Conformational Entropy from Slowly Relaxing Local Structure Analysis

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Article 15

Conformational Entropy from SRLS Analysis of N– H Relaxation in Proteins: Application to Pheromone Binding to MUP-I in the 283–308 K Temperature Range Lukas Zidek, and Eva Meirovitch J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b06049 • Publication Date (Web): 21 Aug 2017 Downloaded from http://pubs.acs.org on August 22, 2017

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The Journal of Physical Chemistry

Conformational Entropy from SRLS Analysis of 15N–H Relaxation in Proteins: Application to Pheromone Binding to MUP-I in the 283–308 K Temperature Range

Lukáš Žídek1 and Eva Meirovitch2,*

Central European Institute of Technology, Masaryk University, Kamenice 5, 62500 Brno, Czech Republic and National Center for Biomolecular Research, Faculty of Science, Masaryk University, Kamenice 5, 62500 Brno, Czech Republic;1 The Mina and Everard Goodman Faculty of Life Sciences, BarIlan University, Ramat-Gan 52900 Israel2

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

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ABSTRACT The slowly relaxing local structure (SRLS) approach is applied to 15N–H relaxation from the major urinary protein I (MUP-I), and its complex with pheromone 2-sec-butyl-4,5dihydrothiazol. The objective is to elucidate dynamics and binding-induced changes in conformational entropy. Experimental data acquired previously in the 283–308 K temperaturerange are used. The N–H bond is found to reorient globally with correlation time, ,, and locally with correlation time, ,, where , >> , . The local motion is restricted by the potential u = – , where is the Wigner rotation matrix element for L = 2, K = 0, and >, evaluates the strength of the potential. u yields straightforwardly the order parameter, <

and the conformational entropy, , both given by = exp(–u). The deviation of the local ordering/local diffusion axis from the N−H bond, given by the angle β, is also determined. We find that ≅ 18 ± 4 and , = 0–170 ps for ligand-free MUP-I, whereas ≅ 15 ± 4 and , = 20–270 ps for ligand-bound MUP-I. β is in the 0–10o range. and , decrease, whereas β increases, when the temperature is increased from 283 to 308 K. Thus, SRLS provides physically well-defined structure-related ( and < >), motion-related (,), geometry-related (β), and

binding-related ( ) local parameters, and their temperature-dependences. Intriguingly, upon pheromone-binding the conformational entropy of MUP-I decreases at high temperature and increases at low temperature. The very same experimental data were analyzed previously with the model-free (MF) method which yielded “global” (in this context, “relating to the entire 283– 308 K range”) amplitude ( ) and rate ( ) of the local motion, and a phenomenological exchange term ( ). is found to decrease (implying implicitly “global” increase in ) upon pheromone binding.


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1. INTRODUCTION NMR relaxation emerged as a powerful method for studying protein dynamics and thermodynamics in solution.1–4 A particularly useful probe is the backbone 15N–1H bond, which provides at any given external magnetic field three relaxation parameters – 15N T1, T2 and

15

N–

{1H} NOE – expressed in terms of five values of the spectral density function, J(ω).5,6 The N–H bond tumbles globally as part of the protein. Spin relaxation analysis can detect local motions with rates larger than the global tumbling; often they are much larger. The local motion differs fundamentally from the global motion in being restricted spatially by the immediate (internal) protein surroundings. In theoretical physical-chemical approaches rotational motions are expressed by diffusion tensors, and spatial restrictions by potentials in terms of which ordering tensors may be defined.7,8 These physical descriptors, including features of local geometry inherent in relative tensor orientations, are key elements of stochastic dynamic models. The solutions of such models are the J(ω) functions.7,8 Thus, on the basis of dynamic models one can extract the information delineated above from the experimental relaxation parameters with datafitting. NMR relaxation in proteins has been analyzed traditionally with the model-free (MF) formalism.9–11 MF is a simple method based on the theory of moments, which assumes that the global and local motions experienced by the probe are decoupled. Within the scope of a modelfree concept, the key quantities are expressed in terms of empirical parameters. MF provides useful semi-quantitative information in the mode-decoupling limit. We developed in recent years the stochastic slowly relaxing local structure (SRLS) approach12–14 for NMR relaxation in proteins15–18. SRLS is a general method, yielding MF in 3 ACS Paragon Plus Environment


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simple limits. It accounts rigorously for mode-coupling, and uses a tensorial representation of the physical quantities.12–18 The global and local motions are described by second-rank diffusion tensors, and , respectively, and the local spatial restrictions by a potential, u. Here we use , = − where θ describes the orientation of the probe in the protein, and is

the Wigner rotation matrix element for L = 2, K = 0. A second-rank local ordering tensor with > may be defined in terms of (which enters the probability principal value < density, Peq(θ) = exp(–u(θ), required to calculate < >. When used in the context of

