Molecular DynamicsâMarkov State Model of Protein Ligand Binding

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A Molecular Dynamics–Markov State Model of Protein Ligand Binding and Allostery in CRIB-PDZ: Conformational Selection and Induced Fit Kelly Marie Thayer, Bharat Lakhani, and David L. Beveridge J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 10 May 2017 Downloaded from http://pubs.acs.org on May 15, 2017

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The Journal of Physical Chemistry

A Molecular Dynamics–Markov State Model of Protein Ligand Binding and Allostery in CRIB-PDZ: Conformational Selection and Induced Fit

Kelly M. Thayer1,3,4*, Bharat Lakhani2,3, and David L. Beveridge1,3 Departments of Chemistry1, Molecular Biology & Biochemistry2, Molecular Biophysics Program3, and Department of Computer Science4 Wesleyan University Middletown, CT 06459 USA *corresponding author. [email protected] phone 860-685-3214

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Abstract Conformational selection and induced fit are well-known contributors to ligand binding and allosteric effects in proteins. Molecular dynamics (MD) simulations now enable the theoretical study of protein-ligand binding in terms of ensembles of interconverting microstates and the population shifts characteristic of “dynamical allostery.” Here we investigate protein-ligand binding and allostery based on a Markov State Model (MSM) with states and rates obtained from all-atom MD simulations. As an exemplary case, we consider the single domain protein par-6 PDZ with and without ligand and allosteric effector. This is one of the smallest proteins in which allostery has been experimentally observed. In spite of the increased complexity intrinsic to a statistical ensemble perspective, we find that conformational selection and induced fit mechanisms can be readily identified in the analysis. In the non-allosteric pathway, MD-MSM shows that PDZ binds ligand via conformational selection. However, the allosteric pathway requires an activation step that involves a conformational change induced by the allosteric effector Cdc42. Once in the allosterically activated state, we find that ligand binding can proceed by conformational selection. Our MD-MSM model predicts that allostery in this and possibly other systems involves both induced fit and conformational selection, not just one or the other.

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Introduction Allostery is a regulatory process in which the functional activity of a protein or other macromolecule is altered by the non-covalent association of an effector ligand at a distal binding site. Early ideas about molecular mechanism in allostery derive from the ideas of Koshland, Nemethy and Filmer 1 (KNF) and Monod, Wyman and Changeau 2 (MWC). The KNF model takes as a point of departure Fischer’s classic lock-and-key model of protein-ligand binding 3, and posits a ligand-induced change in protein structure, or “induced fit.” The MWC model involves ligand binding via the preferential stabilization of binding competent structures intrinsic to the native state of an allosteric protein, now known as “conformational selection.” Historically, there has been considerable debate on the relative significance of conformational selection and induced fit in ligand binding and allostery,4 and recent reviews emphasize that the mechanism allosteric signal transmission is not yet fully clarified.5–7 The earliest molecular models of allostery are based on crystallography, which provide only thermally averaged, “static” structures. Recent studies have called attention to factors such as the role of dynamics, 8,9 the ensemble nature of allostery, 10,11 and ligand-induced population shifts. (REF) Recent advances in force fields, molecular simulations and compute power now enable the theoretical study of allosteric proteins in terms of ensembles of time-resolved microstates. Here we investigate the extent to which an ensemble view of structure can provide new insight into the role of induced fit and conformational capture mechanisms of ligand binding and allostery. In this study, all-atom molecular dynamics (MD) simulations including explicit solvent are applied to an ensemble-based study of allostery in a prototype allosteric protein, the par-6 PDZ domain. Our calculations use the AMBER suite of programs with a protein force field and MD protocol that describes the average structure of stable proteins within ~2 Å RMSD of crystal structures12. MD sampling of a protein conformational space with respect to all variables generates quite large data sets. Subsequent analysis typically involves reduction to a few selected structural parameters, with inevitably some approximations and loss of information. Recently, Markov State Models (MSMs) have provided a novel, network based vantage point on ensemble-based analysis of MD on proteins 13–16. In an MSM, the data reduction problem is dealt with in terms of clusters which differ in collective conformational changes, rather than individual structural parameters such as torsion angles, which can be quite advantageous We describe here a study of binding and allostery based on an MD-MSM research design applied to the single domain protein CRIB–PDZ, in which the binding of peptide ligand activates the cell polarity protein of Par6 17 (Figure 1). Binding of CRIB-PDZ by allosteric effector protein Rho GTPase Cdc42 18 is observed to result in a positive allosteric effect with a ~13-fold increase in affinity for peptide ligand 17. PDZ domains

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form a large family of peptide recognition domains and are well characterized, experimentally 17–21 and theoretically 5.

