Thermodynamics of Biological Processes [Reprint 2019 ed.] 9783110860511, 9783110073126

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Thermodynamics of Biological Processes

Thermodynamics of Biological Processes Editors Ingolf Lamprecht A. I. Zotin

w DE

G

Walter de Gruyter • Berlin • New York 1978

Editors Prof. Dr. Ingolf Lamprecht Institute o f Biophysics Freie Universität Berlin D - 1 0 0 0 Berlin 33 Prof. Dr. A. I. Zotin Institute o f Developmental Biology Academy o f Science of the U.S.S.R. Moscow with 6 9 Figures

CIP-Kurztitelaufnahme der Deutschen

Bibliothek

Thermodynamics of biological processes/ed. : Ingolf Lamprecht; A.I. Zotin. - Berlin, New York: de Gruyter, 1978 ISBN 3-11-007312-9 NE: Lamprecht, Ingolf [Hrsg.]

Library of Congress Cataloging in Publication Data

Thermodynamics of biological processes. Includes bibliographical references and index. 1. Biological physics. 2. Thermodynamics. 3. Developmental biology. I. Lamprecht, Ingolf, 1933 II. Zotin, Aleksandr Il'ich. QH505.T395 574.r91 78-15462

© Copyright 1978 by Walter de Gruyter & Co., Berlin 30. All rights reserved, including those of translation into foreign languages. No part of this book may be reproduced in any form - by photoprint, microfilm or any other means - nor transmitted nor translated into a machine language without written permission from the publisher. Printing: Karl Gerike, Berlin. - Binding: Liideritz & Bauer, Buchgewerbe GmbH, Berlin. Printed in Germany.

V This c o l l e c t i o n of n o n - l i n e a r thermodynamics

s u r v e y s current p r o b l e m s in the

irreversible in b i o l o g y .

and e x p e r i m e n t a l

thermodynamics

p r o c e s s e s and the a p p l i c a t i o n s Problems concerning

substantiation

the

of the p h e n o m e n o l o g i c a l

of d e v e l o p m e n t , g r o w t h and aging

of o r g a n i s m s are

and e x p e r i m e n t a l data are p r e s e n t e d

theory

discussed,

on o o g e n e s i s , a n i m a l

v e l o p m e n t and g r o w t h , and on heat p r o d u c t i o n and energy bolism during concluding

the g r o w t h of m i c r o o r g a n i s m s

of

in c u l t u r e .

e v o l u t i o n and the

demeta-

The

c h a p t e r s treat m o d e r n t h e o r i e s of d i s s i p a t i o n

t u r e s , p r o b l e m s of p r o g r e s s i v e

of

theoretical

struc-

classification

animals.

This m o n o g r a p h w i l l be u s e f u l to b i o p h y s i c i s t s , and e m b r y o l o g i s t s as w e l l as to p h y s i c i s t s and interested

physiologists mathematicians

in m o d e r n p r o b l e m s in t h e r m o d y n a m i c s and the a p p l i -

c a t i o n of this field to

biology.

L i s t of Berlin

authors

(üJest)

R.

Brettel

I.

Lamprecht

K.D.

Loehr

P.

Sayyadi

B.

Schaarschmidt

R. U a l t e r MOSCOUJ:

U.A.

Grudnitzky

U.A.

Kanoplev

I.S.

Nikolskaja

l\!.D. Ozernyuk E.U.

Presnov

E.A.

Prokofiev

L.I.

Radzinskaja

l\l.Sh. S h a g i m o r d a n o v U.E.

Sokolov

U.A.

Uasiliev

S.S.

Uasiliev

I.G.

Uladimirova

A.A.

Zotin

A.I.

Zotin

R.S.

Zotina

IX

Preface The main d i f f i c u l t y , as ue SEE it, is that a general

phenomenological

accompanied

T r u e , two large d i v i s i o n s reversible

theory

by a d i s s i p a t i o n and

linear

of t h e r m o d y n a m i c s

e s t a b l i s h e d ; but the theory a p p r o a c h e s under principles

cf all p r o c e s s e s

of n o n - l i n e a r

of t h e r m o d y n a m i c s ,

(the t h e o r i e s

irreversible

are the creation the a p p l i c a t i o n

of

linear p r o c e s s e s , using

the theory

considerations rather

to say which

of these

a basis for the t h e r m o d y n a m i c s c e s s e s . Yet sential

it is quite

of n o n - l i n e a r

suggest

for solving

p r o b l e m s in p h y s i o l o g y , b i o c h e m i s t r y It should

be noted

recent

that

w a s long

were available

extensive basis

slow heat

It is hoped

the most

of

systems Some

data

important biology.