NMR, SRLS-based analyses can also determine the orientation of the ordering tensor with respect to a known NMR tensor frame. This orientation is expressed by the angle β. Another physical quantity that may be defined in terms of u(θ), emerging thus straightforwardly

from

SRLS

analyses,

is

conformational

entropy,

Sk

given

by

− ln " # $θ (ref 3). A major objective of this study is to elucidate changes in Sk implied by the binding of the pheromone 2-sec-butyl-4,5-dihydrothiazol to the major urinary protein I (MUP-I). We use extensive data acquired previously at magnetic fields of 11.75 and 14.1 T in the 283–308 K temperature-range, and analyzed with the MF method.19 MF does not feature a potential (a key element in this context20–22). Instead it uses a squared generalized order parameter, , to represent the local spatial restrictions at the site of the motion of the probe. Assuming that S is a standard order parameter calculated with Peq = exp(–u), and guessing the form of u, one correlates S and Sk (as both depend on Peq). Numerous studies are based on this rationale.1–4, 23–29 For u representing the wobble-in-a-cone potential, an analytical expression linking Sk to S was developed.3 This strategy was employed in earlier work, where MF9 was applied to MUP-I and its complex with 2-sec-butyl-4,5-dihydrothiazol utilizing data acquired at 11.75 T and 303 K.25 4 ACS Paragon Plus Environment

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The results of ref pointed to increase in conformational entropy upon binding. To explore further this interesting finding, and learn more about the structural dynamics of the MUP-I system, the extended data-set mentioned above was acquired.19 When multi-field and/or multitemperature data-sets are to be analyzed, as in ref 19, often the original MF formalism9 has to be enhanced, typically by including in the analysis the conformational exchange term, Rex.6,30 In principle, Rex represents the contribution of µs-ms motions to the linewidth of the

15

N NMR

signal. It can be measured experimentally and interpreted within the scope of physically sound theoretical methods; a comprehensive review of the related research appears in ref 31. Yet, when determined as fitting parameter, Rex is prone to absorb unaccounted for factors. MF analyses, in general, and the incorporation of Rex, in particular, are carried out utilizing model-selection protocols.6,30 The latter are very sensitive to experimental errors19,32. To forgo such a procedure the authors of ref 19 devised (a) a graphical method based on mathematical spectral density functions, and (b) an MF-based scheme where all of the temperature-dependent data were combined yielding thus “global”, i.e., not temperature-specific, parameters. Both methods feature quite a few Rex contributions. Method (a) classifies the residues of MUP-I qualitatively into four distinct groups. Method (b) yields (in addition to Rex contributions) squared generalized order parameters, , that largely decrease upon pheromone binding, and effective correlation times, ; both parameters are “global” in nature That the temperature-dependences of and are not determined, and conformational entropy, Sk, is not provided by the MF analysis, are primarily consequences of forgoing model-selection. In SRLS, enhancements can be accomplished within the scope of the basic dynamic model. This is achieved by lowering tensor symmetry and/or generalizing features of local geometry. We found recently in related studies20,21 that allowing and to vary in the data5 ACS Paragon Plus Environment


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fitting process does not yield good statistics. On the other hand, allowing and and the angle β to vary yielded good statistics for virtually all of the residues of a given protein. Corresponding MF analyses used , and . β not equal to zero means that the local ordering tensor and the

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N–1H dipolar tensor are diagonal in different frames. The former is

model-related while the latter in NMR-related. Given that they represent different physical properties, having distinct frames is not surprising.15–18 From a physical perspective β not equal to zero means that the orientation of minimum restraints (where u(θ = 0) = – ) does not point along the N–H bond; this is interesting structural information. To gain insight into MUP-I-related features of dynamics and binding not revealed by the MF analysis, we apply SRLS to the experimental data of ref 19. We find that taking the tensor isotropic with , = 1/6 determined by the Stokes-Einstein relation,19 and allowing , = 1/6τ, and β to vary in the data-fitting process, is appropriate both from a physical point of view (see above), and yields good statistics. All of the experimentallyaccessible N–H bonds of ligand-free and ligand-bound MUP-I are characterized in terms of these parameters in a temperature-dependent manner. The change in conformational entropy, Sk, implied by complex formation is calculated in terms of the change in the strength of the local potential, also in a temperature-dependent manner. An intriguing opposite trend in Sk variation upon complex formation at low and high temperatures is revealed and rationalized.

2. THEORETICAL SUMMARY The SRLS approach has been described in previous publications.15–18 For convenience, its basics are summarized in the Supporting Information; here we depict only those aspects that


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are essential for the topic treated. The MF method is developed in ref 9, and its application to NMR relaxation in proteins is described in refs 5, 6 and 32. For convenience, the MF spectral density is depicted in the Supporting Information.

The SRLS potential and order parameter. The exact potential, u, is given in SRLS by the ) 7,8 complete expansion in the basis-set of the Wigner rotation matrix elements, ( . The Wigner

functions have transformation properties related inherently to rotational reorientation, to the frame transformations among the various second-rank tensors involved, and to the standard order parameters defined in terms of = exp −;7,8 hence, this basis-set is particularly appropriate. For practical reasons the expansion of u has to be truncated. With only the lowest (L = 2, K = 0) term preserved, the simple (axial) Maier-Saupe potential:7,8

= − = − 1.5 ./ θ − 0.5

(1)

is obtained. ≡ 1/23 4, where 1 is the potential in kcal/mol, the angle θ denotes the orientation of the probe in the protein, and evaluates the strength of u. We use this potential herein. The (axial) order parameter is defined in terms of u as:7,8

=

7 θ8 ; θ ?θ 566 9:

89: ; θ ?θ

,

(2)