Figure 1. PDZ protein structure. Shown are the average structures from the MDHMM substate/Cluster C for the unbound protein P (cyan) and the ligand bound protein PL(green). The bound protein has adopted a conformation similar to the unbound conformation (backbone RMSD=0.82Å).

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Methods Our MD-MSM study of CRIB-PDZ is based on a general representation of a simple allosteric process as shown in Figure 2, where P refers to the protein, L is the ligand and A is the allosteric effector. In a statistical mechanics view of allostery, conformational selection may occur when the ensemble of structures of P in the absence of L clusters with those of a ligand bound trajectory PL. The coincidence of these substates indicates to what extent P is predisposed to adopting binding competent conformations. Induced fit occurs when an allosteric effector changes the structure of P in order to become binding competent. To elucidate this, MD simulations were performed on four constructs of CRIB-PDZ: unbound protein P, ligand bound PL, allosteric effector bound AP, and finally APL, with both effector and ligand bound. MD simulations including explicit counterions and solvent water were carried out for a total of 400 ns using AMBER 12 23,24 and the parallelized CUDA version of the pmemd routine 25 running on NVIDIA GPUs 25. The parm99SB force field 26 was used for protein and peptide, and TIP3P potential was used for water 27. Minimal salt was added to achieve electroneutrality in each of the simulation cells. Initial structures were obtained from the crystal structure PDBID# 1NF328 containing the allosteric effector Cdc42 and PDZ, and the NMR structure 1RZX 17 of the PDZ domain bound to peptide. The starting structure for the APL construct was obtained from the local coordinate overlay of 12 residues within 4Å (residues 171-177, 198, 199, 201, 231, 235) of two Par-6 PDZ structures (RMSD of ~0.01 Å) with 85% sequence identity. The ligand coordinates were transferred to the 1NF3 set to define the complete allosteric complex, and the remaining constructs were obtained by coordinate deletions. Stability and convergence of the MD were monitored by standard protocols 29. The MD trajectories were analyzed with the AMBER utility cpptraj 30 and the molecular visualization program VMD 31. Markov State models (MSM) were constructed in terms of the nodes and links of a complex network, with the nodes obtained by clustering the microstates. The links were defined from the Chapman-Kolmogorov compliant frequency of direct transitions between nodes 13,14,32 .

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Figure 2. Schematic diagram of the kinetic reaction scheme assumed in this study. The scheme involves a protein P(circle) having one allosteric effector A (rectangle) and binding one ligand L(fragment). Four constructs are required (abbreviations indicated beneath constructs). The relationship between the constructs is shown by arrows; the addition and subtraction of L and A components is shown. (Icons are shown for addition and not subtraction for simplicity.) The protein binding manifold is represented by the left two constructs, and the allosterically assisted manifold appears on the right. These schematically represent the four starting structures of the MD simulations carried out in this study for the allosteric PDZ protein with the Cdc42 regulator and peptide ligand.

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Results The general representation of allostery and a non-allosteric control referred to in this study is shown in Figure 2, where P is protein, L is ligand and A is the allosteric effector. The constructs chosen for this study represent the species in the kinetic reaction scheme. MD simulations were performed on four constructs of CRIB-PDZ: unbound protein P, ligand bound PL, allosteric effector bound AP, and APL, with both effector and ligand bound. The resulting MD trajectories were stripped to include only protein coordinates, concatenated into a single long sequence of structures, and clustered using a k-means procedure 33 clustering based on pairwise RMSD measures. The optimum number of clusters for the CRIB-PDZ project space was obtained by performing individual k-means calculations for the possibility of 2 to 15 clusters, which as shown in Figure 3 converged at 5. The five clusters are situated in somewhat close spatial proximity, and we found it necessary to establish if the difference between them is statistically significant. Distribution functions of the distances of the microstates with respect to each cluster centroid were calculated, and pairwise significance tests based on p-values showed the five clusters to be statistically independent with P < 0.05 for all cases except one, which had P < 0.08. The composition of the clusters reflects what may occur thermodynamically, and the frequency of transitions between cluster determine what does occur, i.e. which transitions are predicted to be kinetically favored. Thermodynamic analysis. The calculated MD-MSM composition of the five clusters is shown in histogram form in Figure 3. The 5 clusters denoted A-E. The contributions of constructs to the clusters are colored blue (P), green (PL), red (AP), and black (APL), and normalized horizontally; i.e. the blue bars going across Figure 3 sum to unity. The use of boldface P notation in P, PL, AP and APL serves as a reminder that our study is protein-centric; for example, PL signifies the construct in which the conformations are composed of protein microstates that originated in the MD on the protein-ligand construct, etc. In the statistical mechanics view of allostery, conformational selection occurs when the ensemble of structures of P in the absence of L encompasses snapshots clustering with those from a ligand bound trajectory. The overlap of these substates between constructs indicates to what extent P is predisposed to adopting binding competent conformations. Induced fit occurs when the presence of the allosteric effector corresponds to an increase in the population of P in one or more binding competent states. In this approach, allostery is permitted to arise from conformational selection, induced fit, or both mechanisms, and the extent of their contributions is an emergent property obtained through machine learning.

