Conformational Entropy from NMR Relaxation in Proteins: The SRLS

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Conformational Entropy from NMR Relaxation in Proteins: the SRLS Perspective Oren Tchaicheeyan, and Eva Meirovitch J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b13034 • Publication Date (Web): 06 Jan 2017 Downloaded from http://pubs.acs.org on January 17, 2017

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The Journal of Physical Chemistry

Conformational Entropy from NMR Relaxation in Proteins: the SRLS Perspective

Oren Tchaicheeyan and Eva Meirovitch*

The Mina and Everard Goodman Faculty of Life Sciences, Bar-Ilan University, RamatGan 52900 Israel

*Corresponding author: [email protected], phone: 972-3-531-8049

1 ACS Paragon Plus Environment


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Abstract Conformational entropy changes associated with bond-vector motions in proteins contribute to the free energy of ligand binding. To derive such contributions we apply the slowly relaxing local structure (SRLS) approach to NMR relaxation from 15N−H bonds or C−CDH2 moieties of several proteins in free and ligand-bound form. The spatial restraints on probe motion, which determine the extent of local order,

are expressed

in SRLS by a well-defined potential, u(θ). The latter yields the orientational probability density,

Peq

=

exp(−u(θ)),

hence

the

related

conformational

entropy,

= − ln sin ( is “entropy” in units of kBT, and θ represents the bond-vector orientation in the protein). SRLS is applied to 4-oxalocrotonate tautomerase (4-OT), the acyl-coenzyme A binding protein (ACBP), the C-terminal SH2 domain of phospholipase Cγ1 (PLCγ1C SH2), the construct dihydrofolate reductase-E:folate (DHFR-E:folate), and their complexes with appropriate ligands, to determine ∆. Eglin C and its V18A and V34A mutants are also studied. Finally, SRLS is applied to the structurally homologous proteins TNfn3 and FNfn10 to characterize within its scope the unusual “dynamics” of the TNfn3 core. Upon ligand-binding the backbones of 4-OT, ACBP and PLCγ1C SH2 show limited, increased and decreased order, respectively; the cores of DHFR-E:folate and PLCγ1C SH2 become more ordered. The V18A (V34A) mutation increases (decreases) the order within the eglin C core. The core of TNfn3 is less ordered structurally and more mobile kinetically. Secondary structure versus loops, surface-binding versus core-insertion, and ligand-size, emerged as important in


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rationalizing ∆. The consistent and general tool developed herein is expected to provide further insights in future work.



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1. INTRODUCTION The free energy associated with the binding process between a protein and a ligand, ∆G, is determined by the balance between favorable and unfavorable contributions.1 We focus here on conformational entropy contributions from locally mobile bond-vectors in the protein, derived with NMR relaxation. Local mobility is contingent upon the availability of excess packing volume. If such surroundings exist, pertinent bond-vectors will exhibit (clearly non-uniform) orientational distribution, resulting from the spatial restraints exerted by the immediate (internal) protein surroundings. Orientational distribution is a measure of “local order”, hence of conformational entropy. The bond-vector motions executed in these constrained spaces are obviously of the restricted, i.e., locally ordered, type. Their characterization in terms of the extent (and symmetry) of the local spatial restraints, related features of local geometry, and motional rates, is the subject matter of NMR relaxation theories. N−H bonds are typical probes for studying backbone dynamics2 and C−CDH2 moieties are typical probes for studying side-chain/core dynamics3,4. Spatial restraints on motion are usually expressed in physical-chemical approaches by potentials, u(θ) (here θ denotes the orientation of the probe in the protein). u(θ) determines the orientational probability density, Peq = exp(−u(θ)), which in turn determines the related conformational entropy given by the following expression:5

= − ln sin .

(1)


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is “entropy” in usual connotation in units of kBT. Thus, physical methods that provide u(θ) also provide Peq, hence . In this study we develop a method for deriving from NMR-relaxation-determined potentials. As shown below, the potentials inherent to this method are suited particularly well for studying restricted motions, in general, and conformational entropy, in particular. The traditional method for NMR relaxation analysis in proteins is model-free (MF).6,7 MF does not feature a potential. Rather, it comprises the squared generalized order parameter, , as representative of the local spatial restraints. To derive from one has to reinterpret S as physical order parameter, i.e., as ensemble average calculated with Peq = exp(−u), since is given by Peq = exp(−u) − cf. eq 1. To make possible the derivation of from S an explicit potential form is required. However, u is not known; hence, its form has to be guessed. This potential – call is u(MF) – may comprise only one coefficient (i.e., it has to be axial and simple) because only one experimental parameter, , is available. There are many potential forms fulfilling these requirements. We found that within the scope of data-fitting (rather than predictive simulations)5 the ensuing ∆ profiles are not necessarily the same. Thus, the generalized nature of entails in this case alleged assumptions and ambiguity. Unless represents the total mean-squared amplitude of all internal motions,8 or S = and is equal to , or ,×2/ (i.e., the MF formula is the limit of the SRLS spectral density for either very weak or very strong local potentials),9,15,16 the physical relevance of derived from is questionable.



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For deuterium C−CDH2 relaxation is parametrized as × , where

is

taken to represent the squared order parameter for fast methyl rotation, and the squared order parameter for C−CDH2 motion.6 However,

!"#

turned out to be a poor

approximation for a standard axial order parameter.10 SRLS11−13 is a two-body (protein and probe) coupled-rotator approach which we developed in recent years for the analysis of NMR relaxation in proteins14−16. SRLS is the generalization of MF, yielding the latter in simple limits.15,16 It accounts rigorously for mode-coupling, ignored in MF, and uses a tensorial representation of the physical quantities involved, not utilized in MF. The global (local) motion is represented in SRLS by a diffusion tensor, $ ($ ). The spatial restraints on probe motion are expressed by a potential, u. To be exact u has to be expanded in a full basis set. The Wigner rotation matrix ' ' ' elements %& (%(& = %& in isotropic solution) were chosen as basis functions by the

pioneers of NMR (and ESR) relaxation analysis17 (see below for particular benefits). Obviously, the full expansion has to be truncated.11 With only the lowest L = 2, K = 0 term preserved, one obtains the axial Maier-Saupe (MS) potential, ) = − % , and the

associated

order

parameter

= < % >

=

0, θ, 0 sin θ dθ / %

sin θ dθ .11,14 For representative sites of the proteins studied18,19 we found that using this potential, and allowing for the angle /01231 (OF − local ordering/local diffusion tensor frame; DF − magnetic

15

N−1H dipolar tensor frame) to vary, yields good statistics

and results that are inherently relevant physically. This setup was applied to all of the sites, which are thus characterized from a structural point of view by two parameters: the


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strength of the local potential, , and the angle /01231 , which is a geometric feature representing local structural asymmetry. The rhombic L = 2 potential (containing the K = 0 and real K = 2 terms), ) = − % − % + %2 , was used by us in the past when more extensive data-sets

were available, or more “flexible” proteins yielding more sensitive data were studied.15,16 This potential has a substantially more intricate form. However, the transformation properties, the inherent relation to rotational reorientation, the direct connection with Wigner rotations among the various tensors involved, and the association with the function, are preserved. Further improvement standard order parameters, akin to the %

(applied when data-sensitivity permits) is done systematically by including terms with higher K and L values. The important features delineated above are preserved in all of these consistently devised SRLS potentials.15,16 In a recent study we used SRLS to derive ∆ for the C−CDH2 moieties of the Cterminal SH2 domain of phospholipase Cγ1 (PLCγ1C SH2) free and bound to the peptide DNDpYIILPDPK (pY1021).10 Substantial discrepancies between formally analogous SRLS and MF parameters, including ∆, were detected in spite of prevalence of large timescale separation, where SRLS was presumed to yield MF. These differences were shown to stem from the accuracy of