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where (as already pointed out) is the probability density for bond-vector orientation. 7

7

= @ A6 566 ; is an approximation to the Boltzmann factor. SRLS allows for additional terms to be included in the expression for u. Thereby one can improve Peq, hence the accuracy of the conformational entropy derived from it. However, determining additional potential coefficients requires more extensive data-sets.16–18

Conformational entropy. It is assumed that the only spatially-restricting factor at a given N–H site is the potential u(θ). The effect of non-zero u(θ) is to change the entropy of the protein by the quantity:3

= − ln " # $θ −BC $ ,

(3)

where Sk is “entropy” in usual connotation in units of kBT. The term −BC $ is independent of u(θ). Hence, in calculating entropy differences, ∆Sk, it suffices to determine how the term − ln " # $θ changes as a consequence of changes in u(θ).3 The following comments are appropriate. (1) The expression for ∆Sk is based on the assumption that the probability density, , is given exclusively by the potential, u.3 However, the conformational exchange process also affects . The implication of this feature on eq 3 is not known. (2). The coefficient, , characterizes the local structure from the viewpoint of potential strength. The angle, β, does so from a geometric perspective associated with the local ordering tensor, which is related the local potential. u(θ) enters the expression for Sk explicitly; β 8 ACS Paragon Plus Environment

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does so implicitly, as would have been different had β not been allowed to vary in the datafitting process. 3. RESULTS AND DISCUSSION A stereo-view of the ribbon diagram of MUP-I, based on the PDB entry 1I06,19 is shown in Figure 1. The compact β-barrel structure, which houses the small hydrophobic ligand in its core, is clearly visible.

3.1. Experimental Data. As a first step we examine the experimental data in the context of the chi-squared function, D , which is minimized in the data-fitting process.6,30 For a single

field data-set D comprises three terms given by E"

F GHIG JF KLM F KLM

σKLM

# : "F KLM#O , for brevity %ΔR/

%SR , where X is 15N T1, T2 or 15N–{1H} NOE (for brevity, T1, T2 and NOE). The quantity %SR is depicted as a function of residue number for ligand-free MUP-I in Figures 2a–2c, and for ligand-bound MUP-I in Figures 3a–3c. Red, orange, yellow, green and blue symbols correspond to 283, 288, 298, 303 and 308 K, respectively. There is substantial diversity in %SR magnitude and trend for a given N–H bond at a given temperature, for a given relaxation parameter at different temperatures, and for a given relaxation parameter associated with the two forms of MUP-I at the same temperature. Figures 2 and 3 show typical experimental 15N relaxation in proteins; hence discussing them is of general interest. In an ideal data-fitting process the %SR values are comparable. All three relaxation parameters affect similarly the optimization. The latter ends when %∆R ≅ %SR for all X. Taking χ ~ 3 (0.05–0.1 critical chi-square distribution for one degree of freedom33) as benchmark, each X contributes 1.



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Let us consider a scenario where the %SR values differ substantially; for example, %SR = 1, 2 and 10 for X = T1, T2 and NOE, respectively. In the beginning the (large) %∆R values are reduced uniformly until %ΔNOE = %σ(NOE) = 10, which is the minimum value of %ΔNOE. The NOE contributes 1 to χ and ceases to affect the process. When %∆(T2) = %σ(T2) = 2 T2 ceases to affect the process, also contributing 1 to χ . From now only T1 is effective until %∆(T1) = %σ(T1) = 1, which is the end-point. The process described in the previous paragraph differs substantially from the ideal process; the implications might be problematic. However, the diversity in %SR is only one of the many factors that affect the optimization (such as the nature of the functional dependence of X on the relevant J(ω) values, the differential sensitivity of J(ω) to the various parameters of the model, etc.). Fortunately, in many cases %SR diversity does not impair substantially the datafitting process, with the results being largely consistent. However, in some cases it does. Thus, we found that sporadic outliers in the best-fit parameter profiles inconsistent with their neighbors in the same structural motif correlate with highly diverse %SR values. This happens for approximately 10% of the best-fit , and β parameters; the respective data were removed from Figures 4 and 5 below.

3.2. Global motion. Compelling evidence that the tensor may be taken isotropic, and using the Stokes-Einstein relation to determine , at 298 K is appropriate, appears in ref 19. It is reasonable to assume that the temperature-dependence of , is given by the temperaturedependence of water viscosity.19 We adopt the strategy of ref 19 with regard to the quantification of the global motion; the diffusion constants used in the SRLS calculations are given in Table 1. 10 ACS Paragon Plus Environment

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Table 1. Global motional diffusion constants, = YZ

[,6

, with , calculated on the

basis of the Stokes-Einstein equation.19

free form)

283 _

288 _

298 _

303 _

308 _

1.15

1.34

1.78

2.02

2.27

1.02

1.34

1.77

2.01

2.26

10a / J bound form) 10a / J

The average , error is estimated in ref 19 at 5%. At 283 K, the , values of ligandfree and ligand-bound MUP-I deviate by +6.5% and –6.5%, respectively, from their mean, and by 12% (which is the difference divided by the mean) from one another. In view of the more stringent spectroscopic conditions at low temperature we consider this error acceptable.

