Consequences of Energetic Frustration on the Ligand-Coupled

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Consequences of Energetic Frustration on the Ligand-Coupled Folding/Dimerization Dynamics of Allosteric Protein S100A12 Weitong Ren, Wenfei Li, Jun Wang, Jian Zhang, and Wei Wang J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b06919 • Publication Date (Web): 25 Sep 2017 Downloaded from http://pubs.acs.org on September 26, 2017

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The Journal of Physical Chemistry

Consequences of Energetic Frustration on the Ligand-Coupled Folding/Dimerization Dynamics of Allosteric Protein S100A12 Weitong Ren†, Wenfei Li*†, Jun Wang†, Jian Zhang†, and Wei Wang*† †National Laboratory of Solid State Microstructure, Department of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China.

ABSTRACT: Allosteric proteins are featured by energetic degeneracy of two (or more) functionally relevant conformations, therefore their energy landscapes are often locally frustrated. How such frustration affects the protein folding/binding dynamics is not well understood. Here, by using molecular simulations we study the consequences of local frustration in the dimerization dynamics of allosteric proteins based on a homodimer protein S100A12. Despite of the structural symmetry of the two EF-hand motifs in the three-dimensional structures, the S100A12 homodimer shows allosteric behaviors and local frustration only in half of its structural elements, i.e., the C-terminal EF-hand. We showed that such spatially asymmetric location of frustration leads to asymmetric dimerization pathways, in which the dimerization is dominantly initiated by the inter-chain binding of the minimally frustrated Nterminal EF-hands, achieving optimal balance between the requirements of rapid conformational switching and inter-chain assembling to the energy landscapes. We also showed that the local frustration, as represented by the double-basin topography of the energy landscape, gives rise to multiple cross-linked dimerization pathways, in which the dimerization is coupled with the allosteric motions of the C-terminal EF-hands. Binding of metal ions tends to reshape the energy landscape and modulate the dimerization pathways. In addition, by employing the frustratometer method, we showed that the highly frustrated residue-pairs in the C-terminal EF-hand are partially unfolded during the conformational transitions of the native homodimer, leading to lowing of free energy barrier. Our results revealed tight interplay between the local frustration of the energy landscape and the dimerization dynamics for allosteric proteins.

Introduction Protein association and recognition play fundamental roles in biological processes 1. By association, proteins may change their structures and dynamics, which are crucial for regulating the downstream cascades of biological events. Previously, studies showed that binding of two identical protein chains from a homodimer is governed by a funnelled energy landscape 2-7 and the native topology largely determines the dimerization mechanism 4, indicating that the energy landscape of dimerization has minimal frustration as shown in protein folding 8. Particularly, depending on the interfacial topology of the homodimer, the two chains can bind either through a folded intermediate or following a two-state mechanism in which the folding and binding are tightly coupled 4-7. For these homodimers studied previously, their unique native structures correspond to the most stable states. However, the situation is quite different for the allosteric proteins which can change their conformations upon the binding of a ligand or protein. In the allosteric proteins, two or more conformational states have comparable stabilities, and the rapid transitions among these conformational states are crucial for their functions 9-11. Recent studies showed that the interactions of the allosteric proteins are often locally frustrated 1215 because the requirements of rapid conformational switching and structural assembling to the energy landscapes are not always consistent. Such local frustration facilitates the functions of the allosteric proteins by reducing the energy barrier of conformational switch or by maintaining the balanced binding specificity and affinity 14, 16. In addition, local frustration often adds new complexities to the folding dynamics of proteins 17-19. Despite of its significant biological implications 15, the question of how such local frustration arising from the allostery requirement contributes to the assembling dynamics of allosteric proteins remains elusive. In this work, we investigated the binding of allosteric proteins based on molecular simulations for protein S100A12, with particular focus on the consequences of local frustration in the dimerization dynamics. S100A12 is a member of Ca2+-binding EF-hand superfamily 20-21 and is involved in a number of key cell processes, including inflammation, host-parasite responses, and so on 22-24. Experimental observation showed that changes in the concentration of Ca2+ can modify the oligomeric state of S100A12 25, which in turn modulates its transportation and interaction with the related extracellular targets. The S100A12 monomer has two EF-hand motifs, and each motif contains one Ca2+ binding site (Figure 1C). The two EFhands are spatially arranged with high symmetry in the native structure of the homodimer. Similar to another well-known Ca2+binding EF-hand protein Calmodulin 26, the S100A12 is a typical allosteric protein. Ca2+ binding can trigger the conformational transition from a closed state to an open one, exposing the hydrophobic region of S100A12 for binding with its downstream target proteins. Different from Calmodulin, for which both the EF-hand motif of the two domains can transit between open and closed conformations 26, the allosteric motions of S100A12 mainly occur at the C-terminal EF-hand (i.e., the canonical EF-hands) of each monomer, whereas the N-terminal EF-hands (i.e., the pseudo EF-hands) always stay at the open conformation regardless of the Ca2+ binding states (Figure 1A,B). Such structurally symmetric arrangement of the two EF-hand motifs with asymmetric locations of the