!"#

being impaired by mode-coupling of the 1st-

type being disregarded in MF, and by the fact that MF parametrizes the measurable spectral density function (SDF) mainly through the parametrization of .10 In this study we apply SRLS to several different proteins in free and ligand-bound form within the scope of 15N−H or deuterium C−CDH2 relaxation.18−24 In all of the cases it has been shown that isotropic % = 1/ 6 ( − correlation time for global diffusion) 7 ACS Paragon Plus Environment


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describes adequately the global motion.18−24 The objective of the present study is to pinpoint the dominant factors that determine ∆ derived with NMR relaxation. We find that a simple model for the local motion consisting of isotropic D2 = 1/ 6 ( − correlation time for local diffusion) and MS local potential − which is formally analogous to the MF set-up comprising the effective correlation time for local motion, τe, and − suffices for the analysis of deuterium C−CDH2 relaxation22−24. For

15

N−H relaxation the

set of variables includes one additional parameter − the angle /01231 between the modelrelated local ordering/local diffusion tensor frame, OF, and the magnetic

15

N−1H dipolar

tensor frame, DF. /01231 ≠ 0 has sound physical basis, as tensors describing different properties are expected to have different Principal Axes Systems. In many cases, including refs 18 and 19, MF also uses an additional (to and ) parameter, Rex, to analyze 15

15

N−H relaxation. This is a term added phenomenologically to

N 1/T2 (T2 − transverse relaxation time) so that the expression (15N 1/T2 + Rex) represents

the calculated counterpart of the experimentally measured dynamic contribution to the 15N linewidth (e.g., see ref 20). Physical Rex represents µs−ms motions.25 However, being external to relaxation, which is probing ps−ns motions, Rex might also be just a fitting parameter that improves the statistics by absorbing unaccounted for factors. Whether Rex is physically relevant can be determined by measuring it independently with relaxationdispersion experiments.25 This was not done for the proteins studied herein.19−21 Moreover, we found that while site-specific data-fitting yields numerous Rex ≠ 0 of considerable magnitude, the 15N


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T1/T2 profiles (T1 − longitudinal relaxation time) show only a few data-points associable with Rex; this is inconsistent with physical Rex. On the other hand, the angle /01231 is invariably well-defined physically. Along with the potential coefficient, , which evaluates the strength of the local potential, it characterizes the local structural restraints. Thus, with /01231 ≠ 0, two different qualifiers distinguish structurally among the N−H sites; the ability to discriminate is enhanced considerably in comparison with the /01231 = 0 scenario. In this article we study with SRLS 4-oxalocrotonate tautomerase (4-OT) and its complex with the inhibitor cis-cis-muconate (4);18 the acyl-coenzyme A binding protein (ACBP) and its complex with palmitoyl-coenzyme A;19 PLCγ1C SH2 and its complex with pY1021;20,21 the binary dihydrofolate reductase-E:folate complex (DHFR-E:folate) and its complex with NADP+ (ref 22). First SRLS is applied to determine , D2 and when relevant /01231 . Then ∆ is calculated from changes in using eq 1. Connection is established between any given ∆ and structural features associated with the respective binding-site. The results are compared to gain new insights into the sources of ∆. We also apply SRLS to native (WT) eglin C and its V18A and V34A mutants23 to investigate the effect of point mutations on . Finally, we study the third fnIII domain from human-tenascin (TNfn3), and the tenth fnIII domain from human-fibronectin (FNfn10),24 which exhibit structural similarity despite limited sequence identity. The feature of interest is the unusually “dynamic” core of TNfn3. We seek to characterize this qualification within the scope of SRLS. The experimental data used are taken from the references cited above.



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2. THEORETICAL SUMMARY The MF method is described in refs 6 and 7. For convenience, we present its basics in section I of the Supporting Information (SI). The SRLS approach as applied to NMR relaxation in proteins is described in our earlier publications (e.g., refs 14−16); for convenience, we present its basics in section II of the SI. The SRLS SDFs used here are depicted below. A given SDF represents the Fourier transform of the time correlation function obtained by solving the appropriate SRLS Smoluchowski equation. We call the individual terms in these linear combinations “eigenmodes”.11 A given eigenmode, i, is associated with an eigenvalue, 1/τ1 (given in units of D2), and a weighting factor, wti.11

2.1. The SDF for N− −H bond dynamics. It is assumed that large timescale . separation, i.e., D2 >> D1, prevails. The local potential is ) = −% For N−H

bond dynamics the potential coefficient, , is relatively large as compared to kBT; consequently the order parameter, = < % >, is relatively large on the 0−to−1 scale.

For simple local geometry, i.e., collinear axial local ordering/local diffusion and magnetic NMR tensors, the measurable SDF is:10

τ

τ

7 ω = 9ω8: τ : + wt => ?@A? 9ωBCDE FGHCF :τ 8

BCDE FGHCF

:

+ 7IJ2KLM.

(2)

The first term represents the global motional eigenmode. The second term is a mixed local-motional eigenmode of the 1st-type. Its eigenvalue, 1/τ=> ?@A? , is close to 1/τ2×( /2) = 1/τren, the eigenvalue of a freely diffusing probe in a strong MS potential27,28; its weighting factor, wt => ?@A?, is close to [1 − ]. The third term, 7IJ2KLM , denotes additional mixed eigenmodes of the 1st-type. 10 ACS Paragon Plus Environment

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When the model-related tensors and the NMR-related tensors are tilted (i. e. , /01231 ≠ 0), the measurable SDF is more intricate. For small angles /01231 the SDF of eq 2 makes the dominant contribution to the measurable SDF.

2.2. The SDF for C− −CDH2 bond dynamics. For methyl-moiety dynamics the potential coefficient, , is relatively small as compared to kBT; consequently the order parameter, , is relatively small on the 0−to−1 scale. For simple local geometry the measurable SDF is:10 τ

τ

7 ω = 9ω8: τ : + ∑&T,, 9 ωR,S: τ 8

R,S

:

wt " + 7Y IJUJVWX .

(3)

The global-motional eigenmode is the same as in eq 2. However, instead of one main mixed local-motional eigenmode of the 1st-type there are three mixed eigenmodes with quite different (from the eigenmode of a freely-diffusion probe which has eigenvalue equal to 6 and weighting factor equal to 1) eigenvalues and weighting factors. For example, for a timescale separation τ2/τ1 = 0.01 one has the eigenvalues 6.20, 5.71 and 7.61, with the corresponding weighting factors of 0.34, 0.33 and 0.21.10 The third term of eq 3 represents additional fast mixed eigenmodes with small individual weighting factors.

3. RESULTS AND DISCUSSION The global motion. Except for DHFR, the MF analyses determined isotropic global diffusion tensors, D1 (see below for procedure). For the DHFR constructs MF determined slightly axial D1 11 ACS Paragon Plus Environment


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tensors with %,|| /%,⟘ ~ 1.15; such small deviation from spherical symmetry may be ignored in SRLS analyses (the deviation of the local spatial restraints from axial symmetry − for which we account by allowing /01231 to vary − is substantially more important26). We adopted the global motional correlation times determined with MF based on the following evidence and considerations. Rigorously speaking isotropic D1 is independent of the local motion in the large timescale separation limit. Hence, D1 values determined with a given MF analysis may be adopted by the corresponding SRLS analysis. However, the MF procedure consists of estimating 1/(6D1) from the trimmed

15

N T1/T2 profile and

subsequently optimizing it within the scope of global analysis; the second step could introduce local-motional effects. To ascertain that these effects are small in the present case, we scanned (as we typically do)15 over a range of ± 0.5 ns around the MF values and compared results.15 We found that within experimental error , determined with MF may be adopted in our SRLS analyses. Recently we investigated mode-coupling of the 1st-type, which exists even in the limit of large timescale separation.10 The results of that work indicate that for the timescale separations, D1/D2, prevailing in this study, , is affected marginally by mode-coupling of the 1st-type. This provides additional support for the utilization of MFdetermined , in our SRLS analyses.

