Biological Magnetic Resonance - Volume 17: Structural Computation and Dynamics in Protein (Biological Magnetic Resonance) [1st ed.] 0306459531, 9780306459535, 9780306470844

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Biological Magnetic Resonance Volume 17

Structure Computation and Dynamics in Protein NMR

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Biological Magnetic Resonance Volume 17

Structure Computation and Dynamics in Protein NMR Edited by

N. Rama Krishna University of Alabama at Birmingham

Birmingham, Alabama

and

Lawrence J. Berliner Ohio State University Columbus, Ohio

KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

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0-306-47084-5 0-306-45953-1

/0110.2345!*.6789!:+7.)4;3+#*$ 633.*+D=-1 ns) buried in internal cavities or in deep and narrow surface pockets. At high frequencies, above the dispersion, the excess relaxation rate (above the bulk water rate) is due to the conventional hydration layer, essentially the water molecules in contact with the protein surface. These water molecules generally have rotational correlation times as well as residence times in the subnanosecond range and therefore do not contribute to the MHz dispersion. In addition, rapidly exchanging labile protein hydrogens can make substantial contributions to the and relaxation rates over the entire frequency range (Denisov and Halle, 1995b; Venu et al., 1997). The theoretical framework needed to analyze NMRD data from protein solutions is based on the “standard model” of water relaxation, first proposed by Lars Onsager (Wang, 1955) and applied in the first detailed water relaxation study of protein solutions by the Krakow group in 1963 (Daszkiewicz et al., 1963). The standard model required two extensions (Halle and Wennerström, 1981b). First, a

frequency-independent term must be added to account for the contribution from mobile surface waters and fast local motions of long-lived waters and labile

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hydrogens. Second, the effect of fast local motions of long-lived water molecules on the dispersion amplitude is accounted for by an order parameter formalism that does not rely on specific assumptions about the nature of this motion.

4.1. Spatial Resolution The relaxation of the water magnetization in a protein solution is governed by molecular motions at two distinct levels. At the level of spin dynamics, translational motion of water molecules transfers magnetization between microenvironments with different intrinsic relaxation rates. If sufficiently fast, such material exchange leads to spatial averaging of the local relaxation rates. At the level of orientational time correlation functions, water rotation averages out the anisotropic spin-lattice coupling and thus determines the intrinsic spin relaxation rate (see Sect. 4.2).

4.1.1. Exchange Averaging The theoretical framework for analyzing relaxation data from nuclei exchanging between discrete states is well established and was, in fact, first developed in connection with studies of water in microheterogeneous systems (Zimmerman and Brittin, 1957). It is not obvious, however, that a discrete-state exchange model provides a valid description of continuous water diffusion in a spatially heterogeneous system such as a protein solution (Halle and Westlund, 1988). There are two aspects to this issue. First, in the fast-exchange regime the actual exchange mechanism is irrelevant, and it is only necessary that the perturbation of water rotation induced by the protein be relatively short-ranged. This is known to be the case: relaxation studies on a variety of microheterogeneous aqueous systems show that only water molecules in direct contact with an interface are significantly perturbed (Woessner, 1980; Carlström and Halle, 1988; Volke et al., 1994). Second, the observed spin relaxation rate depends on the exchange mechanism only in the intermediate exchange regime where the residence times are in the –ms range. Such long residence times are only relevant for buried water molecules and labile protein protons, for which a discrete-state exchange (or jump) model is indeed appropriate. This would not necessarily be the case for water molecules at the protein surface, but they are invariably in the fast-exchange regime. The simplest description of the effect of exchange averaging on the water longitudinal relaxation rate in a protein solution is of the form

Provided that chemical-shift differences can be ignored, an analogous result holds for (see Sect. 3.3.1). Since the contributions and are generally in the extreme-narrowing limit, the subscript 1 is suppressed. The first term in Eq. (32)

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refers to the fraction of water molecules that are unperturbed by the protein and thus have the same relaxation rate as bulk water. The second term refers to the fraction of water molecules that are dynamically perturbed by the protein, but remain sufficiently mobile that their effective correlation times are much shorter than the tumbling time of the protein. These water molecules are responsible for (most of) the excess relaxation at frequencies above the dispersion.

The third term in Eq. (32) refers to the long-lived water molecules responsible for the relaxation dispersion. Each of these water molecules has a distinct residence time and intrinsic longitudinal relaxation rate and, taken together, they

account for a fraction of all water molecules in the sample. The '. and relaxation rates generally contain contributions from water hydrogens as well as labile protein hydrogens. Since labile hydrogens generally exchange slowly compared to the tumbling of the protein, they contribute only to the third term in Eq. (32). The simple form of this term is valid provided that the quantities and are small compared to 1 (Luz and Meiboom, 1964). In typical protein

solutions, they are in the range

so this condition is satisfied with a wide

margin. Equation (32) is an essentially phenomenological description of exchange

averaging and, as such, is of considerable generality. Since the NMRD method lacks

intrinsic spatial resolution, the microscopic significance of the individual terms in Eq. (32) can be deduced only with the aid of extrinsic structural data, such as high-resolution crystal structures. This has been done for a variety of proteins and the general picture is now clear (Denisov and Halle, 1995a, 1996). The short-lived water molecules responsible for the second term in Eq. (32) essentially comprise the traditional hydration layer, i.e., water molecules in contact with the protein surface (hence the subscript S). The quantity is the intrinsic relaxation rate averaged over all surface sites occupied by short-lived water molecules. The long-lived water molecules responsible for the third term in Eq. (32) are usually buried in cavities inside the protein or trapped in deep surface pockets with low accessibility to external water. In the following, we refer to this class of crystallographically identifiable water molecules as internal water molecules (hence the subscript I). (Crystallographers often use this term in a slightly more restrictive sense, including only water molecules that are not within hydrogen-bonding distance of external water molecules.) 4.1.2. Difference NMRD The identification of internal water molecules as the source of the relaxation dispersion has transformed the NMRD method into a quantitative tool for investigating specific water molecules of structural and functional significance and for

exploiting internal water molecules as noninvasive probes of protein structure and dynamics. The most powerful way of conducting such studies is in the form of a

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difference NMRD experiment where the NMRD profiles from two structurally related proteins are compared. In fact, the first demonstration of the crucial role of buried water molecules was a difference NMRD experiment where the NMRD profiles of BPTI and ubiquitin were compared (Denisov and Halle, 1994, 1995a).

These proteins are of similar size and surface structure, but differ qualitatively in one respect: BPTI contains four buried water molecules, ubiquitin none. The result (Fig. 6) is clear-cut: the virtual absence of a relaxation dispersion for ubiquitin must be due to the absence of buried water molecules in this protein. (The tiny ubiquitin dispersion can be attributed to a single weakly ordered water molecule in a surface pocket.) Subsequent work (Denisov et al., 1995, 1996) revealed that the dispersion from BPTI is actually due to only three of the four buried water molecules, the fourth one (W122) exchanging too slowly to contribute significantly at 300 K (see Sect. 5.5). The BPTI–ubiquitin difference experiment relied for its interpretation on high-resolution crystal structures of the two proteins. With the correlation between internal water molecules and NMRD firmly established (Denisov and Halle, 1996),

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useful information can be obtained from difference NMRD experiments even when the structure of one of the two proteins is unknown. Partially folded proteins is a case in point. Figure 7 shows the dispersions from in the native state, in the partially folded A state (“molten globule”) at pH 2, and in the unfolded state (in the presence of 4 M GuHCl and with the four disulfide bonds reduced by dithiothreitol) (Denisov et al., 1999). This experiment provides three pieces of information. First, the dispersion from the A state (corresponding to at least three long-lived water molecules) implies the existence of persistent (>10 ns) structural elements that are not present in the unfolded form. Second, the dispersion frequency is a measure of the hydrodynamic volume of the protein (see Sect. 5.2). The frequency shift (more accurately measured from the dispersions) between the native and A forms suggests a 30% expansion of the latter. Third, the excess relaxation rate on the high-frequency plateau provides a global measure of solvent exposure. This is seen to differ little between the native and A forms, but, as expected, is substantially higher for the unfolded form.

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These two examples can be thought of as global difference NMRD experiments. More detailed information can be obtained from a local difference NMRD experiment where the relaxation dispersion is recorded before and after a site-directed structural perturbation that eliminates one or more of the internal water molecules that contribute to the relaxation dispersion from the unperturbed protein. In a more subtle version of this experiment, the perturbation does not eliminate any internal water molecules but only affects their residence times (e.g., by altering the rate of large-scale conformational fluctuations). If it can be established that the perturbation is local, e.g., from crystal structures of both forms, then should be unaffected and should be the same for all internal water molecules present in both forms. Equation (32) then yields for the difference dispersion

where the sum includes only the displaced water molecules. A local structural perturbation can be induced in several ways. Site-directed mutagenesis is the method of choice for replacing buried water molecules. For example, in the single-point BPTI mutant G36S, the buried water molecule W122 is replaced by the hydroxyl group in the side chain of serine-36. The wild-typeG36S difference dispersions shown in Fig. 8 are thus due to a single buried water molecule. Local covalent modifications can of course also be introduced by conventional chemical methods, e.g., selective reduction of disulfide bonds (this might be a residence time perturbation).

More accessible (but long-lived) water molecules in the native structure can be eliminated (or replaced by short-lived ones) by removing an intrinsic metal ion or cofactor or by adding a high-affinity substrate or inhibitor. If complete removal of an intrinsic ligand cannot be achieved, NMRD profiles can be recorded at a series of ligand–protein ratios and the results extrapolated to zero ligand concentration. This approach can be used, for example, for intrinsic multivalent metal ions that coordinate long-lived water molecules, as illustrated in Fig. 9 for calbindin where each of the two ions coordinates one water molecule (Denisov and Halle, 1995c). The strategy of water elimination by ligand binding is illustrated in Fig. 10 for a B-DNA dodecamer where five water molecules in the minor groove are displaced by the polyaromatic drug netropsin (Denisov et al., 1997a). Due to the relatively short residence time (1 ns), only the low-frequency part of the dispersion could be accessed (see Sect. 5.5). More complete dispersions from DNA solutions were subsequently recorded at 253 K, using an emulsion technique to avoid freezing (Jóhannesson and Halle, 1998). In general, hydrogen exchange is less of a problem in difference NMRD experiments since any labile hydrogen contribution tends to cancel out in the

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difference. This is an important advantage as NMRD data from all three water nuclei can then be quantitatively compared, providing detailed information about residence times (Denisov et al., 1996) and orientational disorder (Denisov et al., 1997b) of buried water molecules. Concern about hydrogen exchange is warranted even in difference NMRD experiments, however, because the structural perturbation might affect the values or exchange rates of labile hydrogens (Denisov and Halle, 1995c). Ligands carrying rapidly exchanging hydrogens may, of course, also present problems (Denisov et al., 1997a). 4.2. Temporal Resolution

By definition, the water molecules responsible for the second term in Eq. (32) do not produce a dispersion in the experimentally accessible frequency range. Even

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for a residence time as long as 100 ps, the dispersion would be centered around 1 or Larmor frequency. The observed relaxation dispersion is due to the frequency dependence of the intrinsic relaxation rates of internal water molecules (and labile hydrogens). Within the BWR regime, as defined in Eq. (2), these rates are related to the spectral density function as shown in Sect. 3. The discussion in Sect. 4.2.1 applies to quadrupolar relaxation as well as to intramolecular dipolar relaxation; hence we omit the Q/D subscript on the spectral density function. Intermolecular dipolar contributions are considered in Sect. 4.2.2. GHz, an order of magnitude above the highest achievable

4.2.1. Intramolecular Spectral Density Function

For an internal water molecule (or labile proton spin pair) tumbling rigidly together with a spherical protein, the spectral density function has the usual

Lorentzian form

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where the effective correlation time

is determined by the residence time in site k and the rotational correlation time of the protein according to (Beckert and Pfeifer, 1965; Hertz, 1967; Brüssau and Sillescu, 1972)

This simple relationship results from two innocuous assumptions. First, water (or labile hydrogen) exchange and protein rotation are statistically independent processes. Second, each exchange event randomizes the orientation of the spin–lattice interaction tensor. In other words, once the internal water molecule or labile hydrogen has exchanged with bulk water, the probability of returning to the same

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site (in the same protein molecule) before the protein has randomized its orientation

is negligible. Note that the residence time

appears at both levels of motional

averaging: Eq. (32) describes spatial averaging of the intrinsic relaxation rates,

while Eq. (35) describes orientational averaging by exchange from a locally ordered site to an isotropic bulk phase. (When treating water and labile hydrogen exchange on an equal footing, we denote the residence time by When either species is referred to, we use the notations and respectively.) Equation (34) is readily generalized to nonspherical proteins with symmetrictop rather than spherical-top rotational diffusion. The spectral density function is then a sum of three Lorentzians, weighted according to the relative orientation of the spin–lattice interaction tensor and rotational diffusion tensor (Woessner, 1962). For most globular proteins, however, the effect of anisotropic rotational diffusion on the shape of the relaxation dispersion is insignificant. Internal water molecules (and labile hydrogens) do not in general tumble

rigidly with the protein, but undergo restricted rotational motions on time scales short compared to If the local rotation is much faster than the global isotropic motion (with correlation time and remains in the extreme-narrowing regime at the highest relevant frequency, then the appropriate generalization of Eq. (34) takes the simple form (Halle and Wennerström, 1981b; Lipari and Szabo, 1982)

where more,

is an effective correlation time for the local restricted rotation. Furtheris the generalized second-rank orientational order parameter for site k, defined through

In our previous work, a generalized order parameter was used. The quantity is more convenient since it has a maximum value of unity for all three water nuclei in the limit of a rigidly attached water molecule. If k refers to an internal water site, is a molecular order parameter defined as

where specifies the orientation of the water-molecule-fixed frame M (Fig. 11) relative to an arbitrary protein-fixed frame P (assuming spherical-top rotation). To relate the generalized order parameters of all three water nuclei to the same set of molecular order parameters we have introduced in Eq. (37) a set of geometric coefficients defined as

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where specifies the orientation of the principal frame F of the spin lattice interaction tensor (Fig. 11) relative to the M frame. The explicit forms of the geometric coefficients for the three water nuclei are collected in Table 2. Since the relaxation rates of these nuclei are not affected by a 180° flip of an internal water molecule around its axis (Denisov and Halle, 1995c; Venu et al., 1997). If k refers to a labile hydrogen site, it is more convenient to define

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the order parameters directly in terms of the orientation tensor with respect to the protein. This corresponds to setting

of the interaction in Eq. (37).

4.2.2. Intermolecular Spectral Density Function When Eq. (32) is applied to NMRD data, the intrinsic relaxation rate of an internal water molecule contains a contribution, given by Eq. (14a), from the intramolecular dipole coupling between the two water protons as well as a contribution, given by Eqs. (18) and (19), from intermolecular dipole couplings

between either water proton and all protein protons. The spectral density function for the intramolecular contribution, where only the orientation of the H–H vector is modulated, is of the same form as for quadrupolar relaxation, Eq. (36), and the generalized intramolecular order parameter is given by Eq. (37) with For the intermolecular contribution, where local motions can modulate both the orientation and the length r of the H–H vector, the spectral density function takes the form

where the sum runs over all internuclear vectors connecting one of the protons of is given by Eq. (12) and the effective dipole frequency averaged by local motions, can be expressed in terms of the generalized intermolecular order parameter as the internal water molecule k with a protein proton i. The dipole frequency

with

involving the solid spherical harmonics of rank Here is the H–H vector, of length and orientation and the are (unnormalized) spherical harmonics. For a rigid water–protein complex without internal motions on the time scale of protein tumbling or faster,

The generalized intermolecular order parameter is most conveniently evaluated in a coordinate system with its origin at the center of symmetry of the internal motion rather than at the proton (Otting et al., 1997). If only one of the two coupled protons undergoes internal motion, the solid harmonics can be transformed to the center of symmetry according to (Chiu, 1964)

Multinuclear Relaxation Dispersion Studies of Protein Hydration

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where and are vectors from the center of symmetry to the mobile and fixed proton, respectively, and is assumed. Furthermore,

If the mobile-proton vector r1 is distributed with spherical symmetry, it follows from the orthogonality of the spherical harmonics that whereby Inserting this into Eq. (42) and using the closure relation for spherical harmonics, one obtains , i.e., the same result as if the spherically disordered proton were fixed at the center of symmetry. For internal

motion of lower symmetry, corrections to this result appear that are proportional to a power of

For cylindrical symmetry, for example, one finds

By employing a two-center expansion for solid harmonics (Chiu, 1964), internal motions of both protons can be handled in a similar way. When both protons are spherically disordered, same as if they were located at the centers of symmetry.

is the

4.3. Water Relaxation in Semisolid Proteins 4.3.1. General Features of Semisolid Systems A substantial fraction of all published NMR studies of water in biological systems are concerned, not with isotropic protein solutions, but with semisolid materials of relatively low water content. In this category we find a diverse

collection of materials, including protein fibers and powders, protein crystals,

protein gels, biological tissues, and partially frozen protein solutions. Protein fibers and powders hydrated from the vapor phase to less than a monolayer of sorbed water may seem ideal for NMR studies of protein hydration since all water molecules interact strongly with the protein, whereas in protein solutions hydration effects are “diluted” by the dominant bulk water response. The structural, energetic, and dynamic properties of sorbed water, however, are qualitatively different from those of water at a protein surface in solution. Furthermore, dehydration may significantly perturb the native protein structure. While studies of sorbed water may therefore not be directly relevant to hydration in solution, they are nevertheless of importance for a variety of applications in food and materials technology. Protein

crystals and gels typically have water contents of 40% or more and are therefore better models for hydration in protein solutions and biological tissues.

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From the point of view of NMR relaxation, the motional-narrowing condition provides a natural demarcation line between semisolids and solutions. In most protein solutions, all orientation-dependent terms in the spin Hamiltonian are averaged to zero by protein tumbling at a rate exceeding the anisotropic coupling frequencies. Under these conditions, the conventional BWR theory of spin relaxation applies (Abragam, 1961). In the semisolid biological materials mentioned

above, the macromolecular component is stationary on this time scale. This has several important consequences. In macroscopically anisotropic systems, incompletely averaged anisotropic couplings may give rise to dipolar or quadrupolar line splittings, the temperature dependence of which can provide information about residence times in the range. Moreover, the relaxation behavior becomes more complex, and richer in information, than in solutions. Relaxation due to relatively fast anisotropic motions becomes orientation dependent and is no longer described by a single spectral density function (as in solutions). Further averaging by slower motions often dominates relaxation. Since the protein molecules are not free to tumble, the actual exchange of internal water molecules (and labile hydrogens) with bulk water can modulate the (residual) couplings, thereby providing direct access to residence times; cf. Eq. (35). If the exchange rates are comparable to the residual couplings, however, relaxation cannot be described by BWR theory. Solutions of large or highly concentrated globular proteins may exhibit such borderline behavior (neither solid nor solution), with overall tumbling rates as well as exchange rates of the same order of magnitude as the residual anisotropic couplings. More importantly, the water relaxation

dispersion in heterogeneous semisolids tends to be dominated by water molecules

with exchange rates comparable to the residual (dipolar or quadrupolar) couplings and then cannot be described by BWR theory. Since water–protein (but not

intraprotein) dipole couplings are modulated by water exchange, cross relaxation (with water as the relaxation sink) can assume much greater importance than in solutions (see Sect. 3.2.3). Since (residual) static dipolar couplings are present, even spin diffusion (in the original sense) can be important for relaxation. 4.3.2. Generalized Relaxation Theory

If protein rotation is sufficiently slow or even inhibited, the correlation time in the spectral density function in Eq. (36) no longer equals the rotational

correlation time If the fractions are small, the mean time during which a water molecule diffuses between two successive visits to a long-lived site

is sufficiently long that, after leaving a given internal site, a water molecule can reach any other site (on the same protein molecule or on a different one) with essentially equal probability. If the semisolid protein sample is macroscopically isotropic or nearly so, as for chemically cross-linked or highly concentrated protein solutions, it then follows that each exchange event brings about complete orienta-

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tional randomization of the anisotropic quadrupole coupling. Equation (35) is then valid and the residence time becomes the correlation time, Since the residence times of internal water molecules span a wide range, from nanoseconds

to milliseconds at least, the motional-narrowing condition, Eq. (2), can be violated. This happens when is of the order of the inverse rigid–lattice coupling frequency or longer, i.e., about 1 for (see Table 1). Under such conditions, the second-order perturbation treatment inherent in the BWR theory must be replaced by a more general theory, such as the stochastic Liouville equation, where spin dynamics and molecular motion appear at the same level of description. A nonperturbative stochastic theory of spin relaxation by exchange among an isotropic distribution of locally anisotropic sites has recently been developed for quadrupolar nuclei (Halle, 1996) and is directly applicable to NMRD data from chemically cross-linked (Koenig and Brown, 1993; Koenig et al., 1993) or highly concentrated (Kimmich et al., 1990) protein solutions. Since the stochastic Liouville equation can be solved analytically for the isotropic exchange model (Halle, 1996), the entire spin dynamical behavior can be calculated within the low-dimensional spin space rather than in the computationally demanding infinite-dimensional direct-product space usually employed in stochastic Liouville calculations. For the experimentally relevant dilute regime the stochastic theory predicts that the longitudinal relaxation is exponential (as observed) with the relaxation rate obtained from Eq. (3a), but with the spectral density function in Eq. (36) replaced by the generalized spectral density function (Halle, 1996):

where is given by Eq. (37) with (since the locally averaged quadrupole tensor is taken to be uniaxial), and where, for The direct contribution from local motions has been neglected here, but can be added a posteriori if necessary (Halle, 1996). A similar (but not identical) result can be obtained less rigorously with the aid of Eqs. (3) and (32). This is not unexpected, because when the motional-narrowing condition in Eq. (2) coincides with the condition for fast-exchange averaging of local relaxation rates and when (so that the effective quadrupole coupling is sparse) BWR theory is approximately valid even when Eq. (2) is violated. As expected, Eq. (45) reduces to (the first term of) Eq. (36) when the motional-narrowing condition, Eq. (2), is satisfied. It should be noted that Eq. (45) is not subject to any restrictions on the relative magnitudes of and It is instructive to cast Eq. (45) on the form of the motional-narrowing spectral density, Eq. (36), as

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with the apparent fraction 1996)

and the apparent residence time

given by (Halle,

If Eq. (36) is used outside its domain of validity, the internal water fraction and residence time deduced from the dispersion profile are the apparent quantities in Eqs. (47). Equation (47b) shows that if then the apparent residence time deduced from the dispersion profile using motional-narrowing theory, is nothing

but the inverse of the residual quadrupole frequency For deuterons in buried water molecules, the residual quadrupole frequency should be close to (Table 1), while the residence times are expected to span a wide range. Figure 12 shows how deuterons with different residence times

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contribute to the magnitude of the dispersion step. The maximum contribution comes from and the relative contribution is reduced by a factor 5 (or 50) when is shifted one (or two) decades away from If there is a distribution of residence times, the relaxation dispersion will thus be dominated by deuterons with residence times near The dispersion profile is therefore expected to show little temperature dependence. It has been demonstrated that these theoretical considerations can account for NMRD data from rotationally immobilized protein samples (Halle and Denisov, 1995). The previous interpretation of these data in terms of a universal residence time of 1

for protein-associated water

molecules (Koenig and Brown, 1993; Koenig et al., 1993; Koenig, 1995) thus appears to be an artifact of using the conventional (fast-exchange) perturbation theory of spin relaxation. In contrast, the nonperturbative, stochastic theory identifies the apparent correlation time of with the inverse of the residual quadrupole frequency, thus explaining its universality (for different proteins) and virtual independence of temperature (Halle and Denisov, 1995). The observed dispersion profiles (Fig. 13) are consistent with a broad distribution of residence times,

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spanning the range. These considerations are also relevant for dipolar relaxation in immobilized protein samples and for understanding the origin of

relaxation-based contrast in MRI images of soft tissues. The BWR theory can break down even for protein solutions if the protein tumbles sufficiently slowly. This should be the case for hemocvanin (9 MDa), with an apparent correlation time of 0.9 deduced from the dispersion (Koenig et al., 1975) and with virtually independent of temperature (Piculell and Halle, 1986). Both these observations can be rationalized by the generalized spectral

density function in Eq. (45). Originally, however, the inference that in hemocyanin solutions was taken as an indication that the standard two-state fast-exchange model is inapplicable (Koenig et al., 1975) when, in fact, it implies that the motional-narrowing condition in Eq. (2) is violated. 5.

