to suggest that the © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J. Jang and S.-B. Paik, Emergence of Functional Circuits in the Early Visual Pathway, KAIST Research Series, https://doi.org/10.1007/978-981-19-0031-0_1

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emergence of diverse functional organizations in the visual pathway could be spontaneously and solely initiated by the haphazard wiring of feedforward neural circuits, providing insight into the developmental principle of the brain, as well as into the advance in machine learning. This book will address how the retino-cortical feedforward mapping of ON and OFF retinal afferents solely initiates the main characteristics of functional maps in V1, including the consistency of spatial periods across animals (Chap. 2), the systematic organization of diverse functional maps (Chap. 3), and the development of disparate organizations across species (Chap. 4). The simulation in Chap. 2 will address the mechanism of how a simple repulsive interaction between nearby retinal cells develops a restricted interference pattern of ON and OFF cell mosaics, which seeds the spatial periodicity of orientation maps so that maps in different animals of the same species develop to have a consistent spatial period. The contents were adapted from Jang & Paik (2017) Interlayer repulsion of retinal ganglion cell mosaics regulates spatial organization of functional maps in the visual cortex. Journal of neuroscience 37:12,141–12,152 [5]. In Chap. 3, the mechanism of how the orthogonal organization among diverse functional tunings in V1 could be initiated by the projection of the structure of retinal cell mosaics will be introduced. The contents were adapted from Jang*, Song*, Kim and Paik (2021) Projection of orthogonal tiling from the retina to the visual cortex. Cell Reports 34:108,581 [6]. In Chap. 4, the mechanism of how different conditions of retino-cortical mapping across species initiate two disparate organizations of orientation tuning observed in mammalian species will be addressed. The contents were adapted from Jang*, Song* and Paik (2020) Retino-cortical mapping ratio predicts columnar and saltand-pepper organization in mammalian visual cortex. Cell Reports 30:3270–3279.e3 [7]. All adaptations of the contents were permitted by all the authors who have copyright and * indicates co-first authors.

1.2 Neuronal Tuning in Visual Cortex 1.2.1 Early Visual Pathway—Feedforward Circuits When visual input first enters the eyes, the signal is sequentially processed by the retina in the eye, the lateral geniculate nucleus (LGN) in the thalamus, and the primary visual cortex (V1) in the occipital lobe. In this section, the anatomy and function of neurons from the retina to V1 will be briefly introduced. In the eye, the visual signal is sequentially processed by several types of cells in the retina (Fig. 1.1). First, photoreceptors convert light, which is visible electromagnetic radiation, into biological signals. Two classic types of photoreceptors are rods and cones, where rods and cones primarily contribute to the scotopic and photopic vision, respectively. After the light is first encoded by photoreceptors, the signal is further

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Fig. 1.1 Structure of the retina. After the light is first encoded by photoreceptors (rods and cones), the signal is further processed by other types of retinal cells (horizontal, bipolar, and amacrine cells) and finally provided as inputs for retinal ganglion cells (RGCs). a Illustrated version. b Real image version. The illustration and image were adapted from the work of OpenStax College [10] under the allowance of the license

processed by other types of retinal cells (horizontal, bipolar, and amacrine cells) and finally provided as inputs for retinal ganglion cells (RGCs). Among these diverse types of retinal cells, the introduction will focus on RGC, which is the final stage of the retina and provides the visual input to further brain regions through the optic nerves. The majority of RGCs innervate the lateral geniculate nucleus (LGN) in the

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Fig. 1.2 Structure of the early visual pathway. The majority of RGCs innervate the lateral geniculate nucleus (LGN) in the thalamus, which is a relay center for the early visual pathway. Most neurons of the LGN directly send their axons to the primary visual cortex, which is the first stage of visual processing in the cortex. The illustration was adapted from the work of Miquel Perello Nieto [11] under the allowance of the license

thalamus, which is a relay center for the early visual pathway. Most neurons of the LGN directly send their axons to the primary visual cortex, which is the first stage of visual processing in the cortex (Fig. 1.2). The visual function of neuron in each region can be examined by measuring the receptive field (RF) of neurons, which indicate the structure of the visual stimulus that elicits the neuron response [8]. Most RGCs and neurons in the LGN have receptive fields that consist of two concentric circles of different sizes, termed center-surround organization [9]. These two circles have opposite polarities among ON or OFF, where ON and OFF, respectively indicate the region activated by light and dark stimulus (Fig. 1.3). For example, ON-center RGC is maximally activated by light spots surrounded by the dark background and vice versa.

1.2.2 Cortical Organization of Orientation Selectivity While most RGCs and neurons in LGN have center-surround receptive fields that function as a light (or darkness) detector, neurons in V1 have much more diverse

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Fig. 1.3 Response dynamics of center-surround ON and OFF RGCs. Yellow indicates the light stimulus, whereas purple indicates the absence of stimulus (or dark stimulus). ON-center and OFF-surround RGC (left) is highly activated when only the center part of the receptive field is activated, while OFF-center and ON-surround RGC is highly activated when only the surround part of the receptive field is activated or a dark stimulus is provided to the center part. The illustration was adapted from the work of Delldot [12] under the allowance of the license

and complicated receptive fields. As the first characterization of receptive fields of neurons in V1, it was observed that some neurons in V1 have elongated subregions of different polarities (Fig. 1.4) [13]. This organization of receptive fields enables neurons to selectively respond to visual stimuli tilted at a certain orientation. For example, if a light bar stimulus aligned to the axis of elongation is given, the neuron would generate a strong response when the stimulus passes on the ON subregion. On the other hand, if a light bar stimulus aligned to the orthogonal direction from the axis of elongation is given, the neuron would generate a weak response because the activation by the ON subregion and the inactivation by the OFF subregion will be canceled against each other. This property was termed orientation selectivity or orientation preference and has been extensively studied with diverse mammalian species as the fundamental function in the visual processing.

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Fig. 1.4 Orientation selectivity of response of V1 neurons. a Orientation-selective response of a V1 neuron. The neuron selectively responds to an optimally oriented stimulus. b Developmental mechanism of the orientation selectivity of a V1 neuron. Hubel and Wiesel (1962) suggested that V1 neurons having orientation preference might receive inputs from LGN neurons having receptive fields arranged along a straight line on the retina [13]. The illustration was adapted from Hubel and Wiesel (1962) [13], under the permission of the copyright holder (© 1962 The Physiological Society)

The advance in the intrinsic optical imaging techniques enabled the simultaneous recording of the orientation preference across the two-dimensional cortical surface [14]. Previously, the neural response to the visual stimulus was usually recorded by single or multiple electrodes at a certain distance. In contrast, intrinsic optical imaging is an imaging method that indirectly records neural activity in a given region by measuring hemodynamic variation initiated by dynamic neural activities [15]. In detail, an external light source is provided onto the cortical surface to examine the spectral absorption property, which varies across oxygenated and deoxygenated hemoglobin [16]. If neural activity around a cortical location is activated, it initiates the deoxygenation of hemoglobin. After then, blood flow is provided and initiates the oxygenation of hemoglobin [17]. This process could be detected by using multiple light sources having different wavelengths. When two light sources are used, one (600–699 nm) targets to monitor deoxygenated hemoglobin and the other (500– 599 nm) targets to monitor blood flow and oxygenated hemoglobin [15]. In higher mammals such as monkeys or cats, these methods have revealed that preferred orientation continuously changes in a quasi-periodic manner, resulting in a columnar organization [18, 19]. Further studies also reported point and line discontinuities (orientation pinwheels and linear fractures) of preferred orientation between

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columnar structures, and these functional neural circuits were termed orientation map (Fig. 1.5) [20, 21]. As the first stage of visual processing in the visual cortex, how such functional circuits could be generated in V1 has been considered as one of the major questions to be solved in order to understand the developmental mechanism of visual functions, whereas it is not completely understood how such periodic organization is initially developed [22–24].

1.2.3 Previous Developmental Models When the orientation selectivity in V1 was first observed, it was suggested that the elongated ON and OFF subregions of the receptive field originate from the ordered arrangement of ON- and OFF-center LGN inputs mapped onto the appropriate retinotopic locations [13] (Fig. 1.4). This circuity was supported by further experimental studies measuring the connectivity between LGN and V1 neurons, reporting that the probability of thalamocortical connection increases as the LGN receptive field largely overlaps with the subregion of the cortical receptive field of the same polarity and vice versa [28, 29]. Based on this notion, much effort has been devoted to suggest a theoretical model for the developmental mechanism of the orientation selectivity, as well as the orientation map. Most of the previous models were built on the assumption that the selective wiring of LGN afferents and the quasi-periodic structure of orientation map are generated by the intra-cortical mechanism—the interaction between neurons in V1. For example, in the bandpass-filtered model, it was suggested that the orientation selectivity of V1 neurons were initially arranged in a disordered manner, but the spatial interaction between nearby neurons with a band-pass kernel initiates the emergence of spatial periodicity in the orientation map [30] (Fig. 1.6). In the essentially complex planforms model, it was suggested that the asymmetric interaction between nearby neurons across the cortical surface generates the periodic pattern observed in the orientation map [31]. Although these models could reconstruct the quasi-periodic pattern of the orientation map, their mathematical assumptions were hardly designed based on biological observation, so the developmental mechanism of the periodicity in the orientation map could be completely understood. Another model was built on a more biologically plausible assumption about a “Mexican-hat” interaction, in which the activation of a cortical location activates nearby neurons and suppresses more distant neurons [32]. However, in further experimental studies, it was reported that the interaction was simply fall-off-shaped, rather than Mexican-hat-shaped [33], so the developmental mechanism of the orientation map has not been completely understood by the above models. Considering that most of the theoretical models do not completely explain the developmental mechanism of the orientation map, new theoretical notions have been proposed to modify the underlying assumptions of the models. Important clues have been found in the observation that cortical orientation tuning originates from feedforward afferents, rather than intra-cortical mechanisms. It was reported that orientation

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Fig. 1.5 Orientation maps in V1 of diverse mammalian species. Preferred orientation changes quasi-periodically across the cortical surface. a Monkey data were adapted from [19]. b Cat data were adapted from [25]. c Tree shrew data were adapted from [26]. d Ferret data were adapted from [27], under the permission of the copyright holders (© 1986, Nature Publishing Group, © 1997 Society for Neuroscience, © 1997 Society for Neuroscience, © 1996 Society for Neuroscience, respectively)

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Fig. 1.6 Bandpass-filtered model for development of orientation map. It was suggested that the orientation selectivity of V1 neurons was initially arranged in a disordered manner, but the spatial interaction between nearby neurons with a band-pass kernel initiates the emergence of spatial periodicity in the orientation map. Images were adapted from Rojer and Schwartz (1990) [30], under the permission of the copyright holder (© 1990, Springer-Verlag)

tuning in V1 is predictable from the local average of ON and OFF thalamic afferents [34]. Although feedforward thalamic inputs are a small portion of the total inputs [35], earlier work reported that the orientation tuning of V1 neurons originates from this feedforward pathway and the orientation preference of a V1 neuron remains consistent when the recurrent cortical circuits are silenced [36–38]. At larger scales, it was reported that the continuous change of orientation tuning across the cortical surface is strongly correlated with the spatial alignment of ON and OFF receptive fields in cats and tree shrews [39, 40] (Fig. 1.7). Considering that the ON and OFF topology in V1 originates from thalamic afferents [34] and given that most thalamic neurons relay retinal afferents [41], these results suggest that neighboring V1 neurons receive ON and OFF retinal inputs from a similar population of nearby RGCs. Therefore, these observations altogether suggest that orientation tuning in the cortical neurons originates from the spatial organization of ON and OFF feedforward afferents; thus, map structures of orientation tuning might be seeded initially from thalamic feedforward projections. Based on these results, it was suggested that the layout of the orientation map would be restricted by the structure of ON- and OFF-center RGC mosaics, as the origin of ON and OFF feedforward afferents. This innovative notion was initially suggested as a conceptual idea that the structure of the periphery of the sensory system—such as RGC mosaics for the visual system—is simply projected to the cortex, providing the structural blueprints of functional maps [3]. This idea was extended to statistical wiring model, suggesting that the orientation selectivity at a given cortical location is restricted by the spatial arrangement of ON and OFF retinal afferents around the same retinotopic location, so the layout of orientation maps is initially seeded by the structure of RGC mosaics (Fig. 1.8) [1, 2]. The key assumption of the model is that the ON and OFF afferents provided to the cortex originate from the output of ON- and OFF-center RGCs and are simply relayed by LGN neurons.

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Fig. 1.7 Clustered ON/OFF retinotopy of neighboring V1 neurons. The location ON and OFF receptive fields of neighboring V1 neurons are highly clustered, resulting in similar orientation preferences among these neurons. a Cat data adapted from Kremkow et al. (2016) [39]. b Tree shrew data adapted from Lee et al. (2016) [40], under the permission of the copyright holder (© 2016, Nature Publishing Group, a division of Macmillan Publishers Limited)

In most mammalian species, neurons in the LGN relay the receptive field of only one to three RGCs, so their receptive fields have a center-surround structure, which is similar to that of RGCs in most cases. In previous anatomical [42] and physiological [43–45] studies in cats, it was reported that most LGN neurons receive feedforward inputs from fewer than six RGCs. Further studies of neural connectomics revealed that the locations and sizes of LGN receptive fields are similar to those of the connected RGC, implying that the activity of LGN neurons is mainly modulated

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Fig. 1.8 Statistical wiring model for development of orientation selectivity. Ringach (2004) suggested that the ON/OFF-segregated receptive field of V1 neurons can arise by sampling the ON and OFF RGC afferents around the corresponding retinotopic location [1]

by a single RGC [41, 46] (Fig. 1.9a). Similar results were also observed in macaques [47]. In mice, where it is reported that more RGCs innervate LGN neurons [48] than in monkeys or cats, it was also reported that an LGN neuron is mainly modulated by approximately three RGC inputs on average [49, 50] (Fig. 1.9b). By expanding this notion, it was suggested that a superposition of hexagonal lattice pattern of ON and OFF RGC mosaics develops a moiré interference pattern and this pattern initiates a quasi-periodicity of the orientation map (Fig. 1.10) [4] or the spatial correlation between the orientation pinwheels of different signs and the cardinal axes of the retinotopic map [51]. These results provide both theoretically solid and biologically plausible explanations of the developmental mechanism of the spatial periodicity of orientation maps. However, the developmental mechanism of a large number of characteristics of cortical functional maps still remains unclear, preventing the statistical wiring model from being accepted as a complete principle underlying the development of functional circuits in the visual cortex.

1.3 Functional Architectures of Visual Cortex 1.3.1 Periodicity of Visual Tuning Maps In each species of higher mammals having columnar orientation maps, one of the major characteristics of the structure of orientation maps is that their spatial periods are consistent across different animals of each species (Fig. 1.11 and Table 1.1) [20, 52]. This implies that the spatial periodicity of orientation maps is regulated by a

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Fig. 1.9 Neurons in the LGN relay the receptive field of a few RGCs. Therefore, their receptive fields have a center-surround structure, which is similar to that of RGCs in most cases. a In cats, locations and sizes of LGN receptive fields are similar to those of the connected RGC, implying that the activity of LGN neurons is mainly modulated by a single RGC. Illustrations describe the receptive fields measured in Usrey et al. (1999) [41]. b In mice, it was also reported that an LGN neuron is mainly modulated by approximately three RGC inputs on average [49]. The graph was adapted from Litvina et al. (2017) [49], under the permission of the copyright holder (© 2017 Elsevier Inc.)

common developmental mechanism in each species, but it still remains unclear how their periods are determined in the visual cortex. Important clues were found from an extended version of the statistical wiring model proposing that moiré interference between the hexagonal lattice of ON- and OFF-center RGC generates a quasi-periodic pattern that can seed the topography of an orientation map at an early stage of development [4]. According to the model, the spatial periodicity of an interference pattern depends on two parameters—the lattice distance ratio (α) and the alignment angle (θ ) between the two lattice patterns (Fig. 1.12). The value of α can be restricted by the cell densities of ON and OFF

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Fig. 1.10 Paik-Ringach model for development of orientation map. Paik and Ringach (2011) suggested that the spatial periodicity of the orientation map arises from a periodic interference pattern of ON and OFF RGC mosaics [4]. a The superposition of hexagonal lattices of ON and OFF RGC mosaics reproduces a moiré interference pattern. b Cortical pooling of neighboring ON and OFF RGCs results in the orientation preference. c Orientation map simulated from a moiré interference pattern of ON and OFF RGC mosaics. Images were adapted from Paik and Ringach (2011) [4], under the permission of the copyright holder (© 2011 Nature America, Inc.)

hexagonal mosaics, but θ also needs to be restricted to a small range to achieve consistent spatial periodicity (Fig. 1.12). Thus, to state explicitly how the consistent spatial periodicity of maps within a species could be achieved, it must be explained how θ is restricted during development. Here, it will be shown that local repulsive interactions between RGCs can restrict θ , and achieve a consistent spatial periodicity in the retinal moiré interference pattern

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Fig. 1.11 Consistency of orientation map periods in a same species. Spatial periods of orientation maps measured from four monkeys are consistent across animals. Orientation map images were adapted from Obermayer and Blasdel (1993) [20], under the permission of the copyright holder (© 1993 Society for Neuroscience)

Table 1.1 Orientation map periods are consistent across animals of a same species, as observed in periods measured from 22 ferrets and 21 cats [55] Orientation map periods in ferret (n = 22)

Orientation map periods in cat (n = 21)

0.64

0.71

0.73

0.76

0.87

0.83

0.92

0.72

0.73

0.71

0.68

0.69

0.76

0.63

0.65

0.72

0.7

0.81

0.74

0.78

0.72

0.71

0.71

0.91

0.7

0.65

0.71

0.68

0.72

0.67

0.75

0.74

0.63

0.67

0.63

0.74

0.78

0.67

0.8

0.75

0.66

0.67

0.61

Unit: mm, Müller et al. (2000)

and the cortical orientation map. Using model simulations, we tested the effect of repulsive interactions between nearby RGCs that induced gradual shifts of cell positions. We first observed that homotypic (ON-to-ON or OFF-to-OFF) interactions could induce a long-range hexagonal organization in each type of RGC mosaic [53], and that the presence of heterotypic (ON-to-OFF) interactions plays an important role in regulating θ . Then, to validate the model, we quantitatively analyzed the structure

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of the RGC mosaics observed in cat data, and found evidence that the heterotypic repulsive interaction is in effect during the development, contrary to the notion from previous research [54].

1.3.2 Orthogonal Organization of Visual Tuning Maps As orientation tuning is observed in the mammalian visual cortex, other functional tunings have also been extensively studied. For example, the ocular dominance of V1 neurons indicates the tendency to prefer visual inputs from one eye to that from the other [57] and the spatial frequency tuning indicates the tendency to selectively responds to visual inputs of a specific spatial frequency [58]. In higher mammals having orientation maps, the quasi-periodic functional maps have also been observed for other functional tunings, such as the ocular dominance map [59] or the spatial frequency map [60] (Fig. 1.13). Although the role of each functional map is under debate [23, 24], correlations between the topographies of different functional maps have been observed, implying their systematic organization. For instance, it was reported that the gradient of orientation tuning intersects orthogonally with that of ocular dominance and preferred spatial frequency in the same cortical area in cats [25]. High-resolution two-photon imaging data revealed that the region of higher spatial frequency tuning tends to align with the binocular region in the ocular dominance map in monkeys [61]. Such structural correlation between the maps is thought to result in efficient tiling of sensory modules and achieve a uniform representation of visual features across cortical areas (Fig. 1.13) [62]. These imply that there may exist a common principle of developing individual functional maps [63], but it is still unclear how such topographical relationships among different maps could arise in V1. Herein, we show that an orthogonal relationship of tuning modules already exists in retinal mosaics and that this can be mirrored to V1 to initiate the clustered topography. First, from an analysis of RGC mosaics data in cats and monkeys, we found that the spatial separation of the ON–OFF feedforward afferents (ON–OFF distance) intersects orthogonally with the ON–OFF alignment angle (ON–OFF angle). These results imply a topographical correlation between the ON–OFF distance and other cortical tunings. As expected, the analysis of published V1 recording data [39] shows that the ocular dominance and spatial frequency in V1 are correlated with the spatial separation of the ON and OFF subdomains of the receptive fields. By combining these analyses of RGC mosaics and V1 recording data, we demonstrate that the regularly structured retinal circuits provide a common framework of various functional maps and topographic correlations among the maps in V1.