The local motion The results of the SRLS and MF

15

N−H and C−CDH2 relaxation analyses differ

often,14−16 in some respects even in the large timescale separation limit10. To what extent they do so in the present circumstances is illustrated and discussed in section III of the SI. 12 ACS Paragon Plus Environment

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3.1. N−H bond dynamics. As delineated above, the rates for (isotropic − see above) global motion of the various proteins and their complexes are taken from the references that contain the experimental data and the respective MF analyses.18−20 3.1.1. The PLCγ1C SH2 system. Data were acquired as 11.7 T, and 303 K for free PLCγ1C SH2 and its complex with the peptide pY1021.20 The free protein prevailed in solution as monomer-dimer equilibrium. Cautiously the authors of 20 focused primarily on trends; we do the same (see below). 3.1.2. The ACBP system. The data of free ACBP and its complex with palmitoyl-coenzyme A were acquired at 14.1 T and 298 K.19 Many 15N−{1H} NOEs, in particular those of the binding-associated α-helices α1 and α2 in the ACBP complex, exceeded the maximum value predicted by MF. When the NOEs were excluded from the analysis, 15N T1 and T2 yielded quite a few non-physical values exceeding 1.19 Consequently only qualitative analysis of the experimental data was conducted.19 On average T1 decreased upon ligand-binding in particular in helices α1, α2 and the Nterminal part of helix α3; this was interpreted as reduction in the amplitude of the local N−H motion. On average the NOE increased upon ligand-binding mainly in helices α1 and α2, and the α2/α3 loop: this was interpreted as higher rate of the local N−H motion.19 That MF (not only the original version6 but also the extended version7) fails to analyze statistically a single-field data set is quite unusual. We subjected these data to SRLS analysis. First only and D2 were allowed to vary; this yielded unsatisfactory results from a statistical point of view. Next we also allowed the angle /01231 to vary;



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this yielded satisfactory results not only from a statistical point of view but also − as delineated above − from a physical point of view. These results are shown in Figure 1B. The errors are on average twice the symbol size except for ∆ (Figure 1Bd) where they are on average 2.5 times the symbol size. The black traces correspond to free ACBP and the red traces to its ligand-bound form. Within helix α1 one has on average = 37 for the ligand-bound form and = 25 for the free form of ACBP; within helix α2 the difference is smaller but still very clearly in evidence of stronger local potentials in the ligand-bound form (Figure 1Ba). A similar trend is observed for the C-terminal half of the α2/α3 loop. Figure 1Bb shows log(D2, 1/s) for free (black) and ligand-bound (red) ACBP. The local motional rates in the ligand-bound form are predominantly smaller; in MF they are estimated to be larger. Figure 1Bc shows the angle /01231 . In helices α1 and α2, and the α2/α3 loop there are many /01231 values in the (−5)−(−10) range, in particular in the ligand-bound form. We found previously that if axial potentials are used /01231 will come out positive, largely in the 5−15o range.29 The reason is that actual potentials at N−H sites are rhombic, with the main ordering axis, ZOF, pointing along Cα−Cα.15−16 Hence the direction perpendicular to Cα−Cα, which is ZOF in the axial potential scenario, is tilted from N−H (i.e., from ZDF), ideally at 11.3o (the standard angle between Cα−Cα and N−H is 101.3o).30 Thus, relatively small and positive angles /01231 most likely represent deviation from potential rhombicity. On the other hand, negative angles /01231 such as detected in helices α1 and α2 of ligand-bound ACBP (Figure 1Bc), most likely represent structural changes/strain induced by ligand-binding. 14 ACS Paragon Plus Environment

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Figure 2a shows ACBP as ribbon diagram in complex with palmitoyl-coenzyme A shown in space-filling representation.31 The α-helices in the back are α1 and α2; it can be seen that they pack tightly against the relatively large ligand. Limited excess packing volume is available at the binding-site, in agreement with our interpretation that negative /01231 angles report on structural strain. Figure 1Bd shows the change in conformational entropy, ∆, implied by ligandbinding. Equation 1 was used, and the difference in between the ligand-bound form and the free form of the protein is shown (this convention applies to all of the cases where ligand-binding is considered). In the ligand-bound form there is substantial decrease in conformational entropy, i.e., increase in local order, primarily within helices α1 and α2 (blue ellipses in Figure 1Bd). On the other hand, except for residue 45, all of the other residues, including those belonging to helices α3 and α4, exhibit limited change in |∆| upon ligand-binding. As shown in Figure 2Bb, the local motional rates decrease upon ligand-binding; the opposite was concluded based on inspection of the experimental data.19 The experimental relaxation parameters depend (through the SDFs) in intricate ways on the physical parameters (e.g., ref 20); the trends exhibited by the former are not necessarily the same as those exhibited by the latter. 3.1.3. The 4-OT system. Data were acquired at magnetic fields of 11.7 and 14.1 T, and 315 K for 4-OT in free form and bound to the inhibitor cis-cis-muconate (4).18 The MF analysis yielded on average = 0.87, typical of single-domain globular proteins.2 Many τe values were found to be zero; those with τe ≠ 0 are largely in the 20−50 ps range, except for the C-terminal segment where they are on average 1.3 ns. A large number of 15 ACS Paragon Plus Environment


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Rex contributions of 1 ± 0.7 \ 2 were obtained; they are significant, given that the average standard deviating in 1/T2 is 1.5 \ 2 .18 MF analysis found that upon ligand-binding seven residues exhibit increased , eight residues exhibit decreased S2, and 44 out of 59 have unchanged .18 Based on a simple formula applying for strong axial local ordering,8,32 the residues with increased (decreased) contribute 3.2 ±1.1 (−1.9 ± 0.1) kcal/mol to the free energy of ligandbinding. Excluding residues A56−R91, which belong to a dangling end, one obtains an overall conformational energy contribution of +0.86 kcal/mol, which is within the error margin. The results of the SRLS analysis are shown in Figure 1A for free (black) and ligand-bound (red) 4-OT. , D2 and /01231 were allowed to vary (for /01231 fixed at the value of zero the results were not satisfactory). The errors are on average twice the symbol size except for ∆ (Figure 1Ad) where they are on average 2.5 times the symbol size. The local potential strength is quite uniform, with = 10 ± 1 (Figure 1Aa). The local motional rates are shown in Figure 1Ab; converted into correlation times (τ2 = 1/(6D2)) for easy comparison with MF, they fall in the 5−50 ps range. The angle /01231 is (5 ± 2)o (Figure 1Ac). These are common values which we observed in previous studies for other proteins.14 Figure 1Ad shows the ∆ profile calculated on the basis of eq 1. ∆ of the 4-OT system is generally smaller than ∆ of the ACBP system (Figures 1Ad and 1Bd). Upon binding cis,cis-muconate (4) some N−H sites of 4-OT experience increase in ∆ while others experience decrease in ∆ (Figure 1Ad). Intriguingly, the changes in upon


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ligand-binding are smaller in the binding-associated loops I and II as compared to the remaining part of the polypeptide chain (blue ellipses in Figure 1Ad). There is no X-ray or NMR structure of the homohexamer of 4-OT in complex with cis,cis-muconate (4). In Figure 2b we show the free homohexamer, as reported in ref 33. The chain segments associated with ligand-binding are the long loops. There appears to be quite a bit of excess packing volume for accommodating the small ligand cis,cismuconate (4), in agreement with our finding than ∆ is on average relatively small.