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allosteric regions (only at the C-terminal EF-hands) make the S100A12 a perfect model system to investigate the effects of the local frustration and the relevant allosteric behavior in protein dimerization.

Figure 1. (A) Three dimensional structure of S100A12 homodimer at closed/apo (left, PDB code: 2WCF) and open/holo (right, PDB code: 1ODB) states. The N-terminal pseudo EF-hand and the C-terminal canonical EF-hand are colored by yellow and red, respectively. The two calcium ions are represented by spheres in purple and pink, respectively. Two zinc ions are colored in wheat. (B) Schematic of the secondary structure arrangement of S100A12 monomer.

By conducting molecular dynamics (MD) simulations using an atomic-interaction based coarse-grained model (AICG) 27-28, we studied the dimerization dynamics of the S100A12. Due to the degeneracy of the open and closed conformations of the C-terminal EF-hands in the native state of the homodimer, the related local energy landscapes can be described by a double-basin topography, which represents energetic frustration arising from allosteric requirement. Whereas, the local energy landscapes of the N-terminal EF-hands are well funneled and centric to a unique native conformation. Meanwhile, by using the frustratometer method 29-30, we showed that the interactions in the C-terminal EF-hands are much more frustrated than those in the N-terminal EF-hands. Such spatially asymmetric distribution of local frustrated interactions leads to the asymmetry of the binding pathways, in which the dimerization dominantly initiates by the binding of the minimally frustrated N-terminal EF-hands, although the EF-hands are arranged with high symmetry in the three dimensional structure, simultaneously meeting the requirements of rapid allosteric motions and inter-chain assembling. We also demonstrated that the double-basin topography of the local energy landscapes of the C-terminal EF-hands results in multiple cross-linked dimerization pathways, in which the dimerization is coupled with the allosteric motions of the C-terminal EF-hands. Binding of Ca2+ reshapes the double-basin energy landscape, which in turn modulates the most probable dimerization pathway. In addition, we revealed the strong correlation between the local frustration of the C-terminal EF-hands and the local unfolding (cracking) during the conformational transitions. Our results provide new insights into the complex interplays between the allosteric features of the energy landscape and the protein dimerization dynamics.

Material and Methods Coarse-grained Modelling of S100A12 Dimerization. In this work, each residue of the S100A12 homodimer was coarsegrained into one spherical bead locating at the Cα position. The interactions between the residues were described by the AICG2+ energy function 28

|

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which includes the bond potential ( ), the flexible local potential ( ), the structure-based local potential ( ), the struc ture-based nonlocal potential (

), and the excluded volume potential ( ). The details of the above terms are described in the Supporting Information. Compared to the conventional structure-based model 31, the strengths of the local and nonlocal native interactions in the AICG2+ model were optimized based on atomic interactions by using multiscale strategy, therefore are sequence dependent 27-28. In addition, the flexible local potential, which was derived by statistical survey to the coil library 32, considered the secondary structure propensity and chain flexibility, by which the unfolded conformations can be more reasonably described.

