Exploration of Multistate Conformational Dynamics upon Ligand

Jan 31, 2018 - HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase) is a monomeric protein with 158 residues, which undergoes large-scale confor...
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Exploration of Multistate Conformational Dynamics upon Ligand Binding of a Monomeric Enzyme Involved in Pyrophosphoryl Transfer Lingci Zhao,†,‡ H. Peter Lu,§ and Jin Wang*,†,‡,⊥ †

College of Physics, Jilin University, Changchun, Jilin 130012, People’s Republic of China State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People’s Republic of China § Center for Photochemical Sciences, Department of Chemistry, Bowling Green State University, Bowling Green, Ohio 43403, United States ⊥ Department of Chemistry and Physics, State University of New York, Stony Brook, New York 11794-3400, United States ‡

S Supporting Information *

ABSTRACT: HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase) is a monomeric protein with 158 residues, which undergoes large-scale conformational changes between apo, open, and holo states responding to ligand binding for its function. It has been explored widely as an excellent target for potential antibacterial drug development. However, little is known about how conformational dynamics between the native states influences the substrate recognition and the functionality of enzymatic catalysis. Here, we report a coarsegrained triple-basin structure-based model upon ligand binding to describe such multiple-state system by the molecular dynamics simulation. With our model, we have made theoretical predictions that are in good agreement with the experimental measurements. Our results revealed the intrinsic conformational fluctuations between apo and open states without ligand binding. We found that HPPK can switch to the activated holo state upon the ordered binding of the two ligands (ATP and HP). We uncovered the underlying mechanism by which major induced fit and minor population shift pathways coexist upon ligand binding by quantitative flux analysis. Additionally, we pointed out the structural origin for the conformational changes and identified the key residues as well as contact interactions. We further explored the temperature effect on the conformational distributions and pathway weights. It gave strong support that higher temperatures promote population shift, while the induced fit pathway is always the predominant activation route of the HPPK system. These findings will provide significant insights of the mechanisms of the multistate conformational dynamics of HPPK upon ligand binding.

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INTRODUCTION Biomolecules are generally not static three-dimensional structures, but can adopt multiple conformations. More and more enzymes carrying out functions have been revealed to be accompanied by large scale conformational changes.1 Although the role of conformational dynamics in the chemical aspects of enzymatic reaction is still a matter of open debate, it is obvious that the multistate conformational transitions are critical for enzymatic catalysis because of the conflicting structural requirements in different stages of the catalytic cycle.2,3 Understanding the process of large scale conformational dynamics is crucial for unraveling the biological functions, especially the enzymatic catalysis. To reach the optimal catalytic efficiency, enzymes are required to maintain fast fluctuations between different unique conformational states. For example, an unbound enzyme must adopt an open conformation to allow its reactants to enter its active site to form a Michaelis complex. © XXXX American Chemical Society

Subsequently, a closed conformation is needed for the formation of precise catalytic geometry to maximize the functional stabilization and prevent side reactions. These conformational changes can happen without any partners and be derived from intrinsic fluctuations,4−6 or can be induced by the binding of other biomolecules, such as proteins7 and nucleotides.8 This is a subject that has attracted much attention recently for exploring the relationship between conformational dynamics and enzyme catalysis, particularly the interplay between functional dynamics and ligand binding. However, it is still a challenge to experimentally obtain global functional dynamics at high resolution. On the other side, theorists put great efforts into modeling conformational changes to trace the Received: December 21, 2017 Revised: January 30, 2018 Published: January 31, 2018 A