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Fig. 1.12 Retinal origin of cortical orientation map and its variation of spatial organization. a Developmental model of orientation map as feedforward projection of ON and OFF retinal mosaics. Receptive field of a V1 neuron is organized from the local projection of ON and OFF retinal mosaics. b The period of the retinal moiré interference pattern (scaling factor, S) is a function of the lattice spacing ratio (α) and the alignment angle (θ) between ON and OFF RGC mosaics. Orientation tuning of a V1 cell is decided from the local structure of ON and OFF RGC mosaics with feedforward wiring, thus the periodic retinal interference pattern seeds a cortical orientation map. Scale bar indicates 5d. c Left, scaling factor S as a function of α and θ. Right, variation in the calculated value of S, when α is fixed to 0.094 as estimated from cat data [56]. d Sample orientation maps developed by moiré interference of RGC mosaics for α = 0.094. Spatial period of maps appears to vary significantly for different value of θ. Left, S = 11.7 of developed map for θ = 0°, Right, S = 3.8 for θ = 15°. Black arrows indicate spatial period of maps. Illustrations and results were adapted from Jang and Paik (2017) [5]

1.3.3 Salt-And-Pepper Organization in Rodents Neural tuning to visual stimulus orientation is one of the hallmarks of the mammalian visual cortex. However, at larger scales, this tuning in V1 is organized into distinct topographic patterns across species. For example, in higher mammals such as cats or monkeys, the preferred orientation continuously changes in a quasi-periodic manner, resulting in a columnar orientation map (Fig. 1.14) [18, 19]. In contrast, the preferred orientation of rodents is arranged in a random-like manner, resulting in a salt-andpepper type of organization (Fig. 1.14) [64]. From the fact that species of distinct cortical organizations are found on separate branches of the mammalian phylogenetic tree, it has been suggested that columnar or salt-and-pepper organization reflect species-specific principles of evolution underlying the development of cortical circuits [65, 66], but it still remains unclear what species-specific mechanism initiates one of the disparate organizations observed in each species. An alternative view is that cortical development is governed by a universal mechanism, but that disparate architectures can arise from variation of specific biological parameters, such as the size of V1 [67], the number of V1 neurons [68], and the range of cortical interaction [69]. However, further analysis of data for various species revealed counterexamples of this simple prediction, implying that V1 organization may not be simply determined by a single anatomical factor [70]. In particular, four species of mammals (ferret, tree shrew, rabbit, and gray squirrel) have V1 of comparable size, but it was observed that two of them have columnar orientation maps, while the others have salt-and-pepper organization. For example, cats with columnar orientation maps have larger V1 (380 mm2 ) [71] than that of mouse without orientation maps (3 mm2 ) [72], but tree shrews with columnar orientation maps have smaller V1 (73 mm2 ) [73, 74] than that of gray squirrels without orientation maps (82 mm2 ) [70, 75]. This suggests that the size of V1 may not be a determinant of V1 patterns. Similarly, other candidate parameters such as visual acuity and body weight also failed to predict V1 organization of orientation tuning among these four species [70]. For example, cats with columnar orientation maps have better visual acuity (6 cycles per degree, cpd) [70] than that of mouse without orientation maps (0.56 cpd) [70], but

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Fig. 1.13 Orthogonal organization among diverse functional maps in V1. a Orientation map, ocular dominance map, and spatial frequency map observed in a same cortical area of cat V1 [62]. Preferred orientation changes in an orthogonal direction against the change of the ocular dominance and the preferred spatial frequency tuning. Map data were adapted from Swindale et al. (2000) [62], under the permission of the copyright holder (© 1969, Nature America Inc.). b Such structural correlation between the maps is thought to result in efficient tiling of sensory modules and achieve a uniform representation of visual features across cortical areas [61, 62]

tree shrews with columnar orientation maps have worse visual acuity (2.4 cpd) [76] than that of gray squirrels without orientation maps (3.9 cpd) [77]. An important clue might be in the observation of the thalamic origin of cortical tuning. In diverse species including higher mammals and rodents, previous studies showed that orientation tuning in V1 is well predicted by the local arrangement of ON and OFF thalamic inputs [34, 38], implying that functional circuits in V1 might initially be structured by thalamic afferents. In a subsequent study, it was

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Fig. 1.14 Columnar orientation map and salt-and-pepper organization of orientation tuning. a Columnar orientation map was observed in V1 of higher mammals. Data were adapted from Ohki et al. (2006) [79]. b Random-like salt-and-pepper organization of orientation tuning observed in V1 of rodents. Data were adapted from Ohki et al. (2005) [64]. c Illustrations of salt-and-pepper organizations observed in rodents and columnar orientation maps observed in higher mammals. Illustrations were adapted from Sirotin and Das (2010) [80]. Images and illustrations were adapted under the permission of the copyright holders (a © 2006 Nature Publishing Group; b © 2005 Nature Publishing Group; c © 2010 Nature America, Inc.)

also suggested that observed variation of thalamocortical projection could play an important role in development of the cortical functions and in maximizing visual acuity [78].

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In addition, considering that neurons in the LGN relay the receptive field of only one to three RGCs in most cases (cat: [41], monkey: [47], mouse: [49]), the structure of the LGN afferents reflects that of the retinal feedforward afferents. Thus, this retinal organization must be taken into account to understand the development of the V1 architecture. Herein, inspired by the statistical wiring model, it will be proposed that the retinocortical feedforward mapping ratio can solely predict cortical organization of each species. From the analysis of data for eight mammalian species, we found that the ratio between the size of V1 and of a retina or the ratio between the number of RGCs and V1 neurons appear higher for species with columnar maps and solely predicts the V1 organization in all the test data. In the following model simulations, it was confirmed that distinct cortical circuits can arise from different V1 and retinal ganglion cell mosaics sizes. These results suggest that both columnar and salt-andpepper organization in V1 develop universally with retinal origin, but may bifurcate due to variation of the feedforward circuit.

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“The repulsive interaction between nearby cells in the eye” (© 2021. Jaeson Jang all rights reserved.)

Chapter 2

Topographical Consistency of Cortical Maps

A consistent spatial periodicity of the cortical orientation map could be achieved by a restricted interference pattern of ON and OFF RGC mosaics. We showed that this restricted interference pattern is initiated by a simple repulsive interaction between nearby RGCs that induces gradual shifts of cell positions. Using a model simulation, we first observed that homotypic (ON-to-ON or OFF-to-OFF) interactions could induce a long-range hexagonal organization in each type of RGC mosaic. More importantly, the presence of heterotypic (ON-to-OFF) interactions plays an important role in restricting the alignment angle between ON and OFF RGC mosaics to a small range, resulting in a consistent spatial periodicity of the interference pattern. To validate the model, our analysis of the structure of observed RGC mosaics data shows that the heterotypic repulsive interaction is in effect during the development, contrary to the notion suggested by previous research.

2.1 Backgrounds In the primary visual cortex (V1) of higher mammals, the spatial distribution of orientation preference across the cortical surface is arranged quasi-periodically, ending in an organized orientation map [1–3]. It is not completely understood how such periodic organization is initially developed [4–6], but clues are found in how the segregation between ON and OFF subregions in the cortical receptive field is developed to originate the orientation tuning in a single V1 neuron [7–9]. In the classical view, it is suggested that a V1 neuron selectively samples feedforward inputs from thalamic neurons to generate an orientation-tuned receptive field [10]. However, experimental observations have suggested that the orientation tuning in V1 might be determined by the spatial distribution of thalamic afferents. Orientation tuning of V1 neurons was well predicted by the local average of thalamic ON and OFF receptive fields [11–13]. Also, the topography of functional maps in V1 is strongly correlated to the spatial distribution of thalamic afferents [14, 15]. These results may reconfirm the earlier observations that the preferred orientation of a © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J. Jang and S.-B. Paik, Emergence of Functional Circuits in the Early Visual Pathway, KAIST Research Series, https://doi.org/10.1007/978-981-19-0031-0_2

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V1 neuron remains consistent without recurrent cortical activity when the thalamic afferents are the only input provided [16–18]. These observations altogether indicate that the topography of cortical orientation maps may be initially seeded by the spatial distribution of ON and OFF thalamic inputs before the postnatal refinement [19, 20] (Fig. 1.7). Given this, how can the spatial distribution of thalamic afferents be organized in a quasi-periodic manner, as observed in the orientation map? Considering that neurons in lateral geniculate nucleus (LGN) relay the receptive field of the retinal ganglion cells (RGC) [21], the statistical wiring model [22, 23] suggests that V1 receptive field structure may be constrained by the spatial organization of ON- and OFF-center receptive fields of RGCs [24]. Based on this notion, a theoretical model [25, 26] proposes that moiré interference between the hexagonal lattice of ON- and OFF-center RGC generates a quasi-periodic pattern that can seed the topography of an orientation map at an early stage of development (Fig. 1.10). However, the model did not state explicitly how the consistent spatial periodicity of maps within a species could be achieved [27, 28]. According to the model, the spatial periodicity of an interference pattern depends on two parameters—the lattice distance ratio (α) and the alignment angle (θ ) between the two lattice patterns (Fig. 1b). The value of α can be restricted by the cell densities of ON and OFF hexagonal mosaics, but θ also needs to be restricted to a small range to achieve consistent spatial periodicity. Thus, it must be explained how θ is restricted during development (Fig. 1.12). Here, we demonstrate that local repulsive interactions between RGCs can restrict θ , and achieve a consistent spatial periodicity in the retinal moiré interference pattern and the cortical orientation map. Using our model simulations, we tested the effect of repulsive interactions between nearby RGCs that induced gradual shifts of cell positions. We first observed that homotypic (ON-to-ON or OFF-to-OFF) interactions could induce a long-range hexagonal organization in each type of RGC mosaic [29] and that the presence of heterotypic (ON-to-OFF) interactions plays an important role in regulating θ . Then, to validate our model, we quantitatively analyzed the structure of the RGC mosaics observed in cat data, and found evidence that the heterotypic repulsive interaction is in effect during the development, contrary to the notion from previous research [30].

2.2 Methods 2.2.1 Development of Hexagonal RGC Mosaics Local repulsive interaction F between nearby cells was designed as a function of distance r between the centers of dendritic fields to induce a gradual shift of cell position (Fig. 2.1). To simulate the development of RGC mosaics, particularly focusing on the effect of local repulsive interactions, we implemented a simplified model

2.2 Methods

27

Fig. 2.1 Model of local repulsion. Repulsive interaction between dendritic fields of nearby RGCs induces a gradual shift of each cell. Modeled repulsive interaction function that regulates the development of mosaic structure. Magnitude of the interaction force F is a function of distance between the cells (r). F is set to diverge to avoid soma overlap and the dashed line indicates the soma diameter, 0.17d, where d is cell distance in the ideal hexagonal lattice. Red and blue curves show different choices of interaction distance R (red and blue arrows)

(Fig. 2.1). Initially, cells are randomly distributed and then a repulsive force, F, between any pair of two RGCs modulates the position of cells in the mosaic (Fig. 2.2). We assumed that (1) F increases as two cells approach and (2) that the somas of two cells should not overlap during the developmental process [23]. Considering the physical definition of potential energy, F was assumed to have the form 1/r 2 and the diameter of the soma (s) was assumed to be 0.17d [29, 31], where the unit distance d is the theoretically estimated lattice distance of mosaics with ideal hexagonal structure assumed (Fig. 2.1). Then, for a given unit distance d, the equation of F is given as 

R−s F(r ; d) =   −ε A =ε r s 2 d −d d A

2

where A is a coefficient for calibration of the strength and the interaction distance R. ε is a fixed constant set to 0.01 for making the interaction disappear at r = R (F(R) = 0). Considering the slight difference between cell densities of ON and OFF RGC, each homotypic interaction (F ON and F OFF ) was defined based on the lattice distance (d ON and d OFF ) as F ON = F(r; d ON ) and F OFF = F(r; d OFF ). From the mosaic in the animal data [32], the relationship between d ON and d OFF was estimated as d ON =

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Fig. 2.2 Modeled process of mosaic development modulated by local repulsion. Top left, in initial cell mosaic, net repulsion for a cell determines the direction of gradual shift at each iteration. Scale bar indicates 1d. Top right, developed mosaic and black arrow indicates displacement of a cell from the initial location. Bottom, Average displacement of a cell during the development for R = 1.1d. The amount of displacement converges as the distribution of cells in the mosaic approaches equilibrium. Red triangle indicates the final state of the simulation ON −1 = 9.4%. Heterotypic interaction (F ONOFF ) was defined 1.094 × d OFF , so α = ddOFF by the average of F ON and F OFF for a given cell distance r as F ONOFF = F(r ; dONOFF ), OFF = 1.05dOFF . where d ONOFF = dON +d 2 For each iteration of mosaic development simulation, the actual shift of a cell was decided by the net force Fnet , the summation of all local repulsive interactions that the cell receives. To avoid any unrealistic oscillatory movement, spatial shifts of the cells were modeled to occur by a unit distance, and only when the net force exceeded a threshold at each iteration. If Fnet exceeded the threshold (10–4 ), the cell was shifted by 0.01d in the direction of Fnet . Otherwise, the cell maintained its location. The simulation was terminated when less than 0.5% of cells moved at each iteration. All simulations and statistical tests were performed using MATLAB R2016b. Bootstrap and Wilcoxon rank-sum tests were performed: bootstrap was used to define the significant peaks in 2D autocorrelation of the cell mosaics (see below for details).

2.2 Methods

29

Autocorrelation of a single mosaic was calculated as a smoothed 2D autocorrelogram, which revealed the relative distribution between every pair of cells. Autocorrelations were smoothed with a Gaussian kernel of standard deviation 0.15d. The value of correlation was normalized so that the self-correlation peak at the center becomes unity, and the center peak was removed after normalization. The significance of a local peak was verified by bootstrap test: the magnitude of a peak was compared with those in the autocorrelations of control mosaics where the y-coordinates of cell positions were shuffled among the cells. To calculate the averaged autocorrelation, every single autocorrelation was rotated so that the strongest peak was aligned in the +y-axis [25]. The significance of local peaks was verified by bootstrap test similarly as above, but the control was obtained by calculating the average of randomly rotated autocorrelations. Based on the observation that the dendritic fields of ON and OFF RGCs are not developed in the same plane, but in separate layers in the inner plexiform layer (IPL), we estimated the ON and OFF inter-mosaic distance in two steps: estimating the width of the IPL and the depth difference between ON and OFF RGC mosaics in IPL. The IPL width was estimated to be 45.6 µm in the cross-sectional image of the retina [33], and the depth difference between ON and OFF layers was 55.6% of the IPL [34]. Considering the unit lattice distance in the OFF RGC mosaic (d) was assumed to be 102 µm, the inter-mosaic distance between ON and OFF RGC mosaics was estimated to be 45.6 µm × 55.6% × (d/102 µm) = 0.248 d.

2.2.2 ON and OFF RGC Mosaics Alignment The angle alignment between simulated ON and OFF mosaics was estimated by matching 2D autocorrelation between the mosaics. Autocorrelation of OFF mosaics was enlarged (increasing α) and rotated (varying θ ) to find the condition at which the similarity to autocorrelation of ON mosaics was maximized. Similarity between autocorrelation was measured by the dot product between the 2D correlation plots within 1.25d from the origin. In this step, every single autocorrelation was smoothed by a Gaussian kernel with a standard deviation of 0.26d, for better estimation of peak positions.

2.2.3 Repulsive Energy Between RGC Mosaics The energy map was calculated to measure the variation of energy state between heterotypic cell pairs when one mosaic is intentionally shifted. When an ON and OFF cell pair induces repulsive interaction, the repulsive energy (E) is derived from the repulsive force

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 E =−

F(r )dr = −

 A A + εr − ε dr = (r − s) (r − s)2

First, the heterotypic energy per ON cell was recorded at the origin of the energy map. For all the other points of the map, the OFF mosaic was intentionally shifted by the spatial vector to the point and the energy per cell was measured in the area of overlap between ON and the shifted OFF mosaic.

2.3 Homotypic Repulsive Interaction for Hexagonal RGC Mosaics Regarding the development of orderly retinal mosaics, it has been reported that somas [29, 32], dendritic fields [35], and receptive fields [36] of one class of RGC are distributed in a quasi-uniform manner across retinal surfaces in adult mammals. This uniform coverage was thought to evolve as a consequence of repulsive interactions between the dendrites of densely located neighboring cells during development to avoid overlap between the functional territory of each cell [37–40]. This leads their dendritic fields to develop in directions opposite from neighboring cells and results in the shifting of their functional territories to minimize overlap, implying the critical role of the repulsive interaction between nearby cells to develop orderly spatial patterns mosaics. If a local repulsive interaction between neighboring cells can induce gradual shifts of RGC dendritic fields across retinal surfaces (Fig. 2.1), this may modulate the spatial organization of RGC mosaics. Here, we assumed that this local interaction between dendrites of neighboring cells may develop the quasi-regular hexagonal distribution of dendritic fields observed in RGC mosaics data [29] and tested the hypothesis by simulating the development of RGC mosaics. We first investigated whether a local repulsive interaction between cells of the same type (homotypic interaction) could develop a hexagonal pattern in the RGC mosaics (Fig. 2.2), which is a necessary condition to achieve moiré interference [25, 29, 36]. In this case, we simulated an arbitrary monotypic mosaic that could be either an ON or an OFF mosaic. From the initial condition where the dendritic fields were randomly distributed, homotypic repulsive interaction gradually rearranged the center of dendritic fields and could generate a quasi-regular structure of a developed dendritic field mosaic (Fig. 2.3). When the interaction distance R was smaller than 1d, dendritic fields were spread to some degree but could not tile the mosaic regularly enough to generate a long-range lattice pattern. However, when the range of interaction was sufficiently large (R > 1d), we could observe a salient pattern of hexagonal lattice in the developed cell mosaics. These results suggest that the local interaction range is a critical factor in the development of regularly structured mosaics. To quantify the lattice pattern developed, we examined the distribution of the lattice angle (ϕ) between neighboring cells [41, 42] (black dash lines in Fig. 2.3).

2.3 Homotypic Repulsive Interaction for Hexagonal RGC Mosaics

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Fig. 2.3 Tiling in a mosaic initiated by a local repulsion. Top left, the initial retinal mosaic. Right, developed cell mosaics, where R = 0.75d and R = 1.1d. Bottom left, average displacement in the developed mosaic for different R. If R is much smaller than 1d, the amount of cell shift is not enough to induce regular packing of mosaics. The displacement increases as R increases, and when R > 1d, cells are orderly packed and the displacement does not increase any more, even for larger R. Red triangle indicates the displacement in the developed mosaic at R = 1.1d

As the interaction distance R increased, the peaks at 60° became stronger, confirming the hexagonal structure of the mosaics (Fig. 2.4). In addition, we examined the distribution of peaks in the autocorrelation of mosaics (black circles in Fig. 2.4b). At R = 0.75d, autocorrelation peaks show weak periodicity in the mosaic lattice, but when R = 1.1d, the angular locations of the local peaks relative to the strongest peak (0°) in the individual mosaics were within ±5° of the multiple of 60° in all trials of the simulation. We also found that this hexagonal pattern was not limited to local mosaic structure, but also had long-range order. When the local repulsive interaction range was sufficiently large (R > 1d), higherorder peaks (up to 6th–7th order) were observed in the autocorrelation of mosaics (black circles in Fig. 2.4c). In addition, the positions of the peaks up to 4th order were matched to those mathematically calculated from an ideal hexagonal lattice (solid white squares in Fig. 2.4c). These results suggest that a local repulsive interaction between RGCs may generate a long-range hexagonal lattice pattern of ON and OFF mosaics.