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In describing the conformational changes of the S100A12, the two AICG2+ energy functions centric to the open and closed structures were interpolated smoothly to construct the energy function with a double-basin topography following the scheme developed by Okazaki and coworkers 33, which is given by

∆ − 2

! − − ∆ " ∆# 2 2 #

where and are the AICG2+ potentials constructed based on the S100A12 crystal structures corresponding to the open 34 (with PDB entry 1ODB) and closed 25 (with PDB entry 2WCF) conformations. In this work, the above double-basin energy function is used for the two monomers and their interface separately. The parameter $ controls the relative stability of the two conformational states. In this work, the $ values of the two monomers were 2.5kcal/model and 2.0kacal/mol, respectively, with which the closed conformation of the homodimer has a major population (~85.0%) in the C-terminal EF-hands without Ca2+ binding. For the interface, the $ value was set as 0. The effects of Ca2+ binding on the shape of the double-basin energy landscape were modelled by an implicit ligand binding model 35, allowing for the description of protein motions on a dynamic energy landscape. In this model, the Ca2+ was not considered explicitly. Instead, the effect of Ca2+ binding was modelled by additional interactions between the liganding residues in the binding site. The binding sites of each Ca2+ were identified by software LigPlot 36-37 based on the crystal structure of the open conformation 34 (PDB code: 1ODB). For the N-terminal pseudo EF-hands, the Ca2+ is mainly chelated via backbone carbonyls, whereas the canonical EF-hand binds Ca2+ mainly via sidechain carboxylates or carbonyls (Figure S12). The contribution of the Ca2+ binding to the overall potential energy is given by Ca2+ binding mediated contacting interactions with the following energy function

%& %'

(

%' 3&% %4

#

./0 − ./0 ! −) *+, 2 3 21 #

where ) is the strength of the ligand mediated interactions. 1 represents the width of interactions for the ligand-mediated contacts and was set as 0.15 Å. ./0 is the distance of ligand-mediated contact between residue I and J in the open state. The binding and unbinding transitions were simulated by Monte-Carlo algorithms. Ligand binding was assumed to be diffusion limited and occurred with the rate given by 6 [Ca2+], where 6 is the rate constant and [Ca2+] is the calcium concentration. In the simulation, the product 6 [Ca2+], as a whole, is the input parameter. By matching the experimental dissociation constant of [Ca2+] binding 20, we can roughly determine the corresponding [Ca2+] (Figure S13). Ligand dissociation rate is dependent on the binding energy of the Ca2+ exponentially. The strength of the ligand mediated interactions for the C-terminal EF-hands is set as 1.16 kcal/mol, with which the open conformation of the homodimer has majority populations (~85.0%) in the C-terminal EF-hands with saturated Ca2+ concentration. The strength of the ligand mediated interactions for the N-terminal EF-hands is set as 0.39 kcal/mol to reproduce the much weaker binding affinity 25. In addition to the Ca2+, two Zn2+ can also bind to the interface of the two monomers. We also simulated the Zn2+ binding using the similar model. Our results showed that binding of Zn2+ can significantly increase the Ca2+ binding affinity (Figure S12), namely, there exists cooperativity between the binding of two kinds of metal ions, which is in line with experimental observations 20. Simulation Details. All the simulations in this work were conducted by Langevin dynamics with friction coefficient γ=0.25. CafeMol2.1 was used for the simulations 38. The three-dimensional structures of the S100A12 taken from the Protein Data Bank (PDB codes: 2WCF and 1ODB) were used as reference structures to build the double-basin model 25, 34. We performed equilibrium simulations under different concentrations of metal ion around the folding temperature Tf (362K) of S100A12. The two chains of the S100A12 were encapsulated within a sphere space with the radius of 3.5, 4.5, and 5.5 nm, respectively. For each case, we carried out multiple trajectories lasting for 4 × 10: MD steps to get efficient sampling of the binding/unbinding events. To explore the dimerization pathway of S100A12, we conducted the simulations at 0.95Tf (345K). Under each concentration of Ca2+, we conducted 200 trajectories initiated from random unfolded structures with the two monomers being well separated. Moreover, we performed equilibrium simulations of the conformational transitions at 0.95Tf to study the role of local frustrations on the allosteric motions of S100A12 homodimer. All the plots were drawn by Matplotlib 39. The protein structures were visualized by PyMOL 40.