3.3. Local motion. Figures 4a, 4b and 4c show the best-fit values of the potential coefficient, , the logarithm of the local motional diffusion constant, log(D2, / J ), and the angle, β,, between the main local ordering/local diffusion axis and the N–H bond, β, respectively. The (reduced as delineated above) experimental data of ligand-free MUP-I acquired at 14.1 T, and the temperatures depicted in the Figures, underlie the respective calculations. Figures 5a, 5b and 5c are the counterparts of Figures 4a, 4b and 4c for ligand-bound MUP-I. The experimental relaxation parameters were deposited in the BioMagResBank (accession code 5995 for free



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MUP-I, and accession code 5996 for MUP-I bound to the pheromone 2-sec-butyl-4,5dihydrothiazol). All of the parameters vary substantially along the protein sequence, and moderately as a function of temperature. That the strength of the local potential, , decreases, and the local motional diffusion constant, D2 (hence also log(D2, / J )), increases with increasing temperature, are straightforward expectations. The extent to which they are fulfilled – given the irregularities visible in Figures 4 and 5 – is discussed below. Quite a few cases where the temperature-dependence of in MF is irregular,34 or expected dependencies are reported only for selected residues,32 appear in the literature. This is so even when Rex, and moreover ,, are also allowed to vary in the data-fitting process (cf. Figures 2 and 5 of ref 34). The effective MF correlation time, , is often not reported, or found to be virtually temperature-independent35. Difficulties encountered with quantitative analyses of temperature-dependent data-sets using MF have lead authors to exclude part of the data (typically

15

N T2) ,36 impose specific restrictions on parameter variability,37 or resort to

qualitative spectral density mapping38–40. The results of SRLS analyses of temperaturedependent data typically abide by straightforward physical expectations.41 Figures 4a and 5a show the potential coefficient, . Red, orange, yellow, green and blue correspond to 283, 288, 298, 303 and 308 K, respectively. It can be seen that the upper part of the distribution is dominated by red and orange symbols, whereas its lower part is dominated by blue and green symbols. While not all of the values in Figures 4 and 5 decrease with increasing temperature, this trend is predominant in carefully-evaluated data-subsets (see below). On average ~ 18 ± 4 for ligand-free MUP-I and 15 ± 4 for ligand-bound MUP-I.


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Figures 4b and 5b depict the logarithm of the local motional diffusion constant, , for ligand-free and ligand-bound MUP-I, respectively. , is at least 50 times, and mostly over 100 times, larger than the global motional diffusion constant, . Mode-coupling is a small effect under these circumstances.16,17 In general, is larger in the ligand-bound form of MUP-I. With regard to its temperature-dependence, quite clear a picture will emerge if the 303 K (green) symbols are disregarded. In that case the lower part of the log(D2, / J ) distribution is dominated by red and orange symbols, indicating relatively slow local motion, whereas its upper part is dominated by blue symbols, indicating relatively fast local motion. Disregarding the 303 K data is justified by the substantial diversity in %σX. Thus, for the ligand-free protein %σX is relatively large and highly dispersed for

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N T2 (Figure 2b, green), and exceptionally

small for 15N–{1H} NOE (Figure 2c, green); for the ligand-bound protein %σX is exceptionally large for 15N T1 (Figure 3a, green). Figures 4c and 5c show the angle β. As pointed out above, that β differs from zero is not surprising. For the ligand-free protein (Figure 4c) the upper part of the distribution in β is dominated by the 308 K and 303 K symbols, whereas its lower part is dominated by the 283 K and 288 K symbols. Figure 5c shows that for the ligand-bound protein β increases gradually from a value not exceeding 2.5o at 283 K, to approximately 10o at 308 K.

3.4. Conformational entropy. The change in conformational entropy, ∆Sk = Sk(ligandbound MUP-I) – Sk(ligand-free MUP-I), calculated according to eq 3 from the corresponding pairs of values, is shown in Figures 6d–6h. Clearly, only N–H bonds that are accessible experimentally for both protein forms are considered. The relatively small differences, ∆Sk, are particularly sensitive to non-uniform percent-error in the underlying experimental data. We 13 ACS Paragon Plus Environment


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excluded all of the outliers that based on Figures 2 and 3 are associated with highly diverse %σX. The 283 K ∆Sk data (Figure 6d) are predominantly positive (blue ellipse), and the 288 K data (Figure 6e) are dominantly positive. At 298 K (Figure 6f) ∆Sk has mixed signs (blue ellipse). The 303 K (Figure 6g) and 308 K (Figure 6h) ∆Sk data are predominantly negative (blue ellipse in Figure 6h). Thus, Figures 6d–6h indicate that at the lower temperatures pheromone binding brings about increase in conformational entropy, contrary to intuitive expectation. On the other hand, at the higher temperatures the commonly-observed decrease in conformational entropy upon ligand-binding is observed. To help rationalize this intriguing finding, we extracted from the 283 and 308 K data in Figures 4 and 5 the and β values of those residues which appear in Figures 6d and 6h. Figure 7 shows these and β values for ligand-free MUP-I (left) and ligand-bound MUP-I (right) at 283 K (black) and at 308 K (red). It can be seen clearly that for both protein forms decreases with increasing temperature (parts a and c),whereas β increases with increasing temperature (parts b and d). The coefficient of the bound form (part c) changes to a considerably smaller extent than the coefficient of the free form (part a), whereas the angle β of the bound form (part d) changes to a considerably larger extent than the angle β of free form (part b). The change in of the bound form in going from 283 K to 308 K (part c) is small as has been quite small already at 283 K; the change in β (part d) is large as β has been unduly small at 283 K. This can be realized by comparing the black curves in Figures 7c and 7d with the other curves in Figure 7 that represent the same parameter. Overall, Figure 7 reinforces the finding illustrated in Figure 6.