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Fig. 2.4 Local repulsive interaction can develop hexagonal patterns in a monotypic cell mosaic. a Distribution of lattice angles (ϕ) of simulated mosaic developed with various R. When R is sufficiently large (> ~0.8d), histogram of ϕ peaked at 60°, implying a hexagonal mosaic structure. b 2D autocorrelation of each cell mosaic for investigation of spatial periodicity: the peak at the origin was removed for better presentation of 1st order peaks. Black circles indicate the significant local peaks (p < 0.05, see Methods for details). Top, R = 0.75d; autocorrelation peaks show weak periodicity of mosaic lattice. Bottom, R = 1.1d; autocorrelation peaks show strong hexagonal periodicity of developed mosaic. c Average of aligned autocorrelation of 100 mosaics developed when R = 1.1d. Black circles indicate significant peaks (p < 0.05) and white solid squares indicate the expected peak position for perfect hexagonal lattice. Note that higher-order peaks suggest that a local repulsive interaction could generate a long-range hexagonal lattice pattern of mosaics. Scale bar indicates 1d

2.4 Heterotypic Interaction for Aligned RGC Mosaics As with the model of single-type RGC mosaic development, we implemented both homotypic [30] and heterotypic repulsive interactions in this model simulations of ON and OFF RGC development (Fig. 2.5a). We modulated the strength of heterotypic interaction (F ONOFF ) by introducing the weight term w, to indicate the relative strength compared to that of homotypic interaction. Based on the experimental observations, we set interlayer distance at 0.25d, where d is the expected average lattice distance in simulated OFF mosaics [33, 43]. The ratio between the expected lattice distances of simulated ON and OFF mosaics (1 + α) was set to 1.094, based on animal data [32]. In the mosaics developed in the absence of heterotypic interaction FONOFF (termed simulated control mosaics; Fig. 2.5b, left), we observed hexagonal patterns from the angular distribution of local peaks in the autocorrelation (Fig. 2.5b, left), similar to the result in Fig. 2.4b. Here, the alignment between ON and OFF hexagonal patterns

2.4 Heterotypic Interaction for Aligned RGC Mosaics

33

Fig. 2.5 Heterotypic interaction can align both ON and OFF RGCs in a similar alignment angle. a Model mosaics separated by interlayer distance dm = 0.25d [33, 43], with and without heterotypic interaction (FONOFF ). When FONOFF exists, a cell receives both homotypic and heterotypic interactions. b Simulated mosaics developed with (right, w = 0.01), and without (left, w = 0) repulsive interaction, FONOFF , from an identical set of initial mosaic structures. c Top and middle, 2D autocorrelations of developed mosaics in b. The local peaks (open circles) show hexagonal patterns. Bottom, the peak locations in b were plotted together (red and blue open circles)

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appeared independent (Fig. 2.5c, left bottom). On the other hand, we observed that a certain level of heterotypic interaction could affect the alignment between the mosaics without interrupting the development of the hexagonal pattern in each mosaic. In the presence of FONOFF (termed simulated model mosaics; Fig. 2.5b, right), each of the simulated mosaics still showed a hexagonal pattern (Fig. 2.5c, right), but the alignment between ON and OFF hexagonal patterns appeared restricted and different from that developed without FONOFF (Fig. 2.5c, right bottom). To further investigate the influence of FONOFF , we measured the angular alignment between simulated ON and OFF mosaics for different w. We estimated the relative ratio of lattice distance (α) and the alignment angle (θ ) between ON and OFF mosaics, by searching the amount of rotation and linear expansion of the autocorrelation of the OFF mosaic that maximizes the similarity to the autocorrelation of ON mosaic (Fig. 2.6). We found that θ was restricted to small angles as w increased (Fig. 2.7a). On the other hand, α was maintained at near the expected level in the model (0.094) (Fig. 2.7b). This is because α is mostly constrained by the ratio between the cell densities. Consequently, the scaling factor S, which is the spatial period of the moiré interference pattern, could be computed based on the obtained θ and α [25]. As w increased, the computed scaling factor was also restricted within a narrow range around the expected level of the scaling factor (S = 10.4 [25], black arrow in Fig. 2.7c). When the heterotypic interaction was sufficiently large (w > 0.02), we confirmed that the obtained θ and the estimated scaling factor S were significantly different from those of the control where ON and OFF mosaics were randomly aligned (*p < 10–21 , Wilcoxon rank-sum test; Fig. 2.8), while they were not distinguishable

Fig. 2.6 Searching the amount of rotation and linear expansion in ON and OFF mosaics. The amount of rotation and linear expansion of the autocorrelation of the OFF mosaic that maximizes the similarity to the autocorrelation of ON mosaic was estimated. To find the relative lattice distance (α) and the alignment angle (θ) between ON and OFF mosaics, autocorrelation of the OFF mosaic was expanded and rotated (black solid circles) to match the autocorrelation of the ON mosaic. From various sets of interference parameters, α and θ were estimated by the set that maximizes the similarity between ON and OFF mosaics. White dashed lines indicate the estimated α and θ

2.4 Heterotypic Interaction for Aligned RGC Mosaics

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Fig. 2.7 Heterotypic interaction can restrict the angle alignment (θ) between ON and OFF mosaics. a Estimated θ from 100 ON and OFF mosaic pairs for different degrees of heterotypic interaction, FONOFF . When FONOFF is absent (w = 0), θ is randomly distributed. As w increased, distribution of θ appears to be limited to small angles. b Estimated α from 100 ON and OFF mosaic pairs as in a. As w increased, α was maintained at near the mathematically calculated value (α = 0.094) from the density of ON and OFF cells in hexagonal lattice. c Scaling factor (S) estimated from a and b. As w increases, value of S is kept consistent. The black arrow indicates the expected scaling factor (S = 10.4) in the theoretical model [25]

from the control for w=0. Considering that the absence of the heterotypic interaction (w = 0) resulted in a failure to restrict the scaling factor to a small range, these results suggest that the heterotypic interaction in RGC mosaics could be the key factor in achieving consistent spatial periodicity in the interference pattern within a species.

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Fig. 2.8 Restricted mosaics alignment with the heterotypic interaction. With the heterotypic interaction, the angle alignment and the scaling factor were significantly different from those of the control where ON and OFF mosaics were randomly aligned. When the heterotypic interaction was sufficiently large (w > 0.02), the obtained θ and the estimated scaling factor S were significantly different from those of the control where ON and OFF mosaics were randomly aligned, while they were not distinguishable from the control for w = 0. Considering that the absence of the heterotypic interaction (w = 0) resulted in a failure to restrict the scaling factor to a small range, these results suggest that the heterotypic interaction in RGC mosaics could be the key factor in achieving consistent spatial periodicity in the interference pattern within a species. a Observed θ from the developed mosaics (w = 0 and 0.04) and the control with randomly aligned mosaics (Wilcoxon rank-sum test, *p < 10–21 , n.s. p = 0.28). b Estimated scaling factor (Wilcoxon rank-sum test, *p < 10–21 , n.s. p = 0.27). Error bars indicate standard deviation

2.5 Heterotypic Interaction in RGC Mosaics Data Next, to validate the central prediction of this model about the presence of the heterotypic interaction, we tried to estimate the influence of the heterotypic interaction during development using experimental data. The typical approaches for measuring interactions between two cell mosaics are two-dimensional crosscorrelograms [23] or 1-dimensional density recovery profiles [30, 44]. However, these methods only focus on the spatial distribution relative to neighboring cells, rather than the relationship at whole-mosaic scale. Thus, to investigate the effect of heterotypic interaction at the whole-mosaic scale, we conducted an analysis of the repulsive energy in each pair of ON and OFF RGC, using simulated mosaics and measured mosaic data from animal experiments (Soma: [29, 32], Receptive field: [36]) (Fig. 2.9). Although this developmental model is for the spatial distribution of dendritic fields, we assumed that this model could also be applied to the mosaic structure of a cell body and receptive field, because it was reported that all three of them are spatially clustered on the retinal surface [45]. Thus, the influence of the heterotypic interaction between dendrites can also be estimated in receptive field and soma mosaics data.

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Fig. 2.9 Repulsive energy map devised to investigate the existence of heterotypic interactions in mosaic data. a A repulsive energy map was plotted from the estimation of heterotypic repulsive energy of each cell pair in overlapped regions of ON and OFF mosaics for each amount of spatial shifts of OFF mosaics. b A theoretical model predicts that the energy map will have a local minimum at the origin. If a repulsive interaction exists during development then ON and OFF RGC locations would be modulated to reduce total repulsive energy. The energy map will have a high energy band around the origin, because the intentional shift of OFF mosaic will increase the repulsive energy level, compared to the stable state at the origin. This pattern will not appear if ON and OFF mosaics were developed independently (simulated control, FONOFF = 0)

As two cells shift away from each other, repulsive energy between the cells would decrease, resulting in a more stable state of the cell pair. Thus, if heterotypic repulsive interaction exists during the development of RGC mosaics, regardless of its strength, the structure of ON and OFF mosaics will be modulated in a way that heterotypic repulsive energy is reduced.

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Therefore, by examining whether the heterotypic repulsive energy of RGC mosaics is minimized in the animal data, we could investigate whether the actual organization of the RGC mosaic is consistent with this model with heterotypic interaction. Under this condition, if either an ON or an OFF RGC mosaic developed with heterotypic interaction is shifted a bit in any direction, the repulsive energy per cell within the areas of overlap of ON and OFF mosaics will increase compared to the original state (Fig. 2.9). On the other hand, ON and OFF mosaics developed without heterotypic repulsive interactions will not show this pattern of energy change. To validate this hypothesis, we examined the repulsive energy, while we varied the amount of spatial shift of an OFF mosaic in all directions in both simulated and observed mosaics (Fig. 2.10). In the simulated mosaic developed with heterotypic interaction, the energy map had a local minimum at the origin, and a band of a higher energy level around it (Fig. 2.11a, left). In contrast, this pattern was not observed in the energy map of simulated control mosaics developed with no heterotypic interaction (Fig. 2.11a, middle). Notably, the energy maps estimated from the RGC mosaics observed in animal studies [29, 32, 36] showed a local minimum at the origin and a higher energy band around it (Fig. 2.11a, right), similar to that from the model simulation. To analyze this energy distribution quantitatively, we investigated the radial distribution of energy by averaging the map in polar coordinates (Fig. 2.11b). In both the model simulation and the animal data, the energy maps showed local minima at the origin and the energy levels of the origin were higher than those in annuli close to the origin, implying that the original RGC mosaics were in stable energy states in terms of ON–OFF RGC repulsive energy (Fig. 2.11b). These results suggest that the observed RGC mosaics in animal data show the vestige of heterotypic interaction during RGC development.

2.6 Robustness of Model Prediction Development of hexagonal pattern does not require a particular form of the repulsive interaction. Although the dendritic maturation of RGC could be affected by various factors (such as stimulus-dependent synaptic activity [46]), it has been observed that RGC mosaics can develop without visual experience [47]. This implies that a simple intercellular interaction in the retina may be sufficient to originate orderly functional structure across retinal surfaces. This model provides a simple explanation of this retinal interaction between neighboring cells during retinal development. In previous studies, it was argued that molecular mechanisms caused avoidance between dendrites of other cells in the retina [37, 38], but it is worth pointing out that the current result is valid as long as both homotypic and heterotypic repulsive interactions exist, regardless of the underlying mechanism. Considering that the exact form of local interaction in retinal mosaics has not been measured, we performed additional simulation for different forms of interaction (Fig. 2.12), just in case the form of

2.6 Robustness of Model Prediction

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Fig. 2.10 Sample ON and OFF mosaics and their energy map. Scale bar indicates 1d, expected hexagonal lattice distance in OFF mosaics. White dashed circles indicate the average heterotypic nearest neighbor distance. a Simulated model mosaics (FONOFF > 0). b Simulated control mosaics (FONOFF = 0). c Three experimental data: Data 1 and Data 2 are cell body mosaics from [32] and [29], and Data 3 is receptive field mosaics from [36]

interaction (∝1/r 2 in the main simulation) substantially affected the conclusion. As long as the interaction distance is sufficient to tile the mosaic (R = 1.1d), all the forms of interaction reproduced regular and hexagonal mosaic structures (Fig. 2.13), consistent with the results in Fig. 2.4. Probably, observations of the retinal mosaic structure during each developmental stage could provide direct evidence of details in this model.

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Fig. 2.11 Observed evidence of heterotypic interactions in animal data. In both the model simulation and the animal data, the energy maps showed local minima at the origin and the energy levels of the origin were higher than those in annuli close to the origin, implying that the original RGC mosaics were in stable energy states in terms of ON–OFF RGC repulsive energy. These results suggest that the observed RGC mosaics in animal data show the vestige of heterotypic interaction during RGC development. a Averaged energy map: Left and middle, average from 100 simulated ON/OFF mosaic pairs. Simulated model mosaics show a local minimum at the origin and a high energy band around it, while simulated control mosaics do not show the pattern. Right, averaged energy map was achieved from the summation of energy maps rotated by 0–360°, with 10° intervals. Note a local minimum at the origin and a high energy band around it, as in the simulated model result. b The average of energy level in the radial direction show a local minimum at the origin and a high energy band around it, both in the simulated model and the animal data. Error bars indicate standard deviation

Alignment between mosaics was kept even with noisy mosaics. One might argue that the simulated mosaics developed in this model have a much more regular organization of the lattice pattern than what is observed in the animal data [29, 32]. Here, we intended to focus on illustration of the mechanism by which local RGC repulsive interaction could develop long-range order in the ON and OFF mosaics, and also regulate the alignment between them (see Discussion). For this reason, the simulation parameters were chosen to best describe the hexagonal lattice structure of

2.6 Robustness of Model Prediction

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Fig. 2.12 Repulsive interaction function defined by the different forms of decaying functions: 1/r , 1/r 2 (used in the main simulation), 1/r 3 , and exp(−r ). All the functions become 0 at r = 1.1d

mosaics and the alignment angle of mosaics (R=1.1d). However, we confirmed that the suggested mechanism also worked under noisy conditions of mosaics by modulating the regularity of the mosaic structure with the interaction range R (Figs. 2.3 and 2.14). We observed that the alignment of ON and OFF simulated mosaics and the computed scaling factor was still restricted (Fig. 2.15) when we reduced interaction range R to produce much less orderly mosaics, consistent with the results in Fig. 2.7. This result suggests that this theoretical model is also applicable to more realistic parameter conditions.

2.7 Limitation of Model Validation from Available RGC Data One may argue that the simplest way to validate this model is to observe the moiré patterns of ON and OFF RGC in the measured mosaics. However, an analytical limitation arises from the size of the measured retinal patches, which is, at most, ~1 mm2 including only ~100 cells for a single type of RGC. This may not be sufficiently large to investigate the emergence of interference patterns between mosaics. To address this issue, we reconstructed a larger mosaic with a level of long-range order similar to that of the measured mosaic and examined whether the size of the mosaic could affect the observation of the interference pattern. As represented in the previous work [25], the current analysis of the autocorrelation of a measured RGC mosaic revealed the hexagonal arrangement of 1st order peaks and many other higher-order peaks (Fig. 2.16a). For quantitative analysis of the hexagonal arrangement at long range in the measured RGC mosaics, we found that the spatial distribution of these higher-order peaks is well fitted to a hexagonal

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Fig. 2.13 Consistency of results with different forms of repulsive function. a Cell mosaics developed by different interactions, from the same initial condition. Inset is the autocorrelation of each mosaic. Although the angular location of local peaks can vary, the hexagonal pattern is maintained across the interaction functions. Only local peaks of significance p < 0.05 were selected, compared with N = 100 autocorrelations of control mosaics where y positions of cells were shuffled. Scale bar indicates 1d. b Distribution of lattice angles (ϕ) in the developed cell mosaic. In all cases, strong hexagonal peaks were observed at 60°

lattice up to 5–6th order, which is the limit of analysis with the given size of measured mosaic (Fig. 2.16b). However, considering that the expected period of the interference pattern in RGC mosaics is larger than this [25], the available range of local peaks may not be large enough to reveal a complete period of the interference pattern. Thus, for further validation of our prediction, we generated large mosaics with level of long-range periodicity equivalent to that of the measured mosaics from the parameter search (Fig. 2.16c). We searched model parameters where simulated mosaics and measured mosaics had the same level of error distance from an ideal hexagonal lattice. Note that as the parameter R increases, the developed mosaic becomes more hexagonal (Fig. 2.4a); so the error distance decreases (Fig. 2.16c).

2.7 Limitation of Model Validation from Available RGC Data

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Fig. 2.14 Sample mosaics developed by the original interaction form for different interaction ranges, R. As R declines, a less orderly mosaic develops

Then, we observed that the mosaics simulated with repulsion range R = 0.9d represented a level of long-range hexagonal periodicity similar to that of the measured mosaics (red arrow in Fig. 2.16c). We used this condition to reconstruct large mosaics in (Fig. 2.17a) and further examined whether the reconstructed large mosaics could reproduce an interference pattern that could seed an orientation map. In the autocorrelation analysis of each mosaic structure, not only the whole reconstructed mosaics but also the cropped mosaics showed a hexagonal arrangement of 1st order peaks (Fig. 2.17b). This implies that both sizes of mosaics show hexagonal lattice patterns, as in Fig. 2.16a. Next, with reconstructed ON and OFF mosaics in (Fig. 2.17a), we simulated orientation maps using the statistical wiring model (Fig. 2.17c) [25]. If ON and OFF mosaics reproduce an interference pattern at long-range, the resulting orientation map must show a hexagonal structure, as predicted by the moiré pattern. As expected, the interference pattern between the largely reconstructed mosaics seeded a hexagonal structure in the orientation map (Fig. 2.17d, left).

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Fig. 2.15 Consistency of results with spatial noise in mosaics. Top, Distribution of estimated θ for mosaics of different interaction ranges. With R= 0.5d, the distribution of the angle does not change as w increases, while the alignment angle is restricted to small angles with R ≥ 0.7d. Black dashed line indicates the average of 10,000 randomly selected angles between 0 and 30°. Bottom, The scaling factor is estimated from the fitted parameters α and θ. For R ≥ 0.7d, the scaling factor increases as the heterotypic interaction becomes stronger. Black dashed line indicates S = 4.9, for randomly aligned mosaics as a control. Shaded regions indicate standard error (N = 100)

However, we also observed that a small part of the reconstructed mosaics that were cropped to the same size as the measured mosaics could not clearly show hexagonal periodicity of a reconstructed orientation map (Fig. 2.17d, right). This implies that among mosaics, sufficient size is necessary for a direct estimation of the long-range periodicity and that the observation of the interference pattern at long-range might not be guaranteed from currently available size of measured mosaics. Thus, this analysis provides a vestige of the long-range periodicity in the measured mosaics

2.7 Limitation of Model Validation from Available RGC Data

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Fig. 2.16 Level of long-range hexagonal periodicity similar to that of the measured mosaics. a Hexagonal arrangement of RGC in the experimental data: Left, receptive fields mosaics of OFF RGC from Gauthier et al. (2009) [36]. Right, autocorrelation of the mosaic shows a hexagonal arrangement of 1st order peaks and the presence of higher-order peaks. b The distribution of local peaks in the autocorrelation is compared with that of an ideal hexagonal lattice, implying the periodicity at long range in the measured mosaic. Black solid circles indicate the local peaks in a and red open circles indicate the fitted hexagonal lattice. c The average distance between the observed peak and the nearest ideal peaks in the autocorrelation (error distance) of our simulated mosaics (w = 0). Red dashed line indicates the average error distance in the experimental data in b. When the interaction range R = 0.9d (red arrow), the simulated mosaics show level of error distance similar to that of the measured mosaics

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Fig. 2.17 Observed RGC mosaics can develop interference patterns, depending on the size of the mosaics. a–d Top, Analysis of the reconstructed mosaics. Bottom, Analysis of a local patch of the reconstructed mosaics cropped to the same size as the measured mosaics in Fig. 2.16a. a The sample model mosaics developed with R = 0.9d as the condition for data reconstruction. Black rectangle indicates the size of the measured mosaics in Fig. 2.16a. b Autocorrelation of the reconstructed OFF mosaics in a. The hexagonal arrangement of the 1st order peaks is also maintained in the analysis of the cropped mosaic. c Orientation map simulated from the reconstructed mosaics in a. d Autocorrelation of the orientation maps in c. Note that reconstructed mosaics could reproduce an orientation map and an interference pattern with hexagonal periodicity (top), but it may not be clearly observed in the analysis of the small retinal mosaic currently available in the data (bottom)

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(Fig. 2.16b), but it remains to be investigated further when larger patches of retinal mosaics could be obtained experimentally. Overall, these results suggest that local repulsive interactions in retinal development may be crucial to the development of the orderly structure of retinal mosaics, and also to the consistent organization of functional architectures in the visual cortex.

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“The structure in the eye mirrored in the brain” (© 2021. Jaeson Jang all rights reserved.)

Chapter 3

Orthogonal Organization of Visual Cortex

The development of the orthogonal relationship of tuning modules in V1 is initiated by the projections of an orthogonal organization that already exists in retinal mosaics. First, from an analysis of RGC mosaics data in cats and monkeys, we found that the spatial gradient of spatial separation of the ON–OFF feedforward afferents (ON–OFF distance) intersects orthogonally with the gradient of ON–OFF alignment angle (ON– OFF angle). Considering the orthogonal organization of orientation tuning and other functional tunings in V1, these results suggest a topographical correlation between the ON–OFF distance and other tunings. As expected, the analysis of published V1 recording data measured in cats shows that the ocular dominance and spatial frequency in V1 are correlated with the spatial separation of the ON and OFF subdomains of the receptive fields. By combining these analyses of RGC mosaics and V1 recording data, we demonstrate that the regularly structured retinal circuits provide a common framework of various functional maps and topographic correlations among the maps in V1.