Reaction Coordinates. In describing the structural features of the conformational states involved in dimerization of the S100A12, we used the fraction of native contacts (; value) as reaction coordinates. According to the various features, different ; values were used, including the ; (or ; ) which represents the ; value with respect to the native structure of the homodi< < mer at the holo (or apo) state, the ;% 4 (or ;% 4 ) which represents the ; value of the intra-chain contacts (or inter-chain con< < tacts), and the ;=>=> (or ;=?=? ) which represents the ; value for the contacts between the two H1 helices (or H4 helices). In describing the conformational transition of the S100A12 homodimer, we used the reaction coordinate @ given by the double-basin model 33. The negative (or positive) value of the @ represents the open (or closed) conformation.

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Results and Discussion Free Energy Landscape of Folding Coupled Dimerization. The simulations of the S100A12 dimerization were performed by using an integrated computational model developed recently for modelling the interplay among ligand binding, protein folding, and allosteric motions of proteins 27-28, 41 (See Methods section for more details). In this model, funnel-shaped energy landscapes are described by the AICG2+ model, which captures the sequence and topological information based on the perfect funnel approximation, and was shown successful in modelling the folding of topologically complex proteins 27. The double-basin feature of the energy landscape, which is the key essential of the allosteric proteins, is modelled by interpolating the two AICG2+ energy functions with the open and closed conformations, respectively, being used as the reference structures, by employing the scheme developed in a previous work 33. In addition, the effects of ligand binding on the shape of the multi-basin energy landscape were modelled by an implicit ligand binding model 35, allowing for the description of protein motions on a dynamic energy landscape modulated by the Ca2+ binding. Based on the above model, we first performed equilibrium simulations for the folding of the S100A12 monomer at the folding temperature with 0 µM and 20.0 µM Ca2+ concentrations. As shown in Figure 2A,B, the S100A12 monomer hops between three conformational states, namely, the unfolded state, the open state, and the closed states. The stability of these states depends on the Ca2+ concentrations. Higher concentrations tend to stabilize the open conformation and destabilize the unfolded and closed conformations (Figure 2C,D). Such results are consistent with previous work for another allosteric protein Calmodulin 28.

Figure 2. (A, B) Representative folding/unfolding trajectories of S100A12 monomer at calcium concentration of 0 (A) and 20.0 µM (B). The red, green and blue dots represent the snapshots of the unfold state, closed state and open state respectively; (C, D) Two-dimensional

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free energy surfaces of S100A12 monomer folding along the reaction coordinates ; and ; at calcium concentration of 0 (C) and 20.0 µM (D); (E, F) Two-dimensional free energy surfaces of S100A12 dimerization along the reaction coordinates ; and ; at calcium concentration of 0 (E) and 20.0 µM (F). The simulations were conducted at the folding/binding transition temperatures at which reversible conformational transitions can be observed. The free energy landscape basins shown in panel (E) were labelled according to the structural features of the sampled conformations (See text for more details).