thermodynamics methods

It w a s not were

until

designed

their wide

will help create a

for the t h e r m o d y n a m i c s

proes-

of i r r e v e r s i b l e p r o -

flows. that

is

is

in

systems.

b e c a u s e no satistact ory

deployment

it

take hold as

irreversible

sensitive m i c r o c a l o r i m e t e r s

and came into common u s e . experimental

stochastic

and d e v e l o p m e n t a l

the i n t r o d u c t i o n

delayed

for measuring

d e c a d e s that

bution and

generalized

occurring

in living

that the t h e r m o d y n a m i c s

c e s s e s could be used as a tool

into biology

basic to n o n -

of this kind

of p h e n o m e n a

e q u i l i b r i u m , particularly

in biology

variational

and

t r e n d s will

obvious that work

to our u n d e r s t a n d i n g

far from

of g r a p h , the

characteristics,

proces-

of t h e r m o d y n a m i c s p r o c e s s e s . At present

difficult

of

the main

of the

local t h e r m o d y n a m i c s theory

r e l a t i o n s and global

are

complete.

of its d e v e l o p m e n t . Among

consideration

as

p r o c e s s e s ) are now uiell

c o n c e p t s of P r i g o g i n e ' s reciprocal

that

of e n e r g y , is far from

irreversible

ses is still at the onset

thermodynamics,

distri-

reliable

of b i o l o g i c a l

pro-

cesses. This m o n o g r a p h laboratories: tute

resulted

from a c o o p e r a t i v e

the B i o p h y s i c a l

for Biochemistry

and

Laboratory

effort

between two

of the C e n t r a l

B i o p h y s i c s at the Free

Insti-

University,

X

West B e r l i n , a n d the L a b o r a t o r y the A c a d e m y

of D e v e l o p m e n t a l

Biology

of S c i e n c e s of the U S S R . Each c o n t r i b u t o r

to

v o l u m e is in some way c o n n e c t e d w i t h one of t h e s e two tories.

As we c o u l d h a r d l y

in w h i c h t h e r m o d y n a m i c s

of this

labora-

e m b r a c e all the f i e l d s of

biology

of i r r e v e r s i b l e p r o c e s s e s m a y

be

a p p l i e d , we c o n f i n e d o u r s e l v e s to the p r o b l e m s w h i c h are being s t u d i e d in our l a b o r a t o r i e s . A c c o r d i n g l y

it s h o u l d be

empha-

sized that the m a i n t h e o r i e s d i s c u s s e d in the book are on the g l o b a l a p p r o a c h to n o n - l i n e a r

irreversible

based

processes,

m o s t of the a u t h o r s being a d h e r e n t s of t h i s a p p r o a c h w h i c h d i s c u s s e d in c o n s i d e r a b l e d e t a i l and s u b s t a n t i a t e d

is

in the first

chapters. The m a t e r i a l p r e s e n t e d w a s t h o r o u g h l y

discussed

beforehand

at the t h e o r e t i c a l p h y s i c s s e m i n a r s of the P h y s i c a l of the A c a d e m y

of S c i e n c e s of the U S S R , at v a r i o u s

and c o l l o q u i a in the same a c a d e m y ' s I n s t i t u t e B i o l o g y , in the S o c i e t y of M a t h e m a t i c a l

of

Institute seminars

Developmental

and P h y s i c a l

Biology

of the G e r m a n D e m o c r a t i c R e p u b l i c , and in the C e n t r a l of B i o c h e m i s t r y

and B i o p h y s i c s of the Free U n i v e r s i t y ,

B e r l i n . U)e are m o s t g r a t e f u l these f r u i t f u l

Institute

to a n u m b e r

of c o l l e a g u e s

West for

discussions.

D o u b t l e s s a book the very b e g i n n i n g

such as this, being

d e v o t e d to a s c i e n c e

of its d e v e l o p m e n t , w i l l c o n t a i n

c i e s or even o u t r i g h t m i s t a k e s . The a u t h o r s w i l l be very ful for all c r i t i c a l r e m a r k s a i m e d at r e m o v i n g d a b l e d e f e c t s of their

these

grate-

unavoi-

work. I. L a m p r e c h t , A . I .