3.1 Backgrounds In higher mammals, the primary visual cortex (V1) is organized into various functional maps of neural tuning such as ocular dominance [1], preferred orientation [2], direction [3], and spatial frequency [4]. Although the role of each functional map in visual information processing is under debate [5, 6], correlations between the topographies of different functional maps have been observed, implying their systematic organization. For instance, it was reported that the gradient of orientation tuning intersects orthogonally with that of ocular dominance [7] and preferred spatial frequency [8] in the same cortical area (Fig. 3.1). High-resolution two-photon imaging data revealed that the region of higher spatial frequency tuning tends to align with the binocular region in the ocular dominance map [9]. Such structural correlation between the maps is thought to result in efficient tiling of sensory modules and achieve a uniform representation of visual features across cortical areas [10] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J. Jang and S.-B. Paik, Emergence of Functional Circuits in the Early Visual Pathway, KAIST Research Series, https://doi.org/10.1007/978-981-19-0031-0_3

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Fig. 3.1 Orthogonal organization of cortical functional maps. Contour of orientation maps and spatial frequency maps intersect orthogonally across the cortical surface. Data were adapted from Nauhaus et al. [8], under the permission of the copyright holder (© 2013 Nature America, Inc.)

(Fig. 3.2). These findings in diverse mammalian species imply that there may exist a universal principle of developing individual functional maps [11], but it is still unclear how such topographical relationships among different maps could arise in V1. Then, how are functional tunings initiated in V1? Important clues regarding the development of the maps have been found in the observation that cortical tuning, such as orientation selectivity, may originate from bottom-up feedforward projections. Although feedforward thalamic inputs are a small portion of the total inputs [12], earlier work reported that the orientation tuning of V1 neurons originates from this feedforward pathway and the orientation preference of a V1 neuron remains consistent when the recurrent cortical circuits are silenced [13, 14]. Recently, it was reported that orientation tuning in V1 is predictable from the local average of ON and OFF thalamic afferents [15] (Fig. 3.3a). At larger scales, it was also reported that the continuous change of orientation tuning across the cortical surface is strongly correlated with the spatial alignment of ON and OFF receptive fields in cats and tree shrews [16, 17]. These observations altogether suggest that visual tuning in the cortical neurons may originate from the spatial organization of ON and OFF feedforward afferents, and map structures of cortical tuning might be also seeded initially from thalamic feedforward projections. Given this, how could the thalamic ON and OFF afferents provide a regularly structured layout of functional tuning to seed an orderly architecture of the map? The statistical wiring model [18, 19] suggested that V1 receptive field structure is

3.1 Backgrounds

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Fig. 3.2 Efficient tiling of diverse tuning in V1. a Diverse functional maps measured from cat V1. White solid arrows represent gradients in each map. Map data were adapted from Swindale et al. [10], under the permission of the copyright holder (© 1969, Nature America Inc.). b Orthogonal relationship between the gradients of diverse cortical tuning maps in [8–10]. c Efficient tiling of diverse tunings is illustrated

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Fig. 3.3 Spatial organization of ON and OFF RGCs might be mirrored to V1 and induces orthogonal tiling of a neural tuning. a Orientation tuning in V1 predicted from the local average of ON and OFF thalamic afferents. Data were adapted from Jin et al. [15], under the permission of the copyright holder (© 2011 Nature America, Inc.). b Illustration of the predicted relationship between the spatial arrangement of ON and OFF RGCs and cortical tunings

constrained by the local structure of ON and OFF mosaics of retinal ganglion cells (RGCs) [20]. In this view, the receptive field of a V1 neuron is generated from the sum of receptive fields of local RGC that provides feedforward afferents, and the V1 neuron is tuned to orientation due to the anisotropy of the receptive fields. Adapting this notion, the Paik-Ringach model further proposed that spatial moiré interference patterns between the hexagonal mosaics of ON and OFF RGC generate a quasi-periodic pattern that seeds the topography of an orientation map early in development [21, 22]. The key assumption that RGC mosaics patterns seed the topography of cortical orientation maps, allowed this model to successfully explain how regularly structured cell mosaics in the retina could seed the early structure of an orientation map [23] and its hexagonal periodicity [24] in diverse species of higher mammals. Herein, expanding this developmental principle of orientation maps, we propose that an orthogonal relationship of tuning modules already exists in retinal mosaics and that this can be mirrored to V1 to initiate the clustered topography of multiple tuning maps. First, we hypothesized that other cortical tunings may also be predictable from a profile of the spatial arrangement of ON and OFF RGCs, which can be expected to change orthogonally with a change in the ON–OFF angle across the retinal mosaics. In this scenario, this spatial organization of ON and OFF RGCs is mirrored to V1 and induces orthogonal tiling of a neural tuning (Fig. 3.3b). From an analysis of RGC mosaics data in cats and monkeys, we found that the topographic map of spatial separation of the ON and OFF RGCs (ON–OFF distance) intersects orthogonally with the map of ON–OFF alignment angle (ON–OFF angle).

3.1 Backgrounds

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This result suggests that these regularly structured retinal afferents provide a common framework for organizing various functional maps in the visual cortex, and this common anatomical substrate results in uniform representation of combinations of sensory modules by organizing topographical correlation between diverse tunings. As expected, our analysis of published V1 recording data measured in cats [16] shows that the ocular dominance and spatial frequency in V1 are correlated with the spatial separation of the ON and OFF subdomains of the receptive fields.

3.2 Methods 3.2.1 Analysis of RGC Mosaics To estimate the ON–OFF angle and distance seeded at each location in the RGC mosaics, we modeled the cortical receptive fields by sampling the receptive fields of local ON and OFF RGCs. We assumed that the RGCs are statistically wired to cortical space with a two-dimensional (2D) Gaussian function with a standard deviation of σcon . The synaptic weighting between ith RGC and jth cortical sites, wi j , was defined as   di2j 1 wi j = √ exp − 2 2σcon σcon 2π where σcon was set to 0.16–0.18 times the expected average lattice distance of OFF RGC mosaics (dOFF ). The local receptive field was calculated at each vertex of a rectangular grid with a spacing distance of 0.1dOFF in the RGC mosaics. The receptive fields of RGCs and V1 neurons were defined as a center-surround model of 2D Gaussian and their linear sum, respectively. The standard deviation and the amplitude of the surrounding region were set to 3 and 0.55 times that of the center region [25].   r2 1 √ exp − 2i 2σRGC σRGC 2π   ri2 0.55 − √ exp − (+ : ON cell, − : OFF cell) 2 18σRGC 3σRGC 2π  = wi j · iRGC

 i,RGC = ±

 j,V 1

i

Here, i,RGC is the receptive field of ith RGC and  j,V 1 is for the jth cortical site where ri is a distance-vector from the center of ith RGC to each position of the visual field. The terms σON,RGC and σOFF,RGC were set to 0.5 times the expected

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average lattice distance of ON and OFF RGC mosaics to satisfy the condition that the receptive fields of ON and OFF RGC mosaics cover all of the visual fields [26]. The ON–OFF angle and distance were measured between the center-of-mass of the modeled ON and OFF receptive fields and then the resultant maps were smoothed using a 2D Gaussian kernel with sigma of 0.8–1dOFF .

3.2.2 Analysis of Multi-electrode Recordings The multi-electrode data recorded from the cats were provided by Jose-Manuel Alonso ([16] and in personal communication) for the analysis in Fig. 3.1. To remove high-frequency spatial noise, the receptive fields were filtered by a low-pass fermi filter in the frequency domain. The filter was designed according to     ω−μ +1 f =1 exp Kμ where μ is the threshold of the frequency (4 cpd) and K is the smoothness coefficient. The ON–OFF angle was estimated from the Fourier transform (ω) of the receptive fields. It is defined as arg(μ)/2, where 

 μ=

|(ω)||ω| exp(2i arg(ω))dω/

|(ω)|dω

Samples for which either the ON or OFF subregion is entirely canceled by the other component were excluded. The ON–OFF distance was defined as the distance between the center of the ON and OFF subregions. The location of the center of the ON and OFF subregions was defined as the strongest peak of each subregion. For multiple subregion samples, the largest subregion was chosen for analysis.

3.2.3 Autocorrelation of Cortical Functional Maps To obtain the autocorrelation of cortical maps, we first digitized the map images from previous studies. To remove high-frequency spatial noise, map images were filtered with a small Gaussian kernel (average σ = 0.05 mm). From these post-processed images, we computed autocorrelation of the whole map image as follows (Fig. 3.4): r (x, y) =

1  (θ (x, y) × θ (x + x, y + y)) N x,y

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Fig. 3.4 Obtaining autocorrelation of measured functional map data. As the first step in the analysis, the map images found in previous publications were digitized using MATLAB. In cases where there was an additional illustration on the image, this illustration was manually removed using an imaging tool. To remove the spatial noise corresponding to high spatial frequency, the image was filtered using a small Gaussian kernel (σ = 0.05 mm on average; less than 5% of the map period) as the only post-processing step. For the filtered map image, autocorrelogram was obtained and it was scaled and rotated to map the local peak onto the point (0, 1) in the plane when it was averaged across different autocorrelograms. Map data were adapted from Hübener et al. [7]

where θ (x, y) is the pixel values of the map image, (x, y) indicates a spatial shift in the autocorrelation and N is the number of total pixels in the overlapping area between original and shifted map areas. Statistical significance of local peaks in the autocorrelation was estimated from comparison with control maps of an isotropic amplitude spectrum matching that of the measured maps (for details, see Supplementary Fig. 3.3 in Paik and Ringach [21]).

3.3 Orthogonal Organization of ON and OFF RGC Mosaics Herein, we show that an orthogonal relationship of tuning modules already exists in retinal mosaics and that this can be mirrored to V1 to initiate the clustered topography (Fig. 3.3). From the observation of the correlation between the ON–OFF angle in the retinal afferents and the cortical orientation tuning, we hypothesized that other cortical tunings may also be predictable from a profile of the spatial arrangement of ON and OFF RGCs, which can be expected to change orthogonally with a change in the ON–OFF angle across the retinal mosaics.

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In this scenario, this spatial organization of ON and OFF RGCs is mirrored to V1 and induces orthogonal tiling of a neural tuning. To validate this scenario, we used RGC mosaics data previously measured in cats [27] (Fig. 3.5a) and examined whether a change of the angle and distance between the local ON and OFF RGC mosaics would have an orthogonal organization. Based on the statistical wiring model [19], we estimated the ON–OFF angle and distance of the sampled receptive field at each position of the RGC mosaics while assuming that RGCs are locally sampled to provide feedforward afferents in the local V1 area (Fig. 3.5a). In this model, neighboring cortical neurons can sample a similar RGC population but generate a different orientation preference depending on the set of several RGCs that provide the dominant inputs to the neuron. Therefore, we calculated the angle of the intersection between the gradients of the ON–OFF angle and that of the distance in smoothed maps (Fig. 3.5b). The smoothed map of the ON–OFF angle covers approximately one period of the columnar structure and is thus comparable to the estimation obtained from the size of the RGC mosaics and the retino-cortical magnification factor [28]. As predicted by our scenario, we found that the angle shows a peak at approximately 90° (Fig. 3.5c). We repeated this analysis for four sets of RGC mosaic data of different eccentricities, obtained from independent experiments, in multiple species (N = 2 for cat [27, 29]; N = 4 for monkey [30–33]) and confirmed the orthogonal intersection between the ON–OFF angle and distance in all sets of tested data (Fig. 3.6a). Each mosaic sample and the average distribution of all datasets showed a peak at 90°, significantly higher than that of the control sets with the shuffled distribution of the ON–OFF angle and distance (Fig. 3.6b; P = 0.01). Notably, the strength of this orthogonal bias is comparable to that observed in the cortex (orthogonality index (OI) = 3.35 ± 0.90 in RGC mosaic; OIPO−OD = 3.90 ± 3.3 and OIPO−SF = 2.72 ± 2.51 in our analysis of V1 tuning in Fig. 3.2b; see Methods for details), implying that the orthogonal bias observed in V1 may be projected from that in RGC mosaics. These results show that the ON–OFF angle and distance in RGC mosaics intersect orthogonally across retinal space and this may provide the blueprint of orthogonal organization of functional tuning maps in V1 (Fig. 3.7).

3.4 Topographic Correlation of ON/OFF Feedforward Projections To validate our prediction of the correlation between the ON–OFF distance and the ocular dominance/spatial frequency tuning, we analyzed recently published cat data [16], where the profile of V1 receptive fields and functional tuning were measured together across the cortical surface (Fig. 3.8). In this dataset, measurements from two electrodes parallel or perpendicular to an ocular dominance column enabled an analysis of the relationship between the cortical receptive fields and the underlying

3.4 Topographic Correlation of ON/OFF Feedforward Projections

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Fig. 3.5 Orthogonal organization between ON–OFF angle and distance in measured RGC mosaic data. a Left, Estimation of angle and distance between local ON and OFF receptive fields from the measured RGC mosaics. RGC mosaic data were adapted from Zhan et al. [27]. Right, ON–OFF angle measured from the RGC mosaics. b Smoothed maps for gradient analysis (within the dashed square in a). c Orthogonal intersection between gradients of ON–OFF angle and distance. Green arrows, the average intersection angle. Inset, Contours of ON–OFF angle (colorful solid lines) and distance (gray sold line) in the white solid square in smoothed maps

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Fig. 3.6 Orthogonal organization between ON–OFF angle and distance in multiple RGC mosaic data. a Similar analyses were performed for five other RGC mosaic data sets (one from cats and four from monkeys). RGC mosaic data were dOFF adapted from Wässle et al. [29], Gauthier et al. [30], Gauthier et al. [32], Rhoades et al. [33], Vidne et al. [31]. Scale bar, the expected average lattice distance of OFF mosaics,. Gray dashed lines indicate the chance level. b Average of the distribution of intersection angle in six RGC mosaic data sets, including the one used in Fig. 4.5.

3.4 Topographic Correlation of ON/OFF Feedforward Projections

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Fig. 3.7 Orthogonal tiling of neural tunings in V1 that is mirrored from the orthogonal organization in the retina

cortical tuning (red and blue electrodes in Fig. 3.8). From the observed receptive fields, we measured the angle and the distance between the center of ON and OFF subfields (Fig. 3.8, bottom) and examined correlations with underlying functional tunings. Notably, previously reported correlations between different functional tunings were all confirmed with the current dataset. As in previous studies [15–17], we observed that orientation tuning is predicted by the angle between the ON and OFF receptive fields (ON–OFF angle; Fig. 3.9a, n = 20, R = 0.59, *P = 6.64 × 10–3 ). Similarly, a correlation between binocularity (1-|ocular dominance|) and spatial frequency tuning [9] was also observed (n = 25, R = 0.41, *P = 0.03), suggesting that this dataset represents profiles that can be used to validate our model prediction of the organization of a correlated topography in the visual cortex. As predicted, we found that the distance between ON and OFF centers (ON–OFF distance, d) periodically changes across the cortical surface (Fig. 3.9b, left). Notably, the spatial period of the ON–OFF distance variation was practically identical to that of the ocular dominance in the same cortical area (~2.9% difference; fitted to a sine curve). As a result, the observed ocular dominance appeared to correlate strongly to the ON–OFF distance (Fig. 3.9b, right, n = 25, R = 0.62, *P = 8.54 × 10–4 ). The ON–OFF distance and spatial frequency tuning were also systematically correlated in the same data. We found that the deviation of the ON–OFF distance from its average (|d|; Fig. 3.9c, left, gray) is correlated negatively with spatial frequency tuning estimated from the fast Fourier transform (FFT) analysis of V1 receptive fields (Fig. 3.9c, right, n = 25, R = -0.44, *P = 0.03).

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Fig. 3.8 Receptive fields and functional tunings recorded across the cortical surface. Top, In Kremkow et al. [16], receptive fields and functional tunings were recorded by the electrodes penetrating cat V1. Electrodes were penetrated in two directions: parallel (pink) or perpendicular (blue) to an ocular dominance column. Bottom, Example of a recording running perpendicular to an ocular dominance column (Fig. 2 modified fromb of Kremkow et al. [16]). ON–OFF angle and distance were measured from the receptive fields

Considering the correlation between the ocular dominance and ON–OFF distance we observed (Fig. 3.9b), this topographic relationship is analogous to the previous observation that spatial frequency tuning and binocularity are correlated positively [9]. These results suggest that the orthogonal organization of the spatial frequency and ocular dominance maps may be initialized by the spatial organization of the ON–OFF angle and distance in the bottom-up projections.

3.4 Topographic Correlation of ON/OFF Feedforward Projections

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Fig. 3.9 Topographic correlation between ON–OFF angle/distance and diverse cortical tunings. Recording data were adapted from Kremkow et al. [16]. a Left, ON–OFF angle estimated from the local receptive field is correlated with the orientation tuning measured at each electrode with N = 20 data points. Right, Correlation between the ON–OFF angle and the preferred orientation. Green solid circles indicate the data adopted from Jin et al. [15]. Inset: Angle difference between the two angles. The average difference is significantly smaller than that of the shuffled pairs (P = 0.01, N = 1000 repeated trials). b Left, ON–OFF distance (d) and ocular dominance vary periodically across the cortical surface. Right, Correlation between d and ocular dominance. c Left, The deviation of ON–OFF distance from its average (|d|) and the spatial frequency tuning measured by the same electrode. Right, Negative correlation between the preferred spatial frequency and |d|

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3.5 Retinal Origin of Orthogonal Organization The development of orthogonal bias in RGC mosaics was previously predicted by the Paik-Ringach model [21]. Based on observations of long-range hexagonal periodicity and the difference between the ON-ON and OFF-OFF distances in data mosaics, the model suggests that the superposition of ON and OFF RGCs generates an interference pattern that initiates a periodic pattern of orientation maps; due to the organized arrangement of RGCs in this geometric pattern, the orthogonal relationship between the ON–OFF angle and distance arises spontaneously (Fig. 3.10, top). In addition, the orthogonal relationship is consistently obtained across different conditions of the moiré pattern, as the ON–OFF angle and distance change in the polar and radial directions, respectively, regardless of the conditions of the lattice distance ratio (α) and/or the alignment angle (θ ). Notably, we estimated α in the measured RGC mosaics used in the above analysis (α = 0.07~0.19) and confirmed that orthogonality is consistently obtained across different conditions of α in the measured range (Fig. 3.10, bottom).

Fig. 3.10 Orthogonal organization in moiré interference pattern of ON and OFF RGC mosaics. Top, Superposition between the hexagonal lattices of the ON and OFF RGC mosaics generates a moiré interference pattern. The angles of the local ON and OFF RGCs gradually adjust toward the polar direction while the ON–OFF distance changes toward the radial direction regardless of the lattice distance ratio (α) and/or the alignment angle (θ). Regularly structured retinal mosaics provide the initial layout of the orthogonal organizations. Bottom left, Lattice distance ratio of ON and OFF RGC mosaics in different animals. Bottom right, Orthogonal intersection between the gradients of the ON–OFF angle and the distance under different conditions of the moiré interference pattern

3.5 Retinal Origin of Orthogonal Organization

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Chapter 2 suggests that such a quasi-uniform tiling in the RGC mosaics of RGCs could be achieved in various ways. One probable scenario [34] is that this form of quasi-uniform tiling can originate from simple local repulsive interactions between neighboring RGCs (Fig. 2.1). In this model, homotypic repulsion (ON-ON or OFFOFF) generates a quasi-hexagonal pattern in ON and OFF RGC mosaics, whereas heterotypic repulsion (ON–OFF), by which ON and OFF cells are not located at the same position, restricts the alignment between these two patterns, resulting in a consistent spatial period of retinal interference patterns. With this result, we confirmed that the orthogonal organization is observed consistently in realistic RGCs mosaics (Fig. 3.11). Notably, we also tested the robustness of these current results under realistic conditions of this model with retinal constraints. To implement realistic conditions, we additionally introduced two factors following observations in our previous studies (Fig. 3.11a): the differences in positions between the soma and the receptive field center [35] and the anisotropic structure of the RGC

Fig. 3.11 Orthogonal organization under realistic conditions of model RGC mosaics. a To test the orthogonality in the realistic conditions of model mosaics of RGC receptive fields, the spatial distance between the soma and the receptive field center [35], and the elliptical structure of RGC receptive fields [36] were additionally considered in the simulation. b Top, Model RGC receptive field mosaics under a realistic level of regularity (regularity index, RI = mean/STD of the nearest neighbor distance = 8.25 ± 0.21; RI = 7.98 ± 1.76 in six measured RGC mosaics used in the above analysis). Bottom, Distribution of the ON–OFF distance in the data and model. c Top, Orthogonal intersection between the gradients of the ON–OFF angle and distance in the model RF mosaics. Bottom, Orthogonality index (OI) of model mosaics is significantly larger than that measured from the shuffled gradient maps. P < 0.01

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receptive fields [36], in contrast to the facts that the location of the receptive field center coincides with that of the soma and that the receptive field is perfectly circular in the original model (Fig. 2.1). As a result, the orthogonal organization of the ON–OFF angle and distance was observed consistently (Fig. 3.11c), supporting the robustness of the orthogonal bias under realistic conditions with retinal constraints. These results suggest that ON and OFF RGC mosaics, with a certain level of spatial regularity as observed in various datasets, are likely to induce a correlated topography of the ON–OFF angle and distance. This then provides a theoretical framework of the developmental mechanism of the orthogonal organization of both the RGCs and cortical maps. Details of the profile of the pattern in RGC mosaics, which plays a key role in the model, can be investigated further when larger retinal patches are achieved experimentally.