QUANTITATIVE ANALYSIS OF NMRD DATA

Throughout most of this section, we assume that the relaxation rate is due entirely to water nuclei, as is always the case for With obvious modifications, however, most of the discussion applies also to labile hydrogens. Some considerations specific to labile hydrogens are presented in Sect. 5.7.

5.1.

Parametrization of the NMRD Profile

For the purpose of analyzing experimental NMRD data, it is convenient to express Eq. (32) on the form

Here, is a normalized dispersion function decreasing monotonically from 1 at the dispersion frequency. Furthermore, is the excess relaxation rate on the high-frequency plateau above the dispersion:

while

measures the magnitude of the dispersion step:

As long as relaxation is exponential, all relaxation rates are linear combinations of spectral densities. The decomposition of the spectral density function in Eq. (36), due to motional time scale separation, then carries over to the intrinsic relaxation rates which may be expressed as

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with

in the extreme narrowing regime at all accessible frequencies. We consider first the simplest case where all water nuclei contributing to the dispersion exchange with bulk water rapidly compared to the intrinsic spin relaxation but slowly compared to the (isotropic) protein rotational diffusion. In the quadrupolar case, the (single-exponential) longitudinal relaxation rate is then given by Eq. (48) with the following identifications:

in Eq. (51) is the average of over all sites contributing to the dispersion (in analogy to the definition of and in Eq. (52) is the average of over these sites. Under the stipulated conditions, the measured relaxation dispersion is fully

characterized by the three parameters and as illustrated for a typical dispersion in Fig. 14. The dispersion function in Eq. (53) is commonly known as a Lorentzian dispersion, although it is, in fact, a sum of two Lorentzians. Nevertheless, it can be accurately approximated by the single-Lorentzian dispersion function (Hallenga and Koenig, 1976)

The difference between the normalized dispersion functions in Eqs. (53) and (55)

varies between + 0.013 and –0.016, with the zero crossing at In the case of relaxation, Eq. (48) should be replaced by

where, under fast-exchange conditions, the dispersion function for the intramolecular contribution is given by Eq. (53) and that for the intermolecular contribution by [cf. Eq. (10)]

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This dispersion function differs by less than 0.009 (over the full frequency range) from

If the small shift of the dispersion frequency is neglected, Eq. (56) can therefore be cast on the form of Eq. (48) with and

Here, is given by Eq. (51) and by Eq. (52) with intramolecular dipole frequency (Table 1)

replaced by the

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with

the H–H separation in the water molecule. The value in Table 1 was derived from the (libration-corrected) intramolecular second moment of ice Ih, obtained by subtracting the calculated intermolecular moment from the measured second moment (Whalley, 1974). When this value is inserted in Eq. (61), one obtains which is the best available estimate of the intramolecular H–H separation in ice Ih (Kuhs and Lehmann, 1986). Finally, is given by

where the sum runs over all protein protons (i), the outer brackets signify averaging over all internal water protons (k), and the inner brackets signify averaging over any local motions, also taken into account via the intermolecular order parameters as defined in Eq. (42). Cross relaxation would alter the frequency dependence of but, as discussed in Sect. 3.2.3, such contributions are generally negligible.

5.2. Correlation Time If all water molecules contributing to the dispersion have residence times such that then the effective correlation time deduced from a fit of Eq. (48) to the NMRD data is simply the rotational correlation time of the protein, as assumed for Eqs. (51)–(54). The assumption that can be checked in several ways. For sufficiently dilute protein solutions, can be estimated from the Debye–Stokes–Einstein relation

with V the hydrodynamic volume of the protein and

the viscosity of the solvent.

This relation is strictly valid only for a protein that behaves as a smooth rigid sphere.

It is common to include a hydration layer in the volume V, but this practice has never been theoretically justified. Bead models have been developed to compute the hydrodynamic properties of real proteins from crystallographic data (Garcia de la Torre et al., 1994; Byron, 1997), thus taking into account surface roughness and nonsphericitv. Independent experimental estimates of may also be available, e.g., from relaxation. The assumption that may also be checked by recording NMRD profiles at different temperatures, since should have the same temperature dependence as (provided the protein structure is invariant), whereas the residence time is expected to vary more strongly (Denisov et al., 1996). If, by any of these means, it can be established that then Eq. (35) yields a lower bound for the residence time of any water molecule that contributes

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significantly to the dispersion, i.e.,

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On the other hand, if the residence

time does not satisfy the inequalities then it can in principle be accurately determined from NMRD data (see Sect. 5.5.2).

5.3. Dispersion Amplitude

According to Eq. (52), the dispersion amplitude parameter contains information about the number of rapidly exchanging internal water molecules with residence times obeying and about their orientational order. It is convenient to express the internal water fraction , with the number of internal water molecules contributing to the dispersion and the total number of water molecules in the solution, both on a per-protein basis. . is typically of order and can be obtained from the protein concentration and the molecular weights of protein and (isotope-labeled) water. For a quantitatively reliable analysis of , an accurate determination of the protein concentration in the NMR sample is essential. This is particularly important in difference NMRD experiments (see Sect. 4.1.2). Whereas uncertainty in extinction coefficients usually limits the accuracy of spectrophotometrically determined protein concentrations to ca. 5% (Gill and von Hippel, 1989), chromatographic analysis of the entire amino acid content of a hydrolyzed aliquot of the protein solution can give protein concentrations to ca. 2% relative accuracy.

5.3.1. Quadrupole Coupling Constants The water and quadrupole frequencies given in Table 1 refer to the rigid-lattice limit of ice Ih. The use of ice values seems a priori justified at least for extensively hydrogen-bonded internal water molecules and is supported by detailed and NMRD studies of the singly buried water molecule W122 in BPTI (Denisov et al., 1995, 1996, 1997b). A wealth of solid-state NMR and NQR data on and QCCs in crystal hydrates and different ice polymorphs (Berglund et al., 1978; Poplett, 1982) as well as large-basis-set quantum-chemical calculations on molecular clusters (Halle and Wennerström, 1981b; Cummins et al., 1985, 1987; Eggenberger et al., 1992, 1993; Ludwig et al., 1995) have established correlations between the QCCs and the geometry of hydrogen bonding (or ion coordination). Judging from such data, the QCC variation among different internal water molecules should be small. In particular, the QCC ratio is nearly invariant at 30.5 1.5 in a variety of hydrogen-bonded solids (Poplett, 1982). Even for water molecules coordinated to ions, such as (Halle and Wennerström, 1981b), (Denisov and Halle, 1995c), and (Thomann et al., 1995), and for water adsorbed on NaX zeolite (Resing, 1976), the QCCs seem to differ little from the ice Ih value. In bulk water, however, the QCCs are 20%–25% larger than in ice Ih but virtually independent of temperature (van der Maarel et al., 1985, 1986;

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Struis et al., 1987; Ludwig et al., 1995). These larger values are probably more appropriate for water molecules at the protein surface than for internal water molecules.

With knowledge about the protein concentration and the rigid-lattice coupling the value derived from the NMRD profile can be used to calculate the quantity

where

is the mean-square generalized order parameter for the

internal water

molecules responsible for the relaxation dispersion. Furthermore, denotes either the quadrupole frequency in Eq. (4) or the intramolecular dipole frequency in Eq. (61). In the 1Hcase, , obtained from Eqs. (60) and (62), should be used with Eq. (64). The available NMRD data from protein solutions suggest that is in the range 0.5–1.0 for buried water molecules. Since, by definition, cannot exceed 1, the quantity provides a lower bound for the number of long-lived internal water molecules in the protein. The actual number of long-lived

water molecules will be larger if

and/or if not all water molecules exchange rapidly with bulk water (see Sect. 5.5). On the other hand, if is known, as might be the case in a difference NMRD experiment, then SI can be obtained directly. If labile-hydrogen contributions (see Sect. 5.7) and intermediate-exchange effects (see Sect. 5.5) can be excluded (or corrected for), then the number should be the same for all three water nuclei. The ratio of the values derived from, say, the and dispersions then yields directly the ratio of the corresponding generalized order parameters, providing information about orientational disorder of internal water molecules.

5.3.2. Libration Amplitudes

The generalized order parameters and describe the effect on the relaxation dispersion of any reorientational motion of buried water molecules that is fast compared to the isotropic tumbling of the protein. Since the nuclear interaction tensors have different orientations with respect to the water molecule (Fig. 11), the three generalized order parameters provide independent information about the internal motion. This information is contained in the second-rank orientational order parameters in Eq. (38). To obtain a quantitative measure of the degree and anisotropy of orientational disorder, these order parameters can be translated into motional amplitudes with the aid of a model. In the anisotropic harmonic libration (AHL) model (Denisov et al., 1997b), the fast local motions are modeled in terms of three independent symmetric libration modes: (i) the rocking of the water molecule around an axis (x) perpendicular to the molecular plane, (ii)

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the wagging of the water molecule around an axis (y) parallel to the H–H vector,

and (iii) the twisting of the water molecule around its axis (see Fig. 11). In addition, the possibility of a fast 180° flip around the axis is included. In the AHL model, the angular variables are the libration angles , and for the rock, wag, and twist modes, respectively. The order parameters , can be expressed in terms of these variables as

where the angular brackets denote averages over the appropriate equilibrium distribution Due to the noncommutability of finite rotations, the order parameters in the AHL model depend on the order in which the rotations are applied. [The result in Eq. (65) corresponds to the order

first and

last.] For the libration

amplitudes of interest, however, this dependence is very weak and can be neglected.

On account of the symmetry of the libration modes, there are only 5 (rather than 25) independent order parameters, namely

In the presence of a

flip, the order parameters

must also reflect the

symmetry of the water molecule, which requires p to be even. The only effect of the flip is thus to make In the AHL model, the five order parameters in Eq. (66) are not independent

since they are all determined by the rms amplitudes

of the three libration

modes. The orientational distribution function for each mode is of the form

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469

This distribution is normalized on the unrestricted interval rather than on The error introduced by this approximation is negligible for the libration amplitudes of interest (say, For the Gaussian distribution in Eq. (67), the five order parameters in Eq. (66) can be expressed in terms of the orientational averages:

with

and 2. Figure 15 shows the effect of each libration mode on the generalized order parameters. Some general observations can be made: (i) is most affected by the twist mode; (ii) is unaffected by the wag mode and is equally sensitive to rock and twist librations; and (iii) only is affected by the flip. Since a fast flip can reduce by as much as a factor 2.7 (in the absence of librational averaging), a comparison of the and dispersion amplitudes may help to diagnose this type of motion. In general, all three libration modes will be more or less excited. The preceding relations are valid for this general case and can be numerically inverted to obtain the three libration amplitudes from the

experimentally determined generalized order parameters. This strategy has recently

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been implemented for several buried water molecules in BPTI and two single-point mutants (Denisov et al., 1997b). While one of these (W122) is as ordered as a water molecule in ice Ih, the others are more disordered. Converting the libration amplitudes to rotational entropies, one finds that the three extensively hydrogenbonded buried water molecules in the Y35G mutant have a configurational entropy comparable to that of bulk water (Denisov et al., 1997b). This result clearly

challenges the conventional wisdom that bound water is highly ordered and suggests that the hydration of nonpolar cavities (Otting et al., 1997) may actually be entropically driven. 5.4. High-Frequency Plateau According to Eq. (51), the high-frequency excess relaxation rate contains contributions from reorientation and/or exchange of mobile surface waters and from local motions of internal water molecules. The latter contribution is usually negligible since and since is generally smaller than While this is certainly the case for subpicosecond librational motions, 180° flips of internal water molecules around the (dipole) axis can make a small but significant contribution to (Denisov and Halle, 1995c). For symmetry reasons, the flip does not contribute to If the flip is slow compared to protein tumbling , not even the relaxation can be affected, since the anisotropic quadrupole coupling then has been averaged to zero before any flips have occurred. The largest flip contribution can be expected when is close to For large proteins (long , water flips in the 1–10 ns range may actually produce an

observable secondary

dispersion step at higher frequencies. Usually, however,

the principal effect of water flips is not the small contribution to but the strong attenuation of (see Sect. 5.3.2). By definition, the contribution refers to water molecules in the extremenarrowing limit at all accessible frequencies. The relaxation rate is therefore proportional to an effective correlation time reflecting more or less restricted local rotation and/or exchange with bulk water. If the QCC is taken to be the same as for bulk water (see Sect. 5.3.1), we thus have If the second term in Eq. (51) can be neglected, we can use the relation andthe known values of and (directly measured on a reference water sample at the same temperature and isotopic composition as the protein solution) to calculate the quantity

where is the average correlation time for the water molecules at the protein surface. From relaxation studies of water in contact with various interfaces, it is

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471

known that the dynamic perturbation is essentially confined to water molecules in direct contact with the surface (Woessner, 1980; Carlström and Halle, 1988; Volke et al., 1994). That this is the case also for proteins is suggested by molecular dynamics simulations (Brunne et al., 1993; Garcia and Stiller, 1993; Lounnas and Pettitt, 1994; Abseher et al., 1996; Rocchi et al., 1997; Kovacs et al., 1997). It is therefore reasonable to estimate for a monolayer, e.g., using the solvent-accessible surface area of the protein (as computed from crystallographic data) and a molecular area of 15 per water molecule. This leads to a dynamic retardation factor of 5–7 for most investigated native globular proteins (Denisov and Halle, 1996). Somewhat larger values for a few proteins, such as trypsin and BSA may be attributed to local motions within clusters of buried water molecules, as represented by the second term in Eq. (51). Although is known, it is useful to quote the ratio (rather than since the ratio depends neither on the tensorial rank of the interaction that induces relaxation (at least for a rotational diffusion model) nor on the isotopic composition of the water (fractionation factors are close to 1). To obtain an estimate for the time taken for a surface water molecule to rotate through one radian, may be multiplied by the (first-rank) dielectric relaxation time of bulk ca. 8 ps at 298 K. For typical globular proteins, one thus obtains values of order 50 ps (at 300 K). Being an arithmetic average over all surface waters, this value is biased toward the longer times in the (probably wide) distribution and may be markedly affected by a few “outliers.” Since both rotation and translation of exposed water molecules at the protein surface should be rate-limited by hydrogen-bond disruption, the 50-ps estimate also gives an indication of the average residence time of surface waters. 5.5. NMRD Time Scales 5.5.1. NMRD Windows For an internal water molecule to contribute fully to the entire relaxation dispersion, its residence time must be long compared to the rotational correlation time of the protein but short compared to the zero-frequency intrinsic relaxation time, If the local motion contribution to is ignored, these conditions can be expressed as

which may be said to define the “NMRD window” on residence times. Of course, water molecules that do not satisfy Eq. (70) may still contribute to the dispersion,

but do so with less than the maximum contribution Using Eqs. (3a), (32), (35), and (36), we can express the relative dispersion step as which becomes 1 when Eq. (70) is obeyed. This quantity is plotted as a function of in Fig. 16 for all three water nuclei, with

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and 100 ns, and from Table 1. (For has been increased by 30% to take intermolecular dipole couplings into account.) Due to the different rigid-lattice coupling frequencies, the intrinsic relaxation time is three orders of magnitude shorter for than for with falling in between (Table 1). The consequent variation of the width of the NMRD windows implies, for example, that some internal water molecules may give a large relative contribution to the dispersion but only a small one to the dispersion. For small to medium-sized proteins, with typically 5–10 ns, such differential window effects are important for residence times longer than a few 100 ns and must be taken into account when comparing values for different nuclei. It is also clear from Fig.

16a that although a large protein (100 kDa, say) may contain numerous buried water molecules, these will only contribute partially to the dispersion. The edge of the NMRD windows is due the competition of protein rotation and water exchange in orientationally averaging the anisotropic coupling, as expressed by Eq. (35). This is a pure correlation time effect and does not affect the value. 5.5.2. Water Residence Time For water molecules on the central plateau of the NMRD window, only lower and upper bounds on the residence time can be established, as expressed in Eq. (70). On the wide flanks of the NMRD window, however, can be accurately determined. On the flank, this requires independent information about (see

Sect. 5.2). Using this strategy, the residence time of water molecules in the narrow minor groove of a B-DNA dodecamer was recently determined to ns (at 277K(Denisov et al., 1997a) and ns at 253 K (Jóhannesson and Halle, 1998). Relatively short residence times, 5–10 ns at 300 K, have also been obtained for water molecules residing in deep surface pockets in ribonuclease A (Denisov and Halle, 1998) and ribonuclease Tl (Langhorst et al., 1999). Longer residence times can be determined by traversing the flank of the NMRD window as the temperature is varied. This is possible even within the restricted temperature range available with protein solutions since long residence times usually are associated with high (apparent) activation enthalpies. Furthermore, with decreasing temperature we not only move to the right on the in Fig. 16, but the edge of the NMRD window is also shifted to the left since increases (this actually shrinks the NMRD window from both sides). Due to the frequency dependence of the intrinsic relaxation rate the fast-exchange condition may be more strongly violated at low frequencies than at high frequencies. Since the dispersion is then more strongly attenuated at lower frequencies, the shape of the dispersion profile is affected. Provided that all water molecules contributing to the dispersion have the same residence time the Lorentzian form of Eq. (53) remains valid to an excellent approximation, but the dispersion is shifted to higher frequency (shorter and the dispersion amplitude

Multinuclear Relaxation Dispersion Studies of Protein Hydratlon

parameter is reduced. To show this, we return to Eq. (32), make use of the decomposition in Eq. (50), and carry out some rearrangements using the (excellent) approximation in Eq. (55). The result is again on the form of Eq. (48), but with in Eqs. (48) and (53) replaced by the effective correlation time

and

in Eq. (48) replaced by the effective amplitude parameter

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If the local motion contribution is in the fast-exchange limit

as is

usually the case, Eqs. (71) and (72) reduce to

where, in general, is given by Eq. (35). If NMRD profiles are recorded at a series of temperatures where the flank of the NMRD window is traversed, the residence time and its activation parameters can be determined from the variation of with temperature, as described by Eq. (73) and a suitable parametrization of (T). (The temperature dependence of is usually known; cf. Sect. 5.2.) The activation parameters are particularly valuable as they provide insight about the mechanism (usually largescale fluctuations of the protein structure) whereby a buried water molecule escapes from within a protein. The residence time can actually be obtained (at one temperature) without assuming a functional form for For example, at the temperature Eq. (73) yields (Often, when is outside the fast-exchange limit.) As an illustration of this approach, Fig. 17 shows the temperature dependence of deduced from and difference dispersions (see Sect. 4.1.2) isolating the contribution from the single buried water molecule W122 in BPTI. A joint fit to the two curves in Fig. 17 yielded a residence time at 300 K and an apparent activation enthalpy (Denisov et al., 1996). The temperature shift between the and curves is quantitatively accounted for by the different quadrupole frequencies of the two nuclei (Table 1). 5.6. Stretched Dispersions