3.2. Conformational entropy from N− −H bond dynamics. Figure 3 shows the ∆ profiles of the 4-OT, ACBP and PLCγ1C SH2 systems on the same vertical scale. The purpose is to pinpoint on the basis of comparison the dominant factors determining ∆ from 15N−H relaxation. 3.2.1. 4-OT:cis,cis-muconate (4) − Figure 3a: 4-OT is a regular globular protein. It features loops as chain segments that surround the binding-site of a small molecule.18 There is ample excess packing volume (Figure 2b). In general, ligand-binding brings about limited change in the local order at the N−H sites of the protein backbone. The contribution of the binding-associated loops to this change is small (red boxes). 3.2.2. ACBP:palmitoyl-coenzyme A − Figure 3b: ACBP binds a relatively large molecule and features α-helices as chain segments that surround the binding-site. There is limited excess packing volume (Figure 2a). In general, the protein backbone becomes more ordered upon ligand-binding. The α-helices located in the vicinity of the bindingsite exhibit the largest increase in local order (red boxes).



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3.2.3. PLCγ1C SH2:pY1021 − Figure 3c: PLCγ1C SH2 features a pTyr bindingsite electrostatic in nature, and a hydrophobic binding-site; both are associated with partial insertion of the ligand into the protein core.20 pY1021 is a large molecule that spans both binding-sites. In general, the protein backbone becomes less ordered upon ligand-binding. The N−H bonds of residues located in the vicinity of the binding-sites exhibit substantial decrease in local order (red boxes). The picture yielded by the three protein backbones studied indicates that the secondary structure of the chain segments associated with ligand-binding is important. This requires cross-talk between side chain and backbone. There appears to be a positive correlation between ligand-size and average backbone |∆| − see results obtained for 4OT and ACBP. As both ligands bind relatively close to the protein surface, this is an interesting observation. pY1021 binds to PLCγ1C SH2 at two binding-sites, with considerable insertion into the protein core. To accommodate such change the protein backbone has to exhibit substantial plasticity, in agreement with the unusual (but not unique)1,34−38 increased disorder upon complexation. Additional cases have to be studied to determine the generality of these findings.

3.3. Deuterium C−CDH2 dynamics. The proteins studied include DHFR,22 PLCγ1C SH2,21 eglin C,23 and the pair TNfn3 and FNfn1024. In all of these cases we assumed that methyl rotation is fast relative to Q = 167 kHz, yielding a partially averaged quadrupole tensor, , with principal value of 55.6 kHz (167×P2(cos(110.5o)) = 55.6; P2 is the second-rank Legendre polynomial and 110.5o is the tetrahedral angle)39. This is


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the standard approach for treating the internal motion of methyl moieties40−42 (also see ref 10). The SRLS model used consists of a local MS potential and isotropic local motion. The rates for the global motion of the various proteins and their complexes are taken from the respective references.21−-24 3.3.1. The DHFR system. 2H T1 and T2 of the binary complex DHFR-E:folate and the ternary complex DHFR-E:folate:NADP+ were acquired at 14.1 and 18.8 T, and 301.5 K.22 A schematic representation of the ternary complex is shown in Figure 4a.43 The Met20 loop (residues 9−24), the BF-BG loop (residues 116−132) and the BG-BH loop (residues 142−150) are associated with the binding-site. Previous MF analysis of 15

N−H relaxation pointed to increased order in these loops upon NADP+-binding.44

Previous MF analysis of C−CDH2 relaxation reinforced these results.22 The Met20 loop changes from “occluded” to “closed” upon NADP+-binding, with M16 being flipped out of the nicotinamide-binding pocket while M20 becomes packed against the nicotinamide ring, and the pterin ring of the substrate.44 In Figure 5 we show and D2 for the binary complex (black) and the ternary complex (red); the average error is twice the symbol size. The boxes on the top depict the loops Met20, FG and GH associated with ligand-binding. The local potential is on average 2 kBT (Figure 5a), in agreement with 2H lineshape analyses of C−CD3 motion in compounds in the solid-state,40−42 and the current view that restricted motions in proteins are approximately the same in solution and in the solid-state.45 The largest increase in local potential strength upon NADP+-binding is experienced by M20 of the Met20 loop and V119γ2 and T123 of the FG loop (Figure 5a). 19 ACS Paragon Plus Environment


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However, SRLS shows that only half of the methyl groups within the Met20 loop experience increase in upon NADP+-binding; the other half experiences decrease in (Figure 5a). The two methyl groups of the FG loop − V119γ2 and T123 − also experience stronger local potential whereas for A143 and A145 of the GH loop there is virtually no change in . The largest decrease in local potential strength is experienced by I61γ. The local motional rates, D2, are shown in Figure 5b. Some methyl groups move faster in the binary complex whereas others move faster in the ternary complex. Of particular interest are M16 and M20 of the Met20 loop: % of M16 increases from 2.7×10 to 4.3×10 \ 2 (τ2 decreases from 62 and 39 ps) whereas % of M16 decreases from 2.4×10 to 1.6×10 \ 2 (τ2 increases from 71 and 106 ps) upon NADP+-binding. D2 of T123 becomes somewhat faster upon NADP+-binding. Figure 6a shows the ∆ profile associated with the binding of NADP+ to DHFRE:folate (the average error is 2.5 times the symbol size). In general, the core of DHFRE:folate becomes more ordered (∆/kBT < 0). Although on average the Met20 loop becomes more ordered, four out eight methyl groups experience decreased local order (in accordance with the changes in − see above). In Figure 6b we show differences in and between the ternary and binary complexes. The average error is 2.5 times the symbol size. It can be seen that the respective patterns differ substantially, indicating that even differences in are quite inaccurate. 3.3.2. The PLCγ1C SH2 system. We studied with SRLS deuterium C−CDH2 relaxation from this protein and its complex with pY1021 in ref 10. Data were acquired at 11.7 and 14.1 T, and 303 K for free and ligand-bound PLCγ1C SH2.21 Figure 4b shows a 20 ACS Paragon Plus Environment

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relatively large peptide binding to PLCγ1C SH2 at two different (in position and chemical nature) sites.46 and τ2 for the free and peptide-bound protein are shown below in comparison with and τ2 for eglin C and either its V18A or its V34A mutant; the purpose is to compare ∆ profiles arising from ligand-binding and point mutation. 3.3.3. Eglin C and its V18A and V34A mutants. In this example we focus on the effect of point mutations on the local order prevailing in the eglin C core. Deuterium T1 and T2 from the C−CDH2 moieties of native (WT) eglin C, and its V18A and V34A mutants, were acquired at magnetic fields of 11.7 and 14.1 T, and 310 K.23 We applied SRLS to these data using the simple model of MS local potential and isotropic local diffusion. A schematic of the eglin C structure is shown in Figure 7a.47 The authors of ref 23 analyzed quantitatively all of the and τe data yielded by the MF analysis. The average error in was estimated at 0.01; the average error inτe was estimated at 1 ps. The core of eglin C is viewed as a dynamic network. The changes in and τ2 are interpreted as follows: the local perturbations induced by the mutations performed are transmitted as (1) contiguous pathways of enhanced dynamics, i.e., decrease in , combined with dispersed changes in τe; and (2) contiguous pathways of attenuated dynamics, i.e., increase in , combined with noncontiguous changes in τe. This is taken to indicate that all of the well-folded proteins inherently possess allosteric features. Figure 8 shows the formally analogous SRLS and MF parameters for WT (native), V18A and V34A eglin C. The differences are substantial; in many cases they are qualitative in nature. If the pathways for the transmission of the perturbations induced by