We then performed equilibrium simulations for the dimerization of the S100A12 monomers. The two monomers are confined in a spherical space with various sizes. We can observe reversible binding/unbinding transitions (Figure S1), with which we constructed the free energy landscape. Compared to the monomer folding, the dimerization showed much more complicated free energy landscape (Figure 2E,F). In addition to the fully unstructured conformations and the native homodimer conformations (either open or closed), one can observe four additional basins with significant populations in the free energy landscape (Figure 2F), which correspond to the metastable states encountered during dimerization. To get more insights into the structural features of the metastable states, we calculated the formation probabilities of the native contacts based on conformations sampled in each of the seven free energy basins in Figure 2E,F. The obtained contact maps are shown in Figure 3A and S2, in which the upper (or the lower) triangle shows the formation probabilities of the native contacts in the closed (or the open) state. The representative structures of the metastable states are shown in Figure 3B. According to the structural features of the two chains and their interface inferred from the contact maps, these conformational states corresponding to each of the seven basins in the free energy landscape can be represented by three-letter acronyms composed of “O” (open), “C” (closed), “I” (partially formed interface), “F” (fully formed interface) and “U” (unstructured), respectively. Hereafter the “O” and “C” refer to the conformational states of the canonical EF-hands since the pseudo EF-hands always stay at the open conformation. For example, “CIU” represents a conformation in which two chains are in closed and unstructured conformations, respectively, and the interface is partially formed. Consequently, the seven basins shown in Figure 2E,F can be denoted as “UUU”, “UIU”, “CIU”, “OIU”, “CFC”, “CFO”, and “OFO”, respectively. The contact maps given in Figure 3A correspond to the metastable states “UIU”, “CIU”, and “OIU”, respectively. Here, the “UIU” represents the first metastable state encountered during dimerization. In this state, the intra-chain contacts between the helices of the monomers remain unformed, although the four helices are structured to a large extent (Figure 3A, left panel). However, the inter-chain contacts between the H1 helices are well formed, suggesting that the H1 helices of two monomers tend to interact with each other at the very beginning of dimerization, act as an “anchor” to bring the two separated monomers together. Surprisingly, in spite of the symmetry in the native structure of the S100A12 homodimer, the opposite pathway, in which the H4 helices bind first, is seldom observed, showing asymmetric dimerization pathways. This behavior will be discussed in more detail later.

Figure 3. Structural features of the metastable states encountered during dimerization. (A) Formation probabilities of the native contacts of the closed (upper triangle) and open (lower triangle) states for the three metastable states, “UIU” (left), “CIU” (middle), and “OIU” (right), respectively; (B) Representative structures of the three metastable states. To be consistent with previous text, the pseudo and canonical EFhands are colored yellow and red respectively. The N-terminal residues and C-terminal residues were represented by purple and cyan beads, respectively.

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Apparently, the dimerization landscape of the S100A12 shown above is much more complicated than that of the homodimers studied previously which have only one unique bound conformation 4-6. According to the work in Ref 4, two identical chains can bind either through one folded intermediate or with a cooperative two-state process, depending on the interface topology of the native homodimers. The observation of inter-chain contacts before the folding of the monomers suggests that the binding and monomer folding are tightly coupled for the S100A12. The tight coupling is also supported by the relatively condensed interface con

tacts and the diagonal shape of the free energy landscape projected onto the reaction coordinates ;% 4 and ;% 4 (Figure S3 and S4). Differently, instead of a two-state cooperative transition, the dimerization of the S100A12 encounters several states, which are mostly arising from the double-basin topography of the energy function intrinsic to the allosteric proteins. Such results suggest that the local frustration, as represented by the double-basin topography of the energy landscape in the allosteric proteins, tends to introduce additional complexity to the dimerization dynamics. Cross-linked Multi-route Dimerization and Ca2+ Binding Induced Pathway Modulation. Ligand binding often modifies the intrinsic energy landscape of allosteric proteins, leading to dynamic energy landscape. To investigate the dimerization pathways and the effects of metal binding, we performed dimerization simulations of the S100A12 starting from fully unstructured conformations at temperature lower than the folding temperature (0.95Tf). For each Ca2+ concentration, we conducted 200 trajectories lasting for 5 × 10B MD steps with the two chains confined in a spherical space with the radius of 3.5nm. We then assigned each of the snapshots of a simulation trajectory to the states identified in Figure 2E and 2F, with which we can construct the dimerization pathways (Figure 4). We also conducted similar simulations with the two chains confined within the spherical space of different sizes, and the results are shown in Figures S5 and S6.