The Lorentzian dispersion function is the fastest decaying function that can result from diffusive (overdamped) molecular motions. On the other hand, experimental dispersion profiles are sometimes found to be more extended than predicted

by Eq. (53). At least three factors can contribute to such dispersion stretching: (i) anisotropic protein rotation, (ii) protein–protein interactions, and (iii) a distribution of residence times extending into either or both flanks of the NMRD window. Depending on the circumstances, these effects can shift the dispersion to higher or lower frequency and/or stretch it over a wider frequency range. While it is straightforward to incorporate the effect of anisotropic rotational diffusion of the protein on the spectral density function, especially in the limit of rigid binding (Woessner, 1962), this generalization introduces not only one or two additional rotational diffusion coefficients as parameters but also requires information (available from high-resolution neutron diffraction data for a few proteins) about the orientation of all contributing internal water molecules (and

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475

labile hydrogens) relative to the principal frame of the rotational diffusion tensor. In practice, this mechanism of dispersion stretching is probably unimportant for most globular proteins (aspect ratio (Denisov and Halle, 1995a). In concentrated solutions, protein–protein interactions may affect the relaxation dispersion. The hydrodynamic interference between nearby protein molecules retards their rotation to some extent; to first order the rotational diffusion coefficient is reduced by a factor at a protein volume fraction (Landau and Lifshitz, 1959; Montgomery and Berne, 1977), but the Lorentzian form of the spectral

density function is not significantly affected (Montgomery and Berne, 1977; Wolynes and Deutch, 1977). Direct interactions (electrostatic, van der Waals, and short-ranged), however, can induce a microscopically heterogeneous solution structure. Little is known about such heterogeneities apart from a few cases of specific association at the dimer or oligomer level. If internal water molecules (or labile hydrogens) experience different local environments on a time scale short compared

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to their spin relaxation times, then the observed relaxation dispersion will be a superposition of Lorentzian dispersions characterized by different rotational correlation times In the case of tight association, also the parameters and could vary. Large-scale heterogeneities that are not sampled on the relaxation time scale would give rise to multiexponential relaxation, but this has not been observed in protein solutions. Most proteins contain several internal water molecules, presumably with different residence times. Unless all residence times happen to fall on the central plateau of the NMRD window (Fig. 16), the Lorentzian dispersion term in Eq. (48) should be replaced by a sum over all contributing internal water molecules, i.e., the relaxation dispersion should be a weighted sum of Lorentzian dispersion functions with different (apparent) correlation times. If some residence times are not much longer than the rotational corelation time of the protein, Eq. (35) must be used. Provided that all contributing water molecules are in the fast-exchange limit, and are still given by Eqs. (51) and (52), but in Eq. (48) we must make the replacement

with as in Eq. (35) and the normalized amplitude factors In the event that all contributing internal water molecules have the same residence time the dispersion is Lorentzian but shifted to higher frequency, with an effective correlation time If or if and are comparable and is known, the residence time can thus be obtained directly from the dispersion. For the quadrupolar water nuclei, where Larmor frequencies above 100 MHz cannot be accessed, the shortest residence time that can be determined in this way is about 1 ns. If the fast-exchange limit is not applicable for all contributing water molecules, the dispersion can again become stretched (even if all In Eq. (48), we must then make the replacement

where

are given by Eqs. (71) and (72) with and as in Eq. (35). This mechanism for stretching and shifting the dispersion (to higher frequency) is particularly important for relaxation, where a large number of labile protons in intermediate exchange can contribute significantly to the dispersion (Denisov et al., 1997a). Stretched dispersions should also be more common for very large proteins: when is about 100 ns or longer, even the NMRD window does not exhibit a plateau region (Fig.

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16a), in which case internal water molecules with different residence times will also have different effective correlation times. For relaxation, an additional complication may arise in the intermediate exchange regime in that the intrinsic relaxation

behavior may be slightly nonexponential (see Sect. 3.1.2). Traditionally, stretched dielectric and magnetic relaxation dispersions (and broad minima) have been accounted for in terms of empirical correlation time distributions (Yager, 1936; Connor, 1964). In connection with water NMRD studies of protein solutions and other aqueous biological systems, a lognormal distribution was favored initially (Blicharska et al., 1970; Kimmich and Noack, 1970a), but in

the past two decades most authors have used a so-called Cole–Cole dispersion for fitting stretched dispersions (Hallenga and Koenig, 1976). The original Cole–Cole dispersion function was used to describe dielectric dispersion data (Cole and Cole, 1941) and can be inverted to yield a particular correlation time distribution (Fuoss and Kirkwood, 1941). When this dispersion function was modified (Hallenga and Koenig, 1976) so as to be dimensionally commensurate with the real part of the spectral density function (which governs nuclear spin relaxation), its physical meaning was lost. In fact, it can be shown that the modified Cole–Cole dispersion does not correspond to any correlation time distribution (Halle et al., 1998). The significance of the effective correlation time extracted from a fit of the modified Cole–Cole dispersion to stretched NMRD data is therefore somewhat obscure. By inverting the Fourier transform in Eq. (5) and setting it follows that

The frequency integral of the modified Cole–Cole dispersion, however, exhibits an

unphysical divergence. A rigorous procedure has recently been developed for analyzing stretched NMRD profiles without the bias of an arbitrarily imposed

correlation time distribution (Halle et al., 1998). This model-free approach allows a separation of the static and dynamic information content of the dispersion data.

5.7.

Labile Hydrogens

Exchange averaging of macromolecular and water hydrogens is a potential pitfall in all water and relaxation work. Failure to appreciate this point has led to even qualitatively incorrect conclusions about hydration behavior. Well-documented cases include a study of poly (methacrylic acid) (Glasel, 1970) and a recent study of an oligonucleotide (Zhou and Bryant, 1996). In both cases, subsequent studies revealed that the relaxation effects that had been attributed to hydration water were entirely due to labile hydrogens (Halle and

Piculell, 1982; Denisov et al., 1997a).

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The labile hydrogen contribution to NMRD data from protein solutions has been characterized in greatest detail for BPTI. By recording and NMRD

profiles over a wide pH range (Fig. 18), the labile hydrogen contribution could be isolated and quantitatively accounted for in terms of known values and hydrogen exchange rate constants and intrinsic relaxation times of the expected magnitude (Denisov and Halle, 1995b). Since the intrinsic relaxation times of labile hydrogens are at least an order of magnitude longer for than for a larger fraction of the labile hydrogens contribute to the dispersion (Venu et al., 1997).

For BPTI, the labile proton contribution appears to dominate over the buried water contribution even at pH 7, where labile protons were previously thought to exchange too slowly to contribute to the dispersion (Koenig and Schillinger, 1969). While hydrogen exchange is a serious complication in and NMRD studies of protein hydration, it can also be used constructively to study side-chain

dynamics (via the intrinsic relaxation rates) and fast hydrogen exchange rates (not readily accessible with high-resolution techniques). More direct access to fast

proton exchange kinetics is provided by the CSM contribution to the transverse

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479

relaxation rate (see Sect. 3.3.1). The CSM contribution usually dominates over the dipolar contribution to at frequencies of and increases strongly at higher frequencies since the chemical shifts are proportional to the magnetic field (Fig. 19). Most labile protons have chemical shifts of 1–5 ppm from the bulk water resonance. Even at moderate fields, therefore, is much larger than typical intrinsic relaxation rates of According to Eq. (29), which then applies, a given type of proton gives a maximum CSM contribution at a value where the (acid and base catalyzed) exchange rate matches the shift difference This gives rise to characteristic maxima in the dependence of (Fig. 19), which help to separate the contributions from different types of labile protons. If the chemical shifts are known, e.g., from high-resolution studies under conditions of slow exchange, a complete separation can possibly be achieved from

480

CPMG dispersions over a wide

Bertil Halle et al.

range (analogous to the

NMRD data in Fig.

18), perhaps including data at several fields.

6. OUTLOOK

Although water NMRD has been applied to protein solutions for nearly three decades, it is only in the last few years that this technique has matured to the stage where it can make significant contributions to protein science. At present, multinuclear NMRD and high-resolution NOE spectroscopy are the two most powerful NMR methods available for probing protein–water interactions in solution. The information provided by these two techniques is largely complementary. While NMRD has unsurpassed temporal resolution by its ability to map out the spectral

density function in the kHz–GHz range, NOE spectroscopy provides spatial resolution by spectral assignments that can establish the proximity of water molecules to specific protein protons. Although the water relaxation rate measured in an NMRD experiment reflects all rapidly exchanging water molecules in the sample, the frequency dependence separates the contributions from the few long-lived

(biologically interesting) water molecules and the many short-lived ones. Moreover, the location of long-lived water molecules can be established by difference NMRD experiments and with recourse to high-resolution crystal structures. (Also

the water NOE method relies on extrinsic structural information to convert chemical shifts into spatial coordinates and to distinguish water NOEs from chemically relayed NOEs.) While the water NOE method has so far been applied only to

solutions of small and medium-sized proteins (up to 22 kDa), the NMRD method is also applicable to very large proteins, subzero temperatures, and semisolid

samples. Labile proton exchange is a serious problem in NMRD as well as in water NOE spectroscopy (cross peaks from direct water NOEs cannot be distinguished from proton-exchange relayed NOEs and may be obscured by intense exchange cross peaks). Oxygen-17 relaxation, however, invariably reports on water molecules. The NMRD and NOE methods will undoubtedly continue to develop in ways that will allow a more detailed structural and dynamic characterization of water

molecules interacting with proteins and will remove some of the present methodological limitations. The ultimate goal is of course to combine the temporal resolution of NMRD with the spatial resolution of multidimensional high-field spectroscopy. The development of FFC instruments with high-field cryomagnets represents a step in this direction. For semisolid protein samples, such as biological tissues, the NMRD approach might be extended in several respects by employing more sophisticated pulse schemes, polarization transfer, and relaxation anisotropy. Building on recent advances in the study of protein hydration in solution, a

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quantitative understanding of the molecular basis of relaxation-based contrast in soft-tissue imaging should also be within reach.

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11

Hydration Studies of Biological Macromolecules by Intermolecular Water-Solute

Gottfried Otting 1. INTRODUCTION

The use of intermolecular water–peptide NOEs (nuclear Overhauser effect) for the detection of solvent exposure was already in 1974 (Pitner et al., 1974). With improved equipment, it is possible today to obtain a much more complete picture of the hydration of biomolecules in aqueous solution. This chapter describes from “Progress in Nuclear Magnetic Resonance Spectroscopy,” Vol. 31, Gottfried Otting, NMR Studies of Water Bound to Biological Molecules, pp. 259–285, 1997, with kind permission from Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands. The exploitation of intermolecular water–solute NOEs in biological molecules was

originally proposed in 1973 by N. Rama Krishna and Sidney L. Gordon in their study of the effects on solutes with coupled spin systems [J. Chem. Phys. 58 (1973), 5687–5696]. The first demonstration of an intermolecular solvent–solute NOE dates back to 1965 when Reinhold Kaiser reported the observation of an enhancement in a chloroform proton signal when the solvent cyclohexane was saturated [J. Chem. Phys. 42 (1965), 1838–1839].

Gottfried Otting • Department of Medical Biochemistry and Biophysics, Karolinska Institute, S-171 77 Stockholm, Sweden. Biological Magnetic Resonance, Volume 17: Structure Computation and Dynamics in Protein NMR, edited by Krishna and Berliner. Kluwer Academic / Plenum Publishers, New York, 1999.

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the use of the nuclear Overhauser effect in high-resolution NMR spectroscopy to detect and localize the water molecules hydrating proteins, DNA and RNA molecules. Other reviews are Kubinec and Wemmer (1992a), Wüthrich et al. (1992), Kochoyan and Leroy (1995), Billeter (1995), and Otting and Liepinsh (1995a). Intermolecular NOEs observed between the water and the solute allow the identification of individual hydration water molecules in the presence of a very large excess of bulk water which appears at the same chemical shift as the signals from the hydration water. This is possible because NOEs are effectively observed only for internuclear distances shorter than 4–5 Å. NOEs observed between the single, averaged water resonance and the solute thus report on direct interactions between the solute and the first shell of hydration. The degeneracy of the chemical shifts of hydration water and bulk water is a consequence of the chemical exchange between the two environments which is fast

on the chemical-shift time scale (milliseconds). Chemical exchange in this context refers not only to the exchange of entire water molecules but also to proton exchange between different water molecules. The proton exchange between water molecules is catalyzed by acids and bases and is slowest at neutral (Meiboom, 1961). Given the proton exchange rates in pure water (ca. at and 25°C, corresponding to an average proton residence time on a water oxygen of 1 ms), it is not surprising that, in general, only a single, averaged NMR resonance is observed for hydration water and bulk water, although it is in principle possible that some proteins contain single water molecules in internal cavities that exchange sufficiently slowly with the bulk water to give rise to resolved NMR signals. To date, such a case has not been reported, illustrating the presence of conformational fluctuations in proteins which trigger the exchange of internal hydration water molecules with bulk water within milliseconds even at temperatures near the freezing point of water. The signal from a hydration water proton exchanging with a rate of with the bulk water would have a linewidth of which would hardly be detectable in the crowded spectrum of a biological macromolecule. In principle, the exchange between different water molecules could be slowed down by the use of organic solvent molecules. For example, the hydration of the peptide antamanide has been studied in chloroform solution (Peng et al., 1996). Water-soluble proteins, DNA and RNA fragments, however, lose their native three-dimensional structure in pure or nearly pure organic solvents. Water molecules can be used with four NMR active isotopes: and Of those, deuterium and relax too rapidly to be suitable for high-resolution NMR spectroscopy and tritium is difficult to handle at high concentration because of its radioactivity. In addition, the magnetization transfer rate due to the NOE between two spins A and B depends on the gyromagnetic ratio of the spins as The high natural abundance of protons in water and biomolecules provides optimum sensitivity for the observation of NOEs at no extra cost.

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In the following, principal differences between intermolecular and intramolecular NOEs are discussed, NMR experiments suitable for the measurement of intermolecular water–solute NOEs are evaluated, and protein hydration studies using intermolecular NOEs are reviewed. A further section briefly summarizes and compares the biophysical information obtained from NOE studies with that obtained from NMRD measurements, X-ray crystallography, and molecular dynamics simulations.

2. THEORETICAL BACKGROUND FOR INTERMOLECULAR NOEs The NOEs can be observed either by the transfer of longitudinal or transverse magnetization between spins. The latter is also referred to as ROE (rotating frame NOE). Throughout this article, the term NOE is used to describe both the cross relaxation in the laboratory frame and the rotating frame; the distinction between NOE and ROE is made only in the terms and which describe the rates of magnetization transfer between two protons by cross relaxation in the respective

frames of reference. The cross relaxation rates and Bothner-By et al., 1984; Griesinger and Ernst, 1987)

where

are defined by (e.g.,

is the spectral density at frequency is the Larmor frequency, is the gyromagnetic ratio of the protons,

is Planck’s constant divided by

and

is the induction

constant. The spectral density functions depend on the model describing the change in length and orientation of the vector connecting the two nuclear spins involved in the dipole–dipole interaction.

Since spectral densities do not assume negative values, is always positive, while can be positive or negative. The values are negative when the high-frequency components of the spectral density function are unimportant compared to its component at zero frequency, i.e., for slow reorientation of the internuclear vector. Negative values are typically observed for intramolecular NOEs between the protons in slowly tumbling macromolecules. Positive

values are observed for the intramolecular NOEs in small, rapidly reorientating molecules and for intermolecular NOEs, if at least one of the compounds is very mobile. Note that positive cross-relaxation rates yield negative cross peaks in NOESY and ROESY spectra (i.e., of opposite sign than the diagonal peaks), whereas negative cross-relaxation rates yield positive cross peaks.

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2.1. NOE between Two Rigidly Bound Protons

Intermolecular water–solute NOEs can be treated like intramolecular NOEs within the solute, if the hydration water molecules are rigidly bound for longer than the rotational correlation time of the solute (typically nanoseconds). This is the case, for example, for hydration water molecules bound in the interior of a protein with hydrogen bonds providing an icelike environment. The spectral density for the simple case of the interaction between two protons attached to an isotropically tumbling sphere (“rigid sphere model,” Fig. 1) is

where r is the interproton distance and the reorientation rate of the sphere.

is the rotational correlation time describing

Plots of and calculated using Eqs. (2) and (3) for different Larmor frequencies are given in Fig. 1 as a function of the rotational correlation time The curves show that (i) the signs of and are the same for small, rapidly tumbling molecules (i.e., small ), and (ii) the sign change of occurs at values of corresponding to 300 ps at a spectrometer frequency of

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For lower Larmor frequencies, the sign change shifts to longer correlation times; i.e., lower magnetic fields favor positive values. The point where changes sign separates the “fast-motional regime” from the “slow-motional regime.” 2.2. NOE between Solute Proton and Bound but Locally Reorientating Water The description of the intermolecular becomes more complicated if the bound water molecule performs motions with a local correlation time shorter than the rotational correlation time of the solute. This situation is quite usually encountered for slowly tumbling proteins and other biological macromolecules. In the extreme case, can be positive for the water-solute interaction, while the rates between protons of the macromolecule are negative. Using explicit models for which analytical expressions of the spectral density function are available, one can show that water–solute NOEs with positive rates are observed with macromolecular systems only if the water molecule is displaced by more than its own diameter within less than a nanosecond, i.e., for rapid exchange

of water molecules (Otting et al., 1991a).

One of the models which can be calculated analytically is the “wobbling-in-acone” model (Fig. 2A) (Richarz et al., 1980; Fujiwara and Nagayama, 1985). Here, a water molecule may be thought to be hydrogen bonded via its oxygen to a proton donor on the solute, with free rotation around the H-bond axis and an additional “wobbling” motion of the axis. The model predicts reduced rates for increased water mobility especially for motions in the time regime, where the rigid-sphere model would predict a sign change. Analytical expressions are also available for a model, where a water proton moves along a line connecting the center of the solute with a solute proton and the water proton (Fig. 2B) (Luginbühl, 1996). This model predicts reduced rates if the water moves rapidly with an amplitude corresponding to complete dissociation and reassociation, but positive values are hardly obtained if the solute is a macromolecule in the slow-motional regime. It appears quite generally that positive rates result more easily from rapid reorientation of the vector with respect to the main magnetic field than if the vector rapidly changes its length. The difficulty of obtaining positive rates by local motions only is also

supported by experimental results: if methane or hydrogen molecules are inserted under pressure into hydrophobic cavities of hen egg-white lysozyme, the values of the intermolecular NOEs observed are negative, although the local reorientation rate of the gas molecules is certainly in the fast-motional regime (Otting et al., 1997). The cross-relaxation rate between a “probe” proton of the solute and a proton of a small molecule trapped inside a cavity of the solute, which reorientates rapidly in the cavity with spherical symmetry, has also theoretically

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been shown to be the same as the NOE between the probe proton and a hypothetical proton located at the center of the cavity (Otting et al., 1997). The most general representation of local motion is obtained by the use of a generalized order parameter

In this case the spectral density is given by (Halle

and Wennerström, 1981; Lipari and Szabo, 1982; Denisov et al., 1997)

where

denotes the correlation time of the rapid local motion, is the correlation time of the overall rotational tumbling of the solute, r is the internuclear distance with indicating time averaging, and ranges between 0 and 1 for complete disorder and complete order, respectively.

2.3. NOE with Rapidly Diffusing Water Molecules In the extreme limit, water may not be bound at all, but simply diffuse past the solute with no further restriction than that imposed by the space excluded by the

solute. Analytical formulas have been calculated by Ayant et al. (1977) for the case

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where solute and solvent molecules are represented by large and small spheres, respectively, with proton spins located at a certain distance underneath the surface of the hard spheres (Fig. 2C). The spectral density describing the intermolecular interaction is

where are the translational diffusion coefficients of the spheres with spins I (protein) and S (solvent)], is the density of the solvent spin S, and and are defined in Fig. 2C. In addition,

where K denotes the modified spherical Besse function of the third kind and

and

and

are the rotational diffusion coefficients given by Stokes’

law:

where k is the Boltzmann constant, T is the absolute temperature, and is the viscosity coefficient. In evaluating the first term of the double sum in Eq. 5, it is helpful to use the relation (Ayant et al., 1977)

Plotting and with Eqs. (5)–(9) as a function of the inverse translational diffusion coefficient D yields curves similar to those of Fig. 1. Using the Einstein– Smoluchowski relationship

the diffusion coefficient D can be translated into an average residence time

of a water molecule at its hydration site on the solute, assuming that the water molecule is exchanged after a displacement x by its own diameter. Calculating and with (Fig. 2C), and for a frequency of 600 MHz, the sign inversion of is predicted for a diffusioncoefficient This value is about six times smaller than

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the self-diffusion coefficient of pure water at 36°C (Hausser et al., 1966). Using Eq. (10) with it corresponds to a residence time of about 70 ps. This time span is four times shorter than the rotational correlation time at which changes sign in the simple model of Fig. 1. It should be noted that the conversion of the diffusion coefficient into a residence time of the hydration water by Eq. (10) assumes three-dimensional diffusion. The corresponding equations for two-dimensional or one-dimensional diffusion, respectively (Villars and Benedek, 1974), would predict twofold or fourfold increased residence times from the same diffusion coefficient. Furthermore, the rotational correlation times and dimensions of the spheres used to represent the solute and the water molecules change the precise value of the diffusion coefficient for which In particular, a smaller radius and a shorter rotational correlation time of the solute predicts positive

rates for longer

residence times. Biological macromolecules present a surface with more curvature to the solvent than a sphere with a smooth surface. Furthermore, the solventexposed chemical groups are often more mobile than corresponding groups in the interior of, for example, a protein. Thus, a positive value of a water–solute NOE indicates a water residence time shorter than about 1 ns, but is difficult to pinpoint more accurately. Intermolecular cross-relaxation rates have also been calculated for a model where the solute is represented by a planar surface, treating bulk water as a self-diffusing continuum (Brüschweiler and Wright, 1994). It was pointed out that

for this and the model of Ayant et al. (1977),

and

with water molecules

in the fast-motional regime are approximately proportional to the inverse of the internuclear distance r, in marked contrast to the dependence usually observed for NOEs (Brüschweiler and Wright, 1994; Wang et al., 1996a). Residence times that are less dependent on the precise parameters of an explicit model can be derived by replacing in Eqs. (3) and (4) by an effective correlation time which depends on the mean residence time and the rotational correlation time of the solute as (Clore et al., 1990; Denisov et al., 1997)

If used with Eq. (3), the resulting model assumes isotropic diffusional rotation of the solute, that the water at the hydration site is rigidly bound to the solute without local mobility, and that the water exchanges between two discrete states: the hydration site and the bulk water. If Eq. (11) is used with Eq. (4), the local mobility of the bound water is taken into account, too. Using this approach it has been demonstrated that the presence of local motions with an order parameter and a local correlation time can shift the sign inversion of to residence times of 1 ns and longer (Denisov et al., 1997).