at

inaccura-

Zotin

XI

Contents

I. G e n e r a l

P r o b l e m s of B i o l o g i c a l

I. L a m p r e c h t

-

Application Classical

Thermodynamics

of the C o n c e p t s

Thermodynamics

1

of

in

Biology A . I . Zotin

-

5

The Second Law, N e g e n t r o p y , modynamics

of L i n e a r

Ther-

Irreversible

Processes E.V. P r e s n o v

-

19

Formalism

of N o n - E q u i l i b r i u m

menolagical II. Q u a l i t a t i v e

Pheno-

Thermodynamics

Phenomenological

Theory

31

of the D e v e l o p m e n t

of O r g a n i s m s A . I . Z o t i n , R.S. Zotina

-

Experimental

Qualitative

Basis

Phenomenological

for Theory

of D e v e l o p m e n t

61

A . I . Z o t i n , R . S . Z o t i n a , V/.A. K o n o p l e v

-

Theoretical

Basis for a Q u a l i t a t i v e Theory

Phenomenological

of D e v e l o p m e n t

E.V. P r e s n o v , R . S . Zotina

-

B5

Stochastic

of C o n s t i t u t i v e

Consideration

P r o c e s s e s and of the

Evolution Criterion E.V. P r e s n o v

-

Strengthened Evolution Criterion Developmental

III. Q u a n t i t a t i v e

99

Phenomenological

in

Biology Theory

105 of

Development

of O r g a n i s m s

111

A . I . Zotin, V . A . K o n o p l e v , E.V. P r e s n o v Phenomenological R . S . Z o t i n a , A . I . Zotin

-

-

Equations

Differential

Developmental

Non-Linear

Biology

Equations

115 of 121

XII

R.S. Z o t i n a , A . I . Zotin

-

Differential

of D e v e l o p m e n t a l

Equations

Biology

U.A. K o n o p l e v , A . I . Z o t i n , E.A. P r o k o f i e v , mordanov

-

R. W a l t e r ,

I. L a m p r e c h t ning

IU. B.

Heat P r o d u c t i o n

-

B.

Growth

of Living

-

-

1^3 163

Heat

Production 167

The C h a n g e of the the G r o w t h

of

Mi-

Cultures

C h a n g e s of ring

Concer-

Equations

F u n c t i o n During

Zotin

135

Processes

S c h a a r s c h m i d t . R. B r e t t e l

A.I.

Equations

Systems

S c h a a r s c h m i d t , I. L a m p r e c h t

crobial

Shagi-

Analysis

Modern Theories

the G r o w t h

in Life

Sh.

Computer

of N o n - L i n e a r

121

181

and

Functions

O o g e n e s i s of X e n o p u s

K.D. L o e h r , P. S a y y a d i , I. L a m p r e c h t

-

Development

and G r o w t h

Laevis

Heat

d u c t i o n and R e s p i r a t i o n

Du191

Pro-

During of two

Insects U.A.

197

G r u d n i t z k y , I.S. IMikolskaja

-

and R e s p i r a t i o n Early U.A. G r u d n i t z k y ,

Heat

B. S c h a a r s c h m i d t

-

P r o b l e m s of E n e r g e t i c s

Relationship Body

Organisms

209

of D e v e l o p m e n t a l Processes

I.S. IMikolskaja, L . I . R a d z i n s k a j a chondria

205

Heat P r o d u c t i o n and

LJeight in Growing Some

the

S t a g e s of G r o w t h

Between

U.

Production

of A x o l o t l e at

During

-

C h a n g e s in

Development

Mito-

and

Growth

of A n i m a l s f\I.D.

Dzernyuk

The Role of M i t o c h o n d r i a

213

217 in

tion of R e s p i r a t i o n During

RegulaOogenesis

229

XIII I.G. V l a d i m i r o v a

-

The E n e r g e t i c s

of

Regeneration

Processes VI.

Dissipative

I. L a m p r e c h t

243

Structures

-

Revieu

257 of the

Theory

of

Dissipative

Structures

261

U.A. Vasiliev

-

Stationary

U.A. Vasiliev

-

Dynamic Dissipative

A.I.

-

Dissipative Fuction

Zotin

S.S. Vasiliev

-

The R o l e Energy

Dissipative

Structures

Structures

Structures

293

and 3D1

of C y c l i z a t i o n

in

277

of

Free

Bio-Physico-Chemical

Processes VII.

Probability

305

State and Orderliness

of

Biological

Systems N.D.

325

Ozernyuk, A.I.

Zotin,

U.A. Konoplev, A.A.

Possible

Mechanism

of t h e

Zûtin Origin

of

Bacteria A.I.

Zotin,

U.A.

Konoplev

329 -

Direction

Evolutionary V.A. Konoplev,

U.E.

Progress

Sokolov, A.I.

Zotin

of O r d e r l i n e s s a n d

of

the

of O r g a n i s m s -

some

341

Criterion Problems

of

Taxonomy A.I.