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the V18A and V34A mutations are significant, they will certainly change within the scope of SRLS analysis. Figures 9a and 9b show and τ2 for WT eglin C (black) and the V18A mutant (blue); Figure 9c shows the corresponding ∆ profile defined as ∆ = (WT eglin C) − (V18A mutant). Figures 9d and 9e show and τ2 for WT eglin C (black) and the V34A mutant (blue); Figure 9f shows the corresponding ∆ profile defined as ∆ = (WT eglin C) − (V34A mutant). Figures 9g and 9h show and τ2 for PLCγ1C SH2 (black) and its complex with the peptide pY1021 (blue); Figure 9i shows the ∆ = (WT eglin C) − (V34A mutant) profile. We estimate the errors to be given approximately by the symbol size except for ∆, where they are approximately twice the symbol size. It can be seen that the ranges within which and τ2 vary are virtually the same for ligand-binding and point mutations; this is interesting. Figures 9c, 9f and 9i show ∆ for the three pairs of protein constructs under consideration. The shaded boxes around the zero line depict the error margin. Intriguingly, the V18A mutation renders the entire eglin C core more ordered (Figure 9c) whereas the V34A mutation renders it mostly more disordered (Figure 9f). The core of PLCγ1C SH2 becomes more ordered upon binding pY1021 (Figure 9i). Let us examine the eglin C system in further detail. As shown in Figure S4 of section IV of the SI, part c, the V18A mutation brings about decrease in the local order for the methyl groups V62γ1 and T17, located in the proximity of the mutation site23 (since exhibits the same trends as , qualitative comparison of trends in is appropriate). However, methyl group V52γ2, which is distant,23 also exhibits decreased order. Figure S2, part f, shows that the V34A mutation brings about decrease in local 22 ACS Paragon Plus Environment

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order for methyl group V52γ2, located in the proximity of the mutation site. However, it brings about increase in the local order for methyl group V54γ1, also located in the proximity of the mutation site. Thus, point mutations may bring about both increased and decreased order at nearby methyl groups.

3.3.4. TNfn3 and FNfn10. These proteins have limited sequence identity but substantial structural similarity.24 A schematic representation of the TNfn3 structure appears in Figure 7b.48 The core of FNfn10 was found to be similar to that of other proteins studied with deuterium C−CDH2 relaxation. Thus, of residues buried deeply in the core is relatively large, decreasing gradually as one proceeds toward the protein surface. By contrast, the TNfn3 core features quite a few methyl groups buried deeply in the core with unusually small ; as one proceeds toward the protein surface increases on average.24 Based on negative correlation between and excess packing volume, evaluated on the basis of several different criteria, lower packing density of the TNfn3 core was invoked as main source for its unusual “dynamics”.24 A molecular dynamics (MD) simulation analysis of THfn3 and FNfn10 explained this observation in atomistic terms.49 We applied SRLS to the experimental 2H relaxation parameters of THfn3 and FNfn10 using the simple model of axial local MS potential and isotropic local diffusion. To make possible comparison with MF we computed from . The formally analogous parameters and are shown in Figures 10a and 10e (10c and 10g) for TNfn3 (FNfn10). The formally analogous parameters τ2 and τe are shown in Figures 10b and 10f (10d and 10h) for TNfn3 (FNfn10). 23 ACS Paragon Plus Environment


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The lower limit of the distribution in is 0.03 for TNfn3 (Figure 10a) and 0.1 for FNfn10 (Figure 10c). Small signifies large disorder. Thus, TNfn3 is structurally more disordered, in agreement with being less densely packed50 than FNfn1024. The upper limit of the distribution is 0.36 in both cases. All of these values are consistent with 2H lineshape analyses in the solid-state40−42 and the current view that restricted local motions in proteins are similar in the solid-state and in solution45. The lower limit of the distribution in is 0.05 for TNfn3 (Figure 10e) and 0.29 for FNfn10 (Figure 10g). The upper limit is in both cases 1.0.4,37,38 Large values are inconsistent with 2H lineshape analyses in the solid-state40−42. The lower (upper) limit of the distribution in τ2 is 40 (540) ps for TNfn3 (Figure 10b); the lower (upper) limit of the distribution in τ2 is 90 (500) ps for FNfn10 (Figure 10d). Thus, TNfn3 is kinetically more dynamic than FNfn10, in the sense that it spans a larger dynamic range with both limits extended. The distribution in τe for TNfn3 (Figure 10f) and FNfn10 (Figure 10h) is virtually the same. Thus, on the basis of the proposed criterion, according to MF these proteins do not differ from a kinetic point of view. The following comment is of interest. The upper limit of the distributions in of TNfn3 (Figure 10a), FNfn10 (Figure 10c), DHFR-E:folate (Figure 2Sa, black, of section I of the SI) and DHFR-E:folate:NADP+ (Figure 2Sb, black, of section I of the SI) is within a good approximation 0.36 (we exclude from discussion eglin C which is very small). The lower limit of the distribution in is 0.03 for TNfn3 (Figure 10a) and 0.1 for FNfn10 (Figure 10c). DHFR-E:folate has 10 methyl groups with ≤ 0.1 (Figure 2Sa, black, of section I of the SI) and DHFR-E:folate:NADP+ has 6 methyl groups with 24 ACS Paragon Plus Environment

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≤ 0.1 (Figure 2Sb, black, of section I of the SI). Thus, = 0.36 appears to represent the upper limit of the local order in protein cores. On the other hand, small values, in general, and the lower limit in , in particular, appear to be proteinspecific. Further studies are required to determine whether these features are general. The fact that the mesoscopic SRLS potentials are physically well-defined makes possible connecting them with corresponding atomistic potentials of mean force derived with molecular dynamics (MD) simulations.51

4. CONCLUSIONS We developed a consistent approach for deriving conformational entropy, , from NMR relaxation within the scope of SRLS. is expressed solely in terms of the orientational probability density, Peq = exp(−u), of the probe, with u determined directly from the experimental data. As any mesoscopic potential, u considered here is approximate. However, it is physically well-defined in terms of meaning, form, transformation properties, and options for improvement. In particular, it is very well suited for treating local order (hence, entropy) associated with restricted rotational reorientation. Conformational entropy changes, ∆, induced by ligand-binding were determined for the backbones and cores of several proteins. Three proteins − PLCγ1C SH2, ACBP and 4-OT − were examined utilizing

15

N−H relaxation. ACBP (PLCγ1C SH2) exhibits

decrease (increase) in conformational entropy upon ligand binding; 4-OT exhibits limited change. Two proteins – the binary DHFR-E:folate complex and PLCγ1C SH2 − were examined

utilizing deuterium

C−CDH2

relaxation;

both


exhibit decrease

in


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conformational entropy upon ligand-binding. Intriguingly, |∆| of the protein cores examined is in general smaller than |∆| of the protein backbones examined. Our results indicate that the secondary structure of the chain segments associated with ligand-binding, the size of the ligand, and whether the latter binds at the protein surface or is to a large extent inserted into the protein core, are important in determining the absolute value of ∆ and its sign. These features have been revealed and quantified here for the first time. Globally point mutations either increase or decrease the conformational entropy of the entire core of the small protein eglin C. Locally both positive and negative ∆ contributions have been observed. Similar MD-based findings were considered surprising;49 here we corroborate this feature experimentally. In characterizing restricted “dynamics” it is useful to distinguish between structural aspects that relate to the local order, and kinetic aspects that relate to the local motion. This perspective helped rationalizing the unusual behavior of the core of TNfn3.