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3. ASSIGNMENTS OF WATER-SOLUTE CROSS PEAKS Water–solute cross peaks in NOESY and ROESY can come about by three principal

mechanisms: (i) direct water–solute NOEs, (ii) exchange-relayed NOEs, where the magnetization is transferred from the water to the solute by chemical exchange and further to another solute proton by an intrasolute NOE, and (iii) chemical exchange between a labile solute proton and the water (Fig. 3). Direct NOEs and exchange-relayed NOEs are readily distinguished from chemical exchange peaks by their different signs in ROESY: in ROESY, chemical exchange peaks have the same sign as the diagonal peaks, whereas NOEs and exchange-relayed NOEs give rise to negative peaks, when the diagonal peaks are plotted as positive peaks. In principle, positive ROESY cross peaks are also observed for magnetization transferred by two subsequent NOE steps during the mixing time (“spin diffusion”) (Farmer et al., 1987) and by TOCSY-type transfers. Since spin-diffusion peaks tend to be very weak in ROESY and TOCSY-type cross peaks are prominent only near the diagonal and antidiagonal of a two-dimensional ROESY spectrum (Glaser and Drobny, 1990), they are disregarded in the following discussion. Since the rotational correlation times of biological macromolecules usually are much longer than , where is the Larmor frequency, intramolecular NOEs invariably lead to positive NOESY cross peaks. Therefore, negative NOESY cross peaks with the water are always direct NOEs. For positive water–solute NOESY cross peaks, which have been shown not to arise from direct chemical exchange by a corresponding ROESY spectrum, it is necessary to consider the possibility of

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exchange-relayed NOEs, before the assignment of a direct water–solute NOE can be made. The distinction between exchange-relayed NOEs and water–solute NOEs is usually not possible experimentally. Therefore, the possibility of exchangerelayed NOEs can be excluded only if the solute proton involved in the water-solute cross peak is at least 4-5 Å from any labile solute proton which exchanges rapidly with the water. It is thus important to know the three-dimensional structure of the solute before assigning water-solute cross peaks.

4. NMR EXPERIMENTS FOR THE DETECTION OF INTERMOLECULAR NOEs WITH WATER 4.1. Water Suppression Water suppression is required because the analog-digital converters (ADC) in commercial NMR spectrometers cannot adequately digitize small signals at the low signal amplification needed to digitize the entire unsuppressed water signal. Although a two-dimensional NOESY spectrum is symmetric with respect to the diagonal, intermolecular NOE cross peaks between water and solute protons can be observed with acceptable sensitivity only in the cross section along the frequency axis (row) taken at the chemical shift of the water resonance, because the corresponding cross section along the frequency axis (column) taken at the chemical shift of the water resonance is obscured by noise from the residual, incompletely suppressed water signal. The intermolecular water–solute NOEs detected in the row along the frequency axis arise from the magnetization transfer, where the water protons are frequency labeled during the evolution time part of the water magnetization is transferred to the solute during the mixing time and subsequently detected at the frequencies of the solute protons during the detection period Thus, the measurement of water-solute NOEs requires that the water suppression takes place after the NOE mixing time and before the detection period Many different experimental schemes are available to excite a spectrum without exciting the water resonance (e.g., Plateau and Guéron, 1982; Hore, 1983; et al., 1987; and Bax, 1987a; Smallcombe, 1993). Most of these assume, however, that the water magnetization is aligned along the positive at the start. (By definition, the is the axis parallel to the main magnetic field; equilibrium magnetization is aligned along the positive ) At the end of a NOESY or ROESY mixing period, however, the water magnetization is usually not simply aligned along the Spin-lock pulses, Watergate, and diffusion filters can be used which suppress the water resonance irrespective of the starting conditions.

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4.1.1. Pair of Spin-Lock Pulses Spin-lock pulses defocus magnetization not aligned along the spin-lock axis by the spatial inhomogeneity of the radio-frequency field. Consequently, spin-lock pulses are most effective when applied at high power. High-power spin-lock pulses of 1 to 2 ms duration are sufficient for nearly complete averaging of the magnetization in the plane orthogonal to the spin-lock axis. A pair of orthogonal spin-lock pulses without interpulse delay suppresses all magnetization. With a free precession delay between the two spin-lock pulses, only the magnetization at the carrier frequency and at multiples of are suppressed. Therefore, the sequence can be used to suppress the water resonance if the carrier is at the water resonance. Solute magnetization which starts as y-magnetization and precesses by 90° during the delay is not suppressed. The resulting excitation profile follows the function where is the frequency relative to the carrier frequency. To avoid echo effects, the spin-lock pulses should be of different length, e.g., 0.5 ms for and 2 ms for If the delay is set to l/(spectral width), the excitation profile covers the spectral halves to the left and to the right of the carrier frequency (water frequency), each with a single lobe of the sine function (Otting et al., 1991b).

If the water suppression sequence follows a NOESY mixing time, the first spin-lock pulse can be replaced by a pulsed-field gradient (PFG) or homospoil pulse during the mixing time. The gradient selects the longitudinal magnetization which is aligned along the y-axis after the pulse at the end of the NOESY mixing time. In an analogous way, the first spin-lock pulse can be replaced by the spin lock of a ROESY mixing period. Spin-lock pulses are the quickest way of adequate water suppression.

4.1.2. Watergate The Watergate sequence (Piotto et al., 1992) uses the sequence 90°(selective)180°-90°(selective) with PFGs before and after the 90° pulses. The 90° pulses are selective for the water resonance. Therefore, the water resonance experiences a 360° or 0° rotation, while the solute resonances, which are not affected by the selective pulses, experience only the 180° pulse. With two PFGs of equal amplitude and sign, any transverse water magnetization is dephased by both PFGs, while the solute magnetization is defocused by the first PFG and refocused by the second. The sequence combines excellent water suppression with a uniform excitation profile which is decreased only near the water resonance, depending on the bandwidth of the 90° pulses. Furthermore, Watergate can be combined with selective water-flipback pulses, which selectively take the residual water magnetization to the positive before the Watergate sequence, which then only purges residual transverse water magnetization. A drawback of the Watergate scheme compared to a pair of spin-lock pulses is the fact that the solute magnetization stays

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transverse for a longer time, causing some signal loss by transverse relaxation and small distortions of the solute signals by scalar coupling evolution. A typical PFG

takes about 0.5–1 ms, and 90° pulses shorter than about 2 ms are no longer very selective, leading to phase and amplitude distortions in the spectrum near the water frequency. Scalar coupling evolution can be refocused if the 180° pulse in the Watergate sequence excites only some of the solute resonances, without exciting their coupling partners (Mori et al., 1994). Another variant of the Watergate sequence uses a pulse train of six hard pulses separated by short free precession delays to replace the 90°(selective)- 180°-90°(selective) sequence ( et al., 1993). The relative amplitudes of the pulses are 3:9:19:19:9:3. This 3-9-19 sequence has the advantage of robustness: no amplitudes and phases of selective pulses have to be optimized to achieve good water suppression. On the other hand, the excitation profile is no longer uniform, with a broad

zero-excitation region around the water and at the ends of the spectrum. 4.1.3. Diffusion Filter

One of the simplest diffusion filters uses the spin-echo sequence, with a strong PFG during each of the delays (van Zijl and Moonen, 1990; Wider et al., 1994; Wu et al., 1995). Water and solute magnetization defocus during the

first gradient and refocus during the second. For sufficiently long and strong gradients, the diffusion of the water molecules during the spin-echo sequence prevents the complete refocusing of the water magnetization, whereas the magnetization of the larger, more slowly diffusing solute is refocused more completely. This results in a preferential suppression of the water signal. Diffusion filters are typically longer than 10 ms, causing significant loss of magnetization by transverse relaxation and impure phases by evolution under scalar couplings. Their main advantages are a uniform excitation profile, which allows the detection of solute signals even under the water resonance, and the possibility of suppressing multiple solvent signals simultaneously (Ponstingl and Otting, 1997a). 4.2. Selective Water Excitation

The NMR signals of all hydration water molecules in proteins and DNAs are at the same frequency, because bound water and bulk water exchange rapidly on the NMR time scale (milliseconds). Consequently, all water–solute cross peaks are observed in two-dimensional NOESY and ROESY experiments in a single cross section. Although the intrasolute cross peaks in the two-dimensional spectra may be helpful for assigning the water–solute cross peaks, the intermolecular water– solute cross peaks could be recorded with better sensitivity and in a shorter

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experimental time by selectively recording the cross section of interest in a onedimensional experiment using selective water excitation. Since two-dimensional spectra can be recorded in a few hours, one-dimensional versions, which may be more complicated to set up, do not provide important time savings. Selective water excitation is thus most important for recording two-dimensional analogs of three-dimensional NMR experiments, which would take days to record with adequate resolution. Studying biomolecular hydration by three-dimensional experiments allows the assignment of the water–solute cross peaks in crowded spectral regions. In these experiments, the magnetization transfer from water to the solute is followed by a second mixing time during which the magnetization is transferred further to other solute spins through scalar couplings

or NOEs (Otting et al., 1991b; Holak et al., 1992). The two-dimensional analogs with selective water excitation can be considered as two-dimensional experiments,

where the starting magnetization is obtained by the prior water–solute magnetization transfer. The selective excitation of the water is complicated by the phenomenon of radiation damping (Abragam, 1961). Radiation damping is caused by the interaction of the precessing magnetization with the detection coil of the probehead. The current induced in the coil acts back on the precessing magnetization like a conventional radio-frequency pulse, causing a rotation of the precessing magnetization toward the positive Consequently, transverse magnetization decays more rapidly than one would expect from relaxation. For inverted, longitudinal magnetization, any minor residual transverse component of the magnetization triggers radiation damping, increasing the amount of transverse magnetization until the magnetization passes through the transverse plane. Thus, the FID of the water signal after a 180° pulse grows and decays, with an envelope reminiscent of a Gauss function. This envelope is a direct measure of the current induced in the coil; i.e., it represents the pulse shape acting back on the water magnetization (Otting and Liepinsh, 1995b). On a 600-MHz NMR spectrometer, radiation damping can turn the water magnetization from the negative to the positive within 50 ms. Thus, no selective pulse can effectively excite the water in the presence of radiation damping if it is longer than 50 ms. Radiation damping is proportional to the intensity of the NMR signal and to the quality factor Q of the probehead. In practice, radiation damping is important only for probeheads with high quality factor as they are common at frequencies above 400 MHz. In a dilute solution of a biomolecule in the water resonance is prone to radiation damping, but the resonances of the biomolecule are not. The selectivity of radiation damping can be assessed quantitatively from the envelope of the FID observed after a 180° pulse, which describes the shape of the selective pulse arising from the current induced in the coil.

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In the following, different selective water excitation schemes are discussed using one-dimensional NOESY experiments as examples. The experiments represent also examples of different solvent suppression schemes.

4.2.1. Selective Water Excitation by a 90° Pulse The simplest one-dimensional experiment would be a NOESY experiment, where the excitation pulse and the evolution time are replaced by a selective 90° pulse at the water frequency (Fig. 4A). As discussed, a long, selective 90° pulse does not provide good sensitivity in the presence of radiation damping. Nonetheless, straight selective or semiselective 90° pulses have been used for water excitation in a couple of examples (Fig. 4B–E). With samples, selective water excitation can be achieved by the use of a heteronuclear filter which suppresses the signals from the labeled sample. Such experiments are discussed in this section, too. It has been noted (Mori et al., 1996a) that E-BURP pulses (Geen and Freeman, 1991) can be used with higher selectivity than, e.g., Gaussian pulses. The reason is that the amplitude of an E-BURP pulse grows toward its end, provoking less radiation damping during the initial half of the pulse. Yet, the recommended pulse duration was not longer than 16 ms, corresponding to the excitation of a fairly wide band (Mori et al., 1996a). In the experiment of Fig. 4B, radiation damping during the rest of the pulse sequence was avoided by the use of a PFG after the selective excitation pulse to defocus the water magnetization (Mori et al., 1994). The subsequent 90° pulse generates longitudinal water magnetization, a second PFG is used to destroy transverse magnetization, and a selective 90° pulse is used to generate transverse coherence for the NH protons. The magnetization is refocused by a gradient which is combined with a second gradient which is part of the following Watergate sequence. This Watergate variant contains only a single semiselective 180° refocusing pulse on the NH protons which does not excite the water. The experiment was proposed for the detection of chemical exchange between water and amide protons in proteins. Because of the use of a defocusing gradient after the selective water excitation which prevents the generation of purely longitudinal magnetization by the following 90° pulse, the sensitivity of the experiment is at most half of the sensitivity of the hypothetical experiment of Fig. 4A. The experiment of Fig. 4C (Mori et al., 1996a) eliminates the sensitivity disadvantage of the experiment of Fig. 4B. All the excited magnetization is longitudinal during the mixing time The selection of longitudinal magnetization is supported by a short strong PFG at the beginning of the mixing time. A weak gradient during the rest of the mixing time prevents the formation of transverse water magnetization which could trigger radiation damping. The mixing time is followed by a hard 90° pulse and a water-flipback pulse, which is a selective pulse

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on the water applied with a phase so that the water magnetization ends up along the positive Residual transverse water magnetization is suppressed by the following Watergate sequence. The water-flipback greatly enhances the sensitivity, since the recovery of equilibrium magnetization of water by relaxation is slow. The water-flipback pulse cannot be phase-cycled independently of the first excitation pulse. This is not expected to lead to artifacts, however, since the magnetization of interest has been transferred from the water to the solute during the mixing time where it is no longer affected by the selective flipback pulse. Since radiation damping prevents the use of a truly selective, long 90° excitation pulse, a spin-echo sequence was proposed to reduce those signals from the macromolecules that are excited by the selective 90° pulse (Fig. 4D) (Mori et al., 1996b). The spin-echo filter relies on the shorter transverse relaxation times of macromolecules compared to water. A PFG is applied both at the start and at the end of the spin-echo delay to prevent loss of water magnetization by radiation damping during the spin-echo sequence. Those PFGs must not be too intense to avoid loss of water magnetization by diffusion. A spin-echo delay of 40 ms was proposed for the use with proteins, where resonances overlap with the water signal. Although this delay is too short for complete relaxation of the protein magnetization, an additional suppression factor is provided by the scalar coupling evolution of the with respect to couplings to amide and which channels much of the magnetization into antiphase coherences which no longer lead to longitudinal magnetization during the NOESY mixing time. It was recommended to use two filter delays, 40 and 60 ms, to check the suppression of the solute resonances (Mori et al., 1996b). Much longer filter delays may result in substantial loss of water magnetization, since the effective relaxation time of water protons in solutions of solutes with exchangeable protons can easily be shorter than 200 ms due to exchange broadening. If proteins are available, the selective excitation problem can be overcome by purging the signals of the protein after semiselective water excitation.

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Purging of the magnetization of protons is particularly efficient, since the constant is large and of very similar size for different CH groups. The experiment of Fig. 4E (Grzesiek and Bax, 1993a, 1993b) uses a short spin-echo sequence of selective pulses on the water resonance. The delay is chosen so that any magnetization excited by the first selective pulse precesses during an effective delay of at which time a 90° pulse converts the antiphase magnetization into unobservable two-spin coherence. Residual in-phase magnetization defocuses again during the second delay into antiphase magnetization which is also converted into unobservable two-spin coherence by the second 90° pulse. If water–protein NOEs with protons are to be observed, the constant-time HSQC sequence with water-flipback following the NOESY

mixing time is an efficient way of measuring the NOEs in a two-dimensional spectrum. The selective 90° water-flipback pulse (the seventh proton pulse in the pulse sequence) is phase-cycled together with the phase of the first selective 90° excitation pulse to align the water magnetization along the in each scan. The following pulses effectively rotate the magnetization back to the before the detection period The magnetization of solute protons not bound to is not removed by the pulses at the beginning of the pulse sequence. In this case, it was proposed to distinguish between intramolecular NOEs and intermolecular water–solute interactions by a control experiment identical to that of Fig. 4E, except that it is preceded by selective water irradiation during the interscan relaxation delay until 200 ms before the first selective 90° pulse (Grzesiek et al., 1994). Water magnetization is removed by the selective water irradiation and does not recover very much during the following 200-ms delay. In contrast, the magnetization of the solute is either not affected by the very selective water preirradiation or it is largely replenished by intraprotein NOEs during the 200-ms delay. Therefore, water–solute NOEs are strongly suppressed in the control experiment, whereas intrasolute NOEs are much less affected. When the solute is 100% labeled with both and the scalar coupling evolution of the protons by the large one-bond and couplings can be used to purge the magnetization from the protons bound to and . thus selectively retaining the water magnetization. This principle was implemented in the HMQC experiment of Fig. 4F which was designed for the observation of water– amide proton cross peaks (Gemmecker et al., 1993). After a nonselective 90° excitation pulse, the magnetization evolves under scalar couplings with respect to and The 90° and 90° pulses after delays of and respectively, turn antiphase magnetization into unobservable two-spin

coherence. The filters are applied twice with slightly different delays to improve the purging quality for different and constants. The original experiment used neither water-flipback nor any special precautions to suppress radiation damping throughout the entire mixing time

Furthermore, the magneti-

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zation of hydroxyl and sulfhydryl protons is not filtered out, even if their chemical shifts are resolved from the water resonance (Knauf et al., 1996).

The experiment of Fig. 4G makes use of the radiation damping effect itself to achieve a long, selective 90° pulse of the water (Otting and Liepinsh, 1995b). A 180° inversion pulse is followed by a gradient to remove any residual transverse magnetization. A long selective pulse of a very small nominal flip angle is used to generate a small amount of transverse magnetization, triggering radiation damping. Once the water magnetization passes through the transverse plane, it is picked up by the following 90° pulse and converted into longitudinal magnetization. The magnetization of the solute is not affected by the radiation damping unless the

signals are very close to the water resonance. In the original sequence, a train of homospoil pulses was used to suppress radiation damping during the NOESY mixing time and the water resonance was suppressed by a spin-lock purge pulse. The radiation damping field generating the selective 90° water pulse is similar to

that of a half-Gaussian pulse, which is similarly selective as the Gaussian pulse (Friedrich et al., 1987). By varying the intensity of the selective the duration of the selective water excitation can be adjusted also on probeheads of not too high quality factor, where radiation damping alone would produce unacceptably

long pulse durations. On a 600-MHz NMR spectrometer, radiation damping produces a 90° flip angle during about 25 ms.