3.6 Hexagonal Topography of Cortical Tuning Maps A key prediction of the model arises from the intrinsic features of RGC moiré interference patterns: hexagonal symmetry. From the fact that ON and OFF RGC mosaics are hexagonal lattices [37], Paik and Ringach (2011) predicted the hexagonal symmetry of cortical orientation maps that is projected from the retinal interference patterns and validated this prediction by analyzing measured orientation map data [21]. Similarly, our model predicts that each functional map that develops from RGC afferents must have hexagonal symmetry in the local region of the map topography, with a consistent map period originating from the common retinal patterns (Fig. 3.12a). We tested this prediction using published animal data on orientation [7, 38–41], ocular dominance [7, 38–40], and spatial frequency maps [7, 39] from different species as was done for orientation maps in the previous study [21]. As predicted, 2D autocorrelation of the individual maps showed a hexagonal pattern of peaks (Fig. 3.12b, top). The statistical significance of the local peaks was tested against control maps that matched the spectral power and spatial periodicity of the original map, but with an isotropic amplitude spectrum instead of hexagonal periodicity (for details, see Supplementary Fig. 3 of [21]). all the hexagonal autocorrelation peaks of individual maps exhibited a significance level of P < 0.05. In the average plot of autocorrelations, the peaks closely matched the expected hexagonal periodicity in three types of functional maps from species as different as cats, ferrets, and galagos (Fig. 3.12b, bottom). Next, we compared the spatial period of different types of functional maps measured in the same cortical area. The spatial period of each map was estimated from the distance between the origin and each local peak in the 2D autocorrelation. As predicted by the model, the spatial period of ocular dominance map closely matched that of the orientation map in the same cortical area (0.99 ± 0.17 times the period of the orientation map; Fig. √ 3.12c, left). The model predicts that the period of the spatial frequency map is 1/ 3 (≈0.58) times that of ocular dominance. This is because frequency tuning is correlated with binocularity, which has minima in both

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Fig. 3.12 Hexagonal periodicity of functional maps. a Hexagonal symmetry is predicted in orientation, ocular dominance, and the spatial frequency map by the moiré interference pattern. b Autocorrelation of functional map. Top, Hexagonal symmetry observed in individual maps of orientation ([39] for Cat 1, [38] for Galago and [7, 40, 41]), ocular dominance [7, 38–40], spatial frequency tuning ([7] for Cat 2 and [39]) in animal data. The autocorrelation functions were rotated and scaled to map each local peak onto (0, 1). Bottom, The average autocorrelation patterns of various functional maps from different species. Peaks (open white circles) in the autocorrelation closely matched the ones in a perfect hexagonal lattice (open white squares). Solid black circles indicate peaks in the autocorrelation of individual maps. The scale bar indicates a period of the map. c Comparison of spatial period across different types of maps in the same cortical area. Observed period of each map data is consistent with our model prediction in all species

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contra- and ipsilateral regions (Fig. 3.12a). In our data analysis, the period of the spatial frequency map was close to the predicted value (0.69 ± 0.05 times the period of orientation map; Fig. 3.12c, right), which also matches the ratio between the two maps in a previous study [9].

3.7 Development of Quasi-Periodic Maps in Realistic Conditions In the above section, we proposed that an interference pattern between ON and OFF RGC mosaics initially seeds the hexagonal layout of diverse functional maps in a cortical patch. If so, would the whole range of functional maps be seeded by a single large interference pattern of RGC mosaics? We hypothesized, in realistic conditions, that cortical maps develop as a patched quilt made of pieces of functional columns, rather than being seeded by a single interference pattern of long-range hexagonal periodicity. Although no mosaic data set large enough for this analysis is currently available, we found evidence that long-range hexagonal periodicity could be broken in realistic conditions. One example is the spatial variation of RGC density with eccentricity that distorted the hexagonal periodicity of RGC mosaics so that cells were aligned at gradually changing angles of axis of the hexagonal lattice across the mosaic area. In addition, even within a mosaic of uniform cell density, hexagonal periodicity may hardly be maintained consistently across large areas of the RGC mosaics due to the spatial noisiness of cell position. To test this, we used the developmental model of RGC mosaics from Chap. 2 [34]. As a result, the axes of hexagonal periodicity in different regions are likely to be aligned at different angles (Fig. 3.13a). This implies that a local hexagonal structure in RGC mosaics can initiate a single cortical column, and then that such local columns continuously patch a quilt, resulting in quasi-periodic functional maps. To test whether a patched quilt of mosaics with local hexagonal structures could develop an orientation map with quasi-periodic layout, we developed model orientation maps from RGC mosaics developed by our previous model [34]. As a result, we observed that the hexagonal axes in local patches of the developed orientation map were aligned at different angles across the map area (Fig. 3.13b). Interestingly, the predicted variation of the aligning axis across the cortical surface was also found in the experimental data, which implies that the retinal mosaic seeding of this map also has such a profile of hexagonal periodicity. In particular, orientation map data in a monkey contains a relatively large number of columns compared to that of the other mammalian species studied, thus hexagonal peaks in the map analysis may hardly be observed due to large variation of the alignment axis across local areas. To validate this prediction, we performed additional analyses of the observed map data, and found that the hexagonal pattern in each local patch is aligned in different angles; thus hexagonal patterns are indeed hard to observe in a large map data set

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Fig. 3.13 Quasi-periodic orientation map seeded by a continuous distribution of local retinal patches. a Even within a mosaic of uniform cell density (generated by the repulsive interaction model of RGC mosaics development [34]), a hexagonal axis is not maintained across a large area of the RGC mosaics. b The orientation map generated by the repulsive interaction model. Regardless of whether the alignment of angles in nearby patches was continuous or random, the local structure of the orientation map appeared hexagonal, but each local patch had a different hexagonal lattice axis

(Fig. 3.14). The autocorrelation analysis of measured orientation map showed that each local patch (~2 map period) contains strong hexagonal periodicity, but that the axis of the periodicity was differently aligned across the patches. This implies that the quasi-periodic orientation map observed in the data might be a patched quilt made of pieces of columns that are seeded by retinal mosaics with local hexagonal periodicity, rather than being seeded by a single interference pattern of long-range hexagonal periodicity. As a result, not a consistent long-range hexagonal periodicity of cortical maps but a quasi-periodic map as a patched quilt of local areas containing hexagonal structures with different axes will be generated. These results also explain why hexagonal periodicity could not be clearly revealed by FFT or autocorrelation analysis of the whole area of the map [42, 43], even though the local structure of each map was observed to be hexagonal [21]. In addition to the above results, Min Song and we performed model simulation showing that the ON–OFF distance and angle in RGC mosaics correspondingly

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Fig. 3.14 Variation of alignment axis in measured orientation maps. Autocorrelation analysis of the measured orientation map shows that each local patch (~2 map period) contains strong hexagonal periodicity, but that the axis of the periodicity is differently aligned across the patches. Map data were adapted from Obermayer and Blasdel [42], under the permission of the copyright holder (© 1993 Society for Neuroscience)

initiate ocular dominance/spatial frequency tuning and orientation tuning, resulting in the orthogonal intersection of cortical tuning maps. Our model simulations suggest that these regularly structured retinal afferents can provide a common framework for organizing various functional maps in the visual cortex. In summary, these results suggest that spatially organized input from the periphery may provide a common framework for various functional architectures in the visual cortex. This common anatomical substrate results in the efficient tiling of sensory modules by organizing a correlated topography of diverse visual tuning. Overall, the structure of periphery with a simple feedforward wiring might provide a parsimonious mechanism to build an initial circuitry for visual function.

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22. Paik S-B, Ringach DL (2012) Link between orientation and retinotopic maps in primary visual cortex. Proc Natl Acad Sci 109:7091–7096. https://doi.org/10.1073/pnas.1118926109 23. Crair MC, Gillespie DC, Stryker MP (1998) The role of visual experience in the development of columns in cat visual cortex. Science (80-)279:566–570. https://doi.org/10.1126/science. 279.5350.566 24. Muir DR, Da Costa NMA, Girardin CC, Naaman S, Omer DB, Ruesch E, Grinvald A, Douglas RJ (2011) Embedding of cortical representations by the superficial patch system. Cereb Cortex 21:2244–2260. https://doi.org/10.1093/cercor/bhq290 25. Croner LJ, Kaplan E (1995) Receptive fields of P and M ganglion cells across the primate retina. Vision Res 35:7–24. https://doi.org/10.1016/0042-6989(94)E0066-T 26. Balasubramanian V, Sterling P (2009) Receptive fields and functional architecture in the retina. J Physiol 587:2753–2767. https://doi.org/10.1113/jphysiol.2009.170704 27. Zhan XJ, Troy JB (2000) Modeling cat retinal beta-cell arrays. Vis Neurosci 17:23–39 28. Jang J, Song M, Paik S-B (2020) Retino-cortical mapping ratio predicts columnar and saltand-pepper organization in mammalian visual cortex. Cell Rep 30:3270-3279.e3. https://doi. org/10.1016/j.celrep.2020.02.038 29. Wässle H, Boycott BB, Illing R-B (1981) Morphology and mosaic of on- and off-beta cells in the cat retina and some functional considerations. Proc R Soc B Biol Sci 212:177–195. https:// doi.org/10.1098/rspb.1981.0033 30. Gauthier JL, Field GD, Sher A, Greschner M, Shlens J, Litke AM, Chichilnisky EJ (2009) Receptive fields in primate retina are coordinated to sample visual space more uniformly. PLoS Biol 7:e1000063. https://doi.org/10.1371/journal.pbio.1000063 31. Vidne M, Ahmadian Y, Shlens J, Pillow JW, Kulkarni J, Litke AM, Chichilnisky EJ, Simoncelli E, Paninski L (2012) Modeling the impact of common noise inputs on the network activity of retinal ganglion cells. J Comput Neurosci 33:97–121. https://doi.org/10.1007/s10827-0110376-2 32. Gauthier JL, Field GD, Sher A, Shlens J, Greschner M, Litke AM, Chichilnisky EJ (2009) Uniform signal redundancy of parasol and midget ganglion cells in primate retina. J Neurosci 29:4675–4680. https://doi.org/10.1523/JNEUROSCI.5294-08.2009 33. Rhoades CE, Shah NP, Manookin MB, Brackbill N, Kling A, Goetz G, Sher A, Litke AM, Chichilnisky EJ (2019) Unusual physiological properties of smooth monostratified ganglion cell types in primate retina. Neuron 103:658-672.e6. https://doi.org/10.1016/j.neuron.2019. 05.036 34. Jang J, Paik S-B (2017) Interlayer repulsion of retinal ganglion cell mosaics regulates spatial organization of functional maps in the visual cortex. J Neurosci 37:12141–12152. https://doi. org/10.1523/JNEUROSCI.1873-17.2017 35. Brown SP, He S, Masland RH (2000) Receptive field microstructure and dendritic geometry of retinal ganglion cells. Neuron 27:371–383. https://doi.org/10.1016/S0896-6273(00)00044-1 36. Suematsu N, Naito T, Miyoshi T, Sawai H, Sato H (2013) Spatiotemporal receptive field structures in retinogeniculate connections of cat. Front Syst Neurosci 7:103. https://doi.org/10. 3389/fnsys.2013.00103 37. Wassle H, Boycott BB, Illing R-B (1981) Morphology and mosaic of on- and off-beta cells in the cat retina and some functional considerations. Proc R Soc B Biol Sci 212:177–195. https:// doi.org/10.1098/rspb.1981.0033 38. Xu X, Bosking WH, White LE, Fitzpatrick D, Casagrande VA (2005) Functional organization of visual cortex in the prosimian bush baby revealed by optical imaging of intrinsic signals. J Neurophysiol 94:2748–2762. https://doi.org/10.1152/jn.00354.2005 39. Issa NP, Trepel C, Stryker MP (2000) Spatial frequency maps in cat visual cortex. J Neurosci 20:8504–8514. https://doi.org/10.1016/j.micinf.2011.07.011.Innate 40. Crair MC, Ruthazer ES, Gillespie DC, Stryker MP (1997) Ocular dominance peaks at pinwheel center singularities of the orientation map in cat visual cortex. J Neurophysiol 77:3381–3385

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“The relatively larger brain of cats and larger eyes of mice” (© 2021. Jaeson Jang all rights reserved.)

Chapter 4

Parametric Classifications of Cortical Organization

In this chapter, it will be shown that disparate organizations of orientation tuning— columnar orientation maps or salt-and-pepper organizations—are initiated by different mapping conditions of the retino-cortical feedforward pathway. From the analysis of anatomical data for eight mammalian species, we found that the ratio between the size of V1 and that of the retina (or between the number of RGCs and V1 neurons) appear higher for species with columnar maps, so the V1 organization of a species could be predicted from these ratios. With a dense mapping condition, the following model simulations show that common retinal afferents are sampled by neighboring V1 neurons, resulting in a continuous and columnar organization of orientation tuning and vice versa. These results suggest that both columnar and salt-and-pepper organization in V1 develop universally with the retinal origin, but may bifurcate due to variation of the feedforward circuit.

4.1 Backgrounds In mammalian visual cortex, neurons selectively respond to various features of external stimuli. These neural tunings often appear as distinct topographic patterns across different species. For example, orientation-tuned neurons in visual cortex are organized distinctively across species into either columnar or salt-and-pepper patterns (Fig. 4.1). It has been debated whether disparate cortical organizations are generated by species-specific developmental principles or simply originate from variation of specific biological parameters. However, it is still unclear if cortical architectures are generated from distinct mechanisms underlying cortical circuit development, or simply destined by specific biological parameters such as cortex size. In detail, selective response of neurons in the primary visual cortex, such as orientation tuning, is one of the hallmarks of the mammalian visual system. Intriguingly, these neural tunings in V1 are organized into distinct topographic patterns across species, such as columnar orientation maps in primates [1] or salt-and-pepper type © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J. Jang and S.-B. Paik, Emergence of Functional Circuits in the Early Visual Pathway, KAIST Research Series, https://doi.org/10.1007/978-981-19-0031-0_4

75

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4 Parametric Classifications of Cortical Organization

Fig. 4.1 Columnar orientation map and salt-and-pepper organization observed in mammalian species. a Left, Columnar orientation map observed in V1 of cats. Data were [12, 2, 13] adapted from Ohki et al. (2006). Right, Random-like salt-and-pepper organization of orientation tuning observed in V1 of rats. Data were adapted from Ohki et al. (2005). b Illustrations of columnar orientation maps observed in higher mammals and salt-and-pepper organizations observed in rodents. Illustrations were adapted from Sirotin and Das (2010). Images and illustrations were adapted under the permission of the copyright holders (a © 2006 Nature Publishing Group and © 2005 Nature Publishing Group; b © 2010 Nature America, Inc.)

organization in rodents [2] (Fig. 4.2a). From the fact that species of distinct cortical organization are found in the separated branches of phylogenetic tree, it has been suggested that columnar or salt-and-pepper organization reflect a fundamental principle of evolution underlying development of cortical circuits in various species (Kaschube 2014; Philips et al. 2017; Weigand et al. 2017).

4.1 Backgrounds

77

Fig. 4.2 Failure of predicting V1 organization from single anatomical parameters. a Columnar and salt-and-pepper organization of orientation tuning observed in mammalian species. b Whether a species has columnar or salt-and-pepper organization cannot be clearly predicted by V1 size, retina size, visual acuity, or body weight

On the other hand, another view has been suggested that disparate organization of cortical neural tuning can simply be predicted by the variation of some biological parameters such as cortex size [3], implying a universal mechanism of cortical development. However, further analysis of data in various species reported counterexamples of this simple prediction, implying that V1 organization may not be simply determined by a single biological factor. For instance, four species of ferrets, tree shrews, rabbits, and gray squirrels have comparable size of V1, but two of them (ferret and tree shrew) have columnar orientation maps, while the others (rabbit and gray squirrel) have salt-and-pepper organizations [4] (Fig. 4.2b). For example, cats with columnar orientation maps have larger V1 (380 mm2 ) [5] than that of mouse

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4 Parametric Classifications of Cortical Organization

without orientation maps (3 mm2 ) [6], but tree shrews with columnar orientation maps have smaller V1 (73 mm2 ) [7, 8] than that of gray squirrels without orientation maps (82 mm2 ) [4, 9]. This suggests that the size of V1 may not be a determinant of V1 patterns. Similarly, other candidate parameters such as visual acuity and body weight also failed to predict V1 organization of orientation tuning among these four species [4]. For example, cats with columnar orientation maps have better visual acuity (6 cycles per degree, cpd) [4] than that of mouse without orientation maps (0.56 cpd) [4], but tree shrews with columnar orientation maps have worse visual acuity (2.4 cpd) [10] than that of gray squirrels without orientation maps (3.9 cpd) [11] (Tables 4.1, 4.2, 4.3 and 4.4). Table 4.1 Retino-cortical size ratio and related experimental data on the retina and V1 anatomy in species having columnar orientation maps (A) V1 size (mm2 ) (B) Retina size

(mm2 )

Macaque

Cat

Ferret

Tree shrew

1257 [4, 14]

380 [5]

83 [15]

73 [7, 8]

636 [16]

510 [17]

84 [18]

122 [19]

(C) Visual acuity (cpd): limit of visible frequency

46 [4]

6 [4]

3.7 [20]

2.4 [10]

(C-1) Visual acuity (cpd): frequency at optimized response/performance

2.7 [21]

0.9 [22]

0.22 [23, 24]

0.26 [25]

(D) Body weight (g)

8000 [4]

3250 [4]

800 [4]

200 [4]

(E) Size ratio (A/B)

1.98

0.75

0.98

0.60

The size ratio (E) in the main text was estimated from previous experimental data in each case. Note that the visual acuity was measured by two different definitions in previous studies (C and C-1); neither of them can predict the V1 organization of diverse species

Table 4.2 Retino-cortical size ratio and related experimental data on the retina and V1 anatomy in species having salt-and-pepper organizations (A) V1 size (mm2 ) (B) Retina size

(mm2 )

Rabbit

Gray squirrel

Rat

Mouse

80 [26]

82 [4, 9]

7 [27]

3 [6]

436 [9, 27]

205 [9]

52 [29]

15 [30]

(C) Visual acuity (cpd): limit of visible frequency

3 [31]

3.9 [11]

1.2 [4]

0.56 [4]

(C-1) Visual acuity (cpd): frequency at optimized response/performance

0.20 [32]

0.5 [11]

0.22 [33]

0.04 [34]

(D) Body weight (g)

2720 [35]

600 [4]

250 [4]

25 [4]

(E) Size ratio (A/B)

0.18

0.40

0.13

0.20

The size ratio (E) in the main text was estimated from previous experimental data in each case. Note that the visual acuity was measured by two different definitions in previous studies (C and C-1); neither of them can predict the V1 organization of diverse species

4.2 Methods

79

Table 4.3 Retino-cortical cell number ratio and related experimental data on the retina and V1 anatomy in species having columnar orientation maps Macaque Cat (cells/mm2 ;

see [376] 3033

(G) Number of V1 neurons (×103 ; A × F)

3812

(F) 2-D density of V1 neurons for details and references) (H) Number of RGC

(×103 )

(I) Cell number ratio, Φ (G/H)

Ferret

Tree shrew

1792

2032

2045

681

169

149

1600 [9]

247 [9] 90 [37] 305 [38]

2.38

2.76

1.87

0.49

The cell number ratio (I) in the main text was estimated from previous experimental data in each case. The two-dimensional density of V1 neurons in rabbit and gray squirrel (F) was estimated from the average density of the other species (except macaques; [36]), based on the previous observation that the surface density of V1 neurons is not noticeably different across diverse species (except primates, [40145])

Table 4.4 Retino-cortical cell number ratio and related experimental data on the retina and V1 anatomy in species having salt-and-pepper organizations Macaque

Cat

Ferret

Tree shrew

(F) 2-D density of V1 neurons (cells/mm2 ; see [36] for details and references)

2021 (Average)

2021 (Average)

2029

2205

(G) Number of V1 neurons (×103 ; A × F)

162

166

14

7

(H) Number of RGC (×103 )

550 [40]

1200 [41]

110 [9]

70 [9]

(I) Cell number ratio, Φ (G/H)

0.29

0.14

0.13

0.09

The cell number ratio (I) in the main text was estimated from previous experimental data in each case. The two-dimensional density of V1 neurons in rabbit and gray squirrel (F) was estimated from the average density of the other species (except macaques; [36]), based on the previous observation that the surface density of V1 neurons is not noticeably different across diverse species (except primates, [39])

4.2 Methods 4.2.1 Analysis of Anatomical Data of Diverse Mammalian Species The anatomical data used in this study were from ref. [4, 9, 14, 16, 42] for macaque, from ref. [2, 4, 5, 9, 17] for cat, from ref. [4, 15, 18, 20, 37, 43, 44] for ferret, from ref. [4, 7, 8, 19, 25, 38] for tree shrew, from ref. [9, 26, 28, 31, 35] for rabbit, from ref. [4, 9, 41] for gray squirrel, from ref. [2, 4, 9, 27, 29] for rat, from ref. [4, 6, 9, 30, 45] for mouse. The details are summarized in Tables 4.1, 4.2, 4.3 and 4.4.