Acknowledgments This work was supported by the Israel Science Foundation (Grant No. 369/15 to E.M.). We thank Prof. Lewis E. Kay of the University of Toronto for the experimental 15N relaxation data of free and pY1021-bound PLCγ1C SH2 domain.

Supporting Information Available: The model-free spectral density functions are depicted in section I of the SI. A summary of the slowly relaxation local structure approach is provided in section II of the SI. Two figures illustrating SRLS versus MF


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results for 15N−H relaxation and C−CDH2 relaxation are provided in section III of the SI. A figure showing that point mutations may either increase or decrease the order prevailing at sites located in the vicinity of the mutation is provided in section IV of the SI. This material is available free of charge via the internet at http://pubs.acs.org.



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References 1. Zidek, L.; Novotny, M. V.; Stone, M. J. Increased Protein Backbone Conformational Entropy upon Hydrophobic Ligand Binding. Nat. Struct. Biol. 1999, 6, 1118-1121. 2. Stone, M. J. NMR Relaxation Studies of the Role of Conformational Entropy in Protein Stability and Ligand Binding. Acc. Chem. Res. 2001, 34, 379-388. 3. Mittermaier, A.; Kay, L. E. New Tools Provide New Insight in NMR Studies of Protein Dynamics. Science 2006, 312, 224 - 228. 4. Wand, J. A. The Dark Energy of Proteins Comes to Light: Conformational Entropy and its Role in Protein Function Revealed by NMR Relaxation. Curr. Opin. Struct. Biol. 2013, 23, 75-81. 5. Yang, D.; Kay, L. E. Contributions to Conformational Entropy Arising from Bond Vector Fluctuations Measured from NMR-Derived Order Parameters: Application to Protein Folding. J. Mol. Biol. 1996, 263, 369-382. 6. Lipari, G.; Szabo, A. Model-Free Approach to the Interpretation of Nuclear Magnetic Resonance Relaxation in Macromolecules. 1. Theory and Range of Validity. J. Am. Chem. Soc. 1982, 104, 4546-4559. 7. Clore, G. M.; Szabo, A.; Bax, A.; Kay, L. E.; Driscoll, P. C.; Gronenborn, A. M. Deviations from the Simple Two-Parameter Model-Free Approach to the Interpretation of Nitrogen-15 Nuclear Magnetic Relaxation of Proteins. J. Am. Chem. Soc. 1990, 112, 4989-4991.


Page 28 of 50

Page 29 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


8. Akke, M.; Brüschweiler, R.; Palmer III, A. G. NMR Order Parameters and Free Energy: an Analytical Approach and its Application to Cooperative Ca2+ Binding by Calbindin D9k. J. Am. Chem. Soc. 1993, 115, 9832-9833. 9. Meirovitch, E.; Shapiro, Yu. E.; Liang, Z.; Freed, H. J. Mode-Coupling SRLS versus Mode-Decoupled Model Free N−H Bond Dynamics: Mode-Mixing and Renormalization. J. Phys. Chem. B 2003, 107, 9898-9904. 10. Thaicheeyan, O.; Meirovitch, E. An SRLS Study of 2H Methyl Moiety Relaxation and Related Conformational Entropy in Free and Peptide-Bound PLCγ1C SH2. J. Phys. Chem. B 2016, 120, 10695-10705. 11. Polimeno, A.; Freed, J. H. A Many-Body Stochastic Approach to Rotational Motions in Liquids. Adv. Chem. Phys. 1993, 83, 89-204. 12. Polimeno, A.; Freed, J. H. Slow-Motional ESR in Complex Fluids: the Slowly Relaxing Local Structure Model of Solvent Cage Effects. J. Phys. Chem. 1995, 99, 10995-11006. 13. Liang, Z.; Freed, J. H. An Assessment of the Applicability of Multifrequency ESR to Study the Complex Dynamics of Biomolecules. J. Phys. Chem. B 1999, 103, 6384-6396. 14. Tugarinov, V.; Liang, Z.; Shapiro, Yu. E.; Freed, J. H.; Meirovitch, E. A Structural Mode-Coupling Approach to

15

N NMR Relaxation in Proteins. J.

Am. Chem. Soc. 2001, 123, 3055-3063. 15. Meirovitch, E.; Shapiro, Yu. E.; Polimeno, A.; Freed, J. H. Protein Dynamics from NMR: the SRLS Analysis Compared with MF Analysis. J. Phys. Chem. A 2006, 110, 8366-8396.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 50

16. Meirovitch, E.; Shapiro, Yu. E.; Polimeno, A.; Freed, J. H. Structural Dynamics of Biomolecules by NMR: the Slowly Relaxing Local Structure Approach. Prog. NMR Spectrosc. 2010, 56, 360-405. 17. Abragam, A.

Principles of Nuclear Magnetism. Oxford University Press

(Clarendon): London, 1961. 18. Stivers, J. T.; Abeygunawardana, C,; Mildvan, A. S.

15

N NMR Relaxation

Studies of Free and Inhibitor-Bound 4-Oxalocrotonate Tautomerase: Backbone Dynamics and Entropy Changes of an Enzyme upon Inhibitor Binding. Biochemistry 1996, 35, 16036-16047. 19. Rischel, C.; Madsen, J. C.; Andersen. K. V.; Poulsen, F. M. Comparison of Backbone Dynamics of Apo-, and Holo-Acyl-Coenzyme A Binding Protein Using 15N Relaxation Measurements. Biochemistry 1994, 33, 13997-14002. 20. Farrow, N. A.; Muhandiram. R. D.; Singer, A. U.; Pascal, S. M.; Kay, C. M.; Gish, G.; Shoelson, S. E.; Pawson, T.; Forman-Kay, J. D.; Kay, L. E. Backbone Dynamics of a Free and a Phosphopeptide-Complexed Src Homology 2 Domain Studies by 15N NMR Relaxation. Biochemistry 1994, 33, 5984-6003. 21. Kay, L. E.; Muhandiram, D. R., Farrow, N. A.; Aubin, Y.; Forman-Kay, J. D. Correlation Between Dynamics and High Affinity Binding in an SH2 Domain Interaction. Biochemistry 1996, 35, 361-368. 22. Schnell, J. R.; Dyson, H. J.; Wright, P. E. Effect of Cofactor Binding and Loop Conformation on Side Chain Methyl Dynamics in Dihydrofolate Reductase. Biochemistry 2004, 43, 374-383.