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The results in Figure 3 show that cluster A is comprised predominantly of protein conformations that originate from construct P, denoted PA. Cluster B is comprised of protein conformations from PL, denoted PLB. The ensemble nature of the analysis is most evident in C, which is composed of protein conformations which originate from constructs P and PL, i.e. a statistical admixture of unbound yet binding competent conformations from MD on P and structures from MD on PL, which are de facto binding competent since they share a substate with a binding competent form. The totality of MD structures of unbound protein P is distributed into two substates, {PA, PC}. In contrast, the ensemble of structures in cluster C are due to fractional contributions from both P and PL. The totality of MD structures from the ligand bound form PL, is likewise distributed between substates B and C, i.e. PL: {PLB , PLC}.

Figure 3. Histogram showing the contributions of the 4 constructs in each of the 5 clusters of the MD- MSM for CRIB PDZ. Colors match to constructs as follows: P (blue), P_L (green), A_P (red), A_P_L (black). The free protein samples clusters A and C, and the ligand bound protein samples B and C. Both sample C, indicating conformational capture. Protein bound to the allosteric effector samples clusters D and E, which both overlap with the effectorbound state. The allosteric effect is seen in the increase of overlap between the free and bound 8 states when the allosteric effector present.Plus ACS is Paragon Environment

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Conformational selection is enabled by the presence of binding competent structures in the MD trajectory of unbound construct P. Since clusters A and B have no substates in common, a transition from A (substate PA) to B (substate PB) must involve a change in structure, i.e. an induced fit. However, conformations from both P and from PL contribute to cluster C, which is to say that in C, a substate of the unbound ensemble overlaps with a substate of the ligand bound ensemble. Since PLC configurations originate from ligand bound constructs, and are de facto binding competent, the configurations PC in cluster C must also be also binding competent. Subsequent binding of ligand (not explicitly shown) will thus preferentially stabilize Cluster C, with a corresponding increase in Boltzmann population. Notably, the fractional increase in the population of PC on ligand binding happens at the expense of PA; this is the essence of describing conformational selection as a “capture” process. Allosterically mediated binding of ligand involves both Clusters D and E. From the point of view of the protein, the configurations of the allosterically activated state AP distribute between clusters D and E, denoted following the above convention, APD and APE . Allosteric activation involves first converting structures of P to the allosterically activated manifold of AP and APL. In the case of CRIB-PDZ, there are no substates in common between the two manifolds, and thus an induced fit mechanism is required for allosteric activation. The bound form of the allosterically active protein, APL contributes substates to D and E, APLD, APLE, respectively. Thus the bound form APL is accessible from allosterically activated AP by conformational selection, “capturing” conformations from the unbound substate AP. Thus, our MD-MSM results predict that ligand binding of allosterically activated CRIB-PDZ can be achieved by conformational selection. However, for the activation of unbound protein to the allosteric manifold, our calculations show that induced fit is required. Summarizing, our MD-MSM model predicts that allostery in CRIB-PDZ involves a sequence: induced fit for allosteric activation, and conformational selection for ligand binding. Kinetic Analysis. The next level of detail to consider is the rates of transitions between substates and the implications thereof. The cluster analysis above has revealed that in this system, each of the constructs {P} and {PL} exhibit two substates {PA, PC} and{PLB, PLC}, respectively. In our analysis, transitions must be considered between all of the substates, and then examined for viability. Figure 4 is a schematic diagram of all possible paths for ligand binding with and without the presence of allosteric effector. Negative log-odds scoring 34 is used to quantitate the transitions and to compare the routes for various processes. Some transitions occur with very low probability, and thus transition counts less than 20 (out of 5500) are considered within the noise level, and neglected. Similarly, less than 5% of the population of AP was found in state E, which

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Figure 4. Schematic diagram of MD-MSM states and for PDZ. The five clusters constitute the states A-C of the MSM. Each state is depicted by a schematic of its graph from Figure 3; colors are preserved. Snapshots for the four constructs were traced through the model to obtain the transitions (arrows). Counts of transition frequencies are shown above the arrows, color coded to their respective construct. Arrows representing transitions without counts are shown in grey.