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The V1 (AV ) and retina (AR ) sizes, and the number of RGCs (N R ), were obtained from the references above. The number of V1 neurons (N V ) in a two-dimensional (2D) section of V1 was estimated by multiplying the V1 area size by the 2-D surface density of V1 neurons. The surface density was estimated from the two-photon imaging data of each species [36], which was observed to be fairly consistent across species (within −11.3 to +9.1% of average) except in macaques (1.50 times higher). This estimation well matched the previous observation that the surface density of V1 neurons is consistent across mice, rats, and cats, but 2.5 times higher in macaques [39]. For precise estimation of retino-cortical mapping across retinal space, both physical cell density and the magnification factor between two areas are required, but this information for all species across eccentricity is currently not available. Instead, we assumed that the mapping ratio is quasi-constant across eccentricity based on the cat and monkey data [46–48]. Then, we estimated the retino-cortical mapping ratio (Φ = number of V1 neurons per RGC) by dividing the average number of V1 neurons by the number of RGCs (N V /N R ).

4.2.2 Connectivity and Receptive Field Models To model a V1 receptive field, we assumed that the RGCs are statistically wired to local V1 neurons around the corresponding cortical location [49]. The connection weight (w) of the retino-cortical projection was constrained by a 2D Gaussian distribution with a standard deviation (σcon ) of 0.4d OFF = 41 µm in the retinal space such that a couple of ON and OFF RGCs strongly contributed to the formation of the receptive field of a V1 neuron [49], where d OFF is the average lattice distance between OFF RGCs (0.102 mm). We assumed that parameters for the retino-cortical projection could be approximated as quasi-constant in the local eccentric area. In particular, we assumed that every cortical cell receives input from a similar number for RGCs regardless of variation in RGCs density and retino-cortical magnification, because the density of the RGCs and retino-cortical magnification are proportional across retinal eccentricity in the observed RGC data at large scale [48, 50]. Synaptic weighting between ith RGC and jth cortical sites (wi j ) was defined as   di2j 1 wi j = √ exp − 2 2σcon σcon 2π where di j represents the distance from the center of the ith RGC to the projected location of the jth cortical site.

4.2 Methods

81

The receptive fields of RGCs were defined as a center-surround 2D Gaussian model. The standard deviation of the surrounding region was set to three times that of the center region [51]. The receptive field of the ith RGC (i,RGC ) was defined as i,RGC

    ri2 ri2 1 − exp − 2 √ exp − 2 2σRGC 18σRGC σRGC 2π 3σRGC 2π (+ : ON cell, − : OFF cell)

 =±

1 √

Here, ri is the distance vector from the center of the ith RGC to each position of the visual field. Additionally, σRGC was set to 43.1 µm for ON and 38.4 µm for OFF RGC based on the two-sigma rule stating that the sigma of the RGC receptive field is around half of the cell-to-cell distance [52]. The receptive fields of V1 neurons were defined by the linear sum of the receptive fields of connected RGCs, so the receptive field of jth cortical site ( j,V1 ) was defined as  j, V1 =



wi j · iRGC

i

All simulations were performed using MATLAB 2017a. The preferred orientation and selectivity of the calculated V1 receptive field were estimated from its Fourier transform (ω). The preferred orientation (θPref ) and preferred spatial frequency (ωpref ) were defined as θPref = arg(μ)/2 and ωpref = |μ|, where μ = ∫|(ω)||ω| exp(2i arg(ω))dω/ ∫|(ω)|dω The orientation selectivity index (OSI) was defined as         OSI = ∫ ωpref , θ  exp(2iθ )dθ / ∫ ωpref , θ dθ

4.3 Failure of Prediction from Single Anatomical Parameters Neural tuning to visual stimulus orientation is one of the hallmarks of the primary visual cortex (V1) in mammals. Intriguingly, this tuning in V1 is organized into distinct topographic patterns across species, such as columnar orientation maps in primates [1] and salt-and-pepper type organization in rodents [2] (Fig. 4.2a). From the fact that species of distinct cortical organization are found on separate branches of the mammalian phylogenetic tree, it has been suggested that columnar or saltand-pepper organization reflect species-specific principles of evolution underlying the development of cortical circuits [53, 54].

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4 Parametric Classifications of Cortical Organization

An alternative view is that cortical development is governed by a universal mechanism, but that disparate architectures can arise from variation of specific biological parameters, such as the size of V1 [3] (Fig. 4.2b, left top), the number of V1 neurons [55] and the range of cortical interaction [56]. However, further analysis of data for various species revealed counterexamples of this simple prediction, implying that V1 organization may not be simply determined by a single anatomical factor [4] (Tables 4.1, 4.2, 4.3 and 4.4). In particular, four species of mammals (ferret, tree shrew, rabbit, and gray squirrel) have V1 of comparable size, but it was observed that two of them have columnar orientation maps, while the others have salt-andpepper organization (Fig. 4.2b, left top). This suggests that the size of V1 may not be a determinant of V1 patterns. Similarly, other candidate parameters such as visual acuity and body weight also failed to predict V1 organization of orientation tuning among these four species [4] (Fig. 4.2b).

4.4 Prediction from Retino-Cortical Mapping Ratio An important clue might be in the observation of the thalamic origin of cortical tuning. Previous studies showed that orientation tuning in V1 is well predicted by the local arrangement of ON and OFF thalamic inputs [57, 58], implying that functional circuits in V1 might initially be structured by thalamic afferents. In a subsequent study, Mazade and Alonso (2017) also suggested that observed variation of thalamocortical projection could play an important role in development of the cortical functions and in maximizing visual acuity [21]. In addition, considering that neurons in the lateral geniculate nucleus (LGN) relay the receptive field of only one to three retinal ganglion cells (RGCs) in most cases (cat: [59], monkey: [50], mouse: [51]), the structure of the LGN afferents reflects that of the retinal feedforward afferents. Thus, this retinal organization must be taken into account to understand the development of the V1 architecture. Herein, from the analysis of data for eight mammalian species, we propose that the retino-cortical feedforward mapping ratio can solely predict cortical organization of each species. In the following model simulations, we confirm that distinct cortical circuits can arise from different V1 and retinal ganglion cell (RGC) mosaics sizes. These results suggest that both columnar and salt-and-pepper organization in V1 develop universally with retinal origin [49], but may bifurcate due to variation of the feedforward circuit. An important clue was found from revisiting the spectrum of single anatomical factors across the species examined in the previous section. Generally, the species with columnar orientation maps (e.g., monkeys or cats) have larger V1 than those with salt-and-pepper organizations (e.g., mice or rats). However, the other four species (ferret, tree shrew, rabbit, and gray squirrel) have V1 of comparable size, but have different organizations of orientation tuning, resulting in failure of predicting V1

4.4 Prediction from Retino-Cortical Mapping Ratio

83

organization from the size of V1. Therefore, it was required to devise a predictor that can divide these four species into two groups depending on their functional organizations. Based on our previous model about the role of retinal afferents for providing blueprints of functional maps, we further examined the size of the retina of these four species. Among these four species, interestingly, the size of the retina was not comparable to that of each other, but the size of the retina of two species having columnar orientation maps was smaller than that of the other two species having salt-and-pepper organizations, which is a tendency opposite to that in the comparison between higher mammals (monkeys or cats) and small rodents (mice or rats) (Fig. 4.3). This implies that these four species might be divided depending on the functional organizations by the predictor considering the size of the retina. Based on this prediction, we first found that the V1 organization of the eight species reported so far can be successfully divided into columnar maps or salt-andpepper organization in linear classification, by considering the size of retina (AR ) and the size of V1 (AV ) together (Fig. 4.4, top and Table 4.1–4.2). In particular, among four species (ferret, tree shrew, rabbit, and gray squirrel; gray shaded area in Fig. 4.4)

Fig. 4.3 Revisiting the spectrum of single anatomical parameters. Among four species having V1 of comparable size, the size of the retina of two species with columnar orientation maps (ferret and tree shrew) was smaller than that of the other two species with salt-and-pepper organizations (rabbit and gray squirrel; the order of blue and red boxes against red-to-blue arrow)

84

4 Parametric Classifications of Cortical Organization

Fig. 4.4 Parametric division of species based on retino-cortical size ratio. Top, V1 organization of eight mammalian species can be divided by a linear classifier (y = 0.46x) in 2D space as a function of V1 and retina sizes. Bottom, V1 organization of each species is well predicted by the ratio between the size of V1 and of a retina

that have V1 of comparable size (~80 mm2 ), two species (rabbit and gray squirrel) with salt-and-pepper organization have larger retinas than do the others, which have columnar maps (ferret and tree shrew; Fig. 4.4, right top). Overall, the ratio between the size of V1 and of a retina (AV /AR ) appears higher for those with columnar maps and solely predicts the V1 organization in all the test data (Fig. 4.4, bottom). Species having V1 of comparable size, in particular, were successfully divided according to their V1 organization, which could not be predicted by any single biological parameter in previous studies. Next, to examine the mapping between two areas in terms of neuronal units, we tested a prediction based on the ratio between the number of RGCs (N R ) and V1 neurons (N V ) and found that this retino-cortical mapping ratio

4.4 Prediction from Retino-Cortical Mapping Ratio

85

(N V /N R ) also successfully predicts the V1 organization of all these species (Fig. 4.5; Tables 4.1, 4.2, 4.3 and 4.4).

Fig. 4.5 Parametric division of species based on retino-cortical cell number ratio. Top, V1 organization of eight mammalian species can be divided by a linear classifier (y = 0.40x) in 2D space as a function of number of V1 neurons and RGCs. Bottom, V1 organization of each species is well predicted by the ratio between the number of V1 neurons and RGCs

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4.5 Model Simulation for Parametric Division of V1 Organization Then, what is the underlying principle that explains this classification of V1 organization by retino-cortical mapping? Based on previous experimental observations that the orientation tuning in V1 can be predicted by the arrangement of ON and OFF feedforward afferents [62, 63], we hypothesized that cortical orientation tuning originates from the spatial arrangement of ON and OFF RGC mosaics [64, 65] and that columnar or salt-and-pepper organization in V1 can simply arise due to a different feedforward mapping ratio between RGC and V1 neurons (Φ = N V /N R = number of V1 neurons per RGC), which determines similarity of the cortical tuning in neighboring V1 neurons. Using observed RGC mosaics data in cats [66], we simulated three scenarios for different sizes of the RGC mosaics and V1 (Fig. 4.6). In the model, it was assumed that the entire retinal area is matched to the whole V1 patch and that each V1 neuron receives feedforward inputs from the same size of local ON and OFF RGCs in the area of the corresponding retinal location (see Methods for details). Then, the orientation tuning of each V1 neuron was calculated from the receptive field (RF) of sampled RGCs [49]. We assumed that every cortical cell receives input from a similar number for RGCs regardless of variation in RGC density and retino-cortical magnification because the density of the RGCs and retino-cortical magnification are proportional across retinal eccentricity in the observed RGC data at large scale [46–48, 50]. When the mapping ratio between RGC and V1 neurons was high (Φ = 2.7; i.e., local RGCs are sampled by a large number of V1 neurons), neighboring V1 neurons had highly overlapping receptive fields due to a high sampling density of mapping from retina to V1 space (Fig. 4.7). Then, neighboring V1 neurons had similar orientation tuning, resulting in a columnar organization of orientation tuning (Fig. 4.7, Top and Fig. 4.8, blue curve). In contrast, when we decreased the mapping ratio (Φ = 0.33) by matching a larger retinal mosaic to the same V1, neighboring V1 neurons received inputs from weakly-overlapping RGC populations due to the sparse sampling density of the mapping (Fig. 16B, left), and induced a salt-andpepper organization (Fig. 4.7, middle and Fig. 4.8, red curve; Φ = 2.7 versus 0.33 (blue vs. red), *p = 6.0 × 10–4 ; two-sample Kolmogorov–Smirnov test). We also observed similar salt-and-pepper organization when we decreased the mapping ratio (Φ = 0.30) by decreasing V1 size for the same RGC mosaics (Fig. 4.7, bottom and Fig. 4.8, green curve; Φ = 0.30 versus 0.33 (green vs. red), p = 0.43; two-sample Kolmogorov–Smirnov test). These results demonstrate that distinct V1 organizations can originate from different retino-cortical mapping ratios, rather than from absolute size of RGC mosaics or V1. The results from comparison of these distinct mapping conditions explain why rabbits and gray squirrels do not have columnar clustering, while ferrets and tree shrews have columnar clustering, even though their V1 sizes are comparable (Fig. 4.7, Top versus Middle).

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Fig. 4.6 Modeled retino-cortical pathways for different mapping conditions. Top, For a high mapping ratio between RGC and V1 neurons (Φ = 2.7), neighboring V1 neurons sample similar populations of RGCs. Scale bar, 100 µm in retina and V1. Middle, When a larger retinal mosaic matches the same V1, the mapping ratio (Φ = 0.33) decreases and sparse sampling density induces weakly-overlapping populations of sampled RGCs. Bottom, A low mapping ratio (Φ = 0.30) can also be achieved due to small V1 size and similarly generates weakly-overlapping populations of sampled RGCs

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Fig. 4.7 Variation of V1 organizations with retino-cortical mapping conditions. From given RGC mosaics, either columnar or salt-and-pepper organizations can be seeded according to the retinocortical mapping condition. Top, For a high mapping ratio between RGC and V1 neurons (Φ = 2.7), neighboring V1 neurons had highly overlapping receptive fields, resulting in a columnar organization of orientation tuning. Scale bar, 100 µm in retina and V1. Middle, When a larger retinal mosaic matches the same V1, the mapping ratio (Φ = 0.33) decreases and sparse sampling density induces weakly-overlapping receptive fields of neighboring V1 neurons, resulting in a saltand-pepper organization. Bottom, A low mapping ratio (Φ = 0.30) can also be achieved due to small V1 size and generates a similar salt-and-pepper organization of orientation preference

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Fig. 4.8 Difference between the preferred orientation of neighboring V1 neurons. For Φ = 2.7 versus Φ = 0.33 (blue vs. red) in Fig. 3.7, *p = 6.0 × 10–4 ; Φ = 0.30 versus Φ = 0.33 (green vs. red), p = 0.43; Φ = 0.30 versus shuffled (green vs. black), *p = 2.1 × 10–2 ; two-sample Kolmogorov– Smirnov test. Shaded areas indicate the standard deviation of the orientation difference. Measured from all pairs of V1 neurons (Φ = 2.7, N = 5.66 × 106 ; Φ = 0.33, N = 8.27 × 104 ; Φ = 0.3, N = 6.82 × 104 pairs from 100 repeated simulations)

In addition to the above results, Min Song and we showed that the Nyquist sampling theorem explains this parametric division of cortical organization with high accuracy [67]. Based on these results, we suggested that both columnar and salt-and-pepper organization in V1 develop universally with retinal origin [49], but may bifurcate due to variation of the feedforward circuit. Our results imply that evolutionary variation of physical parameters may induce development of distinct functional circuitry. Furthermore, we found that even for low Φ, V1 organization of orientation tuning can be slightly clustered as in mice [68, 69], because the sampling of neighboring V1 neurons can partially overlap in the retinal space [70]. Altogether, these findings suggest that both columnar and salt-and-pepper organizations of orientation tuning could originate from retinal mosaics. Based on a universal development process, model simulations show that retino-cortical mapping is a prime determinant of the topography of cortical organization (Fig. 4.9). As above, this prediction was validated by an extensive analysis of neural parameter data from eight mammalian species. This result also suggests that evolutionary change in the size of retina or V1 might have led to development of distinct topographical circuitry of orientation tuning in V1 across species, which does not require species-specific developmental principles.

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Fig. 4.9 A single biological factor predicts distinct cortical organizations across mammalian species. Retino-cortical mapping ratio predicts columnar and salt-and-pepper organization in the mammalian visual cortex, even though only the size or number of neurons in each area were considered

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“The brain circuits seeded from the eye” (© 2021. Jaeson Jang all rights reserved.)

Chapter 5

Discussion: Biological Plausibility of the Model

Previous chapters showed that diverse characteristics of functional maps in V1 could be spontaneously initiated from the feedforward afferents from the retina. However, one might argue that these results have not been obtained from experiments, but from simulations, so this model might not be the fundamental mechanism of functional circuits in the real brain. Although we must admit this inevitable limitation of simulation studies, it is notable that a lot of experimental results supporting the plausibility of our models have been extensively reported. In this chapter, the biological plausibility of the model will be introduced with a wide range of references. The recent experimental studies that were affected by our models will also be briefly introduced. Altogether, these results suggest that the initial circuitry of the brain can provide the beginnings of a mechanism initiating the spontaneous emergence of functions, which provides new insight into the mechanisms underlying the development of the visual functions of the brain, as well as artificial neural networks.