Zotin, V.A. Konoplev,

U.A. Grudnitzky

of IMon-Linearity of O r d e r l i n e s s Concluding

Remarks

349 - The Q u e s t i o n s

for U s i n g

Criterion 361 3S9

References

371

Index

^35

I. General P r o b l e m s of B i o l o g i c a l Thermodynamics

3

None of the fields of theoretical physics is so closely connected with biology o r gives such an effective description of the life p r o c e s s e s as thermodynamics. Although m e c h a n i c s , hydrodynamics, electrodynamics and optics a r e widely applied in biology, they d e s c r i b e phenomena which a r e not a s c h a r a c t e r i s t i c of the living s y s t e m s as heat production and the p r o c e s s of m e t a b o l i s m concerned with it. Modern thermodynamics also includes other concepts e x t r e m e l y important f o r biology such as " t i m e a r r o w s " (see Popper, 1965, 1967 a , b) or various evolution c r i t e r i a specifying the direction of the changes of thermodynamic s y s t e m s (Glansdorff, P r i g o g i n e , 1964, 1971; P r i g o g i n e , 1966; N i c o l i s , 1971; Zotin, 1972, 1974; P r e s n o v , 1973). In spite of this, the problems of applying individual fields of thermodynamics in biology a r e still open to discussion ( L a z a r e v , 1945; Schrodinger, 1945; Ubbelohde, 1947; B r i l l o u i n , 1949, 1955; Raymond, 1950; P a s y n s k y , 1953, 1963; Touloukian, 1956; Volkenstein, 1958, 1965, 1973; Wilkie, 1960; B e r n h a r d , 1964; M o r r i s o n , 1964; R i e g e l , 1965; Calloway, 1966; B l u m , 1967; Molchanov, 1967; T r i n t s c h e r , 1967; Antonov, 1968; Morowitz, 1968, 1970; Kobozev, 1971; Rebane, 1972; Zotin, 1971, 1972, 1974; B l u menfeld, 1974; P r i t z , 1974; Chernavsky, 1975; Nikolaev, 1976). T h e applicability of the concepts of c l a s s i c a l thermodynamics and thermodynamics of l i n e a r i r r e v e r s i b l e p r o c e s s e s to some biological phenomena a r e reviewed below, and b a s i c concepts of the s o - c a l l e d global theory of n o n - l i n e a r i r r e v e r s i b l e p r o c e s s e s a r e presented. Much of the t h e o r e t i c a l and experimental work presented in this book r e s t upon this global theory.

Application of the Concepts of C l a s s i c a l T h e r m o d y n a m i c s in Biology I. L a m p r e c h t

T h e r m o d y n a m i c s was b o r n 200 y e a r s ago when L a v o i s i e r ' s e x p e r i m e n t s on the oxidation b r o k e with S t a h l ' s t h e o r y of phlogiston. At the v e r y beginning of this development, t h e r e w e r e c a l o r i m e t r i c m e a s u r e m e n t s on the heat production of s m a l l a n i m a l s in an ice c a l o r i m e t e r of the L a v o i s i e r - L a p l a c e - t y p e . T h i s s t r o n g connection between biology and t h e r m o d y n a m i c s was n e v e r b r o k e n , and two physicians m a d e the f i r s t s t e p s toward a m o d e r n t h e o r y of e n e r g y : M a y e r and Helmholtz with t h e i r f o r m u l a t i o n of the f i r s t law of t h e r m o d y n a m i c s . Half a c e n t u r y l a t e r , R u b n e r in B e r l i n d e m o n s t r a t e d the validity of the f i r s t law in biology with h i s e x p e r i m e n t s on the m e t a b o l i s m of m i c r o o r g a n i s m s and nowadays living m a t t e r is one of the favoured topics of both c l a s s i c a l t h e r m o d y n a m i c s and (more r e c e n t l y ) the t h e r m o d y n a m i c s of i r r e v e r s i b l e p r o c e s s e s . T h e r e is no question that just this t h e o r y l e a d s to d e e p e r u n d e r s t a n d i n g of living m a t t e r and p r e d i c t s developments which a r e not c o m p r e h e n s i b l e in other w a y s . In this c h a p t e r we s h a l l introduce the c h a r a c t e r i s t i c t h e r m o d y n a m i c a l quantities and explain t h e i r connection with biological p r o c e s s e s .

Internal Energy U Although t h e r e e x i s t s a m a t h e m a t i c a l , a x i o m a t i c deduction of t h e r m o d y n a m i c s which p o s t u l a t e s the e x i s t e n c e of v a r i a b l e s of s t a t e a s cons e q u e n c e of the d i f f e r e n t l a w s , we s h a l l follow a m o r e e m p i r i c a l a p p r o a c h , and define the quantities and r e g a r d the f i r s t and second + l a w s a s prooved by e x p e r i e n c e . +

M . P l a n c k f o r m u l a t e d that the sad fate of the would-be i n v e n t o r s of the p e r p e t u u m mobile is the s t r o n g e s t proof f o r the t r u t h of the f i r s t l a w .