Page 31 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


23. Clarkson, M. W.; Gilmore, S. A.; Edgell, M. H.; Lee, A. L. Dynamic Coupling and Allosteric Behavior in Nonallosteric Proteins. Biochemistry 2006, 45, 7693-7699. 24. Best, R. B.; Rutherford, T. J.; Freund, S. M. V.; Clarke, J. Hydrophobic Core Fluidity of Homologous Protein Domains: Relation of Side-Chain Dynamics to Core Composition and Packing. Biochemistry 2004, 43, 1145-1155. 25. Palmer, A. G. NMR Characterization of Dynamics of Biomacromolecules. Chem. Rev. 2004, 104, 3623-3640. 26. Meirovitch, E.; Shapiro, Yu. E.; Tugarinov, V.; Liang, Z.; Freed, J. H. ModeCoupling Analysis of 15N CSA−15N-1H Dipolar Cross-Correlation in Proteins. Rhombic Potentials at the N−H Bond. J. Phys. Chem. B 2003, 107, 98839897. 27. Polnaszek, C. F.; Bruno, G. V.; Freed, J. H. ESR Lineshapes in the SlowMotional Region: Anisotropic Liquids. J. Chem. Phys. 1973, 58, 3185-3199. 28. Polnaszek, C. F.; Freed, J. H. Electron Spin Resonance Studies of Anisotropic Ordering, Spin Relaxation, and Slow Tumbling in Liquid Crystalline Solvents. J. Phys. Chem. 1975, 79, 2283-2306. 29. Shapiro, Yu. E.; Sinev, M. A.; Sineva, E. V.; Tugarinov, V.; Meirovitch, E. Backbone Dynamics of Escherichia coli Adenylate Kinase at the Extreme Stages of the Catalytic Cycle Studied by 15N NMR Relaxation. Biochemistry 2000, 39, 6634-6644. 30. Lienin, S. F.; Bremi, T.; Brutscher, B.; Brüschweiler, R.; Ernst, R. R. Anisotropic Intramolecular Backbone Dynamics of Ubiquitin Characterized



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 50

by NMR Relaxation and MD Computer Simulations. J. Am. Chem. Soc. 1998, 120, 9870-9879. 31. Lerche, M. H.; Kragelund, B. B.; Redfield, C.; Poulsen, F. M. RDC-Refined NMR Structure of Bovine Acyl-Coenzyme A binding Protein, ACBP, with Palmitoyl-Coenzyme A. 10.2210/pdb1nvl/pdb. 32. Massi, F.; Palmer III, A. G. Temperature Dependence of NMR Order Parameters and Protein Dynamic. J. Am. Chem. Soc. 2003, 125, 11158-11159. 33. Taylor, A. B.; Whitman, C. P.; Hackert, M. L. 3-Oxalocrotonate Tautomerase Observed

as

an

Octadecamer

Rhombohedral

Crystal

Form.

10.2210/pdb4otb/pdb. 34. Akke, M. Conformational Dynamics and Thermodynamics of Protein-Ligand Binding Studies by NMR Relaxation. Biochem. Soc. Trans. 2012, 40, 419423. 35. Stone, M. J. NMR Relaxation Studies of the Role of Conformational Entropy in Protein Stability and Ligand Binding. Acc. Chem. Res. 2001, 34, 379-388. 36. Forman-Kay, J. D. The “Dynamics” in the Thermodynamics of Binding. Nat. Struct. Biol. 1999, 6, 1086-1087. 37. Wand, J. A. The Dark Energy of Proteins Comes to Light: Conformational Entropy and its Role in Protein Function Revealed by NMR Relaxation. Curr. Opin. Struct. Biol. 2013, 23, 75-81. 38. Kasinath, V.; Sharp, K. A.; Wand, A. J. Microscopic Insights in the NMR Relaxation-Based Protein Conformational Entropy Meter. J. Am. Chem. Soc. 2013, 135, 15092-15100.


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39. Tugarinov, V.; Kay, L. E. 1H,13C−1H,1H Dipolar Cross-Correlated Spin Relaxation in Methyl Groups. J. Biomol. NMR 2004, 29, 369-376. 40. Wittebort, R. J.; Olejniczak, E. T.; Griffin, R. G. Analysis of Deuterium Nuclear Magnetic Resonance Line Shapes in Anisotropic Media. J. Chem. Phys. 1987, 86, 5411-5420. 41. Batchelder, L. S.; Sullivan, C. E.; Jelinski, L. W.; Torchia, D. A. Characterization of Leucine Side-Chain Reorientation in Collagen Fibrils by Solid-State 2H NMR. Proc. Natl. Acad. Sci. U.S.A. 1982, 79, 386. 42. Breen, N. F.; Weidner, T.; Li, K.; Castner, D. G.; Drobny, G. P. A Solid-State Deuterium NMR and Sum-Frequency Generation Study of the Side-Chain Dynamics of Peptides Adsorbed onto Surfaces. J. Am. Chem. Soc. 2009, 131, 14148-14149. 43. Sawaya, M. R. Structure of Dihydrofolate Reductase Complexed with Folate. 10.2210/pdb1rx7/pdb. 44. Osborne, M. J.; Schnell, J.; Benkovic, S. J.; Dyson, H. J.; Wright, P. E. Backbone Dynamics in Dihydrofolate Reductase Complexes: Role of Loop Flexibility in the Catalytic Mechanism. Biochemistry 2001, 40, 9846-9859. 45. Agarwal, V.; Xue, Y.; Reif, B. Skrynnikov, N. R. Side-Chain Dynamics as Observed by Solution and Solid-State NMR Spectroscopy: a Similarity Revealed. J. Am. Chem. Soc. 2008, 130, 16611-16621. 46. Pascal, S. M.; Singer, A. V.; Gish, G.; Yamazaki, T.; Shoelson, S. E.; Pawson, T.; Kay, L. E.; Forman-Kay, J. D. Nuclear Magnetic Resonance Structure of



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an SH2 Domain of Phospholipase C-gamma1 Complexed with a High Affinity Peptide. 10.2210/pdb2ple/pdb. 47. Hyberts, S. G.; Goldberg, M. S.; Havel, T. F.; Wagner, G. The Solution Structure of Eglin C Based on Measurements of Many NOEs and Coupling Constants and its Comparison with X-ray Structures. 10.2210/pdb1egl/pdb. 48. Leahy, D. J.; Handrickson, W. A.; Aukhil, I.; Erickson, H. P. Structure of Fibronectin Type III Domain from Tenascin Phased by MAD Analysis of the Selenomethionyl Protein. 10.2210/pdb1ten/pdb. 49. Best, R. B.; Clarke, J.; Karplus, M. What Contributions to Protein Side-Chain Dynamics are Probed by NMR Experiments? A Molecular Dynamics Simulation Analysis. J. Mol. Biol. 2005, 349, 185-203. 50. Halle, B. Flexibility and Packing in Proteins. Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 1274-1279. 51. Tchaicheeyan, O.; Freed, J. H.; Meirovitch, E. Local Ordering at Mobile Sites in Proteins from Nuclear Magnetic Resonance Relaxation: the Role of SiteSymmetry. J. Phys. Chem. B 2016, 120, 2886-2898.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure Captions Figure 1. Class A. Best-fit parameters from SRLS analysis of

15

N−H relaxation

from 4-OT (black) and 4-OT in complex with cis,cis-muconate (4) (red) as a function of residue number: (part Aa), log(D2, 1/s) (part Ab) and /01231 (part Ac). ∆ = (complexed protein) − (free protein) (part Ad). Class B. Best-fit parameters from SRLS analysis of

15

N−H relaxation from ACBP (black) and ACBP in complex with

palmitoyl-coenzyme (red) as a function of residue number: (part Ba), log(D2, 1/s) (part Bb) and /01231 (part Bc). ∆ = (complexed protein) − (free protein) (part Bd). The average error is twice the symbol size in parts a− −c, and two and a half times the symbol size in parts d.

Figure 2. Ribbon diagram of the complex of ACBP with palmitoyl-coenzyme A (shown in space-filling representation), according to PDB accession number 1nvl31 (part a). Ribbon diagram of the homohexamer of 4-OT, according to PDB accession number 4otb33 (part b).