The experiment of Fig. 4H (Wider et al., 1996) uses the same principle in a difference experiment. In the first experiment, the nonselective 90° excitation pulse is followed by a PFG to destroy all transverse magnetization. In the second experiment, the PFG is applied only after some delay which allows for nearly complete return of the water magnetization to the The solute magnetization, which is not affected by radiation damping, remains transverse until the PFG in either experiment and is therefore subtracted when the difference between both

experiments is calculated. Only every second experiment contributes to the desired

signal in the difference experiment, leading to a twofold reduction in sensitivity. The radiation damping field generated by the selective 90° water pulse is similar to that of a time-reversed half-Gaussian pulse. The experiment of Fig. 4I is most similar to that of Fig. 4A. Instead of a continuous selective 90° excitation pulse, a time-shared 90° pulse is used with short free precession delays between the individual pulse segments as in DANTE type (Morris and Freeman, 1978) excitation (Otting and Liepinsh, 1995e). The quality

factor of the rf coil is switched high during the pulses and low during the delays. In this way, radiation damping is suppressed during the delays. Each pulse segment of the excitation pulse is more intense than the corresponding segment of a

continuous pulse of the same duration, because the overall integral of the pulse must be the same for a 90° flip angle. Therefore, the radiation damping field is more easily overcome during short pulse elements. In practice, selective 90° Gaussian pulses of 50 ms duration can be achieved in this way without significant loss of

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water magnetization. The excitation sidebands produced by the DANTE-type excitation are placed outside the spectral width by setting the free precession delays shorter than the dwell time. Switching of the quality factor of the probehead requires special hardware, by which the coil can be connected to electrical ground via a rapid switch. Switch designs are available that hardly affect the sensitivity of the probehead (Anklin et al., 1995). 4.2.2. Selective Water Excitation by a 180° Pulse The simplest conceivable NOE experiment using a selective 180° pulse for water excitation is the difference experiment sketched in Fig. 5A, where an experiment with the 180° pulse on the water resonance is subtracted from an experiment, where this 180° pulse is either absent or applied outside the spectral range of interest. Although it is a difference experiment, all scans contribute to the water–solute cross peaks, retaining the full sensitivity. As discussed before, the simple scheme does not allow for a very selective pulse in the presence of radiation damping. Nonetheless, the scheme has been used for selective water excitation with

pulse durations of up to 50 ms (Kriwacki et al., 1993). Similarly as in the experiment of Fig. 4D, the use of a diffusion filter has been proposed to help distinguish direct water–solute NOEs from intrasolute NOEs which are less strongly affected by

diffusion during the delay (Fig. 5B) (Kriwacki et al., 1993). A different scheme for a long, water-selective 180° pulse is presented by the experiment of Fig. 5C. The experiment presents a difference experiment, where the selective 180° pulse is composed of a DANTE-type series of small flip-angle pulses interleaved by short free precession delays (Böckmann and Guittet, 1996). Short bipolar gradients ( , 1995; Zhang et al., 1996) are applied during the delays to suppress radiation damping. In the second part of the difference experiment, the phase of the small flip-angle pulses is reversed in the second half of the selective excitation pulse, leading to an effective 0° flip angle for the water magnetization. The following NOE mixing time starts with a PFG to support the selection of longitudinal magnetization followed by a weak gradient throughout the mixing time to prevent radiation damping. Each bipolar gradient first defocuses and then refocuses the water magnetization. It has been shown that weak bipolar gradients of as little as 0.2 G/cm are sufficient to suppress radiation damping during the evolution time of a two-dimensional experiment ( , 1995). In the scheme of Fig. 5C, the free precession delays and thus the PFGs must be of the order of the dwell time or shorter to exclude the appearance of excitation sidebands in the spectrum. To achieve significant defocusing during

the short delay, each individual PFG must be relatively intense, yet sufficiently weak to avoid troubles from eddy currents. Figure 5D presents a scheme, where radiation damping is used to achieve a near-180° rotation of the water magnetization (Otting and Liepinsh, 1995b). Like

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the scheme of Fig. 5A, the experiment is a difference experiment. Following a nonselective 160° pulse, a series of homospoil pulses or PFGs is applied in one experiment but not in the other. With the homospoil pulses, any transverse magnetization is defocused and radiation damping is suppressed. Without the homospoil pulses, the transverse component of the water magnetization triggers radiation damping, which turns the water magnetization back to the positive while the magnetization of the solute remains unaffected as long as it precesses with different frequencies than the water magnetization. The effective field produced by the radiation damping resembles a Gaussian pulse. The experimental scheme of Fig. 5D yields optimum sensitivity, since almost no water magnetization is lost during the radiation damping process. In contrast, the water signal intensity observed after a selective radio-frequency pulse is always somewhat less than that observed after a nonselective pulse, mostly due to relaxation. A drawback of the excitation scheme of Fig. 5D is the poor definition of the mixing time, since the water magnetization is not longitudinal during the entire mixing time in half of the scans. As in all difference experiments based on selective 180° pulses, the water–solute NOE building up during the selective excitation scheme is not completely subtracted in the difference experiment, which may become noticeable when the excitation scheme is followed by a short ROE mixing time. Finally, it has been noted that difference experiments based on selective 180° inversion pulses tend to suffer from subtraction artifacts (Otting and Liepinsh, 1995b; Mori et al., 1996a), perhaps because of dipolar field effects (see below). The experimental schemes of Fig. 5E–G use a selective 180° refocusing pulse in the middle of a spin-echo period, during which the water magnetization is transverse. Radiation damping is suppressed by defocusing the magnetization by a PFG applied before the selective refocusing pulse. Thus, long, selective pulses can be used without interference from radiation damping. In these schemes, magnetization transfer between water and solute during the selective excitation scheme does not result in a net magnetization transfer; i.e., the NOE or ROE mixing times in these experiments are well defined and given by It must be remembered, though, that the exchange of protons between water and solute can lead to rather short effective relaxation times of the water magnetization. Furthermore, care must be taken to adjust the phase of the selective 180° refocusing pulse. If phase-shifted by 45° relative to the phase of the hard pulses, no longitudinal magnetization is generated at the start of the mixing time. The experiment of Fig. 5E uses PFGs of opposite polarity on either side of the selective 180° pulse; i.e., the second PFG defocuses the water magnetization even

further (Dalvit, 1995; Dalvit and Hommel, 1995a). Thus, only half of the water magnetization is longitudinal during the subsequent NOE mixing time, resulting in twofold reduced sensitivity. The magnetization transferred to the solute is refocused during the Watergate scheme, which also contains PFGs of opposite polarity. The

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PFGs in the Watergate sequence must be of different strength to avoid undesired echo effects. The experiment of Fig. 5F is another variant of the experiment of Fig. 5E, where the water magnetization is refocused by the PFG after the selective 180° pulse, so that all water magnetization is longitudinal during the mixing time and full sensitivity is retained (Dalvit and Hommel, 1995b). Radiation damping is suppressed during the mixing time by a weak, continuous gradient. The mixing time ends with the combination of a selective 90° pulse and a nonselective 90° pulse,

which together return the water magnetization to the positive

The following

conventional Watergate sequence effectively does not excite the water resonance. Thus, high sensitivity is retained in this experiment even if the repetition rate is fast

compared to the relaxation time of the water. The excitation schemes of Figs. 5E and 5F have also been implemented in off-resonance ROESY experiments for the detection of exchange cross peaks with water (Birlirakis et al., 1996). The experiment of Fig. 5G (Wider et al., 1996) relies on a diffusion filter to separate the magnetization of the water and the solute. The selective 180° refocusing pulse is relatively short (4.1 ms) and therefore of little selectivity. The selectivity of this pulse is, however, not very important, since the water signal is selected based on the different diffusion rates of water and solute rather than frequency. The experiment is a difference experiment. In the first experiment, all magnetization

excited by the initial nonselective 90° excitation pulse is defocused by the following PFG. Only the magnetization refocused by the following selective 180° pulse is refocused by the subsequent PFG. Only little water magnetization is refocused, however, because the PFGs are applied with very high amplitude (i.e., 115 G/cm), leading to efficient suppression of the water magnetization by diffusion. In the second experiment, the first pair of PFGs is applied with weak amplitude (i.e., 10 G/cm) so that radiation damping is suppressed but magnetization losses by diffusion are unimportant. The difference between both experiments yields the cross peaks

with the water resonance and suppresses the intrasolute cross peaks between nonlabile or slowly exchanging protons. Since the diffusion of the solute during the excitation scheme also affects the solute magnetization, the total gradient power in each of the experiments is kept constant; that is, weak PFGs are used during the

Watergate sequence, if strong PFGs were used during the excitation scheme, and vice versa. In this way, the Watergate sequence acts as a diffusion filter like the excitation scheme. For comparable diffusion filtering effects, the duration of the

excitation scheme is the same as the duration of the Watergate sequence The advantage of the experiment is the suppression of intrasolute NOEs even if the solute’s resonances are at exactly the same chemical shift as the water. As in all

other experiments of Figs. 4 and 5, however, exchange-relayed NOEs (Fig. 2B) are not suppressed. A disadvantage is the twofold loss in sensitivity, since water magnetization is retained only in every second experiment. Furthermore, the

experiment is prone to eddy current artifacts from the strong gradients. Finally, the

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duration of the Watergate sequence is relatively long to match the duration of the excitation sequence.

4.3. Nonselective Experiments Nonselective experiments have the advantage that spectral artifacts such as and are readily identified, whereas they would appear as subtraction artifacts in experiments using selective water excitation. Furthermore, selective pulse shapes tend to produce negative excitation sidelobes (Hajduk et al., 1993), requiring special care in later spectral analysis. Otherwise, NOEs from solute protons excited with negative sign could easily be interpreted as negative NOESY cross peaks with the water. Nonselective experiments of higher dimensionality, however, tend to be less sensitive than selective experiments. Since quadrature detection in the indirect dimension requires that the phase of the first pulse be incremented in steps of 90°, the water magnetization cannot be channeled into longitudinal magnetization during the NOE mixing time for all FIDs as in the analogous experiments of lower dimensionality which employ selective waterexcitation schemes. Thus, water-flipback schemes cannot readily be implemented. Much of the sensitivity lost in experiments scrambling the water magnetization can, however, be recovered by the use of relaxation reagents which shorten the relaxation time of the water and therefore allow faster repetition rates (Otting and Liepinsh, 1995c). One of these is Gd-diethylenetriamine pentaacetic acid-bismethylamide [Gd(DTPA-BMA)], a nonionic relaxation reagent which is routinely used in MR imaging to shorten the relaxation time of water protons. Gd(DTPA-BMA) has been shown not to bind to plasma proteins and is effective at submillimolar concentrations.

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The pulse sequence of Fig. 6A shows how the water magnetization can be steered into reproducible positions during the mixing time of a NOESY experiment.

The 90° pulse preceding the mixing time is phase-shifted by 45° with respect to the first 90° excitation pulse of the pulse sequence (Driscoll et al., 1989). With the carrier at the water frequency, half the water magnetization becomes longitudinal at the start of the mixing time, while the other half becomes transverse, independent of whether the first 90° excitation pulse is applied along the x- or y-axis. In this way, the amount of water magnetization that needs to be suppressed is the same for every scan. The transverse magnetization is destroyed by the strong PFG at the start of the mixing time. Radiation damping during the rest of the mixing time is suppressed by a long, weaker gradient, and the remaining water magnetization is suppressed by some water suppression scheme, e.g., a spin-lock purge pulse or a Watergate sequence. Radiation damping during the evolution time would lead to broadening of the water signal in the dimension, but can be suppressed by the use of a bipolar gradient, by which the water magnetization is first defocused and then refocused ( , 1995). Alternatively, if PFGs are not available, a Q-switch (Anklin et al., 1995) or spin-lock pulses before the first 90° pulse and after the second 90° pulse (Otting, 1994) can be used for the same purpose. Three-dimensional experiments for the observation of water–solute NOEs are straightforward extensions of the corresponding two-dimensional experiments. Only a few illustrative examples are discussed here. In three-dimensional experiments, water magnetization can be suppressed either after the first or second mixing time. Figure 6B shows a pulse sequence for a 3D NOESY–TOCSY experiment, where transverse water magnetization during the first mixing time is suppressed by a PFG during and longitudinal water magnetization is suppressed by the sequence where the free precession interval before the spin-lock purge pulse SL introduces a sine-shaped excitation profile in the frequency dimension (Otting et al., 1991b). Alternatively, the water suppression scheme can be implemented right before the detection period placing the nonuniform excitation profile in the dimension (Holak et al., 1992). The hydration of or labeled solutes is conveniently studied by 3D NOESY–HSQC experiments. HSQC experiments are not only very sensitive, but also offer simple ways of combining various water suppression schemes with the delays already present in the pulse sequence. For example, water suppression by spin-lock pulses can be incorporated into the first INEPT step of the HSQC sequence, as illustrated by the experiment of Fig. 6C (Messerle et al., 1989). With the carrier at the water frequency, the magnetization of the protons bound to precesses during the INEPT delay by 90°, while the water magnetization stays aligned along the y-axis and is defocused by the spin-lock purge pulse. Since one-bond coupling constants are very similar for different groups, the heteronuclear coherence is hardly affected by the spin-lock purge pulse, resulting in a uniform excitation profile in all dimensions. The

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Watergate sequence is implemented with similar ease in the reverse INEPT step of a 3D NOESY–HSQC experiment (Fig. 6D) ( et al., 1993). Isotope-labeled samples offer the additional option to use gradients for coherence selection with the possibility to totally remove the residual water magnetization (Hurd, 1991). For example, a pair of PFGs of opposite polarity around a 180° pulse can be used to defocus the magnetization of the spins without dephasing the proton magnetization. The coherences of interest are refocused by a corresponding gradient applied to the proton magnetization immediately before detection (Fig. 6E). In the implementation of Fig. 6E, a factor of in sensitivity is lost by the use of gradients in an echo–antiecho mode (Keeler et al., 1994). Using an HSQC sequence with sensitivity enhancement, up to twofold better sensitivity can be obtained (Kay et al., 1992). 4.4.

Dipolar Field Effects

The effective magnetic field experienced by solute and water spins depends also on the orientation of the water magnetization with respect to the main magnetic field. Thus, solute signals appear shifted by about 1 Hz, depending on whether the

bulk magnetization of the water is parallel or antiparallel to the main magnetic field (Edzes, 1990). The effect is present locally, too, i.e., if the water magnetization is parallel to the main magnetic field in some areas of the sample and antiparallel in others. Such inhomogeneous magnetization patterns arise when the magnetization is defocused by a PFG and partially converted into longitudinal magnetization by a following 90° pulse (Bowtell, 1992). The field shift can lead to subtraction artifacts in difference experiments and impure line shapes (Kubinec et al., 1996). It can be shown to cancel when PFGs are applied along the magic angle (54.7°) with respect to the main magnetic field (Warren et al., 1993). Both classical and quantum-mechanical descriptions are available for quantitative descriptions of this so-called dipolar field or demagnetization field effect (Broekert et al., 1996; Levitt, 1996; Richter et al., 1995).

5. APPLICATIONS

5.1. Studies of Protein Hydration

After initial reports on intermolecular water–peptide NOEs observed in 1D NOE difference experiments with angiotensin II (Pitner et al., 1974) and oxytocin (Glickson et al., 1976), hydration studies by intermolecular NOEs do not seem to have been pursued any further, perhaps because of the limited sensitivity of the NMR instrumentation or the difficulty in suppressing subtraction artifacts in the 1D NOE difference experiments.

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The use of intermolecular NOEs for the identification of individual hydration water molecules in proteins was first demonstrated with bovine pancreatic trypsin

inhibitor (BPTI) (Otting and Wüthrich, 1989). This study used NOESY and ROESY spectra to distinguish between chemical exchange and NOE or exchangerelayed NOEs. The cross peaks that could be assigned to intermolecular water– BPTI NOEs could all be explained by NOEs with the four internal hydration water molecules buried in the interior of BPTI, which had previously been identified by X-ray crystallography in all single-crystal structures of BPTI. The cross peaks were positive in NOESY and their intensities comparable to intraprotein cross peaks. It was noted that all water protons and most hydroxyl protons appeared at the chemical shift of the bulk water. Later, the exchange between hydration water and bulk water was formally verified by adding the paramagnetic shift reagent which shifts the frequency of the bulk water signal (Otting et al., 1991c). The experiment showed that the NOEs with hydration water molecules were shifted together with the bulk water signal.

BPTI was further used to develop homonuclear 3D NMR experiments for the study of protein hydration by intermolecular water–protein NOEs (Otting et al.,

1991b; Holak et al., 1992). The improved resolution in these experiments allowed the assignment of many more cross peaks. Negative NOESY cross peaks were observed for surface protons of BPTI, indicating little hindered diffusion rates of the hydration water molecules on the protein surface. A control experiment performed with a 50 mM solution of oxytocin at 8°C showed that negative water–peptide NOESY cross peaks can be observed for all

protons (Otting et al., 199la). At 8°C, all intrapeptide cross peaks were positive in NOESY. Lowering the temperature to –25°C (with the addition of 40% acetone to prevent freezing), the sign of the water–oxytocin NOESY cross peaks turned positive, indicating water residence times at the very low temperature (Otting et al., 1992). As a side result of the hydration studies, exchange cross peaks were observed between water and the hydroxyl protons of BPTI at low temperatures. Their

exchange rates were subsequently measured at 4°C as a function of (Liepinsh et al., 1992a). This study was later complemented by measurements of the proton exchange rates of the labile side-chain protons of lysine, arginine, threonine, serine, and tyrosine in the free amino acids in the temperature range 4–36°C and as a function of (Liepinsh and Otting, 1996). It was also shown that carboxyl protons of solvent-exposed side chains are not readily detected by water–polypeptide NOEs (Liepinsh et al., 1993). BPTI was also used as an example for a comparative hydration study of a protein with and without the presence of 200 mM

using a modified NOE–

TOCSY sequence with selective excitation by radiation damping (Fig. 5D). Unfortunately, the presence of artifacts and impure phases of the cross peaks interfered with a detailed spectral analysis (Böckmann and Guittet, 1995). The same excitation

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scheme worked well for the same authors in a proton exchange study (Böckmann et al., 1996). An early protein hydration study by water–protein NOEs was performed with (Clore et al., 1990). The experiment used was a 3D ROESY HMQC using a spin-lock purge pulse for water suppression. 15 water–protein NOEs were identified and interpreted by 11 water molecules previously detected in the single-crystal structure. Although no NOESY experiment was performed, residence times were attributed to the detected hydration water molecules based on Eq. (11) and on the fact that their NOEs were sufficiently intense for detection. human was used in a later study (Ernst et al., 1995) to detect water–protein NOEs with methyl groups in a WNOESY experiment (Fig. 4E) (Grzesiek and Bax, 1993a). NOEs were detected with methyl protons lining a hydrophobic cavity of about volume in the interior of the protein, although no water molecules had been located in this cavity in any of the crystal structures. It was argued that the lack of hydrogen-bonding partners in the cavity wall could lead to a delocalization of the hydration water molecules, which would make their observation difficult by X-ray crystallography.

In a hydration study of reduced human thioredoxin, four hydration water molecules were detected by six water–protein NOEs with the amide protons in a 3D ROESY HMQC experiment (Forman-Kay et al., 1991; Clore et al., 1990). A structure calculation was performed using these NOE distance constraints supplemented by H-bond restraints with nearby carbonyl oxygens and lower-limit distance constraints for amide protons, for which no intermolecular NOE had been observed. Only those two water molecules which were characterized by two NOEs each were located at unique sites in the protein structure. Their orientation appeared disordered. The 3D ROESY HMQC experiment (Clore et al., 1990) was further used

to study the hydration of the immunoglobulin binding domain of streptococcal protein G (Clore and Gronenborn, 1992). Two solvent-exposed water molecules were identified by three NOEs with amide protons and their binding to the protein modeled with bifurcated hydrogen bonds. A structure computation including internal water molecules was further performed with an FK506-binding protein–ascomycin complex (Meadows et al., 1993; Xu et al., 1993). The protein was and 11 water–protein NOEs were detected in 3D ROESY HMQC (Clore et al., 1990) and 3D NOESY HMQC experiments using a spin-lock purge pulse for water suppression. The NOEs defined three internal water molecules at 30°C. The NOE distance constraints were supplemented by 18 hydrogen-bond constraints based on the crystal structure. The resulting structures were reported to be better defined in the vicinity of the water molecules, when the water molecules were explicitly included in the structure calculation. The same three internal water molecules were detected

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in a later study using FK506-binding protein with the PHOGSY pulse sequence (Fig. 5E) (Dalvit and Hommel, 1995a). The possibility of detecting hydration water molecules at the interface between a DNA-binding protein and DNA by intermolecular water–protein NOEs was demonstrated for a complex between an Antennapedia homeodomain mutant and a 14-base-pair DNA duplex (Qian et al., 1993). The 3D NOESY

and spectra with water suppression by spin-lock purge pulses (Fig. 6C) (Messerle et al., 1989) were recorded with samples of the complex containing protein. Three intermolecular water–protein NOEs

were identified. The experiment (WNOESY, Fig. 4E) was first demonstrated with a complex between calmodulin and an unlabeled 13-residue peptide, where intermolecular water–protein cross peaks were observed with numerous methyl groups (Grzesiek and Bax, 1993a). The same technique was used to quantify the magnetization exchange rates between water and protein protons in a sample of calcineurin B (Grzesiek and Bax, 1993b). In the absence of a three-dimensional structure, however, direct water–protein NOEs could not be distinguished from exchange-relayed NOEs.