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we considered negligible. In both cases, renormalization considering these exclusions was applied. Four MD-MSM paths are observed to be significant in the P → PL transition. The total score is the sum of the four scores, either in probability or log odds space. Four independent MD-MSM paths were also found for the allosteric P→AP→APL, transition. All begin with the free protein P, found in clusters A or C. Addition of the allosteric effector caused transition from P to the AP state, which for the unbound state is a transition to state D. Both D and E in the allosteric manifold have substates in which AP and the liganded state APL. Now, effective rates are calculated from the product of the probabilities for each step, and the allosteric effect can be quantified The probability of protein P to bind to ligand L in the control manifold was found to be 0.161, whereas the probability to bind ligand in the allosteric manifold P→AP→APL was found to be 0.1921. Thus, kinetic network analysis of our model predicts that PDZ protein binds to peptide ligand with a roughly twelve-fold greater probability in the allosteric route pathway as opposed the simple ligand binding route pathway. This supports positive allosteric enhancement observed for this system and distinctly captures the trend of the enhancement observed in the experimental data for CRIB-PDZ17.

Discussion This study is focused on protein-centric aspects of ligand binding and allostery, using MD to obtain a sampling of protein configuration space and construction of an MSM to elucidate the ensemble of states, substates and rates involved in the relevant conformational transitions. The method identifies positive allostery as an increase in substate overlap between the bound and unbound forms AP and APL as compared with the overlap between P and PL. Analogously, negative allostery would have been identified as an initial high overlap between P and PL decreased in the presence of the allosteric effector. A marked advantage of defining the problem in terms of constructs is that MD sampling is directed into the subspace of the protein energy landscape pertinent to allostery. Our results indicate that describing the mechanism of any protein-ligand binding or allosteric process in terms of exclusively conformational capture or induced fit may be oversimplified, a point made independently from the observed kinetics of ligand binding processes by Hammes et al. 35 The continuum of dynamically interchanging conformations in the MD described ensemble in conjunction with MSM can be used to differentiate the role of the two mechanisms. Several key ideas about ligand binding and allostery can be inferred from the results on CRIB-PDZ. An ensemble-based view of simple ligand binding suggests a

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general principle: conformational selection is possible only when bound and unbound states, P and PL, respectively have a binding competent substate in common, i.e. with minima on the free energy landscape that coincide. Otherwise, the probability of the unbound ensemble having a binding competent substate available for conformational capture will be negligible. Our results on CRIB-PDZ showed that a ligand bound state (Cluster C) involves fractional contributions from interconverting unbound and ligand bound constructs PC and PLC which indicates energy minima that coincide and enable conformational selection. Ligand binding to preferentially stabilizes C, the binding competent substates, and the corresponding increase in the Boltzmann population can be viewed as the bound state AP “capturing” structures from other substates of the unbound P state. There are several implications of the MD-MSM model that may well have general applicability. First, conformational selection, which must involve the presence of binding competent substates in an unbound ensemble, requires an average structure that does not change significantly on ligand binding. This is expected to be the case for only a small subset of allosteric proteins. In MD-MSM the interesting and provocative idea of “allostery without a change in structure” advanced by Cooper and Dryden 36,37 would be a limiting case of 100% conformational capture, since all clusters would have substates in common. Second, the lack of a substate shared between allosteric effector bound and unbound states eliminates the possibility of a conformational selection mechanism. In this case, some extent of induced fit will be required if a transition is to be made. We find from the analysis on CRIB-PDZ that there is no substate in common in transitioning from the non-allosteric to allosteric binding manifold, which leaves no opportunity for conformational selection and indicates that an induced fit will be required for allosteric activation. The allosteric AP state is formed by the allosteric effector inducing P into a fully binding competent state. Once activated, ligand binding in the allosteric manifold is able to proceed by a conformational selection mechanism. Third, the MD-MSM model indicates to us that conformational selection and induced fit are not only intuitively but formally complementary to each other. Conformational selection requires a substate of unbound and bound protein configurations that coincide on the free energy landscape, i.e. they have similar structures, whereas induced fit will be necessary for binding when there are no overlapping substates and thus no opportunity for conformational selection. Finally, from a thermodynamic perspective, both conformational selection and induced fit may contribute to mechanism, 38,39 can either be sequential or, from a statistical point of view, simultaneously. However, conformational selection is intuitively