5.1 Local Repulsion for Development of Hexagonal Mosaics How is the consistent spatial periodicity of an orientation map retained within a species? In the present study, we proposed a developmental model of RGC mosaics to provide an answer to this fundamental question by addressing a scenario with both homotypic and heterotypic interactions. We first showed that a local repulsive interaction between same-type (homotypic) RGCs developed a long-range hexagonal pattern in ON and OFF simulated mosaics. Then we showed that the relatively weak interaction between ON and OFF (heterotypic) RGCs constrains the alignment angle between the two mosaics, even though it is not strong enough to significantly modulate the structure of the mosaic of the other type. This restricted alignment between mosaics induces a consistent periodicity of retinal moiré interference patterns that will seed a cortical orientation map. Last, in the analysis of the observed RGC mosaics of the experimental data, we found evidence of heterotypic interaction that supports the model prediction. This suggests that both homotypic and heterotypic © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J. Jang and S.-B. Paik, Emergence of Functional Circuits in the Early Visual Pathway, KAIST Research Series, https://doi.org/10.1007/978-981-19-0031-0_5

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retinal interactions may be crucial to the organization of functional architecture in the retina, which would initiate the functional architectures in V1 [1–3]. Because the quasi-uniform tiling of a retinal cell mosaic has been observed [4], the developmental origin of this regular spacing has been studied in some molecularbiological and genetic studies (Lin et al. 2004; Zipursky and Grueber 2013; Lefebvre et al. 2015). In particular, Eglen et al. (2005) suggested a mathematical model for the developmental process of the regularly structured retinal mosaic. The developmental mechanism implemented in this study was based on the pairwise interaction point process (PIPP), where cells were created or removed by conceptual birth-and-death steps. In the PIPP model, each RGC is repeatedly removed and relocated to random positions until all the positions of cells are accepted by a process of stochastic interaction. Consequently, the PIPP model could not generate a hexagonal pattern in mosaics, leading to the conclusion that local interaction between nearby RGCs does not reproduce a hexagonal pattern [5]. However, the PIPP process did not consider the actual process of development, where cells are not really created and removed every time. The model did not address the possibility that the position of RGCs is gradually modulated by repulsive interactions so that they might generate a wellpacked organization of dendritic fields and receptive fields as observed [6]. In this present study, instead of the conceptual birth-and-death steps, we introduced a more biologically plausible mechanism based on the observed pattern of dendritic field growth. The developmental mechanism allowed a continuous change of dendritic field area, which enabled close-packing of cells into a hexagonal lattice pattern. Furthermore, this simulation showed that the closely-packed local hexagonal lattice could generate a long-range order of lattice [4, 6–8]. One of the simplest ways to validate this model would be to confirm a longrange hexagonal pattern in the RGC mosaics data, but a technical problem arises from the limited size of the observable mosaics: No data is currently available in which all RGC receptive fields are plotted over a sufficiently large area of the retina to confirm multiple cycles of retinal interference pattern. In the previous analysis of RGC mosaics, Hore and colleagues (2012) analyzed the autocorrelation of cell mosaic using a scatter plot and claimed that hexagonal arrangement of clusters was not observed. In their analysis, however, simple visual inspection with a scatter plot made it impossible to find hexagonal periodicity. This is because the plotted raw data contained a considerable amount of positional noise of the mosaics. In the revised analysis, we introduced a density map achieved using an appropriate level of filtering of the raw autocorrelogram [9]. As a result, we found a hexagonal pattern that was not observed in the raw scatter plot in Hore et al. (2012), because the method in the original study seemed not appropriate to find such patterns in noisy realistic mosaics. Hore and colleagues presented the autocorrelogram of cell mosaics as a scatter plot and concluded that the hexagonal arrangement of clusters was not observed (Fig. 5.1a). In this scatter plot, however, it is difficult to clearly investigate if there is a particular pattern generated because the location of every single dot plotted contains errors from the local noise of the mosaics. To investigate the structure of mosaics in this study more precisely, we introduced a density map achieved from an appropriate level of filtering of the raw autocorrelogram. As a

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Fig. 5.1 Hexagonal patterns observed in the density map of RGC mosaics. a Hore and colleagues (2012) presented the autocorrelogram of RGC mosaics as a scatter plot and concluded that the hexagonal arrangement of clusters was not observed. Data were [5] adapted from Hore et al. (2012), under the permission of the copyright holder (© Cambridge University Press 2012). b To investigate the structure of mosaics more precisely, a density map was achieved from an appropriate level of filtering of the raw autocorrelogram. As a result, a hexagonal pattern that was not observed in the raw scatter plot was achieved. c The number of 1st-order peaks across different sizes of filters shows a plateau around six, implying that the observed hexagonal pattern is not a filtering artifact and is independent of size of the filter

result, we found a hexagonal pattern that was not observed in the raw scatter plot (Fig. 5.1b). To double-check that this was not a filtering artifact, we examined the number of 1st -order peaks while varying the size of filters and confirmed a plateau around six, implying that the observed hexagonal pattern is independent of size of the filter (Fig. 5.1c). In addition, our intensive analysis of available RGC mosaics data showed evidence that long-range hexagonal periodicity exists in the RGC mosaics [9], which can generate a periodic interference pattern. Using OFF type RGC mosaic data from Gauthier et al. (2009a), which is one of the largest retinal mosaic data sets published, we examined the spatial distribution of higher-order peaks in the autocorrelogram. We found that the local peak positions were well fitted to a hexagonal lattice of up to 5–6th order, which is the upper limit of the analysis within the size of the given mosaics (Fig. 2.16). This analysis provided a vestige of the long-range periodicity in

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the measured mosaics. Future experiments to obtain larger patches of retinal mosaics will enable direct investigation of retinal interference patterns. In the aspect of the role of heterotypic interaction, in a previous study, it was assumed that ON and OFF RGC mosaics develop independently [10]. Based on the analysis of whether a density of one type of cell is dependent on the position of the other types of cells, the researchers concluded that the distribution of the cells was uniform, implying that the location of an RGC does not provide any information about the location of other types of cells. However, the authors neglected the chance that relatively weak heterotypic interactions between ON and OFF RGCs exist. An important point is that heterotypic interaction is not as strong as homotypic interactions, thus it does not interrupt development of the hexagonal patterns in each mosaic. Notably, a previous analysis suggested that the heterotypic repulsive interaction, if it exists, must be much weaker than homotypic interaction. The density profile of other cells around any single cell shows that “neighbor-avoidance-distance” appears large for same-type cell pairs, but is relatively small for different-type cell pairs, resulting in a weak spatial dependency between the ON and OFF cells (Fig. 1 of Ref. [10]; Fig. 5.2). Because the dendritic fields of ON and OFF RGCs occupy different tissue planes [11], the actual distance Fig. 5.2 Density recovery profiles of RGC mosaic data. The density profile of other cells around any single cell shows that the neighbor-avoidance-distance (red solid arrows) appears large for same-type cell pairs (ON–ON), but is relatively small for different-type cell pairs (ON–OFF), suggesting that the heterotypic interaction is not as strong as homotypic interactions. Data were [10] adapted from Eglen et al. (2005), under the permission of the copyright holder (© 2005 Cambridge University Press)

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of a heterotypic RGC pair could be larger than what is measured in previous 2D data, where ON and OFF RGCs were assumed to be in the same plane [4, 10, 12]. Thus, the repulsive interaction between heterotypic RGCs may not appear as significant as that between homotypic RGCs. For better realization of a biologically plausible model, we may implement some additional factors in a future model that we did not apply to the current model for the convenience of theoretical argument. For example, variation in the spatial aspect ratio of receptive fields [13] implies the elliptic and anisotropic development of RGC dendritic fields, and this may develop more realistic and noisy structure of RGC mosaics. Thus, it remains to be determined how much the restricted alignment between the mosaics can be maintained by local repulsion under noisy conditions. Because the model predicts that the orderly structure of RGC mosaics is necessary for the development of orientation maps, it can be also tested whether incomplete tiling of RGCs induces abnormal development of the cortical map. Controlled experiments on the abnormal development of RGC mosaics, such as in mutant animals with the shrinkage of repulsion between RGC dendrites [14–17] might give an answer to this argument. To validate the model prediction further, more precise investigation is needed about what is required in the feedforward and recurrent circuits to seed quasiregular orientation maps from the simulated mosaics. For example, the convergence of retinogeniculate [18] and thalamocortical [19, 20] feedforward connections need to be examined carefully because they significantly affect the receptive field structure and orientation tuning developed in V1 neurons. Note that the present scope of the model is limited to explaining how the cortical map structure is initially organized by the retinal origin [2]. For the complete comprehension of the visual cortical functions [21, 22], the postnatal activity-dependent development of recurrent cortical circuits should be taken into account to explain observations such as the cortical responses for multiple orientations [23, 24] or the matching process between orientation maps through two eyes [25]. It is worth pointing out that the basic concept of the model is connected to other disciplines that also investigate the spatial distribution of particles or their local interaction. In solid-state physics, the hexagonal arrangement of atoms has been widely observed to maximize the volume of the virtual spheres between atoms when they are closely packed in a limited space [26, 27], supporting that the hexagonal arrangement would be an efficient strategy for uniform tiling of cells. In physical chemistry, the role of local interaction between nearby particles was extensively discussed in phase transition [28, 29]. These previous studies in various disciplines suggest the crucial role of local interaction in the organization of regular spacing of particles. Considering that the repulsive energy function weights local interactions more strongly, this function was referred to motivate to define the inter-mosaic coordination energy (IMCE). Using this function, Roy et al. (2021) found that ON and OFF RGC mosaic pairs are anti-aligned, so the amount of encoded information could be maximized [30]. My results about the spatial dependence between ON and OFF RGC mosaics, which are inconsistent with the most related studies reporting the statistical independence between two mosaics, were also referred to motivate

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the analysis of anti-alignment explained by the efficient coding theory [31]. The role of ON–OFF segregated thalamocortical afferents in the development of cortical maps was reminded to motivate the propose a common organizing principle of the ocular dominance maps, resulting in the orthogonal intersection between the slowest retinotopic gradient and the ocular dominance stripes [32]. Overall, these results suggest that local repulsive interactions in retinal development may be crucial to the development of the orderly structure of retinal mosaics, and also to the consistent organization of functional architectures in the visual cortex.

5.2 Initialization of V1 Tunings from Magnocellular and Contralateral Pathway How are various functional maps developed to have topological correlations with each other? Could a common developmental principle of each functional architecture induce such correlation? With these questions in mind, we introduced a novel notion assuming that all the observed functional maps arise from projection of the structure of retinal mosaics and that this common origin induces systematic organization of different maps (Fig. 4.7). These results support our idea of a single common principle active in the developmental mechanism of diverse functional maps in the V1. There are two independent visual pathways, magnocellular and parvocellular, and one may question the role of each pathway during the development of functional maps. In this study, we hypothesized that a magnocellular pathway (parasol retinal ganglion mosaic) initially seeds the orientation map because it contributes predominantly to V1 when orientation selectivity is initially observed in V1. Previously, it was reported that orientation selectivity of the primary visual cortex in cats is observed between developmental stages E57 and P0 [33–35], during which both magnocellular and parvocellular pathways are connected to V1 layer 4. However, orientation selectivity is observed only in sublayer 4Cα, where the magnocellular pathway is predominantly connected. Furthermore, cortical cells in V1 layer 2/3 connected to the parvocellular pathway are not even completely migrated until postnatal week 3. Thus, it is reasonable to infer that the magnocellular thalamocortical input is the only source when orientation selectivity is observed initially. Overall, we inferred that the orientation map may emerge from early magnocellular connectivity and that it is then refined by parvocellular connectivity after eye-opening, though further studies may reveal the detailed mechanism by which these two pathways contribute to the development of functional maps. Similarly, we hypothesized that a contralateral pathway initially seeds the cortical tunings because the contralateral thalamocortical projections from the contralateral eye arrive at V1 layer 4 ahead of those from the ipsilateral pathway. In early developmental stages of the cat (P0–P9), contra-dominant cortical cells are observed in the primary visual cortex, but ipsi-dominant cells are not observed until 20–24 days postnatal. Thus, it is possible to infer that the contralateral input has priority over

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the cortex between P0 and P21. Considering that orientation selectivity is already observed in the early stages of development (P6–9), this functional tuning is probably developed initially from contralateral inputs [36]. Another study reported that orientation preference from the ipsilateral pathway initially shows very weak selectivity (P14), and then is refined after development with visual experience (P30) so that binocular orientation preferences are matched [25]. Such results suggest that ipsilateral connections may develop between P14 and P30, after contralateral development. Altogether, these results suggest that a contralateral pathway first develops before eye-opening (around P7) to initialize orientation tuning, and then an ipsilateral pathway develops later and matches it. The development of orthogonal bias in RGC mosaics was previously predicted by the Paik-Ringach model [2]. In this model, the superposition of ON and OFF RGCs generates an interference pattern that initiates a periodic pattern of orientation maps; due to the organized arrangement of RGCs in this geometric pattern, the orthogonal relationship between the ON–OFF angle and distance arises spontaneously (Fig. 4.10). Such a spatial organization of RGCs can simply originate from local repulsive interaction between nearby RGCs, as reported in Chap. 4. These results suggest that ON and OFF RGC mosaics, with a certain level of spatial regularity as observed in various datasets, are likely to induce a correlated topography of the ON–OFF angle and distance. This then provides a theoretical framework of the developmental mechanism of the orthogonal organization of both the RGCs and cortical maps. Details of the profile of the pattern in RGC mosaics, which plays a key role in the model, can be investigated further when larger retinal patches are achieved experimentally. Compared to other maps, a relatively complicated architecture for spatial frequency maps may have caused difficulty in precise analysis of the location of orientation pinwheels on spatial frequency maps and resulted in contradictory results across some observations. Once, it was reported that pinwheels are preferentially located around the center of ocular dominance domains [37] where binocularity is relatively low. Because it was observed that the binocularity in the cortical neurons has positive correlation with the preferred spatial frequency across the cortical surface [38], pinwheels were expected to be located in regions encoding low spatial frequency. However, in other, more precise optical imaging studies, the orientation pinwheels are reported to be more probably located at either low or high spatial frequency domains [39, 40] or in the positions between high- and low-frequency regions [41]. Considering that estimating the pinwheel location can be affected by the pre-processing condition found in the optical imaging methods (see Fig. S2 in Kaschube et al. 2010), further studies imaging larger patches with higher resolution could provide a clue to resolve this contradiction. This model also provides the explanation for the inter-map relationship between orientation and direction maps—direction preference flips to the opposite direction along the center of iso-orientation domains (Fig. 5.3) [42, 43]. Based on the model, we initially predicted that direction selectivity originates from the temporal delay between ON and OFF RGC afferent to a V1 neuron and that its preferred direction would be from ON to OFF. However, further analysis showed that there also are

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Fig. 5.3 Flip of preferred direction at the center of iso-orientation domains. Direction tuning discontinuity appears in iso-orientation domains in cat V1 [42, 43]. The model predicts that the ON-to-OFF or OFF-to-ON direction of RGCs suddenly flips where their orientation is consistent. Map data were [42][43] adapted from Shmuel and Grinvald (1996) and Kisvˇarday et al. (2001), under the permission of the copyright holders (© 2013 Nature America, Inc. and © Oxford University Press 2001, respectively)

counterexample data showing that the preferred direction appears to be from OFF to ON. First, from additional analysis of the previously reported data [44], we observed that the preferred direction was not always from ON to OFF subregions, but was from OFF to ON in some sample units (Fig. 5.4). In addition, we found that the temporal delay between ON and OFF afferent signals appeared different in previous studies: the ON pathway appears faster in a study [45], but the OFF pathway was faster in other studies [46–48]. Interestingly, however, we found that this tendency of temporal delay between ON and OFF pathways appears consistent (either ON-to-OFF or OFF-to-ON) within the same sample in each study [45–51]. Therefore, with the fact that the temporal delay between spatially separated input is an important source of direction tuning in general [52–55], we suggest that “Cortical direction selectivity is initially seeded by temporal disparity between ON and OFF afferents, and it could be either ON-to-OFF or OFF-to-ON in each animal or in each cortical region”. In other words, if the ON– OFF delay is consistent in a local region of V1, the preferred direction within the region will be organized in either ON-to-OFF or OFF-to-ON direction. In this case, the preferred direction suddenly flips to the opposite direction near the region where the ON–OFF phase of the afferent flips, regardless of whether the direction tuning is constrained by the ON-to-OFF (Fig. 5.3, left) or OFF-to-ON direction (Fig. 5.3, right). Therefore, this model predicts that a moiré interference pattern of ON and OFF RGC mosaics contains linear fractures of ON-to-OFF direction, forming preferred

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Fig. 5.4 Direction preference aligned with ON-to-OFF or OFF-to-ON directions. The preferred direction was not always from ON to OFF subregions but was from OFF to ON in some sample units. Data were [44] adapted from Kremkow et al. (2016), under the permission of the copyright holder (© 2016, Nature Publishing Group, a division of Macmillan Publishers Limited)

direction discontinuities. In this view, direction discontinuities would appear in the middle of the iso-orientation domain (Fig. 5.3, bottom). Notably, this is the simplest and probably the only model to explain the observed topographic relationship between the orientation and direction tuning maps, and this model prediction does not particularly depend on whether the preferred direction is ON-to-OFF or OFF-to-ON. Although we cannot specifically predict the direction of preference at this moment, this is not the central prediction of this model, and the observation from the data that there is overlap between the direction fracture and the iso-orientation domain is readily explained by the model in both cases direction polarity. Thus, this model is not only based on the plausible assumption but also provides an explanation for the inter-map relationship, the mechanism of which has been elusive for more than two decades [56]. From this, the model predictions became less specific but still provide a possible explanation of the main questions, “Why does the direction preference in the map “flip” (direction fracture) along the center of iso-orientation domains?” and “What developmental mechanism can explain this topographic correlation between the two maps?” [42, 43]. Although the luminance preference also shows quasi-periodic variation [44] and clustered topography in V1 [57], it is yet unclear whether the luminance preference has any specific inter-map relationships with other maps. Rather, the intersection angle between orientation tuning in ferret V1 did not show any bias to any orthogonal or parallel organization (Fig. 5.5), implying that the layout of the luminance map might not be seeded by the retinal afferents. Further experiments measuring the

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Fig. 5.5 Weak inter-map relationships between the luminance map and other maps. Although the luminance preference also shows quasi-periodic variation [44] and clustered topography in V1 [57], it is yet unclear whether the luminance preference has any specific inter-map relationships with other maps. The intersection angle between orientation tuning in ferret V1 did not show any bias to any orthogonal or parallel organization. Data were [57] adapted from Smith et al. (2015), under the permission of the copyright holder (© 2015 Elsevier Inc.)

luminance and receptive fields together will help to clarify whether the luminance map also organizes a systematic structure as with other cortical maps. The present scope of our model is limited to explaining how retinal inputs can provide the “original” blueprint for each functional map. However, it is obvious that the refinement of the circuits from the cortical activity and from visual experience is also a critical factor in modifying the layout of functional maps [25, 58]. To understand fully the development of the cortical circuits, which component of the cortical circuit activity, such as cross-orientation suppression [24], plays an important role in each visual processing function must be investigated in future studies. In summary, this study suggests that spatially organized input from the periphery may provide a common framework for various functional architectures in the visual cortex. This common anatomical substrate results in the efficient tiling of sensory modules by organizing a correlated topography of diverse visual tunings. Overall, these results suggest that the structure of periphery with simple feedforward wiring can provide the beginnings of a mechanism by which to build the initial circuitry for the visual function.