The WNOESY and WROESY experiments (Fig. 4E) (Grzesiek and Bax, 1993a) were also used for the detection of intermolecular water–protein cross peaks

with GATA-1 in complex with a 16-base-pair DNA duplex, for which 20 direct water–protein NOEs were reported (Clore et al., 1994). Only eight NOEs were detected in the WNOESY experiments (recorded with NOE mixing times of 60 and 100 ms), one of them with the same sign as in the WROESY experiments (which were recorded with 60-ms mixing time). NOEs present in the WROESY and absent from the WNOESY experiment were ascribed to water molecules with residence times of 200–300 ps. Curiously, numerous water–protein

NOEs were observed with solvent-exposed methyl groups with good intensities in the WROESY experiment. Usually, the water–protein NOEs with solvent-exposed methyl groups yield cross peaks of the same sign and similar intensity in NOESY and ROESY (e.g., Otting et al., 1991a; Kubinec and Wemmer, 1992b; Liepinsh et al., 1992b; Radhakrishnan and Patel, 1994a). WNOESY and WROESY experiments (Grzesiek and Bax, 1993a) were further used to detect buried water molecules in the catalytic domain of stromelysin-1 complexed with a small inhibitor (Gooley et al., 1996). Seven water–protein NOEs were reported, giving evidence for three water molecules which had also been detected in the crystal structure by X-ray crystallography. A homonuclear hydration study of horse heart ferrocytochrome c and ferricy-

tochrome c using 2D NOE–TOCSY and ROE–TOCSY experiments with selective water excitation by a simple, sine-shaped 90° pulse and water suppression by spin-lock purge pulses reported five (six) hydration water molecules in the interior of ferri(o)cytochrome c, one of which changed position between the different

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oxidation states (Qi et al., 1994). Thirty-four NOEs defined six water molecules. Two of these had not been detected by X-ray crystallography. A water molecule was detected at the interface between HIV-1 protease and a chemically synthesized inhibitor by one NOE with an amide proton (Grzesiek et al., 1994). The assignment was based on the crystal structure. A different inhibitor, designed to replace this water molecule, was shown to abolish the intermolecular water–amide proton NOE. The water–amide proton crossrelaxation rate was quantitatively measured using WNOESY and WROESY experiments (Fig. 4E) (Grzesiek and Bax, 1993a) and found to match the internuclear distance measured in the single crystal. Hence, a residence time longer than the rotational correlation time of the complex (9 ns) was attributed to this water molecule. Corresponding cross-relaxation rate measurements were performed later to characterize the hydration of HIV-1 protease in complex with the inhibitor KNI-272 (Wang et al., 1996b) and of HIV-1 protease in complex with DMP323 (Wang et al., 1996a). Four to six water molecules with residence times ns were reported for the complex with KNI-272, but only one to three such water molecules were found at the inhibitor binding site in the complex formed with DMP323. The quantitative measurement of intermolecular water–peptide NOEs in the

turn-forming peptide SYPYD demonstrated differential solvation of the proline residue under conditions of cis and trans prolyl peptide bonds and 1.8/30°C, respectively) (Yao et al., 1994). Two-dimensional ROESY and NOESY experiments were used with spin-lock purge pulses for water suppression (Otting et al., 1991b). Reduced intermolecular NOEs were observed in the cis proline form, indicating low solvent accessibility of the proline ring in the turn structure. An NOE study of human dihydrofolate reductase in complex with methotrexate and NADPH revealed six bound water molecules, five of which were also observable in the absence of NADPH (Meiering and Wagner, 1995). The observed water molecules were highly conserved between different crystal structures. It was noted that these water molecules were buried with less than 80% solvent accessibility and had low-temperature factors in the crystal structures and at least two hydrogen bonds. Three different mutants of the protein were prepared which removed a hydrogen bond to one of the water molecules (Meiering et al., 1995). Weaker water–protein NOEs were subsequently observed for this water molecule, possibly because of a shortened residence time. The experiments used were 3D (Clore et al., 1990), 3D (Messerle et al., 1989), and corresponding two-dimensional spectra using a 10-ms hyperbolic secant 90° pulse for water excitation were recorded. A homonuclear hydration study of a ribonuclease C-peptide analog showed negative NOESY cross peaks with the water resonance for all protons of all 13 residues, as far as the signals could be resolved in 2D NOESY and 3D NOESY– TOCSY spectra, although CD spectra indicated 60% (Brüschweiler et

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al., 1995). Spin-lock purge pulses (Otting et al., 1991b) were used for water suppression. The e-PHOGSY pulse sequence (Fig. 5F) was demonstrated using hen eggwhite lysozyme. The detection of at least three not further specified hydration water molecules was reported (Dalvit, 1996). Like hen egg-white lysozyme contains internal hydrophobic cavities, where no hydration water was detected in the crystal structures, whereas water–protein cross peaks with the protons lining the cavity walls were detected in NOESY and ROESY experiments using spin-lock purge pulses for water suppression (Otting et al., 1997). In contrast to the experiments with interleukin only weak intermolecular NOEs were observed, suggesting partial occupancies of the cavities. Partial occupancy is further suggested by the fact that one of the cavities is so small that only a single water molecule can be accommodated at a time. Thus, the difficulty of observing this water molecule by X-ray crystallography cannot be attributed to a delocalization of the hydration water. Using unlabeled, and samples, the hydration of oxidized flavodoxin from Desulfovibrio vulgaris was studied (Knauf et al., 1996) by way of homonuclear 3D NOESY–TOCSY (Otting et al., 1991b; 3D (Clore et al., 1990) and MEXICO (Gemmecker et al., 1993) experiments. The 3D NOESY–TOCSY experiment used spin-lock purge pulses for water suppression, but was modified by an additional 4-ms water-selective 90° Gaussian pulse at the end of the NOESY mixing period. The pulse was applied with orthogonal phase relative to the following hard 90° pulse. Its purpose was to improve the water suppression by turning any longitudinal water magnetization present at the end of the mixing time into the transverse plane with a phase so that it was not affected by the following 90° hard pulse, resulting in optimum defocusing by the following spin-lock purge pulse which was applied with orthogonal phase relative to the hard 90° pulse (Otting et al., 1991b; Knauf et al., 1996). Four hydration water molecules were defined by about 10 intermolecular water–protein NOEs, one of which lies in a bridging position between the protein and the ribityl side chain of the FMN ligand. Interestingly, some of the buried hydration water molecules reported by the single-crystal structure seemed to be absent in solution. Finally, four to five intermolecular water–protein NOEs detected in 3D (Messerle et al., 1989), 3D and the corresponding ROESY experiments of E. coli flavodoxin were used for the identification of two to three buried hydration water molecules (Ponstingl and Otting, 1997b).

5.2. Studies of DNA and RNA Hydration An early attempt to detect intermolecular

NOEs between water and

DNA by two-dimensional NOESY spectra failed because the imino and amino

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protons of the DNA fragment exchanged too rapidly with the water under the conditions chosen (van de Ven et al., 1988). A quantitative analysis of exchangerelayed NOEs showed that all cross peaks observed with the water resonance could be interpreted as exchange-relayed NOEs. The first study demonstrating intermolecular water–DNA NOEs appeared four years later (Kubinec and Wemmer, 1992b). Using spin-lock purge pulses to suppress the water resonance in two-dimensional NOESY and ROESY experiments (Otting et al., 1991b), it was shown that the hydration water in the vicinity of the adenine 2 protons and some of the sugar protons in the minor groove of the

self-complementary DNA fragment has sufficiently long residence times to give rise to positive water–adenine 2H cross peaks in the NOESY spectrum. Negative NOESY cross peaks were reported with the thymidine methyl protons and G12

indicating short water residence times near these protons.

Positive NOESY cross peaks observed with the terminal nucleotides of the DNA duplex were probably falsely attributed to bound hydration water molecules, since the presence of hydroxyl groups at the terminal sugar moieties provides the possibility of exchange-relayed NOEs. The same DNA fragment and pulse sequences were used in a study published

shortly after, detecting the same water molecules of the spine of hydration in the minor groove and negative NOESY cross peaks with thymidine methyl groups,

guanine 8H, and some of the protons (Liepinsh et al., 1992b). Furthermore, the fragment was studied by the same techniques, where positive NOESY cross peaks with the adenine 2 protons of the central part of the duplex indicated the presence of a spine of hydration even there.

The DNA fragment sample, where A5 was selectively labeled with

was again studied later with a at positions 2 and 8 of the base

(Kubinec et al., 1996). The level of tritium labeling was sufficient to observe intermolecular water–proton to DNA–tritium NOEs in a heteronuclear NOESY experiment which was derived from the conventional three-pulse NOESY sequence by replacing the last 90° pulse by a 90° pulse with subsequent tritium detection. Since the water did not contain tritium, the spectrum could be recorded without water suppression. It was noted, however, that the water–proton to tritium cross peaks were mostly dispersive at short mixing times, regaining pure phase at mixing times of 100 ms or longer. It is likely that the phase distortions arose from demagnetization field effects (Edzes, 1990; Bowtell, 1992; Kubinec et al., 1996; Warren et al., 1993; Broekaert et al., 1996; Levitt, 1996; Richter et al., 1995). Using ROESY experiments with a spin-echo water suppression sequence, the water–DNA NOEs with four different phenazine-tethered matched and mismatched DNA duplexes were measured in a study that tried to correlate the intensities of the water–DNA NOEs with imino proton exchange rates and the thermodynamic stabilities of the duplexes (Maltseva et al., 1993). The validity of

the conclusions reached in this study was perhaps compromised by the fact that the

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water suppression scheme used (Bax et al., 1987; and Bax, 1987b) had not been designed for the observation of intermolecular NOEs with water, producing markedly unequal amounts of water magnetization with even and uneven FIDs recorded with different phase increments for quadrature detection in the indirect frequency dimension. Furthermore, large exchange cross peaks were observed and the possibility of exchange-relayed NOEs was not convincingly ruled out. NOESY and ROESY spectra recorded of the non-self-complementary duplex using water suppression by spinlock purge pulses (Otting et al., 1991b) confirmed the presence of a spine of hydration in the minor groove with water residence times above about 1 ns, since positive NOESY cross peaks were observed with several adenine 2 protons near the center of the duplex (Fawthrop et al., 1993). Interestingly, no hydration water molecules were observed at the central A–T step in the crystal structure of a closely

related duplex. The thymidine methyl groups showed negative NOESY cross peaks as all B-DNA type duplexes studied to date. The residence time of the water molecules of the spine of hydration in the minor groove were reported to be slightly shorter near the AT base pairs in than in since water–adenine 2H cross peaks were absent from the NOESY spectrum of the former, but positive in the latter DNA fragment, while the corresponding ROESY cross peaks were intense in both fragments (Liepinsh et al., 1994). It was speculated that the different residence times could arise from a different minor groove width. The experiments were two-dimensional NOESY and ROESY experiments using spin-lock pulses for water suppression (Otting et al., 1991b).

A subsequent study of three different DNA fragments containing TTAA and AATT segments showed that positive water–adenine 2H NOESY cross peaks can be observed also with TTAA segments (Jacobson et al., 1996). The experiments used the Q-switched water-selective 90° pulse in two-dimensional NOE–NOESY and ROE–NOESY experiments (Otting and Liepinsh, 1995c), where the water– DNA cross peaks lie on the diagonal and off-diagonal peaks assist with the assignment of the diagonal peaks. It was shown that NOEs could be observed on the diagonal free from interference with the strong exchange cross peaks of the terminal hydroxyl protons which otherwise appear in the spectral region of the resonances. Negative NOESY cross peaks were observed for base protons other than adenine 2H, most of the sugar protons, and all thymidine methyl groups. The 2H resonances of adenines next to GC base pairs also yielded mostly negative NOESY cross peaks. The conclusion of the study was that the residence time of the hydration water in the minor groove of TTAA segments depends on the nucleotide sequence context. The hydration of DNA triplexes and a parallel-stranded DNA duplex has been studied by two-dimensional NOESY and ROESY experiments using spin-lock purge pulses for water suppression (Radhakrishnan and Patel, 1994a, 1994b; Wang

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and Patel, 1994). Positive water–DNA NOESY cross peaks were observed at -3 to –4°C for some of the protons lining the grooves in these unusual DNA structures. It was argued that these hydration water molecules could contribute to the conformational stability of the structures by shielding against unfavorable electrostatic interactions. A hydration study of RNA was recently performed with the fragment (Conte et al., 1996). Two-dimensional NOESY and ROESY spectra were recorded using Watergate for water suppression. Weak positive water-RNA cross peaks were observed in the NOESY spectrum with two of the adenine 2H and several protons. Since the minor groove in RNA is wider than in DNA, it was argued that groove width is less important for long water residence times than opportunities for hydrogen-bond formation. The NMR signals of the hydroxyl groups were resolved in the spectra, but gave rise to large exchange cross peaks with the water. It was therefore not trivial to exclude the possibility that the cross peaks with the nonexchangeable minor groove protons originated from exchange-relayed NOEs, in particular since the exchange cross peaks with the hydroxyl protons were about 100 times more intense than the water-RNA cross peaks with the nonexchangeable RNA protons, i.e., of similar

intensity as the diagonal peaks. The argument that only weak cross peaks were observed does not mean that these NOEs are weak, since there was also very little diagonal peak intensity for the resonances due to the rapid exchange with the water during the mixing time.

6. 6.1.

SUMMARY OF THE RESULTS Residence Times

By fortuitous coincidence, the sign of the NOE cross-relaxation rate changes for water residence times in the range 0.1–1 ns. Hydration water on protein surfaces and in the minor groove of DNA exhibits residence times exactly in this time range. Thus, NOE measurements provide a tool to distinguish “slow” and “fast” water molecules on this time scale. A second fortuitous coincidence is the fact that water molecules with longer residence times are much easier to detect by water-solute NOEs than rapidly diffusing water molecules. The NOE intensities increase with the residence time until the residence time becomes longer than the rotational correlation time of the solute. Therefore, water-solute NOEs cannot discriminate between different residence times in the regime above the rotational correlation time of the solute (typically several nanoseconds). Since only a few water molecules from the hydration shell of a biomolecule are in the slow-motional regime, the water–solute NOEs provide a filter for the preferential observation of these water molecules

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which usually are in more intimate contact with the solute than rapidly diffusing

water. The upper limit of the residence times of slowly exchanging hydration water molecules is in the millisecond time range. A residence time of at least about 20 ms would be required to enable the observation of a NOESY cross peak at a chemical shift separate from that of the bulk water (Otting et al., 1991c). A residence time of 1 ms would broaden the signal of the water molecule by about 300 Hz, which would be difficult to observe in the one-dimensional NMR spectrum of a biomolecule. Definitely, upper limits of 100 to 200 cannot be deduced from water–solute NOE studies as claimed (Ernst et al., 1995). Attempts to distinguish rapidly diffusing bulk water from hydration water diffusing at the rate of the macromolecule in an experiment with strong PFGs yielded an upper limit of 1 ms for the residence times of the internal hydration water molecules in BPTI at 4°C (Dötsch and Wider, 1995). Since proton exchange rates between water molecules in the bulk phase occur with rates of and faster (Meiboom, 1961), all these upper limits pertain strictly speaking only to the residence times of the water protons but not the entire water molecules. Residence times in the subnanosecond time range, as documented by negative NOESY cross peaks, must be due to the exchange of entire water molecules, unless proton exchange is very strongly catalyzed. In bulk water, proton exchange lifetimes become shorter than 1 ns at (25°C) (Meiboom, 1961). Recent work by Halle and co-workers showed that accurate residence times in the nanosecond to millisecond time range can be measured for individual hydration water molecules using nuclear magnetic relaxation dispersion (NMRD) of the water nuclei and (Denisov and Halle, 1995a, 1995b, 1995c; Denisov et al., 1996; Venu et al., 1997). The NMRD data predominantly reflect the exchange of the few hydration water molecules with extended residence times on the macromolecular solute. The measurements report on the entire hydration of the solute, not only in the vicinity of solute protons as the water–solute NOE measurements. Although only the relaxation times of the average water NMR signals are measured, information on individual hydration water molecules can be obtained by comparison between samples with and without solvent accessible hydration sites. Hydration sites can be rendered inaccessible by site-directed mutagenesis [for example, the internal water molecule 122 in BPTI is replaced by the hydroxyl group of Ser 36 in the mutant BPTI(G36S) (Berndt et al., 1993)] or by the addition of a ligand [for example, a drug binding to the minor groove of DNA replaces hydration water molecules from the spine of hydration (Denisov et al., 1997)]. The technique yields not only residence times but also order parameters for the solute-bound water

molecules. Furthermore, the number of water molecules bound with long residence times can be determined with good accuracy.

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6.2. Structural Relevance

Since intermolecular water–solute NOEs single out buried hydration water molecules with residence times longer than 1 ns, it is tempting to believe that these water molecules are of importance for the three-dimensional structure of the biomolecules. The energetic implications of slowly and rapidly exchanging hydration water molecules are, however, not so clear. A slowly exchanging hydration

water molecule may not be “more stably” bound than a water molecule that is more

easily exchanged by another water molecule. This is particularly apparent for water molecules in hydrophobic cavities where hydrogen-bonding partners are missing. The problem is also well illustrated by the hydration water molecules mediating specific contacts in the trp repressor/operator-DNA cocrystal structure (Otwinowski et al., 1988). Some of these hydration water molecules appear to be approximately conserved in the single-crystal structure of the free DNA (Shakked et al., 1994). In the free DNA, these water molecules are highly solvent exposed and are probably characterized by residence times in the subnanosecond time range. Thus, rapidly exchanging water molecules may be structurally important as slowly exchanging water molecules may be of little structural relevance. The observation

of hydration water molecules with residence times longer than 1 ns in the interior of proteins and in the minor groove of DNA is primarily a consequence of the fact that these water molecules are buried or at least largely protected from access to the bulk solvent. Hydration water molecules buried inside a protein or located in the minor groove of DNA are almost invariably also detectable by X-ray crystallography, where they are often characterized by low B-factors. These water molecules are thought to play a structural role, when the crystal structure shows several well-defined hydrogen bonds with the solute. Usually, many more hydration water molecules are detected by X-ray crystallography than by NOE experiments, but not all hydration water molecules of the first shell of hydration are detected. This is readily explained by the fact that the electron density of the water molecules must be spatially well localized in order to be observable by X-ray crystallography. Thus, continuously diffusing or disordered water escapes X-ray detection, whereas rapidly exchanging water molecules may be observable if they exchange in a

“hopping” motion. It is not surprising that many of the hydration water molecules detected by X-ray crystallography contact one or two solute molecules in the crystal lattice. Negative water–solute NOESY cross peaks observed in solution show that most of these hydration water molecules have residence times of less than 1 ns in solution. More puzzling are reports on water molecules with residence times longer than about 1 ns near solvent-exposed methyl groups (Ernst et al., 1995; Clore et al., 1994). Rapid rotation of water pentagons about the methyl groups has been proposed to explain the fact that these water molecules were not observable in single-crystal X-ray studies, but molecular dynamics simulations do not support this interpretation.

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The molecular dynamics (MD) of a protein or DNA molecule in water can be simulated with explicit water molecules for up to a few nanoseconds. The residence times of the hydration water molecules on protein surfaces predicted by the MD simulations range from tens of picoseconds to a few hundred picoseconds (Ahlström et al., 1988; Brunne et al., 1993; Knapp and Mügge, 1993; Billeter et al., 1996).

6.3. Future Perspectives

Currently, water–solute NOEs can be observed for the entire surface of small peptides, but not for protein or DNA molecules. With improved sensitivity of the

NMR equipment, intermolecular water–solute NOEs should become observable for all solvent-exposed protons of the biomolecular macromolecules. Equipment with improved sensitivity would further allow the use of heteronuclear NOEs to study the hydration of chemical groups devoid of protons, such as carbonyl groups. The principle feasibility of such studies has been demonstrated with small organic molecules (e.g., Seba and Ancian, 1990; Canet et al., 1992). The distinction between direct and exchange-relayed NOEs continues to be a problem if the three-dimensional conformation of the solute is not known. Theo-

retically, diffusion filters could be used to separate the signal of rapidly diffusing

bulk water from that of hydration water diffusing at the rate of the solute, but much stronger PFGs would have to be applied in a much shorter time span than what is technically possible today. The attempt to identify direct NOEs in the presence of exchange-relayed NOEs by a quantitative measurement of the NOE cross-relaxation rates failed (Wang et al., 1996a). Usually, many water–solute cross peaks are observed (Fig. 7), but only a few of them can be attributed to direct water–solute NOEs in an unambiguous way and the number of water molecules identified by these is even less. Automation of the spectral analysis will greatly enhance the attractiveness of

the technique. The detection of hydration water molecules at the interface between a protein and a small organic ligand molecule would suggest the design of a new ligand which could bind with higher affinity by replacing the water molecules by functional groups (Grzesiek et al., 1994). It may be conceived that future MD simulations will cover a sufficiently long time span to allow the calculation of water–solute NOEs with all protons of the solute, which will allow the further refinement of the force fields describing biomolecular hydration and lead to a model in quantitative agreement with the experimental NMR data.

7. CONCLUSION What have we learned from hydration studies of biological macromolecules using water–solute NOEs? Perhaps the most interesting result are the short residence

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times of the hydration water molecules on protein and DNA surfaces. Hydration–

dehydration events would not be expected to be rate-limiting steps in protein folding and intermolecular recognition. Most of the water molecules detected by X-ray crystallography were shown not to be kinetically stable in solution. The possibility of obtaining this information for many individual water molecules in aqueous solution is unique to the NOE method. The hydration studies of proteins and other biological macromolecules by intermolecular water–solute NOEs certainly triggered the development of numerous new pulse sequences dedicated to the detection of intermolecular water–solute cross peaks. In the field of selective water excitation, the experiments with the most colorful acronyms are perhaps not the most attractive in practice. Yet the ideas developed in the context of biomolecular hydration studies may prove invaluable in the development of pulse sequences applicable to the study of NOEs between biological macromolecules and organic cosolvents in aqueous solutions. The first NOE studies of protein–organic solvent interactions are currently emerging (Liepinsh and Otting, 1997; Ponstingl and Otting, 1997a). They may significantly enhance our understanding of altered enzyme specificity observed in nonaqueous environments and provide a tool for rational drug design.

NOTE. Abergel et al. recently demonstrated an elegant modification of the selective excitation scheme of Fig. 5D, where an electronic feedback circuit is used to eliminate or enhance radiation damping at any time during the pulse sequence (Abergel, D., Louis-Joseph, A., and Lallemand, J.-Y., 1996, J. Biomol. NMR 8:15).

ACKNOWLEDGMENTS. The author thanks Dr. Edvards Liepinsh for the spectrum of Fig. 7 and helpful discussions, Dr. Bertil Halle for a critical reading of the manuscript, and the Swedish Natural Science Research Council for financial support. REFERENCES Abragam, A., 1961, Principles of Nuclear Magnetism, Clarendon Press, Oxford. Ahlström, P., Teleman, O., and Jönsson, B., 1988, J. Am. Chem, Soc. 110:4198. Anklin, C., Rindlisbacher, M., Otting, G., and Laukien, F. H., 1995, J. Magn. Reson. B 106:199. Ayant, Y., Belorizky, E., Fries, P., and Rosset, J., 1977, J. Phys. (Paris) 38:325. Bax, A., and Davis, D. G., 1986, J. Magn. Reson. 65:355.