© 1978 by Walter de Gruyter & Co., Berlin • New York Thermodynamics of Biological Processes.

6

If a s y s t e m , separated by fixed or movable walls from its environment, undergoes a change of state, this might involve a flow of heat to or from the system and work done by or on the s y s t e m . If a negative sign is assigned to energy which is delivered to the surroundings, the influx of heat is Q, while the work on or produced by the s y s t e m is A . T h e r e e x i s t s a variable of s t a t e , the internal energy U , which combines these two p a r a m e t e r s in the equation: A U »

AQ

A.A

(1.1)

V e r y often the work done is an expansion of a gas against an outside p r e s s u r e . Following the B o y l e - M a r i o t t e law we find: AA

- -pAV

and inserting this value in (1. 1): A U

-

AQ

-

f>AV

(1.2)

B y integrating ( 1 . 2 ) we could obtain the value of the internal energy U, but in the most experiments we a r e only interested in the change AU» when the s y s t e m p a s s e s from a state 1 to a state 2. The value of A Q is measured c a l o r i m e t r i c a l l y , while the following t e r m may be obtained by calculation f o r a known reaction o r by m a n o m e t r i c e x p e r i m e n t s . T h e r f o r e , we have to distinguish three different c a s e s : a) The c a l o r i m e t r i c v e s s e l is open to the surrounding, so that no change in p r e s s u r e can o c c u r , i . e .

Ap = 0.

b) The c a l o r i m e t r i c v e s s e l is closed, the p r e s s u r e changes ( A p t 0), but the volume stays constant, i. e.

A V = 0.

c) Although one of the two c a s e s a) and b) must be fullfilled, we have A V = A p = 0 , if no gaseous p a r t s a r e involved in the observed r e action. L e t us explain these differences with a simple example of great importance in biology. During glycolysis the sugar glucose is d e c o m posed by a chain of enzymes to ethanol or to l a c t i c acid. In the f i r s t

7

c a s e , the r e a c t i o n follows the equation: C

2 C 6H12°6 — > 2H5°H+2C02F o r s i m p l i c i t y , we take one mole of s u g a r dissolved in one l i t e r of w a t e r

which is contained in a two l i t e r v e s s e l . If it is open to a i r ( A p = 0), we have to c a l c u l a t e AV, which f o r two m o l e s of the gas is 2 x 2 2 . 4 l i t e r = 3 44, 800 cm . With a n o r m a l p r e s s u r e of 760 m m Hg we get: - p AV = 1 , 0 1 3 k p / c m 2 • 44, 800 c m 3 = 454 mkp = 4 , 4 5 0 J = 1060 c a l . The heat exchanged in this p r o c e s s is AQ = -17 k c a l / m o l e , so that the total change in i n t e r n a l e n e r g y i s : AlA=" A Q - - p A V =

-fe3Ymole .

It was a s s u m e d in o u r calculation that the w a t e r was s a t u r a t e d by c a r b o n dioxide s o that none of the gas g e n e r a t e d went into solution. The r o l e of work is s m a l l and negligible in m o s t biological e x p e r i m e n t s . When glucose is metabolized to l a c t i c acid the r e a c t i o n i s : C^H, „ O . *• 2CHOHCOOH o IZ b with no production of g a s . The change of the i n t e r n a l e n e r g y e q u a l s the production of h e a t , which a m o u n t s to -151 k J / m o l e = -36 k c a l / m o l e . The e r r o r due to neglecting work in the e n e r g y calculation inc r e a s e s with the amount of gas p r o d u c e d . In the c a s e of r e s p i r a t i o n of glucose, 6 m o l e s of c a r b o n dioxide a r e f o r m e d f o r each mole of g l u c o s e . T h e e f f e c t of work is thus t h r e e t i m e s a s high a s when ethanol is p r o duced, but a s the change in i n t e r n a l e n e r g y AU = - 6 7 8 k c a l / m o l e , the e n e r g y contribution f r o m work is negligible. Equation (1.1) is one f o r m u l a t i o n of the f i r s t law of t h e r m o d y n a m i c s : that a l l e n e r g y added to the s y s t e m is to be found in the i n t e r n a l e n e r g y . M o r e i m p r e s s i v e l y , e n e r g y is n e i t h e r c r e a t e d n o r d e s t r o y e d . T h i s law, f i r s t f o r m u l a t e d f o r p h y s i c a l (e. g. gaseous) s y s t e m s , was s u c c e s s f u l l y checked f o r biological entities as well. R u b n e r showed at the beginning of this c e n t u r y , in a s e r i e s of p a p e r s f o r m i c r o b i a l c u l t u r e s , that the e n e r g y content of the nutrient was c o m p l e t e l y divided into t h r e e p a r t s , the sum of which r e m a i n s constant: the e n e r g y wasted a s heat and t r a n s -