Figure 4. Pathways of S100A12 dimerization with the calcium concentrations of 0 (A), 20.0 µM (B), and 200.0 µM (C) at temperature of 0.95Tf with the open conformation being used as the final state of the dimerization. The metastable states are represented by three-letter acronyms. The probabilities of the pathways are represented by line breadth and percentage numbers, and different pathways are represented by arrow lines with different colors. Only the four most probable pathways are shown.

Figure 4 shows the four most probable dimerization pathways at different Ca2+ concentrations, which are represented by the arrowed lines with different colors. In constructing the dimerization pathways, the homodimer with open conformation was set as the final state of the dimerization. The results with closed conformation being set as the final state are shown in Figure S7. Obviously, the dimerization of S100A12 follows multiple routes. These routes are cross-linked, forming a kinetic network. Particularly, the dominant dimerization pathways are different for the Ca2+ concentrations of 0 µM, 20.0 µM and 200.0 µM. At low Ca2+ concentration of 0 µM, the pathway “UUU”→“UIU”→“CIU”→“OFU”→“OFO” is dominant. In comparison, at Ca2+ concentration of 200.0 µM, the pathway “UUU”→“UIU”→“OIU”→“OFO” is dominant. Such results demonstrate that the binding of Ca2+ modulates the dominant dimerization routes. Interestingly, even at high (or low) Ca2+ concentration, in which the energy landscape favors the open (or closed) conformation, the dimerization pathways via an intermediate with one of the monomer adopting a closed (or open) conformation have significant populations. For example, at high Ca2+ concentration, the “UIU” state can proceed with one of the monomer folding to the closed conformation “CIU”, then it transits to the open conformation “OIU”, which is followed by the folding of the other monomer to the open conformation “OFO”. In addition, at both the low and high Ca2+ concentrations, the dimerization pathways may involve a hybrid intermediate “OFC”, in which one chain is in the closed state and the other chain is in the open state. Obviously, such cross-linked multi-route feature of the dimerization processes are the results of the double-basin topography of the energy landscape of allosteric proteins and is distinct from the two (three)-state binding/unbinding transitions of the proteins with unique native structures (4-6). These results suggest that the functional constraint to realize rapid allosteric motions is not fully consistent with the requirement for rapid dimerization, and such frustration adds new complexities to the dimerization dynamics, rendering the dimerization a cross-linked multi-route processes.

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Local Frustration of the Allosteric Energy Landscape Induces Asymmetry in Dimerization Pathways. From the contact maps shown in Figure 3A, the inter-chain contacts between the H1 helices are mostly formed in the “UIU” state. In comparison, the inter-chain contacts between the H4 helices are seldom formed in this state. Therefore, the dimerization tends to initiate by the packing of the two H1 helices locating at the N-terminal EF-hand. At the final stage of dimerization, the two H4 helices associated together and lock the native homodimer conformation as a latch. More detailed analysis demonstrated that the pathways initiating by binding of the two H1 helices account for the majority of the dimerization pathways, although the two EF-hands in each of the monomers are spatially arranged with high symmetry in the native structure of the S100A12 homodimer. Consequently, the opposite pathways initiating by the binding of the two H4 helices are very rare (=> and <