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Figure 8 shows (parts a and c) and β (parts b and d) of the ligand-free (black) and ligand-bound (red) forms of MUP-I at 283 K (left) and 308 K (right). As in Figure 7, only the residues appearing in Figures 6d and 6h are considered. At 283 K the values of the bound form (part a, red) are substantially smaller than those of the free form (part a, black) for virtually all of the residues. The angle β is mostly smaller than 4o for the free form (part b, black) and smaller than 2.5o for the bound form (part b, red). Thus, at low temperature ligand-binding involves reduction in the strength of the local potential, and the establishment of simple local geometry, where the local ordering/local diffusion axis is the same as the N–H bond. (ligandbound MUP-I) < (ligand-free MUP-I) implies increase in conformational entropy (eq 3), in agreement with Figure 6d. At 308 K the differences in are less consistent. Qualitatively, (ligand-bound MUPI) (red) is larger than (ligand-free MUP-I) (black) for somewhat over 50% of the residues (part c of Figure 8); β (ligand-bound MUP-I) (red) is larger than β (ligand-free MUP-I) (black) for approximately 75% of the residues (part d of Figure 8). Quantitative evaluation of ∆Sk using eq 3 points to overall decrease in conformational entropy upon ligand-binding (Figure 6h). Experimental data acquired at 11.75 T, and combined 297 K, 11.75 K and 298 K, 14.1 T as well as 302 K, 11.75 T and 303 K, 14.1 T data,19 were also analyzed. The 11.75 T data are less precise, and the constituents of the two-field data-sets are associated with somewhat different temperatures. The results associated with local dynamics are forgone, but the results associated with conformational entropy, which is the focus of this article, are explored. Interestingly and rewardingly, we find that once outliers associated with highly diverse %σX are removed, the temperature-dependence of ∆Sk from the 11.75 T data (Figure 6a–6c), and



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from the combined 11.75 and 14.1 T data (Figures 6i and 6j), reproduce qualitatively the temperature-dependence of ∆Sk from the 14.1 T data (Figure 6d-6h). Given that the change in trend from the usual decrease in conformational entropy upon ligand-binding at high temperature to the unusual increase in it at low temperature is one of the main findings of this study, the information inherent in the first and third columns of Figure 6 is important. Supported by Figures 6a–6c, 6i and 6j, we offer Figures 6d-6h as a reliable picture of ∆Sk changes as a function of pheromone-binding to MUP-I in the temperature-range of 283–308 K. ∆ < 0 obtained with MF analysis at 303 K using 11.75 T data in ref 25, and ∆a0 < 0 (a0 is a mathematical parameter signifying S when the mathematical spectral density has the same form as the spectral density of ref 9) obtained with “global” analysis in ref 19, are consistent with ∆Sk > 0 in Figure 6d. Correlating ∆Sk with a physically well-defined local potential, and characterizing the N–H sites in terms of the strength of a well-defined local potential form ( ), a geometric feature (β) which allows for the local ordering/local diffusion axis to deviate from the N–H bond orientation, and a kinetic-in-nature local-motional diffusion constant (D2), is unique to the SRLS analysis. So is the change in the sign of ∆Sk in going from 283 to 308 K.

Mesoscopic interpretation of ∆Sk. Why is pheromone-binding associated with increase in conformational entropy at the lower temperatures, and decrease in it at the higher temperatures, of the 283-308 K range? The 308 K case describes a situation wherein a substantial portion of the protein structure becomes more compact upon ligand-binding, implying decrease in conformational 16 ACS Paragon Plus Environment

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entropy. Such scenarios have been encountered often.1,2,4,6,20,21,23–29,32,34,36,42 In the present case compactness is implied by stronger local potentials at the N–H sites. In addition, the angle β increases in most cases, in evidence of more intricate local geometry, where the local ordering/local diffusion axis is not pointing along the N–H bond. This is consistent with the moieties in the immediate surroundings (which exert the local potential) moving closer to the N–H bond. At the same time, the minimum-restraint-orientation (i.e., the orientation of the local ordering/local diffusion axis) is shifting away discernibly from its assumed (for simplicity) identity with the N–H bond orientation. The 283 K case describes a situation wherein ligand-binding renders the protein structure less compact, implying increase in conformational entropy. Such scenarios are much rarer.19,24,25,26,29,32,42 The angle β decreases upon pheromone-biding, rendering the local geometry simpler. This is consistent with the moieties in the immediate surroundings moving away from the N–H bond, with the minimum-restraint-orientation relaxing to its simple N–H bond orientation. Pheromone-binding consists of insertion of the ligand into the interior of the compact βbarrel structure. At 308 K sufficient higher-energy states are populated to render this process possible through thermal motions, within the scope of the changes described above. At 283 K binding is facilitated by other factors, possibly of an induced-fit type. These changes exhibit trends opposite to those associated with the 308 K scenario. Most of the previous binding-related MF studies report on increase in “local order” upon ligand-binding; some report on decrease in it.19,25,26,29,42 To our knowledge, reports on changes in trend as a function of temperature do not appear in the literature.