8 mitted to the surroundings, the energy stored a s c e l l m a t e r i a l ( m e a sured by bomb c a l o r i m e t r y ) and the energy left in the medium as m e t a bolites. L a t e r o n Sedlaczek (1964) repeated this m e a s u r e m e n t with higher a c c u r a c y for various b a c t e r i a , such as E . coli, P . v u l g a r i s , S. aureus and P . f l u o r e s c e n s . He compared the decrease, in heat content ( m e a sured as heat of combustion) between the initial and the final medium with the sum of energy converted to heat and the heat of combustion of the b a c t e r i a l c r o p . L e t us consider one example, the growth o f E . heat of combustion of the initial medium

- 17, 338 cal

heat of combustion of the final medium

- 16, 264 "

difference

coli:

1,074 "

heat of combustion of b a c t e r i a l crop

-

528 "

energy converted to heat during growth

-

468 " 996 cal

T h e r e is a discrepancy of 1 , 0 7 4 - 996 = 78 c a l o r 7. 3 % of the calculated heat, but when we take into account that the d e c r e a s e in energy content is found as a s m a l l difference between two l a r g e f i g u r e s , the d i s c r e pancy is negligible (78 c a l of 17, 338 c a l a r e just 0 . 4 %). T h e experiments a r e in full agreement with the f i r s t law.

Enthalpy H As shown above, the change in internal energy might be due to a heat flux and an expansion of gas against an outside p r e s s u r e . T h i s energy i s called the work of volume. As it is e s s e n t i a l in all reactions c o m bined with a production of gas, a new function is defined by: -H -

U

-ya.V

(1.3)

which is called the enthalpy of the s y s t e m . In differential f o r m we may write: A+t *» A U + A ( - p . v ) = A"U. + V A - p + -jo AV

9

and t o g e t h e r with (1.2) A t t « A Q - ' p A V + V A - p + - p A V ~ A Q + VA>|p .

(1.4)

In the c a s e that the p r e s s u r e does not change d u r i n g the e x p e r i m e n t (i. e. that the v e s s e l is open in a biological c a l o r i m e t e r ) , A p equals z e r o and the change in enthalpy is the heat consumed o r produced in the r e a c t i o n . As in m o s t r e a c t i o n s , the p r e s s u r e s t a y s constant, the i n c r e a s e in e n thalpy is the heat of r e a c t i o n of the p r o c e s s . We have pointed out above that the amount of work e n e r g y i s s m a l l c o m p a r e d with the h e a t . T h e r e f o r e , the v a l u e s obtained f o r the i n t e r n a l e n e r g y a r e n e a r l y the s a m e a s f o r the enthalpy; or put a n o t h e r way, a l though c a l o r i m e t r y e v a l u a t e s heat e x c h a n g e s , these v a l u e s can be taken f o r the enthalpy, too.

Temperature T B e f o r e we explain the next t h e r m o d y n a m i c v a r i a b l e of s t a t e , the e n t r o p y , we have f i r s t to i n t r o d u c e the t e m p e r a t u r e , well known f r o m the daily l i f e . In c o n t r a s t to i n t e r n a l e n e r g y , enthalpy and e n t r o p y , t e m p e r a t u r e is an intensive quantity which c h a r a c t e r i z e s the s t a t e of a s y s t e m . By definition two bodies in contact have the s a m e t e m p e r a t u r e (independ e n t l y of the s c a l e used) if t h e r e is no heat exchange between t h e m . N o r m a l l y two d i f f e r e n t s c a l e s f o r t e m p e r a t u r e a r e used: the C e l s i u s s c a l e with 100 c e n t i g r a d e between the two fixed points of w a t e r and the Kelvin s c a l e with only one fixed point (triple point of w a t e r ) set equal to 273. 15 K above absolute z e r o . It h a s r e c e n t l y been r e c o m m e n d e d that only this s c a l e should be u s e d . T e m p e r a t u r e is a v e r y i m p o r t a n t p a r a m e t e r f o r living s y s t e m s . Although one is usually i n t e r e s t e d only in changes in i n t e r n a l e n e r g y and enthalpy, one n e e d s to know the absolute value of the t e m p e r a t u r e r a t h e r than the change in t e m p e r a t u r e . N o r m a l life

is bound to a v e r y s m a l l r e g i o n of t e m p e r a t u r e , p e r -

10 h a p s (let us say) between 10 and 40 d e g r e e s c e n t i g r a d e . Some h i g h e r o r g a n i s m s have developed s p e c i a l s y s t e m s to withstand e x t r e m e t e m p e r a t u r e s , i. e . between - 1 0 0 ° C and p e r h a p s +55° C at the upper end. Howe v e r , t h e r m o p h i l i c o r g a n i s m s a r e known, e s p e c i a l l y b a c t e r i a and a l g a e , which a r e s o well adapted to t h e i r biotops that they even grow n e a r +100° C, and one b e l i e v e s that life m a y e x i s t a s long a s liquid w a t e r is p r e s e n t . On the o t h e r hand, the f r e e z i n g of w a t e r at l o w e r t e m p e r a t u r e s l i m i t s life at the l o w e r l i m i t , although the f r e e z i n g point m a y be shifted by high c o n c e n t r a t i o n s of s a l t s o r o r g a n i c s u b s t a n c e s .