< < ;=?=? , which shows that conformations with high ;=?=? and low ;=>=> are rarely populated (Figure 5B). Considering the symmetric arrangement of the two EF-hand motifs in the three-dimensional structure of the S100A12 homodimer, it is surprising to observe the highly asymmetric dimerization pathways. Therefore, it is important to further investigate the relation between the energetics and asymmetry of the dimerization pathways. In the current computational model, the local frustration can be represented by two aspects, i.e., the double-basin topography of the energy landscape 15 and the sequence dependence of the interactions which shows that the contacting interactions between the residue pairs specific to one of the functional states are much weaker than those shared by different functional states (Figure S8) 13. As a control, we first conducted simulations with the single-basin Go model 31, in which both the double-basin topography and the sequence dependence of the interactions are omitted. One can see that with the single-basin Go model, the probability of the dimerization pathways initiating by the binding of the H4 helices has significant populations (~30%, the green bars in Figure 5A), leading to roughly symmetric populations of the dimerization pathways (Figures S9 and S11). The remaining bias of the dimerization pathways with the single-basin Go model is resulted from the slightly more condensed native contacts between the N-terminal EFhands than those between the C-terminal EF-hands (Figure S10). We also conducted simulations with the single-basin AICG2+ potential which considered the sequence dependence, therefore the allosteric feature, of the interactions. The resulted probability of the dimerization pathways is between those of the double-basin AICG2+ potential and the single-basin Go model (~10%, blue bars in Figure 5A), suggesting that both aspects of the local frustration of the allosteric proteins contribute to the asymmetry of the dimerization pathways, with the contribution from sequence dependence of the interaction strengths dominated. Particularly, several exceptionally strong inter-chain contacts between the H1 and H2 helices have significant contribution to the asymmetry of the binding pathways (Figures S8 and S10).

Figure 5. Asymmetry in the dimerization pathways. (A) Probabilities of the pathways initiated by the association of the two H4 helices with the double-basin AICG2+ potential (red bars), the single-basin AICG2+ potential (blue bars), and the single-basin Go potential (green bars) at temperatures of 310K, 320K, and 330K; (B) Two-dimensional free energy surfaces of S100A12 dimerization along the reaction

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< < coordinates ;=>=> and ;=?=? at the folding temperature; (C) A representative trajectory of the backtracking event plotted in the conforma< < < < tional space formed by the reaction coordinates ;=>=> and ;% 4 (blue) and by the reaction coordinates ;=?=? and ;% 4 (red); (D) Probabilities of the trajectories with the two H4 helices associated first (green bars) and the probabilities of the backtracking events for these trajectories.

As the N-terminal EF-hand has nearly identical conformations in the apo and holo homodimers, the energy landscape of the Nterminal EF-hands is well funneled in the current model framework. Such funneled energy landscape, together with the stronger inter-chain interactions, guide the two H1 helices to quickly form the most stable conformation once encountered, leading to a relatively long-lived metastable state, which is crucial for the subsequent dimerization steps. In comparison, due to the frustration in the C-terminal EF-hands, it takes much longer time to find the most stable conformation of the two H4 helices after their encountering as indicated by the high free energy of the conformations locating at the bottom-right corner of Figure 5B. Quite often, the two H4 helices break up before its further dimerization (Figure 5C,D). Such a process is very similar to the backtracking events observed in the folding of other topologically complex proteins 27, 42-43. Consequently, the dimerization events initiated by the association of the two H4 helices are much less probable compared to the two H1 helices, leading to asymmetry of dimerization pathways. Therefore, the asymmetry in the dimerization pathways is resulted from the asymmetric location of frustration in the N-terminal EF-hands and the C-terminal EF-hands. It is reasonable to believe that the coexistence of the pseudo EF-hands and the canonical EF-hands in the S100 family proteins is the results of comprise between the requirements of rapid association and allosteric motions. Cracking and Local Frustration in Allosteric Motions of S100A12 Homodimer. The local frustration of the C-terminal EFhands can also be demonstrated by the “frustratometer” results. Using the methods developed by Ferreiro and coworkers 29-30, we identified the residue pairs with high frustration (Figure 6A,B). One can see that the C-terminal EF-hands show much more significant frustration compared to the N-terminal pseudo EF-hands. Particularly, the frustration is mostly focused on the H3 helices. Such local frustration around the residues involved in the conformational motions are the common features of the allosteric proteins, as demonstrated in Ref 44-47. To investigate how such local frustration contributes to the conformational changes of the S100A12 homodimer, we conducted equilibrium simulations at 0.95Tf to sample the reversible open-closing conformational motions. Our results show that during the conformational changes, the C-terminal EF-hand involves significant cracking events (local unfolding), as demonstrated by much larger root mean square fluctuations around the C-terminal EF-hand region, especially around the H3 helices (Figure 6C). We also calculated the average number of the formed native contacts involving the H3 helices as a function of the reaction coordinate χ (Figure 6C, see the Methods for the definition of χ.). We can see that the native contacts involving the H3 are broken to a large extent around the transition state region of the conformational change, supporting the cracking events (red lines in Figure 6D). For comparison, we also showed the average number of the native contacts involving the less frustrated H2 helices, which remain structured well throughout the conformational transition (blue lines in Figure 6D). Early studies of conformational transition of adenylate kinase revealed that such cracking events can significantly reduce the free energy barrier of the conformational motions by increasing the conformational entropy around the barrier region, therefore speeding up the conformational transitions 44-46, 48-49. Subsequent experimental data supports the role of the cracking on the conformational changes of the proteins 50-52 . As a control, we performed additional simulations with the native contacts in the H3 helices being constrained with a harmonic potential to prevent the H3 helices from partial unfolding. As expected, constraining the H3 helices significantly elevate the free energy barrier of the conformational transition of the S100A12 homodimer (Figure 6E), suggesting the importance of the cracking to the conformational transitions of the S100A12 homodimer. Such results clearly demonstrate the tight interplay between the local frustration and the allosteric motions.