DOI: 10.1021/acs.jpcb.7b12562 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Figure 1. The free energy landscapes and schematic representation of the conformational dynamics of HPPK upon ligand binding. Free energy is shown as a function of RMSDa and RMSDo.The picture on the top left corresponds to the free form of HPPK, which interconverts rapidly between the open and apo states. On the top right is shown the conformational dynamics between three native states of HPPK upon ligand binding. The monomeric protein contains four α helices and six β strands, and the three flexible loops are colored red and labeled on the native structures. The loops act as the characteristic fingers to cover and expose the rigid palm, which consists of the rest of protein. The ligands introduced in our model contain ATP and HP, and the ligand−protein contacts are extracted from the holo native structur e(1Q0N) .To describe the conformational dynamics upon the ligand binding, the induced fit and population shift are the two essential mechanisms. For the former case, the apo state of HPPK changes into the holo form directly (the black arrows, A→H); for the latter case, HPPK arrives at the holo basin through the open basin (the orange arrows, A→O→H).

theoretical efforts have been made to investigate the functional dynamics near the bottom of the funneled landscape using the coarse-grained structure-based models, including the microscopic,9,10 macroscopic,11−13 and mixed contact map4−7 models. These models, with the reduction of degrees of freedom and the consequent extension of accessible time scales, have been proven successful to explore the kinetic and

dynamics of proteins at the atomistic scale in recent years. But it is rather difficult for computational explorations of large scale conformational transitions in all-atom details having in mind that the time scale of the conformational changes of the medium sized proteins are often on the order of subseconds to minutes, while that of the molecular dynamics simulations are on the order of microseconds. An increasing number of B

DOI: 10.1021/acs.jpcb.7b12562 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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Figure 2. The effects of ligand binding on thermodynamics with increasing εHP from 0.0 to 1.0. The free energy surfaces are shown in the twodimensional space of RMSDo and R89−116. (a) εHP = 0, εATP = 0.0. There are two free energy minima without ligand binding. One corresponds to apo state at (2.3,0.36), the other corresponds to open state at (3.1,0.18). (b−e) εHP = 0.4, 0.6, 0.8, and 1.0 and εATP = 0.3. There is a free energy minimum corresponding to holo state at (1.5,0.47) next to the apo basin. (f) The typical time trajectories as a function of RMSDs. It shows the three distinct states and the switching among them.

fluorescence-magnetic tweezers microscopy.26−28 In their molecular dynamics simulations, Duan et al. found that loop 2 and loop 3 in the apo structure can open up in the absence of MgATP using a locally enhanced sampling technique. The simulations by Gao et al. showed that multiple conformations of loop 2 and loop 3, including the open, semiopen, and closed conformations, are all accessible to the apoenzyme. The abovementioned theoretical simulations both investigated the loop dynamics around the conformations of a single native structure. While the conformational transitions among multiple native structures remain largely unknown. There are several representative atomistic structures along the catalytic cycle of HPPK that have been experimentally determined via X-ray crystallography and NMR. Previous studies have been accumulating evidence that HPPK is capable of executing large-scale conformational fluctuations without any ligand. The holo state (1Q0N) can emerge after both ligands bind to the enzyme. Thus, several mechanistic questions arise: What are the processes of the conformational changes with and without ligand binding? Is the system better described by populations shift or induced fit mechanism? How does the ligand binding influence the conformational changes? How many transition pathways are there? What are their importance and the corresponding weights? Which parts of the enzyme play a key role in the conformational changes? To address these questions, we have developed a coarse-grained triple-basin structure-based model, with explicit consideration of ligands, to explore the underlying mechanisms of the conformational dynamics of HPPK. In the present work, we extended our previous structurebased model (SBM) by introducing explicit ligands, which were