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It is of interest to correlate the mesoscopic picture delineated above with atomistic results provided by previous molecular dynamics simulations.43 The simulation conducted on the ligand-free form at 300 K pointed to possible weak interactions between the turn joining the

β-strands C (green in Figure 1) and D (magenta in Figure 1), and the chain segment 27–36. These interactions are necessarily stronger at lower temperature and weaker at higher temperature. One might hypothesize that at low temperature the structural constituents of these weak interactions get pushed apart to make possible pheromone insertion into the β-barrel, reducing structural compactness. This effect overrides the common increase in structural compactness upon ligand-binding. At high temperature the latter effect dominates. It was also found that several hydrogen bonds between the turn joining the β -strands E (cyan in Figure 1) and F (red in Figure 1), and the turn joining the β -strands G (black in Figure 1) and H (pink in Figure 1), broke in the course of the 300 K MD simulation of the ligandbound form.43 This effect is likely to be more frequent at higher temperature, further loosening the average structure, and less frequent at lower temperatures, further tightening the average structure. The temperature-dependence of the conformational entropy, Sk, can provide heatcapacity.32 We defer such studies to future SRLS-based work, to be carried out within the scope of enhances, i.e., combined multi-field, data-sets. This makes possible allowing for rhombic potentials, hence deriving more accurate conformational entropy. It is of interest to determine to what extent the overall picture, in particular the conformational-entropy-related aspects, will be improved thereby. Comparison with results obtained previously within the scope of a comprehensive study (comprising several methods) of a MUP protein with a somewhat different


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sequence, in free form and bound to two ligands differing from the pheromone used herein,44,45 is also an interesting prospect.

4. CONCLUSIONS 15

N–H relaxation from the major urinary protein-I, in free form and bound to the

pheromone 2-sec-butyl-4,5-dihydrothiazol, has been studied in the 283–308 K range with SRLS. Physically well-defined parameters that relate to the local structure (potential strength, ), the local motion (diffusion constant, ), the local geometry (angle β), and ligand-binding (conformational entropy, ) were determined. The temperature-dependence of and abides by straightforward physical expectations and that of β provides interesting new information. At 308 K MUP-I features increased structural compactness upon ligand-binding implying the usually-observed decrease in conformational entropy. The local geometry deviates from its simplest form, eventually to accommodate the increase in potential strength. Sufficient high-energy states are populated to make possible the insertion of the pheromone into the βbarrel. At 283 K the local potential decreases upon pheromone-binding. This signifies reduced structural compactness, which implies increase in conformational entropy. The local geometry simplifies, in agreement with reduced structural strain. These trends are opposite to those detected at the higher temperatures. Because fewer high-energy states are populated at 283 K, factors additional to those active at 308 K are operational. A previous MF analysis of the same relaxation data describes the dynamics of MUP-I and its complex with the pheromone 2-sec-butyl-4,5-dihydrothiazol in terms of “global”



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squared generalized order parameter ( ) and effective local motional correlation time ( ), and quite a few conformational exchange terms ( ). “Global” decreases upon pheromonebinding. An earlier MF study determined decrease in , and from it increase in conformational entropy upon pheromone binding, at 11.75 T and 303K.

Supporting Information Available: A summary of the slowly relaxation local structure approach; the original model-free spectral density.

5. Acknowledgments This work was supported by the Israel Science Foundation (Grant No. 369/15 to E.M.).


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8.

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Clore, G. M.; Szabo, A.; Bax, A.; Kay, L. E.; Driscoll, P. C.; Gronenborn, A. M.

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Polimeno, A.; Freed, J. H. A Many-Body Stochastic Approach to Rotational

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15

N NMR Relaxation in Proteins. J. Am. Chem.

Soc. 2001, 123, 3055-3063.


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16.

Meirovitch, E.; Shapiro, Yu. E.; Polimeno, A.; Freed, J. H. Protein Dynamics

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Meirovitch, E.; Shapiro, Yu. E.; Polimeno, A.; Freed, J. H. Structural Dynamics

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Tool for Interpreting NMR Spin Relaxation in Proteins. J. Phys. Chem. B 2009, 113, 13613. 19.

Křížová, H.; Žídek, L.; Stone, M. J.; Novotny, M. V.; Sklenár, V. Temperature-

Dependent Spectral Density Analysis Applied to Monitoring Backbone Dynamics of Major

Urinary

Protein-I

Complexed

with

the

Pheromone

2-sec-butyl-4,5-

2

H Methyl-Moiety

Dihydrothiazole. J. Biomol. NMR 2004, 28, 369-384. 20.

Tchaicheeyan, O.; Meirovitch, E. An SRLS Study of

Relaxation and Related Conformational Entropy in Free and Peptide-Bound PLCγ1C SH2. J. Phys. Chem. B 2016, 120, 10695-10705. 21.

Tchaicheeyan, O.; Meirovitch, E. Conformational Entropy from NMR Relaxation

in Proteins: the SRLS Perspective. J. Phys. Chem. B 2017, 121, 758-768. 22.