Entropy S A v e r y e s s e n t i a l but often m i s u s e d and m i s i n t e r p r e t e d t h e r m o d y n a m i c value of s t a t e i s the e n t r o p y of the s y s t e m , an extensive f i g u r e like i n t e r nal e n e r g y , enthalpy and v o l u m e . If at a given t e m p e r a t u r e T an amount Q of heat is exchanged with the s u r r o u n d i n g s , it is a c c o m p a n i e d by a r e v e r s i b l e change in entropy: A S

-

A O .

/ T

.

A c c o r d i n g to the second law of t h e r m o d y n a m i c s , total entropy can not diminish in an isolated s y s t e m . In the ideal r e v e r s i b l e e x p e r i m e n t it s t a y s constant (being a function of s t a t e !), but in a l l r e a l isolated s y s t e m s , the entropy tends to r e a c h a m a x i m u m . In this way, the i n c r e a s e in e n tropy is closely connected to the p a s s a g e of time; it is " t i m e ' s a r r o w " . B o l t z m a n n was able to explain this tendency of e n t r o p y to a t t a i n a m a x i m a l value by his s t a t i s t i c a l t h e o r y . He showed that e n t r o p y is c o m bined with the probability "F^. of a s t a t e by the equation: £

-

¿rv

P

T

(1.5)

11 with k the Boltzmann-constant.

A s a system always tends to more

probable states, the increase in entropy is to be deduced. An increase in entropy as demanded by the second law corresponds (see (1.5)) to an increase of probability, i. e. a loss of order. As growing organisms seem to contradict this statement, it was often argued that the second law could not hold true for living matter. However, this law deals only with isolated systems, and no organism may be isolated from its environment f o r long. If we want to use the concept in the classical way, we have to build up an isolated system of organism plus environment. In this new system, there is a small (living) part the entropy of which decreases at the expense of the larger (inanimate) one. In spite of the partial diminution, the total change in entropy is always positive. Following Schrödinger (1945) we ascertain that living matter draws a steady stream of negative entropy ("Negentropy") from the environment, compensating in this way for its own continuous production of entropy: animals are feeding on negentropy! The same idea was published 90 years ago by the Austrian physicist Boltzmann (see Broda, 1970) in a very modern form: "Der allgemeine Lebenskampf der Lebewesen ist daher nicht ein Kampf um die Grundstoffe - auch nicht um Energie, welche in F o r m von Wärme leider unverwandelbar, in jedem Körper reichlich vorhanden ist - sondern ein Kampf um die Entropie (more exactly: Negentropy E. B . ) , welche durch den Übergang der Energie von der heißen Sonne zur kalten Erde disponibel wird. Diesen Übergang möglichst auszunützen, breiten die Pflanzen die unermess-

+

Shannon (1948) deduced an identical looking equation for the information content of a state. This was the reason for introducing the name "entropy" into information theory, too. Although there are some similarities between the negative entropy and the information, this connection should not be overestimated (a dimension of J per degree for information is useless).

12

liehen F l ä c h e n i h r e r B l ä t t e r aus und zwingen Sonnenenergie in noch une r f o r s c h t e r W e i s e , ehe sie auf das Temperaturniveau der E r d o b e r fläche herabsinkt, chemische Synthesen auszuführen, von denen man in unseren L a b o r a t o r i e n noch keine Ahnung hat. " + Let us illustrate these facts with two e x a m p l e s . (1) Animals feed on plants or other animals and take t h e i r negentropy from them. But where do the plants get their negentropy? They a r e the f i r s t step in producing m a c r o m o l e c u l e s from carbon dioxide and water in the p r e s e n c e of light and in diminishing the entropy of the s u b s t a n c e s . The temperature of the sun T surface of the earth T g

( 5 , 5 0 0 K) is nearly 20 times that of the s (290 K). According to the laws of radiation, the

maximum intensity of an emitted spectrum corresponds to the t e m p e r a ture of the s o u r c e . T h e r e f o r e , if an amount Q of s o l a r radiation is absorbed on earth and reemitted there is a change in entropy: AS " qr ~ — T«. Ts