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expected to be kinetically more facile, since a binding competent substate is intrinsically a part of the unbound conformational ensemble and need not require the time to be induced. From this vantage point, “pure” conformational selection or induced fit are limiting cases with a continuous range of fractional contributions possible, depending on the system. In the crib-PDZ system, we observed that an activation by induced fit was necessary to allow the protein to access the allosteric manifold, the domain of clusters D and E. If the system is in the allosteric manifold, the effector-bound protein and ligandbound states share both of their substates, which enables a conformational selection mechanism. The role of the allosteric effector is to induce a transition between the two manifolds, and conformational capture is then the mechanism of ligand binding in both manifolds. Recently, Steiner and Caflisch22 have reported a rigorous simulation study and free energy landscape model of ligand binding for the related protein PDZ3 using the cFEP method. The role of conformational capture in ligand binding in CRIB-PDZ is consistent with their findings22. Several recent papers have described a dependence of conformational selection and induced fit based on concentration of allosteric effector. At low allosteric effector concentration, the mechanism is expected to proceed by conformational selection, whereas at high concentration, induced fit is preferred. While our studies do not directly consider a continuous range of effector concentrations, we do address the limiting cases: low concentration of A by the effector unbound constructs P and PL (top branch of Fig. 3), and high concentration of A through the bound constructs AP and APL (lower branch of Fig.3). Our results support a conformational selection mechanism at low effector concentration, and induced fit at high effector concentration. Interestingly, the AP and APL had considerably more conformational overlap than P and PL, and the conformations involved were distinct in the two regimes. We are pursuing the generality of these observations over a range of allosteric systems, including those with both large and small conformational changes, small proteins, large proteins, and intrinsically disordered. While one cannot speculate on the relative contribution of conformational selection and induced fit strictly by inspection, we do know ensemble dynamics is common to all biomolecules. In the kinetics of allostery increased binding affinity for the ligand originates from a coincidence of substates in the presence of the allosteric effector, and is reflected in the scoring (Table S1). In the absence of allosteric effector, the free protein adopts binding competent conformations in PC for about 35% of the conformations, whereas after activation by the effector, both substates of AP are binding competent, namely APD with APLD and APE with APLE. In the presence of the allosteric effector, AP is binding competent no matter which substate it adopts. Notably, Nussinov and co-workers propose that allosteric signal transmission might occur via a sequence of induced fit and conformational selection events40 and is supported by recent experiments41,42. Our results support this idea, since we propose that 13



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these two basic mechanisms are the only two possibilities that are involved in any noncovalent interaction, either intermolecular or intramolecular. This mechanism would generally be expected to attenuate with distance, whereas long range allosteric communication may involve binding sites ~100 Å or more. There is always the possibility that allostery in some systems may occur when an effector ligand simply induces some perturbation of the free energy landscape that modulates a functional interaction.

Conclusions Our MD-MSM results on CRIB-PDZ support a positive allosteric effect, consistent with experimental observations. Analysis from ensemble based perspective resolves clearly the complementary contributions from MWC conformational selection and KNF induced fit. The idea that allostery may involve both conformational selection and induced fit may transcend the debate over whether the mechanism is one or the other. The MD-MSM approach in principle introduces a theoretical methodology that can be used to assess the nature of allostery in any system. Note also that induced fit and conformational selection refer to general aspects of ligand binding and might well be referred to as “semi-molecular.” The detail of exactly which specific interactions are mechanistically involved in either case would be required to complete the picture at the molecular level.

Supporting Information Table S1. Scoring of Allosteric and Non-Allosteric binding pathways. The four major pathways representing P->PL (A) and the four major pathways representing P->AP>APL (B) were considered. The paths are indicated in the headers and correspond to paths through the model in Figure 4. The probabilities for a protein to be in a state are taken from Figure 3, and the transition probabilities are taken from the normalized transition probabilities reported above the arrows for the respective transitions in Figure 4. Scores are computed both in percentage space (as the product of events) and in log odds space. The totals are the sum over the four paths for the respective binding processes. The total percentage for binding in the case of the allosteric effector (B) is approximately 12-fold greater than the percentage without the allosteric effector (A).

Acknowledgement 14


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The authors wish to thank Stephen C. Harvey for a critical reading of the manuscript. Technical assistance with high performance computing from Henk Meij is gratefully acknowledged. We thank Wesleyan University for computer time supported by the NSF under grant number CNS-0619508 and CNS-0959856. This work was supported by the molecular biophysics training grant NIH/NIGMS 5 T32 GM008271.

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Molecular DynamicsâMarkov State Model of Protein Ligand Binding

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