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Figure 6. Local frustration and cracking. (A, B) Residue pairs with maximal (blue) and minimal (grey) frustration identified by the frustratometer method plotted in the closed (A) and open (B) conformations; (C) The fraction of native contacts (; value) involving the H3 helices (red) and that involving the H2 helices (blue) as a function of the reaction coordinate @ at the calcium concentration of 0 (dashed lines) and 20.0 µM (solid lines); (D) Root mean square fluctuations of the residues at different stage of the conformational transition. Black and white colors represent high and low fluctuations, respectively. (E) Free energy surface of the conformational transitions along the reaction coordinate @ with (blue) and without (red) restraints to the H3 helices.

Conclusion In summary, we investigated the interplay between the local frustration and protein dimerization dynamics of typical allosteric protein S100A12. Our results showed that the local frustration, as represented by the double-basin topography of the energy landscape, adds new complexities to the dimerization dynamics of the allosteric proteins, rending the dimerization of allosteric proteins a cross-linked multi-route process, which can be further modulated by the binding of Ca2+. We also showed that the spatially asymmetric location of the local frustration along the two EF-hands leads to the asymmetry in the dimerization dynamics although the two EF-hands are arranged symmetrically in the three-dimensional structure of the homodimer. The initialization of dimeriza-

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tion by the binding of the EF-hand motifs with minimal frustration ensures rapid inter-chain recognition, achieving optimal balance between the seemly conflicting requirements from structural assembly and allosteric motions. In addition, by employing the frustratometer method, we demonstrated that the residue pairs with maximal frustration tend to be partially unfolded during the conformational transition of the S100A12 homodimer, which contributes to the lowing of the free energy barrier of the allosteric motions. Our results provide new insights into the interplay between the local frustration of energy landscape, allostery, and protein dimerization dynamics.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. Details of the simulations; Figure S1Figure S13 (PDF) .

AUTHOR INFORMATION Corresponding Author * [email protected] or [email protected]

ACKNOWLEDGMENT The authors thank Shoji Takada for discussions. This work was supported by the National Natural Science Foundation of China (Nos. 11334004, 11574132, 11274157) and the High Performance Computing Center of Nanjing University.

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Consequences of Energetic Frustration on the Ligand-Coupled

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