energetic details of the allosteric transitions of typical proteins, such as maltose binding protein (MBP),7 adenylate kinase (ADK),4−6,9,10,14 Rop dimer,15 glutamine-binding protein,16 protein kinase A,17,18 and DNA Y-family polymerase IV (DPO4),8 etc. To study the enzyme dynamics−function relationship, we chose HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase) as a model system. HPPK, a small, stable, monomeric protein of 158 residues, catalyzes the transfer of pyrophosphate from ATP to 6-hydroxymethyl-7,8-dihydropterin (HP), leading to the biosynthesis of folate, a vitamin essential for all forms of life.19 Humans obtain folates from their diet, however, without an active transport system, most microorganisms must synthesize folates de novo. Hence, HPPK plays an important role in microbial growth and this catalytic pyrophosphorylation reaction is a promising target for potential antibacterial drug development.20,21 There are three flexible loops of HPPK involved in the enzymatic catalysis reaction. Therefore, the open to closed transition of HPPK is mostly dictated by the relative positions of the three flexible loops with respect to the core region (the major rigid portion of HPPK). Among them, loop 3 undergoes dramatic open-close conformational changes in each catalytic cycle, correlating with ligand binding. Yan et al. proposed that the conformational change of HPPK is hand-like,22 and the flexible loops act as the characteristic fingers to cover or move away from the rigid palm (the core region). It is evident that conformational dynamics, especially movements of the loop regions, plays an important role in the catalytic reaction. There has been a number of computer simulations2,3,23 and experiments24,25 carried out for HPPK, such as our recent studies with single-molecule C

DOI: 10.1021/acs.jpcb.7b12562 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B typically ignored or implicitly considered in most SBMs, and simulated the detailed process of conformational transitions. We revealed the intrinsic conformational fluctuations between the apo and open states of HPPK. More accurate and realistic investigations of functional transitions responding to ligand binding benefited from the explicit modeling of ligands. The holo state can be induced upon the ordered ligand binding with ATP first. Our methods illustrated the detailed process of conformational dynamics with and without ligand binding and the accompanying pathway distributions, and thus further enriched our understanding of the relationship between enzymatic dynamics and functions of HPPK.

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RESULTS AND DISCUSSION Functional Landscapes with and without Ligand Binding. In this work, we studied the structures of three states of HPPK to explore the conformational transition mechanism. After calibration of interaction parameters according to the experimentally determined structures (Figure 1), the dynamical equilibrium between native states can be achieved from our triple-basin model (see details in the Supporting Information). The free energy landscapes F (RMSDa, RMSDo), with and without ligand binding, are shown in Figure 1 as a function of RMSDa and RMSDo. RMSDa is the root-mean-square displacement of the state relative to apo state, while RMSDo is the root-mean-square displacement of the state relative to open state. They describe the structural similarity to the respective native states, and are both in units of nanometers. In the two-dimensional free energy surfaces along the residual distance between TRP89 in loop 3 and TYR116 in the core region R89−116 and RMSDo (Figure 2), (R89−116, RMSDo) = (2.3,0.36) is for the apo state conformation, (R89−116, RMSDo) = (3.1,0.18) is for the open state conformation, and (R89−116, RMSDo) = (1.5,0.47) is for the holo state conformation. In Figure 2a−e, we can see clearly that HPPK is capable of sufficiently sampling a wide range of conformations between the apo and open basins. This is comparable to the conclusion that the range of loop conformations accessible in the apo state overlapped with that of the open state.23 The typical trajectories in time as a function of RMSDs are shown in Figure 2. It indicates the typical transitions among the three native states. Compared to the dynamical equilibrium between apo and open states within free HPPK (Figure 2), we can achieve all of the three native states when the two ligands, ATP and HP, are bound. Four individual MD simulations were performed on each system of ligand-free HPPK, HPPK−ATP complex, HPPK− HP complex, and HPPK−ATP−HP ternary complex to analyze the root-mean-square fluctuations (RMSF), which is the time average of RMSDs for each residue in the protein with reference to the average structure during the simulation.3,29 As displayed by RMSF curves calculated from the MD trajectories (Figure 3), the conformational changes during the simulations are mainly located at the loop regions, consistent with previous theoretical results2,3 and NMR order parameters from NMR structures. At the simulation temperature, the scale of structural fluctuations is comparable with those obtained using the physics-based explicit solvent model at 303 K (Figure S8). Loop 3 showing the highest RMSF values actually makes the most direct interactions with ATP, and constitutes the pocket of the active center with another flexible loop 2. This seems to be the region responsible for HP-binding. It is worthwhile pointing out that loop 2 in the binary−ATP complex has