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Contents of Previous Volumes

VOLUME 1 Chapter 1

NMR of Sodium-23 and Potassium-39 in Biological Systems Mortimer M. Civan and Mordechai Shporer

Chapter 2

High-Resolution NMR Studies of Histones C. Crane-Robinson Chapter 3

PMR Studies of Secondary and Tertiary Structure of Transfer RNA in Solution Philip H. Bolton and David R. Kearns

Chapter 4 Fluorine Magnetic Resonance in Biochemistry J. T. Gerig

Chapter 5

ESR of Free Radicals in Enzymatic Systems Dale E. Edmondson 529

530

Contents of Previous Volumes

Chapter 6 Paramagnetic Intermediates in Photosynthetic Systems Joseph T. Warden Chapter 7

ESR of Copper in Biological Systems John F. Boas, John R. Pilbrow, and Thomas D. Smith

Index VOLUME 2 Chapter 1

Phosphorus NMR of Cells, Tissues, and Organelles Donald P. Hollis Chapter 2

EPR of Molybdenum-Containing Enzymes Robert C. Bray

Chapter 3

ESR of Iron Proteins Thomas D. Smith and John R. Pilbrow

Chapter 4

Stable Imidazoline Nitroxides Leonid B. Volodarsky, Igor A. Grigor’ev, and Renad Z. Sagdeev Chapter 5

The Multinuclear NMR Approach to Peptides: Structures, Conformation, and Dynamics Roxanne Deslauriers and Ian C. P. Smith

Index

Contents of Previous Volumes

531

VOLUME 3

Chapter 1 Multiple Irradiation Experiments with Hemoproteins Regula M. Keller and Kurt Wüthrich Chapter 2

Vanadyl(IV) EPR Spin Probes: Inorganic and Biochemical Aspects N. Dennis Chasteen

Chapter 3

ESR Studies of Calcium- and Protein-Induced Photon Separations in Phospatidylserine-Phosphatidylcholine Mixed Membranes Shun-ichi Ohnishi and Satoru Tokutomi Chapter 4

EPR Crystallography of Metalloproteins and Spin-Labeled Enzymes James C. W. Chien and L. Charles Dickinson Chapter 5

Electron Spin Echo Spectroscopy and the Study of Metalloproteins W. B. Mims and J. Peisach Index VOLUME 4 Chapter 1

Spin Labeling in Disease D. Allan Butterfield

Chapter 2

Principles and Applications of Ian M. Armitage and James D Otvos

to Biological Systems

532

Contents of Previous Volumes

Chapter 3

Photo-CIDNP Studies of Proteins Robert Kaptein Chapter 4

Application of Ring Current Calculations to the Proton NMR of Proteins and Transfer RNA Stephen J. Perkins Index VOLUME 5 Chapter 1

CMR as a Probe for Metabolic Pathways in Vivo R. L. Baxter, N. E. Mackenzie, and A. I. Scott

Chapter 2

Nitrogen-15 NMR in Biological Systems Felix Blomberg and Heinz Rüterjans Chapter 3

Phosphorus-31 Nuclear Magnetic Resonance Investigations of Enzyme Systems B. D. Nageswara Rao

Chapter 4

NMR Methods Involving Oxygen Isotopes in Biophosphates Ming-Daw Tsai and Larol Bruzik Chapter 5

ESR and NMR Studies of Lipid-Protein Interactions in Membranes Philippe F. Devaux Index

Contents of Previous Volumes

VOLUME 6 Chapter 1 Two-Dimensional Spectroscopy as a Conformational Probe of Cellular Phosphates Philip H. Bolton Chapter 2 Lanthanide Complexes of Peptides and Proteins Robert E. Lenkinski Chapter 3 EPR of Mn(II) Complexes with Enzymes and Other Proteins George H. Reed and George D. Markham

Chapter 4 Biological Applications of Time Domain ESR Hans Thomann, Larry R. Dalton, and Lauraine A. Dalton Chapter 5 Techniques, Theory, and Biological Applications of Optically Detected Magnetic Resonance (ODMR) August H. Maki

Index VOLUME 7 Chapter 1 NMR Spectroscopy of the Intact Heart Gabriel A. Elgavish Chapter 2 NMR Methods for Studying Enzyme Kinetics in Cells and Tissue K. M. Brindle, I. D. Campbell, and R. J. Simpson

533

534

Contents of Previous Volumes

Chapter 3

Endor Spectroscopy in Photobiology and Biochemistry Klaus Möbius and Wolfgang Lubitz Chapter 4

NMR Studies of Calcium-Binding Proteins Hans J. Vogel and Sture Forsén

Index VOLUME 8 Chapter 1

Calculating Slow Motional Magnetic Resonance Spectra: A User’s Guide David J. Schneider and Jack H. Freed

Chapter 2

Inhomogeneously Broadened Spin-Label Spectra Barney Bales Chapter 3

Saturation Transfer Spectroscopy of Spin-Labels: Techniques and Interpretation of Spectra M. A. Hemminga and P. A. de Jager Chapter 4

Nitrogen-15 and Deuterium Substituted Spin Labels for Studies of Very Slow Rotational Motion Albert H. Beth and Bruce H. Robinson

Chapter 5

Experimental Methods in Spin-Label Spectral Analysis Derek Marsh Chapter 6

Electron-Electron Double Resonance James S. Hyde and Jim B. Feix

Contents of Previous Volumes

535

Chapter 7

Resolved Electron-Electron Spin-Spin Splittings in EPR Spectra Gareth R. Eaton and Sandra S. Eaton

Chapter 8

Spin-Label Oximetry James S. Hyde and Witold S. Subczynski

Chapter 9

Chemistry of Spin-Labeled Amino Acids and Peptides: Some New Mono- and Bifunctionalized Nitroxide Free Radicals Kálmán Hideg and Olga H. Hankovsky

Chapter 10 Nitroxide Radical Adducts in Biology: Chemistry, Applications, and Pitfalls Carolyn Mottley and Ronald P. Mason

Chapter 11

Advantages of and Deuterium Spin Probes for Biomedical Electron Paramagnetic Resonance Investigations Jane H. Park and Wolfgang E. Trommer

Chapter 12

Magnetic Resonance Study of the Combining Site Structure of a Monoclonal Anti-Spin-Label Antibody Jacob Anglister Appendix

Approaches to the Chemical Synthesis of Spin Labels Jane H. Park and Wolfgang E. Trommer Index

and Deuterium Substituted

536

Contents ofPrevious Volumes

VOLUME 9

Chapter 1 Phosphorus NMR of Membranes Philip L. Yeagle

Chapter 2

Investigation of Ribosomal 5S Ribonucleotide Acid Solution Structure and Dynamics by Means of High-Resolution Nuclear Magnetic Resonance Spectroscopy Alan G. Marshall and Jiejun Wu Chapter 3

Structure Determination via Complete Relaxation Matrix Analysis (CORMA) of Two-Dimensional Nuclear Overhauser Effect Spectra: DNA Fragments Brandan A. Borgias and Thomas L. James

Chapter 4

Methods of Proton Resonance Assignment for Proteins Andrew D. Robertson and John L. Markley Chapter 5

Solid-State NMR Spectroscopy of Proteins Stanley J. Opella Chapter 6

Methods for Suppression of the Signal in Proton FT/NMR Spectroscopy: A Review Joseph E. Meier and Alan G. Marshall Index VOLUME 10 Chapter 1

High-Resolution

Magnetic Resonance Spectroscopy of

Oligosaccharide-Alditols Released from Mucin-Type O-Glycoproteins Johannis P. Kamerling and Johannes F. G. Vliegenthart

Contents of Previous Volumes

537

Chapter 2

NMR Studies of Nucleic Acids and Their Complexes David E. Wemmer Index VOLUME 11 Chapter 1

Localization of Clinical NMR Spectroscopy Lizann Bolinger and Robert E. Lenkinski Chapter 2

Off-Resonance Rotating Frame Spin-Lattice Relaxation: Theory, and in Vivo MRS and MRI Applications

Thomas Schleich, G. Herbert Caines, and Jan M. Rydzewski Chapter 3 NMR Methods in Studies of Brain Ischemia Lee-Hong Chang and Thomas L. James

Chapter 4

Shift-Reagent-Aided Whole-Organ Systems

NMR Spectroscopy in Cellular, Tissue, and

Sandra K. Miller and Gabriel A. Elgavish

Chapter 5

In Vivo

NMR

Barry S. Selinski and C. Tyler Burt

Chapter 6

In Vivo

NMR Studies of Cellular Metabolism

Robert E. London

Chapter 7

Some Applications of ESR to in Vivo Animals Studies and EPR Imaging Lawrence J. Berliner and Hirotada Fujii

Index

538

Contents of Previous Volumes

VOLUME 12

Chapter 1

NMR Methodology for Paramagnetic Proteins Gerd N. La Mar and Jeffrey S. de Ropp

Chapter 2

Nuclear Relaxation in Paramagnetic Metalloproteins Lucia Banci

Chapter 3 Paramagnetic Relaxation of Water Protons Cathy Coolbaugh Lester and Robert G. Bryant

Chapter 4

Proton NMR Spectroscopy of Model Hemes F. Ann Walker and Ursula Simonis

Chapter 5 Proton NMR Studies of Selected Paramagnetic Heme Proteins J. D. Satterlee, S. Alam, Q. Yi, J. E. Erman, I. Constantinidis, D. J. Russell, and S. J. Moench Chapter 6

Heteronuclear Magnetic Resonance: Applications to Biological and Related Paramagnetic Molecules Joël Mispelter, Michel Momenteau, and Jean-Marc Lhoste Chapter 7

NMR of Polymetallic Systems in Proteins Claudio Luchinat and Stefano Ciurli

Index

Contents of Previous Volumes

539

VOLUME 13 Chapter 1 Simulation of the EMR Spectra of High-Spin Iron in Proteins Betty J. Gaffney and Harris J. Silverstone Chapter 2

Mössbauer Spectroscopy of Iron Proteins Peter G. Debrunner

Chapter 3 Multifrequency ESR of Copper: Biophysical Applications Riccardo Basosi, William E. Antholine, and James S. Hyde Chapter 4 Metalloenzyme Active-Site Structure and Function through Multifrequency CW and Pulsed ENDOR Brian M. Hoffman, Victoria J. DeRose, Peter E. Doan, Ryszard J. Gurbiel, Andrew L. P. Houseman, and Joshua Telser Chapter 5

ENDOR of Randomly Oriented Mononuclear Metalloproteins: Toward Structural Determinations of the Prosthetic Group Jürgen Hüttermann

Chapter 6 High-Field EPR and ENDOR in Bioorganic Systems Klaus Möbius Chapter 7

Pulsed Electron Nuclear Double and Multiple Resonance Spectroscopy of Metals in Proteins and Enzymes Hans Thomann and Marcelino Bernardo

Chapter 8 Transient EPR of Spin-Labeled Proteins David D. Thomas, E. Michael Ostap, Christopher L. Berger, Scott M. Lewis, Piotr G. Fajer, and James E. Mahaney

540

Contents of Previous Volumes

Chapter 9

ESR Spin-Trapping Artifacts in Biological Model Systems Aldo Tomasi and Anna Iannone

Index VOLUME 14 Introduction: Reflections on the Beginning of the Spin Labeling Technique Lawrence J. Berliner Chapter 1

Analysis of Spin Label Line Shapes with Novel Inhomogeneous Broadening from Different Component Widths: Application to Spatially Disconnected Domains in Membranes M. B. Sankaram and Derek Marsh

Chapter 2 Progressive Saturation and Saturation Transfer EPR for Measuring Exchange Processes and Proximity Relations in Membranes Derek Marsh, Tibor Páli, and László Horváth Chapter 3

Comparative Spin Label Spectra at X-band and W-band Alex I. Smirnov, R. L. Belford, and R. B. Clarkson

Chapter 4

Use of Imidazoline Nitroxides in Studies of Chemical Reactions: ESR Measurements of the Concentration and Reactivity of Protons, Thiols, and Nitric Oxide Valery V. Khramtsov and Leonid B. Volodarsky

Chapter 5

ENDOR of Spin Labels for Structure Determination: From Small Molecules to Enzyme Reaction Intermediates Marvin W. Makinen, Devkumar Mustafi, and Seppo Kasa

Contents of Previous Volumes

Chapter 6

Site-Directed Spin Labeling of Membrane Proteins and PeptideMembrane Interactions Jimmy B. Feix and Candice S. Klug Chapter 7

Spin-Labeled Nucleic Acids Robert S. Keyes and Albert M. Bobst

Chapter 8

Spin Label Applications to Food Science Marcus A. Hemminga and Ivon J. van den Dries Chapter 9

EPR Studies of Living Animals and Related Model Systems (In-Vivo EPR) Harold M. Swartz and Howard Halpern

Appendix Derek Marsh and Karl Schorn

Index VOLUME 15 Chapter 1 Tracery Theory and NMR Maren R. Laughlin and Joanne K. Kelleher Chapter 2

Isotopomer Analysis of Glutamate: A NMR Method to Probe Metabolic Pathways Intersecting in the Citric Acid Cycle A. Dean Sherry and Craig R. Malloy Chapter 3

Determination of Metabolic Fluxes by Mathematical Analysis of Labeling Kinetics John C. Chatham and Edwin M. Chance

541

542

Contents of Previous Volumes

Chapter 4 Metabolic Flux and Subcelluar Transport of Metabolites E. Douglas Lewandowski Chapter 5

Assessing Cardiac Metabolic Rates During Pathologic Conditions with Dynamic NMR Spectra Robert G. Weiss and Gary Gerstenblith

Chapter 6

Applications of Labeling to Studies of Human Brain Metabolism In Vivo Graeme F. Mason Chapter 7

In Vivo NMR Spectroscopy: A Unique Approach in the Dynamic Analysis of Tricarboxylic Acid Cycle Flux and Substrate Selection Pierre-Marie Luc Robitaille

Index VOLUME 16

Chapter 1

Determining Structures of Large Proteins and Protein Complexes by NMR G. Marius Clore and Angela M. Gronenborn

Chapter 2

Multidimensional NMR Methods for Resonance Assignment, Structure Determination, and the Study of Protein Dynamics Kevin H. Gardner and Lewis E. Kay Chapter 3

NMR of Perdeuterated Large Proteins Bennett T. Farmer II and Ronald A. Venters

Contents of Previous Volumes

Chapter 4

Recent Developments in Multidimensional NMR Methods for Structural Studies of Membrane Proteins Francesca M. Marassi, Jennifer J. Gesell, and Stanley J. Opella Chapter 5

Homonuclear Decoupling to Proteins Hiroshi Matsuo, and Gerhard Wagner Chapter 6

Pulse Sequences for Measuring Coupling Constants Geerten W. Vuister, Marco Tessari, Yasmin Karimi-Nejad, and Brian Whitehead Chapter 7 Methods for the Determination of Torsion Angle Restraints

in Biomacromolecules C. Griesinger, M. Hennig, J. P. Marino, B. Reif, C. Richter, and H. Schwalbe

Index

543

Index

Acyl carrier protein, 55 distance constraints, 24 Aggregation symmetric, 132 ,449 ALFA, 59, 60 Alignment, see Molecular alignment ALPS, 59, 60 Ambiguous restraints, 67 Ambiguous distance restraints (ADRs), 131, 140–142, 155–156, 157 assignment of, 145 symmetric, 140–142 Analytical expressions for the transferred NOESY of a two-spin system, 238 Angle search, 64, 39 Anisotropic interactions, see Interactions, anisotropic magnetic susceptibility, see Magnetic susceptibility, anisotropic reorientation, see Molecular alignment Annealing protocols, 142–144 naming convention, 143 ANRS method, 61 Apo-kedarcidin, 58 Applications of water-solute NOEs, 511 Arc motion, see Motion, arc model ARIA, 145 Assessment of conformational flexibility, 209 Assignment of NOEs, 136, 155 of resonances, 136 Assignment methods, 43 Assignments of water-solute cross peaks, 493 Asymmetric labeling, 137–138 Atom swapping, 63 Atomic B-factors, 12

AURELIA, 38 AUTOASSIGN, 56, 67 Automated methods, 40 Automated peak picking, 68 Automated resonance assignments, 40, 57 ALPS, 85 AUTOASSIGN, 85–97 CONTRAST, 84–85 FELIX, 83 NOESY spectra assignment, 67 program of Abbott Laboratories NMR Group, 84–85 program of Bristol-Myers Squibb NMR Group, 83 stereospecific assignments, 33 Averaging sum, 141 Back calculation of NMR spectra, 206 transferred NOESY spectra, 265, 281 Backbone dynamics derived from relaxation rates, 385 analysis of the multispin relaxation of 386 experiments to determine the relaxation rates, 391 heteronuclear NOE, 389 relaxation time, 387 relaxation time 387 Backbone dynamics derived from relaxation rates, 370 calculation of microdynamical parameters, 377 experimental details, 370 interpretation of microdynamical parameters, 381 processing of spectra and determination of relaxation rates, 376 sensitivity-enhanced HSQC experiment (SE-HSQC), 370 water-flipback HSQC, 371 Basic fibroblast growth factor (FGF-2), 90, 94, 97 Bayesian parameter estimation, 331

545

546 Bayesian posterior probabilities, 86 Bicelles, see Molecular alignment, Protein alignment Blood group A trisaccharide, 283, 289 Boltzmann average, 4, 28 constant, 6 ensemble, 5, 6 factor, 5 probability distribution, 15 sampling, 21 Bovine pancreatic ribonuclease, 90–97 Bovine seminal ribonunclease, 46 BPTI, 51, 448, 450, 474–475, 478–479 Branched polymers, 22 BSA, 461 Calbindin D9k, 450, 452 Calculation of concentrations, 247 Calmodulin, 58 CARNIVAL, 206 Cellobiohydrolase I, 65 Channel blocker, 214 Chemical exchange, 493, 501 Chemical shift dispersion degeneracy, 136–141 symmetry degeneracy, 136, 137, 140–141 Chemical shifts, 4,12,19,23 CLAIRE, 45 Coherence-transfer delays, 124 Cold-shock protein (Csp A), 90, 97 Comonomer NOEs, 137, 138, 146 Complete hybrid matrix, 204 Complete relaxation matrix, 165, 204, 282 CORCEMA, 223 CORMA, 203 IRMA,172 MARDIGRAS, 172, 204 MORASS, 172 PDB2 NOE, 285 Cone motion, see Motion, cone model Conformational annealing search, 142–144 averaging, 210 exchange, 224

heterogeneity, 86 sampling, 214 Conformational exchange matrix, 233

Constraint

adiabatic distance, 24 methods, 6 propagation, 56, 87 CONTRAST, 84 CORCEMA, 223, 265 analysis of transferred NOESY data, 289–301 calculations for finite delays, 232 program, 246, 248 theory, 230

Index Corepressor tryptophan with repressor-operator

complex, 297 CORMA, 203, 224 Correlation time, 204, 453, 465–466 COSY (ECOSY), 328 Coupling constants, 203, 207 Couplings, measurement of effects of cross correlation, see Spin relaxation, cross correlation effects of dynamic frequency shifts, see Spin relaxation, dynamic frequency shifts frequency based experiments, 323–325, 328–333 intensity based experiments, 325, 333–336 precision of measurement, 323, 325, 330–332 systematic errors, 324, 335–336 Couplings, residual dipolar angular constraints, 312, 319, 321–322; see also Structure determination determination of sign, 320 field dependence, 313, 319, 323, 325 field induced, 311 history of observation, 320–322 in the study of motion, see Motion measurement of, see Couplings, measurement of separation from scalar, 319 theory, 314–320 Couplings, scalar measurement of, see Couplings, measurement of CPMG, 443, 444

Crambin, 73 Cramér-Rao lower bound (CRLB), see Couplings, measurement of, precision of measurement Cross validation, 217 Degeneracy dispersion, 136, 141 symmetry, 136, 137, 140–141 Determination of protein dynamics in the microsecond time window, 406 in the millisecond time window, 409 Diamagnetic susceptibility, see Magnetic susceptibility, diamagnetic Diamagnetic systems, see Magnetic susceptibility, diamagnetic DIAMOD, 69 DIANA, 65

Difference NMRD, 447 Difference spectroscopy, 138 Diffraction, 3, 8

Diffusion filter, 496 Dipolar field effects, 511 Dipolar relaxation with chemical exchange, 439 Dipolar couplings, see Couplings, residual dipolar, field-induced

Index Dipolar (cont.) Hamiltonian, 315, 316; see also Couplings, residual dipolar, theory shifts (pseudocontact shifts) 341 DISGEO, 66 Dispersion amplitude, 466 function, 463, 474–477 stretched, 474–477 Distance constraints, 6, 24 holonomic, 24 Distance geometry, 61–63, 202 DISGEO, 66 DGEOM, 282 self-correcting, 143 Distance restraints (constraints), 62 ambiguous, 140–142 bounds, 141 restraint function symmetry restraints, 139–140, 156–157 DNA and RNA hydration, 516 DNA, 450, 453, 472 DNA duplexes, 207 complexed to GATA-1, see Structure determination, examples, GATA-1 complexed to DNA

magnetic susceptibility, see Magnetic susceptibility,

diamagnetic, in DNA structure refinement, 322; see also Structure determination, examples, GATA-1 complexed to DNA DNA three way junction, 190–194 final structure, 192–193 hybrid-hybrid matrix refinement, 190–194 refinement summary, 192 sequence, 190 Dolichos biflorus lectin, 283, 287 Double-quantum-filtered COSY (2QF-COSY), 207 Dynamic frequency shift, see Spin relaxation, dynamic

frequency shifts Dynamic matrix, 230, 238 Dynamic shift, 436–437 Dynamics of protein structures, 311, 357 from field-induced dipolar couplings, 311 from and relaxation, 357

general features of dynamics, 357 microdynamic motional parameters, 359 ECOSY spectroscopy, 328 Effect of ligand-receptor ratio on tr-NOESY, 270 Effect of motions of transferred NOESY, 278 Electric field alignment, see Molecular alignment, using electric field Electron density, 5, 12 Electron spin, see Magnetic susceptibility, paramagnetic, in myoglobin Encounter complexes, 240

547 Energy, see potential minimization, 144 Ensemble, 6, 29 average, 14, 19, 29 calculations, 201 generation of, 6, 8

Ensemble of structures, 212 Equations of motion, 5, 6, 23, 24 Er-2, 72 Error analysis, 205

E-selectin, 290 Euler rotations, see Rotations, Euler Ewald techniques, 27 Exchange rate, 202 Experimental NMR restraints, 202

accuracy, 202, 206 internal inconsistencies, 213, 217 redundancy of restraints, 219 Extended system restraining methods, 6 Fast conformational exchange, 236 Fast field cycling, 421, 424–429 FELIX, 38, 47 3D data set to process, 191 Ferrocytochrome c, 60