Figure 3. ∆ from SRLS analysis of 15N−H relaxation from the 4-OT system (part a), the ACBP system (part b), and the PLCγ1C SH2 system (part c), as a function of residue number. The chain segments associated with ligand-binding are depicted. The boxes around the zero lines represent the error margin.

Figure 4. Ribbon diagram of the ternary complex DHFR-E:folate:NADP+ (E:folate:NADP+ shown in stick representation), according to PDB accession number 35 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1rx743 (part a). Ribbon diagram of PLCγ1C SH2 in complex with the peptide pY1021 (shown in stick representation), according to PDB accession number 2ple46 (part b).

Figure 5. Best-fit parameters from SRLS analysis of deuterium C−CDH2 relaxation from DHFR-E:folate (black) and DHFR-E:folate:NADP+ (red): (part a) and D2 (part b). The binding-associated loops are depicted on the top. The abscissa represents methyl groups numbered as they appear along the protein sequence. The γ2 methyl of valine, the δ2 methyl of leucine and the δ1 methyl of isoleucine are denoted with a “prime” symbol. The γ2 methyl of Ile appears before the δ1 methyl. The average error is twice the symbol size.

Figure 6. ∆ from SRLS analysis of deuterium C−CDH2 relaxation of the ternary and binary complexes of DHFR (part a). ∆ = (ternary complex) − (binary complex) from SRLS and ∆( ) = (ternary complex) − (binary complex) from MF22 (part b). The binding-associated loops are depicted on the top. The abscissa is specified in the captions of Figure 5. The average error is two and a half times the symbol size.

Figure 7. Ribbon diagram of the complex of eglin C, according to PDB accession number 1egl47 (part a). Ribbon diagram of the protein TNfn3, according to PDB accession number 1ten48 (part b).


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Figure 8. Best-fit parameters from SRLS analysis of deuterium C−CDH2 relaxation analysis: from SRLS (black) and from the MF23 (red) for WT eglin C (part a), the V18A mutant of eglin C (part c), and the V34A mutant of eglin C (part e);

τ2 from SRLS (black) and τe from the MF23 (red) for WT eglin C (part b), the V18A mutant of eglin C (part d), and the V34A mutant of eglin C (part f). The abscissa represents methyl groups numbered as they appear along the protein sequence. The average error is roughly the symbol size.

Figure 9. Best-fit parameters from SRLS analysis of deuterium C−CDH2 relaxation of WT eglin C (black) and the V18A mutant (red): (part a) and τ2 (part b); ∆ = (WT eglin C) − (V18A mutant) (part c). Best-fit parameters from SRLS analysis of deuterium C−CDH2 relaxation of WT eglin C (black) and the V34A mutant (red): (part d) and τ2 (part e); ∆ = (WT eglin C) − (V34A mutant) (part f). Best-fit parameters from SRLS analysis of deuterium C−CDH2 relaxation of PLCγ1C SH2 (black) and PLCγ1C SH2 bound to pY1021 (red): (part g) and τ2 (part h); ∆ = (complexed protein) − (free protein) (part i). The abscissa represents methyl groups numbered as they appear along the protein sequence. The boxes around the zero lines represent the error margin. The average error is roughly the symbol size in parts a, b, d, e, g and h, and twice the symbol size in parts c, f and i.

Figure 10. Best-fit parameters from SRLS analysis of deuterium C−CDH2 relaxation: from TNfn3 (part a) and FNfn10 (part c); τ2 from TNfn3 (part b) and FNfn10 (part d). Best-fit parameters from MF analysis24 of deuterium C−CDH2 37 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

relaxation: from TNfn3 (part e) and FNfn10 (part g); τe from TNfn3 (part f) and FNfn10 (part h). The abscissa represents methyl groups numbered as they appear along the protein sequence. The average error is twice the symbol size.


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TOC graphics



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

β 1 loop I

c 02

α -helix

loop II β 2

β -hairpin

A

40

a

α 1 -helix

20

0 12

0 12

10 log(D2, 1/s) 8

α 2 -helix

α3 -helix

40

20

b

Page 40 of 50

α 4 -helix

B

b

10 8 c

10 β 0 -10

c 10 0 -10

o

0.5 ∆S

a

d

0.5

0

0

-0.5

-0.5

-1

-1 0

10

20

30 40 residue

50

60

d

0

10

ACS Paragon Plus Environment

20

30

40 50 residue

60

70

80

Page 41 of 50


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

4-OT system

loop I

0.4

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PLC γ 1C SH2 system

ACBP system

loop II helix α1

helix α 2

∆S 0

hydrophobic pTyr binding site binding

-0.4

site

-0.8

a 0

20 40 residue

60

c

b 0

20

40 60 residue

80


0

20 40 60 80 100 residue

Page 43 of 50



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

1

5 × 10

3 × 10

1 × 10 9

0 M1 I2g I2d L4 L4’ I5 I5’ A6 L8 L8’ A9 V10 V10’ V13’ V14’ M16 M20 L24 L24’ A26 L28’ T35 L36 L36’ V40’ I41 I41’ M42 T46 I50 I50’ L54’ I60 I60’ I61 I61’ l62’ L62’ V72 V72’ T73 V75’ V78 V78’ A81 I82 I82’ A84 V88’ I91 I91’ M92 V93 V93’ I94’ V99’ L104’ A107 L110 L112 L112’ I115 I115’ V119’ T123 V136’ A143 A145 !155 I155’ L156 L156’


3

c 02

M16

D2 , 1/s M42

M1


Page 44 of 50

Met20 FG GH

M42 I61’

a

M92

2

M20

M1

9

M92

b

M16

M20

9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

∆S

-0.2

2 ∆ Saxis

M1 I2g I2d L4 L4’ I5 I5’ A6 L8 L8’ A9 V10 V10’ V13’ V14’ M16 M20 L24 L24’ A26 L28’ T35 L36 L36’ V40’ I41 I41’ M42 T46 I50 I50’ L54’ I60 I60’ I61 I61’ l62’ L62’ V72 V72’ T73 V75’ V78 V78’ A81 I82 I82’ A84 V88’ I91 I91’ M92 V93 V93’ I94’ V99’ L104’ A107 L110 L112 L112’ I115 I115’ V119’ T123 V136’ A143 A145 !155 I155’ L156 L156’

Page 45 of 50 The Journal of Physical Chemistry

Met20 FG GH

0.2

a

0.1

0 M16

-0.1

M20

0.2

∆ ( S 02 ) 2

b

0.1

0

-0.1

-0.2




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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


0.9 ( S 02 )2 2 S axis

WT

a

V18A

c

V34A

e

0.6

0.3

0 600 τ2 , ps τ e , ps 400

d

b

f

200

0

methyl

methyl ACS Paragon Plus Environment

methyl


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

3

Eglin C: WT & V18A

c 02

Page 48 of 50

SH2 free & bound

Eglin C: WT & V34A

g

a

d

b

e

h

WT more disordered f

i

2 1 0 800

τ2 , ps

400

0

c

0.1

∆S

0 -0.1

0.1 0

WT more ordered

methyl

-0.1

bound

methyl ACS Paragon Plus Environment

more ordered

methyl

Page 49 of 50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


1 (S 02 ) 2 0.8

TNfn3

SRLS

FNfn10

c

a

TNfn3 2 Saxis

MF

FNfn10

g

e

0.6 0.4

0.36

0.36 0.29

0.2 0.1

0 800 600

τ2

0.03

0.05

d

b 540

f 500

ps

h

τpse

400 200 0

40

methyl

107

107

18

18

90

methyl

methyl


methyl


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

127x95mm (72 x 72 DPI)


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Conformational Entropy from NMR Relaxation in Proteins: The SRLS

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