Zerbetto, M.; Meirovitch, E.

15

N–H-Related Conformational Entropy Changes

Entailed By Plexin-B1 RBD Dimerization: A Combined Molecular Dynamics/NMR Relaxation Approach. J. Phys. Chem. B 2017, 121, 3007-3015.



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23.

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Lee, A. L.; Sharp. K. A.; Kranz, J. K.; Song, X. J.; Wand, A. J. Temperature

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Bracken, C.; Carr, P. A.; Cavanagh, J.; Palmer III, A. G. Temperature

Dependence of Intramolecular Dynamics of the Basic Leucine Zipper of GCN4: Implications for the Entropy of Association with DNA. J. Mol. Biol. 1999, 285, 21332146. 25.

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Conformational Entropy upon Hydrophobic Ligand Binding. Nat. Struct. Biol. 1999, 6, 1118-1121. 26.

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. 27.

Marlow, M. S.; Dogan, J.; Frederick, K. K.; Valentine, K. G.; Wand, A. J. The

Role of Conformational Entropy in Molecular Recognition by Calmodulin. Nat. Chem. Biol. 2010, 6, 352-358. 28.

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Entropy and its Role in Protein Function Revealed by NMR Relaxation. Curr. Opin. Struct. Biol. 2013, 23, 75-81. 29.

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Binding Studies by NMR Relaxation. Biochem. Soc. Trans. 2012, 40, 419-423. 30.

Fushman, D.; Cahill, S.; Cowburn, D. The Main-Chain Dynamics of the Dynamin

Pleckstrin Homology (PH) Domain in Solution: Analysis of Monomer/Dimer Equilibrium. J. Mol. Biol. 1997, 266, 173-194.


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N Relaxation with

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31.

Meirovitch, E.; Shapiro, Yu. E.; Tugarinov, V.; Liang, Z.; Freed, J. H. Mode-

Coupling Analysis of

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N CSA-15N–1H Dipolar Cross-Correlation in Proteins. Rhombic

Potentials at the N–H Bond. J. Phys. Chem. B 2003, 107. 9883-9897. 32.

Palmer III, A. G. Chemical Exchange in Biomolecules: Past, Present and Future.

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Spiegel, M. R.; Liu, J. Mathematical Handbook of Formulas and Tables, 2nd ed.;

Shaum’s Outline Series; McGraw-Hill: New York 1999, p. 266. 35.

Syracopoulis, L.; Lavigne, P.; Crump, M. P.; Gagné, S. M.; Kay, C. M.; Sykes, B.

D. Temperature Dependence of Dynamics and Thermodynamics of the Regulatory Domain of Human Cardiac Troponin C. Biochemistry 2001, 40, 12541-12551. 36.

Chang, S.-L.; Tjandra, N. Temperature-Dependence of Protein Backbone Motion

from Carbonyl 13C and Amide 15N NMR Relaxation. J. Magn. Res. 2005, 174, 43-53. 37.

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Motions of Calmodulin Probed by NMR Relaxation at Multiple Fields. J. Am. Chem. Soc. 2003, 125, 11379-11384. 39.

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Mispelter, J.; Stern, M.-H.; Lhoste, J.-M.; Roumestand, C. Refined Solution Structure



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and Backbone Dynamics of 15N-Labeled C12A-p8MTCPI Studied by NMR Relaxation. J. Biomol. NMR 1999, 15, 261-288. 40.

Jin, C.; Liao, X. Backbone Dynamics of a Winged Helix Protein and its DNA

Complex at Different Temperatures: Changes of Internal Motions in Genesis upon Binding DNA. J. Mol. Biol. 1999, 292, 641-651. 41.

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Shapiro, Yu. E.; Kahana, E.; Meirovitch, E. Domain Mobility from NMR/SRLS.

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Figure captions Figure 1. Stereo ribbon diagram of MUP-I (PDB entry 1IO6, with the C-terminal residues added). The β-strands are color-coded as follows: A, blue; B, yellow; C, green; D, magenta; E, cyan; F, red; G, black; and H, pink. The short β-strand, I, and the helical regions, are shown in gray. The cysteine side-chains forming a disulfide bond are shown in yellow.

Figure 2. Percent error in X, %σX = "

F GHIG JF KLM F KLM

#:"

σKLM F KLM

#, where X denotes 15N T1 (part a),

T2 (part b), and 15N–{1H} NOE (part c), as a function of residue number for the ligand-free form of MUP-I. The data, X, acquired at 14.1 T, and the corresponding errors, are taken from ref 19. Data corresponding to 283, 288, 298, 303 and 308 K are depicted in red, orange, yellow, green and blue, respectively.

Figure 3. Percent error in X, %σX = " T2 (part b), and

15

F GHIG JF KLM F KLM

σKLM

# : "F KLM#, where X denotes 15N T1 (part a),

N–{1H} NOE (part c), as a function of residue number for the ligand-bound

form of MUP-I. The data, X, acquired at 14.1 T, and the corresponding errors, are taken from ref 19. Data corresponding to 283, 288, 298, 303 and 308 K are depicted in red, orange, yellow, green and blue, respectively.