FFC, see fast field cycling Field-induced residual dipolar couplings, 311 Field variation, 421 Finite receptor off-rates, 227, 268 FKBP, 67 Floating chirality, 63, 64, 67 Force Field, 5, 7, 9, 19 GROMOS, 20, 87 GROMOS 43A1, 9 parameters, 142 Forssman pentasaccharide, 287, 289 Frequency domain experiments, see Couplings, meas-

urement of, frequency domain experiments

Function of off-rate, 277 Fuzzy graphs, 47 GAL 4, 62 GARANT, 50, 51 GATA-1 magnetic susceptibility, see Magnetic susceptibility,

diamagnetic, in DNA structure refinement, see Structure determination, examples, GATA-1 complexed to DNA GCN4 homodimer, 149–151

Generalized intensity (I) matrix, 234 Generalized kinetic (K) matrix, 234 Generalized relaxation rate (R) matrix, 233 Generic spin system object, 86 Genetic algorithms, 50 Global optimization, 50

GLOMSA, 64, 65

548

Index

Glutamine-binding protein, 60 Goodness of refinement, 186 Graph theory, 41, 49 Grid search, 63 HABAS, 63, 65 Hamiltonian, see Dipolar Helix motion in myoglobin, see Motion, in myoglobin relative orientations, see Structure determination,

example, myoglobin Hemocyanin, 462 High temperature approximation, 318 Hinge-bending motion, 228–229, 240–243 Hirudin, 72 HIV integrase fragment dimer, 134 HnRNP C RNA-binding domain, 58 Holonomic distance constraints, 24 HSQC, 323–324; see also Couplings, measurement of

Human fibrinopeptide analogs, 282 Human RNP C RNA-binding domain, 58 Human transforming growth factor (hTGF), 57 Hybrid duplex, 216

Hybrid-hybrid matrix method, 163–199 advantages, 196–198 effect of added noise, 176 experimental refinement, 190–194 for 3D NOESY-NOESY data analysis, 171–176 iterative refinement calculation, 179–190 procedure, 175 refinement of a duplex DNA, 177–190 refinement of a DNA three way junction, 190–194 theory, 173 Hybrid-matrix-based algorithms, 265 IRMA, 172 MARDIGRAS, 204 MORASS, 172 Hybrid matrix of NOE intensities, 204 Hydration studies by intermolecular water-solute NOEs, 485 Indices of agreement, 209; see also R-factor and NOE R-factor crystallographic R-factor, 210 sixth-root-weighted

factor, 210

Insulin hexamer, 135, 154–155 Integration time step, 23, 24, 25, 26, 27 Intensity based experiments, see Couplings, measurement of, intensity-based experiments Intensity-restrained refinement, 264

Interaction function, 5, 7, 9, 19, 23 Interaction tensor, 455 Interactions anisotropic dipolar, see Couplings, residual dipolar, theory

electric quadrupole, 314; see also Quadrupolar

Interactions (cont.) isotropic scalar couplings, 314

Zeeman, 314 Interface filter, 147 Interleukin-8 dimer, 147, 148, 149 Intermolecular ligand-receptor dipolar relaxation, 227 Intermolecular NOE hydration studies, 485 in transferred NOESY, 229, 244, 255, 277 solvent-solute, 485, 523 theory, 487 water-DNA, 516 water-protein, 511 water-solute, 485

Intermolecular potentials, 141 Intermolecular transferred NOESY, 229, 244, 255, 277 methods for observing, 255–261 Intermonomer NOEs, 137–146

Internal motion, 202 Interproton distance restraints, 203, 217

dynamically averaged distances, 206 Intramonomer NOEs, 137 Irreducible spherical tensor (IRE), see Tensor, irreducible spherical tensors Isolated spin pair approximation (ISPA), 224, 437 Isotope-selected/filtered methods, 261 Isotropic

interactions, see Interactions, isotropic reorientation, see Molecular alignment Iterative structure calculation, 145, 157 4,12,16,19, 23 J-modulation experiments, 328 J-resolved spectroscopy, 328 Jun homodimer, 148, 149–151 Karplus relation, 5, 12, 31 Killer toxin, 72 Kinetic matrix, 230 Labile hydrogens, 477–480 Lac repressor, 47 Ladder, 56, 58 Leakage-shell model, 298, 299

Leucine zipper homodimers, 146, 148, 149–151 Libration amplitudes, 467

Ligand motions in the bound state, 229 Ligand-protein intermolecular dipolar relaxation, 272 Ligand-protein/DNA complex, 297 Ligand-protein intermolecular NOESY intensity, 277 Ligand-receptor complexes, 223 calculation of concentrations, 247–249 reversibly binding, examples of, 225, 226

Index Ligand-receptor interactions, 233 encounter complex, 240 multistate models, 240 two-state model, 233 LINSHA, 207 Liquid crystals, see Molecular alignment, using liquid crystals LISP, 96 Local-elevation search method, 21 Logical constraint propagation, 56 Magnetic field alignment, see Molecular alignment, using magnetic field Magnetic susceptibility anisotropic, 313, 316–328, 340–342, 348, 350 concentration dependence, 348 determination, 320–322, 340–342, 348 diamagnetic, in ubiquitin, 324–326 in aromatic systems, 317, 319–322 in DNA, 322, 326, 342 in myoglobin, 321, 340–342, 348 interaction with magnetic field, see Molecular alignment, using magnetic field

origin of, 321 paramagnetic determination, 340, 341 in myoglobin, 323–325, 340–341 in small inorganic complexes, 321 origin, see Magnetic susceptibility, paramagnetic, in myoglobin principal axis system, see Principal axis system, magnetic susceptibility Magnetization transfer, 438-442 Main chain directed strategy, 39 MARCOPOLO, 43 MARDIGRAS, 204, 281 Maximum common subgraph, 42 Mean-field approximations, 22 MEDUSA, 213 Met repressor dimer, 147, 148, 149 Metalloprotein, 209 Methods for relaxation rate determination, 361 determination of the heteronuclear NOE, 369 determination of the longitudinal relaxation time 366 determination of the transversal relaxation time 368 experiments for the determination of relaxation rates, 365 theory of relaxation in proteins, 361 Methods for suppressing or identifying proteinmediated spin diffusion, 249 Methylphosphonate, 216 Metric tensor, 25, 27, 31 Model free expressions for transition probabilities, 231

549 Molecular alignment, see also Protein alignment using bicelles, 327 using dilute liquid crystals, 313, 327 using electric field, 320 using magnetic field, 312, 314, 316–322; see also Magnetic susceptibility Molecular complexes, 224, see also Ligand-receptor complexes Molecular conformations, 202 pool of conformers, 202, 213 Molecular dynamics in torsion angle space, 157 simulated annealing with, 142–144 Molecular dynamics (MD) simulation, 9, 13, 14, 21, 23, 29 in four-dimensional Cartesian space, 22 Molecular motion libration, 467–470 models, 444–446 Monte Carlo, 59 Monte Carlo simulation, 6, 21 MORASS, 172, 174–194 3D version of, 174 iterative refinement cycles, 191

Motion, see also Motions amplitudes, 346–347 arc model, 344–347 cone model, 344–348 effects on magnetic susceptibility, 341, 348 effects on NOE measurement, 344 effects on residual dipolar couplings, 344–345, 348–352 in myoglobin function, 345 librations from spin relaxation, see Spin relaxation order parameters and time scales order matrix analysis, see Order matrix, motion characterization slow collective motion in myoglobin, 346–347 Motional model, 204 Motions bond-angle bending, 24, 26 bond-stretching, 24, 26 dominated by Coulomb interactions, 24, 27 dominated by van der Waals contacts, 24, 27 torsional, 26 water librational, 26 Multiple copy refinement, 212 Multiple-time-step algorithms, 23, 25, 27 Multiple-quantum coherence, 434–436 Mutual information method, 50 Myoglobin diamagnetic susceptibility, see Magnetic Susceptibility, diamagnetic, in myoglobin motion, see Motion paramagnetic susceptibility, see Magnetic Susceptibility, paramagnetic, in myoglobin

550 Myoglobin (cont.) structure refinement, see Structure determination, examples, myoglobin Network editing sequences, 253 Neural networks, 52 Neutron diffraction intensities, 4, 19 NMR CLUST, 212 NMR data, 202 NMR experiments for intermolecular NOEs with water, see Pulse sequence for water-solute NOEs NMR methods for suppressing protein-mediated spin diffusion, 250

NMRD, see Nuclear Magnetic Relaxation Dispersion NOAH, 71, 44 NOAH/DIAMOD, 40, 47 NOE, 203, 311–312, 342; see also Motion, effects on NOE measurement between solute proton and bound but locally reorientating water, 489 between two rigidly bound protons, 488 connectivities, 45, 74

with rapidly diffusing water molecules, 490 intermolecular, 255–261 NOE assignment between symmetry mates, 156 comonomer, 137, 146 intermonomer, 137, 146 intramonomer, 137 restraint potential, 142

NOE-NOESY, 522 NOE R-factor, 298, 299; see also R-factor NOESY, 420; see also NOE 3D NOESY-NOESY data deconvolution of, 173–176, 191 gradient method for the analysis of, 165 simulation studies, 167–171 Non-bonded potential, 143 Non-crystallographic symmetry, 138–139, 156–157 Nonselective experiments, 508 Nonspecific binding, 229, 244 Non-structural protein (NS-1) from influenza A virus, 90, 97

Non-symmetric aggregation, 132 Normalization of calculated and experimental intensities, 267 Nuclear Overhauser enhancement (NOE)

Index Nuclei

319, 326, 338 see Quadropolar , 323–325 , 431, 432 Nucleic acid, see DNA

, 214 Order, magnetic field induced, 314 Order matrix, 348 diagonalization, 349 motion characterization, 350–353

ordering director, 348, 350–351 relation to magnetic susceptibility parameters, 350 structure determination, 349–352 theory, 348–350 Order parameter, 29, 231, 490 intermolecular, 456–545 intramolecular, 454–456, 467–470 Order parameters from residual dipolar couplings, see Order matrix, theory from spin relaxation, see Spin relaxation, order parameters and time scales tetramerization domain, 136, 135, 148, 151–152 Packing restraints, 146 Pair of spin-lock pulses, 495 Paramagnetic susceptibility, see Magnetic susceptibility, paramagnetic Paramagnetic systems, see Magnetic susceptibility, paramagnetic

PARSE, 212 Particle-particle-particle-mesh methods, 27 Partial relaxation, 205 Pathogenesis-related protein from tomato, 72 PDB2 NOE, 282, 285 PDQPRO, 213, 214, 218 Peak ambiguity, 39 Peak picking for resonance assignments, 99 Penalty function, 6, 7, 13, 31 for lower-bound restraining, 7 for upper-bound restraining, 7 Perdeuterated receptors, 249 Phage 434 represser, 72 Pitfalls in structure determination, 31 Platelet factor4/lL-8 chimer tetramer, 152

distance bounds, 12, 15, 19, 23

Point groups, 132–133, 134–135

intensities, 4, 12, 15, 19

Potential distance symmetry, 139–140, 156–157 NOE, 142 non-crystallographic symmetry, 139–140, 156–157 repel, 143

relaxation matrix calculation, 12, 23, 165, 204, 223 Nuclear magnetic relaxation dispersion (NMRD), 419– 421 data Analysis, 462 difference, 447–451 window, 471–473

soft-square, 139, 142

square-well, 139, 142

Index Principal axis system (PAS) dipolar interaction, 315 magnetic susceptibility, 315-319, 323 order tensor, see Order matrix, ordering director and diagonalization Probabilities of conformers, 213 PROSPECT, 45 Protein alignment, see also molecular alignment magnetic field induced, 311,316 using bicelles, 327 using liquid crystals, 313, 327 Protein association, 132 Protein hydration, 511 Protein-hydration, 419 semisolid sample, 457–458 Protein-leakage effects, 277 Protein-mediated spin-diffusion effects, 228, 272 methods for suppressing, 249–255 Protein motions at the active site, 228, 229 Proteins, see GATA-1, myoglobin and ubiquitin Protocols for symmetric oligomers, 143 Pseudoatom, 62 Pseudorotation phase angle, 208, 217 Pseudosymmetry, 133–134 Psuedocontact shifts, see dipolar, shifts Pucker amplitude, 208 Pulse sequences amplitude modulated HSQC, 333 CBCA(CO)NH,121 CBCANH, 121-125 CPMG for 369 for 393,397 for 393,408 for NOE, 397 for heteronuclear NOE, 394 for NOE, 372, 374 for .. 372, 374 for 372, 374 for transverse SIIS cross relaxation, 403 HNCA, 108, 110 HN(CA)CO, 104, 107 HACA(CO)NH, 109–113 HACANH, 114–116 HNCO, 104, 105 HSQC, 101–103 inversion recovery sequences for 367 multiple-quantum triple-resonance spectra, 127 NOESY-NOESY, 164 phase modulated HSQC, 334 phase-type triple-resonance spectra, 115–120, 126–127 selective coupling enhanced HSQC, 329 water flip-back HSQC, 371 Pulse sequences for water-solute NOEs ID NOE, 499 3D NOESY-TOCSY, 509

551 Pulse sequences for water-solute NOEs (cont.) 3D , 509 3D 509 90° excitatin by radiation damping, 499 HYDRA-N, 505 MEXICO, 499 PHOGSY, 505 water excitation by 180° pulse, 505 with 160° water excitation, 505 with diffusion filter, 505 with Q-switched selective 90° pulse, 499 with WANTED sequences, 505 with WEX-I filter, 499 with WEX-II filter, 499 WNOESY, 499 Q-switch, 503 Q(l/6) factor, 180 Quadratic objective function, 214 Quadratic programming algorithm, 213 Quadrupolar relaxation, 433 Quadrupolar coupling constant, 321 interaction, see Interactions, anisotropic, electric quadrupole nuclei, see Nuclei, splittings, 320–321 Quadrupole coupling constant, 466–467 Quantitative J, see Couplings, measurement of, intensity based experiments Quasi-symmetry, 133 example of leucine zippers, 133 Quiet-bird-NOESY, 255 Quiet-EXSY, 255 Quiet-NOESY, 255 R-factor, 29, 156, 157, 180, 210, 298, 299; see also NOE R-factor averaging, 65, 67 summation, 65, 67 Radiation damping, 497 Ramachandran map, 326 RANDMARDI, 205 Real space assignment, 39, 61 Relaxation filters, 257–260 spin-echo, 257–260 spin-lock, 257–260 Relaxation rate, 214 Relaxation rate matrix, 165, 230 Relaxation-reagent, 508 Relaxation time, 24, 25 Relaxation BWR theory, 433, 458 chemical-shift modulation, 442–443, 479–480 cross, 437–442 due to isotropic couplings, 442

552 Relaxation (cont.) deuteron, 431, 433–434 dipolar, 437–442 dispersion, see Nuclear Magnetic Relaxation Dispersion effectively exponential, 434 exchange averaging, 446–447 filters, 257-260 generalized theory, 458 mechanisms, 432–444 oxygen-17, 431–432, 434 proton, 430–431 quadrupolar, 433–437 scalar, 443–444 stochastic theory, 458–462 temporal resolution, 351 time measurement, 422, 428 Reliability distance, 71

Reorientation local, 489 Repel potential, 143 Residence limes, 519 Residual dipolar couplings, see Couplings, residual dipolar Restrained molecular dynamics, 202, 208 time-averaged molecular dynamics, 212 trajectories, 212 Restraints, 138–140 comonomer, 146 distance symmetry, 139-140, 156–157 NOE distance, 142 non-bonded, 143 non-crystallographic symmetry, 138–139, 156–157 packing, 146 space group, 132 Reversibly binding molecular complexes, 225, 226 Ribonuclease, 472 RID method, 56, 57 RNA DNA hybrid, 207, 217 RNA hairpin, 206 ROESY, 206 Hartmann-Hahn transfer of magnetization (HOHAHA), 206 Rotations Euler, 315–318, 351 Wigner, 316–318, 351 SAR-by-NMR, 301 Saturation of receptor resonances, 251 Sauson-Flamsteed projection, 350–351 Screening of compound libraries, 301 SECODG, 40, 67, 68 Selective water excitation, 496 Selective water excitation by a 90° pulse, 498 Selective water excitation by a 180° pulse, 504 Self-correcting distance geometry, 40, 67, 68

Index SERENDIPITY, 39, 46, 49 SH3, 66 SHAKE method, 26 Sialyl tetrasaccharide, 290, 294 complexed to E-selectin, 297 Side-chain derived from relaxation rates, 395 dynamical parameters derived from relaxation times and steady state NOE, 396 SIIS Cross Relaxation, 402 Simulated annealing, 59, 60 see Structure determination, simulated annealing using molecular dynamics, 142–144 Simulated temperature annealing, 22, 25 Simulated transferred NOESY, 267 Simulation of NMR cross-peaks, 207 Single target function, 264 Soft-square potential, 139, 142 Spectral Density Function, 452–457 SPHINX, 207 Spin relaxation contributions to multiplets, 336–338 CSA/dipole-dipole, 336–337 dipole-dipole/dipole-dipole, 337–338 dynamic frequency shifts, 337–339 effects on couplings measurement, 337–339 nuclear dipole/Curie spin-nuclear dipole, 339 order parameters and time scales, 344–346 Square-well potential, 139, 142 dimer (Single-stranded DNA binding protein), 148, 149 Staphylococcal protein A, 57 Stereoconfiguration, 217 STEREOSEARCH, 64, 65 Stereospecific assignment, 209 Stereospecific assignment, 62, 63 Stochastic dynamics (SD) simulation, 21, 23 restraining methods, 6 Structural relevance, 521 Structural restraints, 203 Structure based design, 227, 301, 302 factor, 5, 12, 19, 23 refinement, 24, 202 well defined, 144 Structure calculation iterative, 145, 157 protocols, 142, 144 Structure determination examples, 322–344 GATA-1 complexed to DNA, 326 myoglobin, 322–323, 342–344 order matrix approach, see Order matrix, structure determination protocols, 339 simulated annealing, 339–344

Index Structure determination (cont.) ubiquitin, 324–326 Structure-based drug design, 302 Structure-based filters, 70, 71 Studies of protein hydration, 511 Studies of DNA and RNA hydration, 516 Sugar conformation, 208

Surface hydration water, 470–471 SYMM, 205 Symmetric oligomers, 131

examples of, 148 interface between, 147 possible point group symmetries, 133–135 solved by NMR, 131, 149–151, 152–155 structure calculation method, 138–147 Symmetric aggregation, 132 dimers, 133, 134–135 hexamers, 133, 134–135 oligomers, 131 pentamers, 133, 134–135 trimers, 133, 134–135 tetramers, 133, 134–135 Symmetrization matrix, 235 Symmetry ADR method, 138 problems, 155 pseudo, 133–134 quasi, 133 Symmetry degeneracy, 136, 137, 138 linear group, 132 point group, 132–133, 134–135

spin-echo relaxation filters, 257

spin-lock filter, 257 Temperature used in simulated annealing, 143–144 Temperature control, 423

553 Toxin III, 66 Tr-NOESY-based screening of compound libraries, 301 Transferred NOESY, 223, 225 analytical expressions for a two-spin system, 238 CORCEMA theory of, 223 effect of finite off-rates, 227, 268–270 effect of ligand-receptor ratio, 270–272 effect of motions in the protein-ligand complex, 278–281 effect of protein-mediated spin diffusion, 227, 228, 272–277

effect of protein-leakage, 228, 272–270 in structure-based design, 227, 301 intermolecular, 229, 277–278 for multi-state models, 240–243

for two state models, 233–240 on systems with encounter complexes, 240 screening of compound libraries, 301 simulation using CORCEMA, 289–301 simulation using PDB2 NOE, 282, 285 Transferred NOESY difference spectroscopy, 256 Transferred NOESY with short mixing times, 250 Transverse relaxation, 336 Treatment for more than two states, 240

Triple-resonance NMR, 82; see also Pulse sequences Troponin C EF hand, TNCIIIdimer, 147, 148, 149 Trp-repressor-complex operator, 227, 297 Twin-range method, 25 Two-dimensional ROESY, 251 Two-state model of ligand-receptor interactions, 233 Ubiquitin, 448 diamagnetic susceptibility, see Magnetic susceptibility, diamagnetic, in ubiquitin structure refinement, see Structure determination, examples, ubiquitin United-atom model, 8 Upper distance constraints, 74

Tendamistat, 19, 51

Variable target function, 21, 68, 69, 264

Tensor irreducible spherical (IRE), 315–319 magnetic susceptibility, see Magnetic susceptibility operators, 315–319 order, see Order matrix Theoretical background for intermolecular NOEs, 487 Thermolysin-inhibitor complex, 241 Three dimensional volume matrix, 166

VTB, B subunit of verotoxin, 135, 154–155

Three-spin effects, 224 Thrombin, 282 Time averaging, 14, 15 restraining, 14, 15, 16, 18, 21, 31 structure refinement, 15 Torsion-angle dynamics, 27, 31 Torsion angle restraints, 207 Toxin OSK1, 66

Water excitation, selective, 496 Water flipback, 502 Watergate, 495 demagnetizing fields, 511 diffusion filter, 496 dipolar field effects, 506, 511

spin-lock pulses, 495 Water-internal, 447 residence time, 453, 472–475 Water-protein magnetization transfer, 438–439 Water relaxation in semisolid proteins, 457 Water residence time, 491, 519 Water suppression, 494 Weak-coupling restraining methods, 6

554 Well-defined structure, 144 Wigner rotations, see Rotations, Wigner X-ray diffraction intensities, 4, 15, 19 scattering factors, 12

Index X-filtered spectroscopy, 138, 156 X-PLOR, 138, 139 XEASY, 38, 51 Z-Domain of staphylococcal protein A, 90, 97 Zeeman interaction, see Interactions, isotropic, Zeeman