=

Gl(4 - 4 ) I«, is

>

A S may be calculated: A S = 150 n c a l / d e g . mole with n the number of quanta n e c e s s a r y for the formation of one molecule of sugar in photosynthis: 6 C

+

0

2

+

6 H

2

0 —

C6H1206+ 6 02

" T h e general struggle for existence among living things is therefore not competition for b a s i c substance - nor for energy, which is abundantly in the inconvertible form of heat, in e v e r y body, but for the entropy (more exactly: negentropy E . B . ) , which b e c o m e s available in the transit of energy from the hot sun to the cold e a r t h . In order to take best advantage of this transition, the plants spread out the i m m e a s u r a b l e surface of their l e a v e s and force the s u n ' s energy, before it sinks to the temperature of the e a r t h ' s u r f a c e , to c a r r y out chemical syntheses of which we in our l a b o r a t o r i e s a r e s t i l l totally ignorant. "

13

with an entropy d e c r e a s e of A S = - 4 0 c a l / d e g . m o l e . Roughly 3 quanta a r e used p e r mole CO , so that +450 c a l / d e g . mole compensate for - 40 c a l / d e g . m o l e . An efficiency of 10 per cent suffices to fullfill the r e quirements of the second law (Britten, Gamov, 1961). M o r e o v e r one may calculate a m a x i m a l density of plants for the total s u r f a c e of e a r t h , so that the entropy change by growth and t e r m a l denaturation equals the s o l a r entropy influx. T h i s density could be a s 4 2 2 high as 2 . 1 0 / g / c m of plants compared with approximately 1 / g / c m found on the earth (Stein, 1960). (2) L e t us choose another example which shows that the limit of the second law is never touched. The multiplication of a m i c r o o r g a n i s m may be written (Morowitz, 1960): 1 c e l l + substrate

—

2

c e l l s + metabolites.

Different parts of growth have to be distinguished: condensation of nutrients into the cell; arranging of substrate molecules into c e l l s t r u c t u r e , i n c r e a s e in entropy during the metabolism of the substrate; heat flux to the environment. The destruction of substrate to 0 . 0 3 g waste m a t e r i a l per g new c e l l m a t e r i a l would be enough to meet the second law. Instead of this we find a figure of 4 . 9 5 for E . c o l i . The entropy production is thus 150 times bigger than n e c e s s a r y . In c a l o r i m e t r i c experiments with yeast we find during fermentation a A S of + 128 c a l / d e g . mole to be compared with a negentropy of c e l l s of - 7 c a l / d e g . m o l e . Even if the reaction v e s s e l guides all the metabolic heat into the environment, the entropy flux i s - 85 c a l / d e g . mole, keeping the balance positive, as n e c e s s a r y for the second law.

F r e e Energy F According to the f i r s t law of thermodynamics the maximum work A which can be obtained f r o m a reaction is given by: A A =» L M - - A G l

14

and t o g e t h e r with ( 1 . 5 ) f o r r e v e r s i b l e c o n d i t i o n s : AA -

A U - T A S = AT 7 .

T h i s c h a n g e in i n t e r n a l e n e r g y d i m i n u i s h e d by t h e e n t r o p y t e r m i s i n t r o d u c e d a s the f r e e e n e r g y F . If AU i s i n d e p e n d e n t of t e m p e r a t u r e ,

the

d i f f e r e n t i a t i o n of A A l e a d s to: d A / oLT =

-

AS

and A=F = A U - T . o t A / c L T

(1. 7)

the e q u a t i o n of Gibbs and H e l m h o l t z . Only at T = 0 o r with a v e r y s m a l l t e m p e r a t u r e c o e f f i c i e n t of the m a x i m a l w o r k i s t h e r e a d i r e c t c o n v e r s i o n of i n t e r n a l e n e r g y to w o r k .

F r e e E n t h a l p y (Gibbs F r e e E n e r g y ) G In the s a m e w a y a s f o r the f r e e e n e r g y a s e c o n d " f r e e " f i g u r e i s i n t r o d u c e d by Gj -

4+ -

T. S

(1.8)

o r in the d i f f e r e n t i a l f o r m ( A T = 0); AG] = A t t -

T.AS .

(1.9)

T h e c h a n g e in the f r e e e n t h a l p y i s e s s e n t i a l f o r the d i r e c t i o n of a r e a c t i o n . A c h e m i c a l s y s t e m c a n v a r y i t s s t a t e s p o n t a n e o u s l y only if t h i s c h a n g e i s c o m b i n e d with a n e g a t i v e A G , i . e . the r e v e r s i b l e r e a c t i o n p r o d u c e s w o r k . T h e n e g a t i v e s i g n of A G m a y b e due to a s t r o n g e x o thermic effect ( A H