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5.3 Functional Implication of Disparate V1 Organizations Findings in Chap. 3 suggest that both columnar and salt-and-pepper organizations of cortical circuits originate from retinal mosaics and by a universal development process. Analysis of anatomical data from eight mammalian species suggests that retino-cortical mapping is a prime determinant of the topography of cortical organization of orientation tuning. This result implies that evolutionary variation of the size of retina and V1 has led to development of distinct topographical circuitry in V1, even without species-specific developmental principles. The discussion regarding the effect of other characteristics of rodent visual systems on the cortical organization of orientation tuning is provided in the published version of this work [59]. Although the manner by which each V1 organization is projected onto the next stage has not yet been directly measured, previous studies suggest distinct functional impacts of the two organizations on further visual pathways. In a salt-and-pepper organization, orientation tuning is distributed in a random-like manner such that receptive fields with different preferred orientations can sample a visual scene more uniformly [60]. Considering that connections from rodent V1 project to very different visual areas [61–63], the salt-and-pepper organization may be the structure providing unbiased visual inputs for diverse visual pathways specialized for distinct visual functions, such as motion-related versus pattern-related computations [64]. In contrast, local orientation tuning in a columnar organization is more biased toward a specific orientation, but this structure enables an efficient tiling of diverse functional modules for ocular dominance or spatial frequency tuning, maximizing the representation of different stimulus combinations for each cortical location [38, 65]. One can argue that each V1 organization may originate from the different dynamics of recurrent cortical circuits across species, but experimental observations provide evidence that the cortical organization of orientation tuning is initialized by feedforward afferents rather than by recurrent circuits [20]. It was recently reported that orientation tuning is initially seeded by randomly sampled ON and OFF feedforward afferents and that recurrent circuits can modulate further refinement of the receptive field [66]. Indeed, cortical orientation tuning and its columnar organization are observed before the complete development of recurrent circuits, and the spatial layout of this initial organization is maintained through the development stage [25, 67, 68]. This indicates that the cortical organization of orientation tuning is initially seeded by feedforward afferents and can be fine-tuned by various types of synaptic plasticity in feedforward and recurrent circuits (Park et al. 2017; Lee et al. 2020). Note that the current study is based on a comparative study of only eight species, and additional investigations of other species will provide further support for this model. For example, the galago (bush baby) is another primate species with orientation columns [69]. Although its anatomic parameters are seemingly different from that of macaques (retina size, 332 [70] vs. 636 mm2 ; V1 size, 212 [71] vs. 1257 mm2 ), This model predicts that this species would have orientation columns because the ratio between the size of V1 and the retina (212/332 = 0.64) has been found to be

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a condition initiating the columnar organization (>0.46; Fig. 15A), consistent with experimental observations. In addition, ongoing observations of orientation columns in wallabies [72] may provide additional data sets with which to test this model predictions. A key assumption of the current model is that neighboring V1 neurons receive feedforward inputs from a similar population of nearby RGCs, as suggested by the statistical wiring model [1, 12]. Although such feedforward projections have not yet been directly measured due to a lack of experimental techniques capable of tracing the retino-cortical connectome while also measuring corresponding receptive fields, recent studies have reported a vestige of such local pooling, where the location ON and OFF receptive fields of neighboring V1 neurons are highly clustered, resulting in similar orientation preference of these neurons [44, 73]. Considering that the ON and OFF topology in V1 originates from the thalamic afferents [20] and that most thalamic neurons relay retinal afferents [18], these results suggest that neighboring V1 neurons receive ON and OFF retinal inputs from a similar population of nearby RGCs. In Tables 4.1–4.4, one might argue that the visual acuity of ferrets is too high, considering previous experimental results [74, 75]. To address this issue, we found that this discrepancy arose from two different definitions of visual acuity that have been interchangeably used in previous studies: the upper limit of the frequency of the visible stimuli (Fig. 5.6a, red dashed line) or the frequency at the optimized response (Fig. 5.6b, blue dashed line). Fig. 5.6 Two different definitions of visual acuity that have been interchangeably used in previous studies. a The upper limit of the frequency of the visible stimuli or the frequency at the optimized response. b Visual acuity measured by optimized frequency of eight species studied

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To avoid any confusion, both values of each species were separately summarized in row C and C-1 of Tables 4.1–4.4 and we confirmed that both of them fail to predict the V1 organization of species (Figs. 4.2 and 5.6b). For example, the visual acuity of ferrets in our previous manuscript was measured using the upper limit of the frequency of the visual stimuli (3.35–4 cpd [76]). However, in other studies, the acuity was measured by the frequency for the optimized neuronal response or behavioral performance (0.18~0.25 cpd [74, 75]), resulting in lower visual acuity than that measured by the first definition. Recently, Ho et al. (2021) suggested the mouse lemur, one of the smallest living primates, as the counterexample of our model [79]. They observed the columnar orientation map of mouse lemur and reported that the retino-cortical size ratio of mouse lemur is 0.37 (the size of V1 is 48 mm2 and the size of the retina is 130 mm2 ), while we predicted that species having the retino-cortical ratio smaller than 0.46 would not have columnar orientation maps (0.6 in tree shrew with orientation map, but 0.4 in gray squirrel and 0.18 in rabbit without orientation map; Tables 4.1–4.4 and Fig. 4.4). Regarding this issue, we would like to point out that the higher cortical cell density in primates might increase the practical retino-cortical mapping ratio to be greater than the ratio estimated from the size comparison. In our model, the most important parameter is the amount of neural resources in the retina and V1 of species (Fig. 4.6). Although the number of cells is a more direct estimator for the amount of neural resources than the size of the region, we initially used the size as the estimator in our previous analysis by assuming that the physical cell density in each area is comparable across species. As assumed, the 2D surface density of V1 neurons was observed to be consistent across non-primate species. However, it was 2.5 times higher in primates compared to that in other nonprimate species (mouse, rat, and cat vs. macaque) [80]. Therefore, to estimate the retino-cortical mapping ratio more directly considering the higher V1 cell density of primate species, the size ratio should increase by 2.5 times as the estimator for primate species but stay consistent for non-primate species. After this calibration process, the greatest ratio of species having salt-and-pepper organizations is 0.4 (gray squirrel), and the lowest ratio of species having columnar orientation maps is 0.6 (tree shrew; 0.37 (original size ratio) × 2.5 = 0.93 for mouse lemur), so the species are still divided into two groups depending on their functional organizations. The functional role of the columnar and salt-and-pepper organization has been debated [24, 81] and future studies are needed to reveal whether each type of organization is the optimized form of functional circuits under different physical constraints in each species. These findings may provide advanced insight into the study of distinct cortical architectures under a universal principle of development process.

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5.4 Emergence of Visual Tunings in Untrained Artificial Neural Networks The above results suggest that the functional circuits encoding low-level visual cues in V1 could be solely initiated by hard-wired feedforward projections from the retina. Extending this notion, it is expected that higher cognitive functions might also spontaneously arise in further visual areas by sampling elementary functional modules in V1, which does not require any learning process. Important clues were found from the innate number sense observed in newborn animals, implying that the initial development of higher cognitive functions also might not require a training process modulated by the visual experience. Number sense is an ability to estimate numbers without counting [82, 83]. It has been reported that this capacity is observed in humans and various animals in the absence of learning. Newborn human infants can respond to abstract numerical quantities across different modalities and formats [84], and newborn chicks can discriminate quantities of visual stimuli without training [85]. In single-neuron recordings in numerically naïve monkeys [86] and crows [87], it was observed that individual neurons in the prefrontal cortex and other brain areas can respond selectively to the numerosity of visual items. These results suggest that numerosity-selective neurons arise before visual training and that they may provide a foundation for an innate number sense in the brain. Recently, model studies with biologically inspired artificial neural networks have provided insight into the development of various functional circuits for visual information processing [88–91]. For example, the brain activity initiated by various visual stimuli has been successfully reconstructed in deep neural networks (DNNs) [92–94] and the visual pattern designed to maximize the response of DNNs also maximized the spiking activity of cortical neurons beyond their naturally occurring levels [95]. These results suggest that studies using DNN models can provide a possible scenario for the mechanism of the brain activities encoding visual information. Regarding the spontaneous emergence of the number sense, important clues were found from a randomly initialized, untrained feedforward network able to initiate various cognitive functions [96]. It was reported that selective tunings, such as number-selective responses, can emerge from the multiplication of random matrices [97] and that the structure of a randomly initialized convolutional neural network can provide a priori information about the low-level statistics in natural images, enabling the reconstruction of the corrupted images without any training for feature extraction [98]. Based on these results, Gwangsu Kim and we showed that abstract number tuning of neurons can spontaneously arise even in completely untrained DNNs, and that these neurons enable the network to perform number discrimination tasks [99]. Using an AlexNet model designed based on the structure of a biological visual pathway, we found that number-selective neurons are observed in randomly initialized DNNs in the complete absence of learning and that they show the single- and

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multi-neuron characteristics of the types observed in biological brains following the Weber-Fechner Law. Our findings suggest that number sense can emerge spontaneously from the statistical properties of bottom-up projections in hierarchical neural networks. Also, these findings provide insight into the understanding of biological brains, specifically in relation to how number neurons or number sense similarly arise in a wide range of different species, from mammalian [86] to avian [87], separated in the phylogenetic tree by nearly 300 million years [100, 101]. In particular, observations of number neurons in these naïve animals of various species suggest that number tuning emerges regardless of the species-specific design of the neural circuitry, such as different numbers of layers in the neocortex. Instead, these findings suggest that number neurons can originate from much simpler and more common components in the feedforward afferents. This may provide the simplest theoretical scenario for the spontaneous emergence of number neurons with different organizations of the cortical circuits, which may also inspire new designs of artificial neural networks that function analogously to biological brains. Lastly, these findings here can provide insight into the understanding of the development of early cortical circuits in the brain. In the early development stage before visual experience, the visual pathway from the retina to the cortex is initialized by retinotopic projections of feedforward afferents [1–3, 9, 12, 102]. During this stage, local wirings for feedforward convergence projection are noisy and the receptive fields of individual neurons are not yet refined [103, 104]. This is comparable to the condition of a convolutional filter in a randomly initialized neural network before training for a task. In this stage of DNNs, a convolutional process is simply a local sampling of feedforward inputs with random weights. It was previously believed that convolutional filters must be refined by training for the network to perform a function, but here we suggest that the network can perform certain innate functions with these untrained filters. In the case of a biological neural network, spontaneous tunings generated in this early condition will initialize various functions, possibly leading to highly effective refinement of the receptive fields when learning begins with sensory inputs. In summary, we conclude that the innate number tuning of neurons can spontaneously arise in a completely untrained deep neural network, solely from the statistical variance of feedforward projections. Similarly, we recently found that units selective to faces also emerge robustly in randomly initialized networks [105]. These findings suggest that various cognitive functions originate from the organization of the random initial wirings of deep neural circuits, providing new insight into the mechanisms underlying the development of cognitive functions in biologically inspired artificial neural networks.

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5.5 Concluding Remark The nature-versus-nurture debate has been one of the most challenging issues in neuroscience. Does intelligence appear from nothing as described by the tabula rasa [106], or is the initial seed of intelligence innately given and then strengthened afterward? Although much effort has been devoted to studying the reinforcement of intelligence through a training process in the fields of machine learning and neuroscience, most parts remain elusive regarding how such intelligence or cognitive functions arise initially. One possible approach would be to reveal how the blueprints of the development of functional neural circuits are genetically encoded and inherited through generations. Regarding this issue, the results in this book suggest that the hard-wired feedforward neural network can solely provide the foundation for the emergence of functional circuits, even without any visual experience. Therefore, for the initial emergence of the intelligence, it would be sufficient to save the blueprints for the hard-wired architecture of neural circuits, such as the retino-cortical feedforward connections or the repulsive interaction between nearby retinal cells, even though intelligence would be strengthened through the experience modulated by further mechanisms. Overall, several examples for the development of functional circuits or cognitive functions originating from the unrefined wiring of the feedforward neural network were presented in this book. These results suggest that the hard-wired circuity of the brain can initiate the spontaneous emergence of cognitive functions, even under the complete absence of further training or refining processes. These findings might provide new insight into the mechanisms underlying the development of the visual functions of the brain, as well as artificial neural networks.

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Curriculum Vitae

(Lastly updated on December 21, 2021) Jaeson Jang, Ph.D. [email protected] EDUCATION 2016.03–2020.08 Ph.D.

Bio and Brain Engineering (Advisor: Se-Bum Paik) KAIST, Daejeon, Republic of Korea

2014.03–2016.02 M.S.

Bio and Brain Engineering (Advisor: Se-Bum Paik) KAIST, Daejeon, Republic of Korea

2010.02–2014.02 B.S.

Bio and Brain Engineering, Mathematical Sciences (Double major) Business and Technology Management (Minor) KAIST, Daejeon, Republic of Korea

RESEARCH EXPERIENCE 2020.09–Current

Research scientist, Looxid Labs - Eye-tracking/EEG data analysis

2014.03–2020.08

Graduate researcher, KAIST - Modeling visual processing in the retino-cortical pathway - Examining functions of untrained artificial neural networks

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 J. Jang and S.-B. Paik, Emergence of Functional Circuits in the Early Visual Pathway, KAIST Research Series, https://doi.org/10.1007/978-981-19-0031-0

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PEER-REVIEWED PUBLICATIONS * Co-first, † Co-corresponding authors As first author Koh HY*, Jang J*, Ju SH*, …, Sohn JW† , Paik SB† & Lee JH† , “Non-cell autonomous epileptogenesis in focal cortical dysplasia”, Annals of Neurology (2021) [https://onlinelibrary.wiley.com/doi/abs/10.1002/ana.26149] Song M*, Jang J*, Kim G & Paik SB, “Projection of orthogonal tiling from the retina to the visual cortex”, Cell Reports (2021) [https://www.cell.com/cell-rep orts/fulltext/S2211-1247(20)31570-9] Kim G*, Jang J*, Baek S, Song M & Paik SB, “Visual number sense in untrained deep neural networks”, Science Advances (2021) [https://advances.sciencemag. org/content/7/1/eabd6127] Jang J*, Song M* & Paik SB, “Retino-cortical mapping ratio predicts columnar and salt-and-pepper organization in mammalian visual cortex”, Cell Reports (2020) [https://www.cell.com/cell-reports/fulltext/S2211-1247(20)30199-6] Jang J & Paik SB, “Interlayer repulsion of retinal ganglion cell mosaics regulates spatial organization of functional maps in the visual cortex”, Journal of Neuroscience (2017) [https://www.jneurosci.org/content/37/50/12141?etoc=] Featured article: This Week in The Journal: Orientation Maps May Depend on Repulsion in the Retina [https://www.jneurosci.org/content/37/50/i] Sailamul P*, Jang J* & Paik SB, “Synaptic convergence regulates synchronization-dependent spike transfer in feedforward neural networks”, Journal of Computational Neuroscience (2017) [https://link.springer.com/art icle/10.1007/s10827-017-0657-5] As co-author Baek S*, Song M*, Jang J, Kim G & Paik SB, “Spontaneous generation of face recognition in untrained deep neural networks”, Nature Communications (2021) [https://www.nature.com/articles/s41467-021-27606-9] Kim G, Jang J & Paik SB, “Periodic clustering of simple and complex cells in visual cortex”, Neural Networks (2021) [https://www.sciencedirect.com/sci ence/article/pii/S0893608021002343] Kim J*, Song M*, Jang J & Paik SB, “Spontaneous retinal waves generate longrange horizontal connectivity in visual cortex”, Journal of Neuroscience (2020) [https://www.jneurosci.org/content/40/34/6584] (Cover article) Koh HY, Kim SH, Jang J, … & Lee JH, “BRAF somatic mutation contributes to intrinsic epileptogenicity in pediatric brain tumors”, Nature Medicine (2018) [https://www.nature.com/articles/s41591-018-0172-x]

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PRE-PRINTS Lee B*, Lee T*, …, Shin C† & Jang J† , “Synergy through Integration of Wearable EEG and Virtual Reality for Mild Cognitive Impairment and Mild Dementia Screening: Protocol Design and Feasibility Study”, JMIR Preprints (2021) [https://preprints.jmir.org/preprint/30028/submitted] Under review in IEEE JBHI CONFERENCE PRESENTATIONS International oral presentations 1

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Annual Computational Neuroscience Meeting (CNS) 2019, Jaeson Jang*, Min Song* & Se-Bum Paik, “Development of Periodic and Salt-And-Pepper Orientation Maps from a Common Retinal Origin” Society for Neuroscience (SfN) 2018, Jaeson Jang*, Min Song*, Gwangsu Kim & Se-Bum Paik, “A Unified Developmental Model of Functional Maps in the Primary Visual Cortex”

International poster presentations 1

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Computational and Systems Neuroscience (Cosyne) 2021, Jaeson Jang*, Gwangsu Kim*, Seungdae Baek, Min Song & Se-Bum Paik, “Abstract Number Sense in Untrained Deep Neural Networks” CSHL Meeting—from Neuroscience to Artificially Intelligent Systems (NAISys) 2020, Jaeson Jang*, Gwangsu Kim*, Seungdae Baek, Min Song & Se-Bum Paik, “Emergence of Number Selectivity in Untrained Deep Neural Networks” Annual Computational Neuroscience Meeting (CNS) 2020, Jaeson Jang*, Gwangsu Kim*, Seungdae Baek, Min Song & Se-Bum Paik, “NumberSelective Units Can Spontaneously Arise in Untrained Deep Neural Networks” Computational and Systems Neuroscience (Cosyne) 2019, Min Song*, Jaeson Jang*, Gwangsu Kim & Se-Bum Paik, “Topographic Organization of Distinct Tuning Maps for Optimal Tiling of Sensory Modules in Visual Cortex” International Brain Research Organization (IBRO) 2019, Jaeson Jang*, Min Song* & Se-Bum Paik, “Retinotopic Mapping as a Determinant of Columnar and Salt-And-Pepper Organization of Orientation Tuning in Visual Cortex” Society for Neuroscience (SfN) 2019, Jaeson Jang*, Min Song* & SeBum Paik, “Principles of Columnar and Salt-And-Pepper Organizations of Orientation Tuning in Visual Cortex” Korean Society for Brain and Neural Sciences (KSBNS) 2018, Jaeson Jang*, Min Song*, Gwangsu Kim & Se-Bum Paik, “Universality of the Developmental Origins of Diverse Functional Maps in the Visual Cortex” Annual Computational Neuroscience Meeting (CNS) 2018, Jaeson Jang*, Min Song* & Se-Bum Paik, “Retinal Development of Cortical Functional Circuits”

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Korean Society for Brain and Neural Sciences (KSBNS) 2017, Jaeson Jang & Se-Bum Paik, “Regularly Structured Retinal Mosaics Can Induce Structural Correlation Between Orientation and Spatial Frequency Maps in V1” Annual Computational Neuroscience Meeting (CNS) 2017, Jaeson Jang & Se-Bum Paik, “Regularly Structured Retinal Mosaics Can Induce Structural Correlation Between Orientation and Spatial Frequency Maps in V1” Society for Neuroscience (SfN) 2017, Jaeson Jang*, Min Song* & Se-Bum Paik, “Retinal Origin of Various Functional Maps in Visual Cortex” Annual Computational Neuroscience Meeting (CNS) 2016, Jaeson Jang & Se-Bum Paik, “Local Repulsive Interaction Between Retinal Ganglion Cells Can Generate a Consistent Spatial Periodicity of Orientation Map” Society for Neuroscience (SfN) 2016, Jaeson Jang*, Changju Lee* & Se-Bum Paik, “Quasi-Regular Structure of oN and oFF Retinal Mosaics Provides a Common Organizing Principle of Functional Maps in V1” Annual Computational Neuroscience Meeting (CNS) 2015, Jaeson Jang & SeBum Paik, “Local Interaction in Retinal Ganglion Cell Mosaics Can Generate a Consistent Spatial Periodicity in Cortical Functional Maps” Society for Neuroscience (SfN) 2014, Jaeson Jang, Pachaya Sailamul & SeBum Paik, “Local Repulsive Interactions in Retinal Mosaic Generate LongRange Order and Consistent Periodicity”

Domestic poster presentations 1

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Korean Society for Computational Neuroscience (Cbrain) 2017, Jaeson Jang & Se-Bum Paik, “Regularly Structured Retinal Mosaics Originate Structural Relationship Between Orientation and Spatial Frequency Maps in V1” Korean Physical Society Spring Meeting (KPS) 2017, Jaeson Jang & Se-Bum Paik, “Regularly Structured Cell Mosaics in Retina Can Induce a Geometrical Correlation Between Orientation and Spatial Frequency Maps in Brain” Korean Physical Society Spring Meeting (KPS) 2016, Jaeson Jang & SeBum Paik, “Repulsive Interaction Between Two Lattice Mosaics Can Develop Consistent Spatial Organization of Functional Maps in Brain” Korean Society for Computational Neuroscience (Cbrain) 2015, Pachaya Sailamul*, Jaeson Jang* & Se-Bum Paik, “Synchronization-Dependent Spike Transfer Modulated by Convergent Wiring in Feedforward Networks” Korean Physical Society Spring Meeting (KPS) 2015, Jaeson Jang & Se-Bum Paik, “An Interference Pattern of Cell Mosaics Developed by Local Interaction Can Generate a Periodic Structure of Functional Maps in the Brain” Korean Society for Computational Neuroscience (Cbrain) 2014, Jaeson Jang, Pachaya Sailamul & Se-Bum Paik, “Local Repulsive Interactions in Retinal Mosaic Develop a Consistent Spatial Periodicity in Cortical Functional Maps” Korean Physical Society Spring Meeting (KPS) 2014, Jaeson Jang & Se-Bum Paik, “An Interference Pattern Generated by Intrinsic Geometrical Factors Can Develop a Periodic Structure in Biological System”

Curriculum Vitae

121

PATENTS Se-Bum Paik, Gwangsu Kim, Jaeson Jang, Seungdae Baek, Min Song, US Patent, 17/000,887 (2020) “Electronic device for recognizing visual stimulus based on spontaneous selective neural response of deep artificial neural network and operating method thereof” HONORS and AWARDS Ph.D. Thesis Award for Excellence, Department of Bio and Brain Engineering in KAIST, 2021 Student Travel Awards, Annual Computational Neuroscience Meeting (CNS), 2019 Best Student Poster Presentation Award, Annual Computational Neuroscience Meeting (CNS), 2017 Best Poster Presentation Awards, The Korean Physical Society Spring Meeting (KPS), 2015 Excellence Award, Computational Neuroscience Winter School, 2015 Best Poster Presentation Awards, Korean Society for Computational Neuroscience Annual Meeting (Cbrain), 2014 Best Poster Presentation Awards, The Korean Physical Society Spring Meeting (KPS), 2014 FUNDING and SCHOLARSHIP Government Scholarship, Korea Student Aid Foundation (2014–2019, 6 years) National Scholarship for Science and Engineering Students, Korea Student Aid Foundation (2010–2013, 4 years)