Figure 4. Best-fit parameters from SRLS analysis of

15

N–-H relaxation as a function of

residue number: coefficient evaluating the strength of the local potential, (part a); logarithm of the local-motional diffusion constant, / J (part b); and angle, β, between the principal axes of the local ordering and

15

N–1H dipolar tensors (part c), for ligand-free MUP-I. Parameters



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Page 28 of 39

corresponding to 283, 288, 298, 303 and 308 K are depicted in red, orange, yellow, green and blue, respectively. The black bars on the right show the average error. The

15

N chemical shift

anisotropy (CSA) was taken as −172 ppm, the N–H bond length as 1.02 Å, and the

15

N−1H

dipolar/15N CSA tensor tilt (accounted for rigorously in SRLS) as −17o.16−18


15

N–-H relaxation as a function of

residue number: coefficient evaluating the strength of the local potential, (part a); logarithm of the local-motional diffusion constant, / J (part b); and angle, β, between the principal axes of the local ordering and

15

N–1H dipolar tensors (part c), for ligand-bound MUP-I. Parameters

corresponding to 283, 288, 298, 303 and 308 K are depicted in red, orange, yellow, green and blue, respectively. The black bars on the right show the average error. Information on fixed physical parameters used in the calculations appear in the captions of Figure 4.

Figure 6. Conformational entropy differences, ∆Sk = Sk(ligand-bound MUP-I) – Sk(ligandfree MUP-I) obtained from the corresponding pairs of values according to eq 3 as a function of residue number. ∆Sk obtained from experimental data acquired at 11.74 T are shown in parts a–c. ∆Sk obtained from experimental data acquired at 14.1 T are shown in parts d–h. ∆Sk obtained from combined experimental data acquired at 11.75 and 14.1 T are shown in parts i and j. The corresponding temperatures are depicted. The black bars on the right show the average error. Information on fixed physical parameters used in the calculations appear in the captions of Figure 4.


Page 29 of 39

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15

N–H relaxation of the residues

which appear in Figure 6d for the 283 K data, and in Figure 6h for the 308 K data, as a function of residue number. of ligand-free MUP-I at 283 K (black) and 308 K (red) (part a); angle β of ligand-free MUP-I at 283 K (black) and 308 K (red) (part b); of ligand-bound MUP-I at 283 K (black) and 308 K (red) (part c); angle β of ligand-bound MUP-I at 283 K (black) and 308 K (red) (part d). The black bars on the right show the average error. Information on fixed physical parameters used in the calculations appear in the captions of Figure 4.


15

N–H relaxation of the residues

which appear in Figure 6d for the 283 K data, and in Figure 6h for the 308 K data, as a function of residue number. at 283 K of ligand-free MUP-I (black) and ligand-bound MUP-I (red) (part a); angle β at 283 K of ligand-free MUP-I (black) and ligand-bound MUP-I (red) (part b); at 308 K of ligand-free MUP-I (black) and ligand-bound MUP-I (red) (part c); angle β at 308 K of ligand-free MUP-I (black) and ligand-bound MUP-I (red) (part d). The black bars on the right show the average error.



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TOC graphics


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Page 31 of 39


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


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14.1 T

Page 32 of 39

ligand-free MUP-I

20

T1

a

T2

b

NOE

c

283 K 288 298 303 308

15

% error 10

5

0

0

40

80 120 160 residue

0

40

80 120 160 residue

ACS Paragon Plus Environment

0

40

80 120 160 residue

Page 33 of 39

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


14.1 T

20

T1

ligand-bound MUP-I

a

T2

b

NOE

c

283 K 288 298 303 308

15

% error 10

5

0

0

40

80 120 160 residue

0

40

80 120 160 residue


0

40

80 120 160 residue


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

14.10 T

Page 34 of 39

ligand-free MUP-I

a 20

c 20 10 283 K

288

298

303

308

0

b 16.7 ps 167 ps 1670 ps

10 log(D2, 1/s) 8

c

10

β

o

0 0

20

40

60

80 residue

100


120

140

160

Page 35 of 39

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


14.10 T

ligand-bound MUP-I

a 20

c 20 10 0

b 16.7 ps 167 ps 1670 ps

10 log(D2, 1/s) 8

c 10

β

o

0 0

20

40

60

80 residue

100


120

140

160


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

11.75 T

Page 36 of 39

11.75 & 14.10 T

14.10 T

0.1

283 K

d

e

∆S k 0 -0.1 0.1

291 K

a

288

297

b

298

∆ Sk 0 -0.1 0.1

∆ Sk 0

297.5 K

f

-0.1

0

302

0.1

∆Sk 0

c

303

g

308

h

100 50 residue

150

50

100

i

150

302.5 K

j

100 50 residue

150

-0.1 0.1

∆ Sk 0 -0.1

0

100 50 residue

150

0


0

Page 37 of 39

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


free

30

c 20

283 K - black 308 K - red

bound

a

c

b

d

20

10

10

β

o

0

0

50

100 residue

150

0


50

100 residue

150


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

283 K

30

c

2 0

Page 38 of 39

free - black bound - red

308 K

a

c

b

d

20

10

10

β

o

0

0

50

100 residue

150

0


50

100 residue

150

Page 39 of 39

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


0.1 ∆Sk

283 K

308 K

0 residue

-0.1 0

100

residue 0

100


Conformational Entropy from Slowly Relaxing Local Structure Analysis

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