Figure 3. RMSF difference (nm) curves of binary−ATP, binary−HP, and ternary HPPK−ATP−HP complex minus apo HPPK, as well as the individual RMSF (nm) curves of apo HPPK, HPPK−ATP binary complex, HPPK−HP binary complex, and HPPK−ATP−HP ternary complex. The HPPK structure is colored with RMSF values (nm). It is obvious that the three loop regions are very flexible with large RMSF values. The typical residues around the active center and at both ends of the protein that were selected as reaction coordinates to monitor the conformational changes are also shown.

similar RMSF values as that of apo HPPK, indicating that the binding of ATP has hardly any effect on loop 2. In contrast, the interactions between HP and HPPK influence both loop 2 and loop 3. Loop 2 was significantly stabilized upon HP binding. The most obvious fluctuation occurs only in the ternary complex, with both ATP and HP joining in. This implies that the movements of loop regions, especially loop 2 and loop 3, play a critical role in the conformational transitions of HPPK in response to ligand binding. It is clear that these conformational fluctuations must be influenced by the existence of both ligands. So we first investigated the effects of ligand binding by tuning the relative strength of ligand−protein contacts and that of ligand-bound holo state-specific contacts. The probability distributions of D

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Figure 4. Shift of conformational distribution. εLJ = 1.0, εcore = 1.0, εspe = 0.5, εapo = 0.7, and εopen = 2.7. Gradually increasing εligand while keeping εholo constant (a), and vice versa (b,c,d). The shift of conformational distributions is measured by RMSD relative to open state. It shows the simulated measurement of probability distributions for the free HPPK and the ligand-bound enzyme. Our model is robust to attain the three native states with modestly varying the energetic parameters relative to ligand binding.

RMSD relative to the native open structure (PDB: 1EQ0), with increasing εligand or εholo, are shown in Figure 4. We found that the holo state stays at very low probability density until the ligand raised to 0.5. We also ran a series of trajectories with varying εholo under small and modest ligand concentrations quantified by the strength, respectively. As seen, we can achieve more holo state with increasing εholo, and even more with larger εligand in the conformational dynamics. The ligand binding thus biases toward the holo state. There is mounting evidence that the HPPK-catalyzed reaction follows an ordered kinetic mechanism with the ATP binding first.30−32 However, it is still unclear about how the functional dynamics of HPPK is modulated by the two ligands and their binding sequence. To further address the detailed effects of either ligand interacting with HPPK on the conformational dynamics at a microscopic level, we carried out the molecular dynamics simulations by developing an explicit-ligand model, which consists of two ligands, ATP and HP (see more details of modeling of both ligands in the Supporting Information). The strength of contacts between ATP and protein (εATP) were tuned to match the experimental 33 KATP d . As shown in Figure S1, we calibrated the εATP = 0.30 so that the disassociation constant of ATP is comparable to the experimental data (Kd = 38 μM). The probability distributions of the Cα distance between Ala86 and Phe101, with different modeling of the ligands, are shown in Figure 5. The distance between two typical residues, Ala86 in the most flexible loop 3 and Phe101 at the bottom of the core region with little mobility, is the frequently used reaction coordinate in the conformational transition studies of HPPK.2,3 It indicates the conformational redistributions upon ligand binding with the simulated measurement of apo, binary, and ternary models. These theoretical results are consistent

Figure 5. Conformational redistributions upon ligand binding. The probability densities are measured by the Cα distance between two typical residues, Ala86 in the most flexible loop 3 and Phe101 at the bottom of the core region, for apo, binary-ATP, and ternary models.

with earlier experimental findings that the free HPPK, with flexible loops, is capable of fluctuating between the apo and open conformations.2 With the further participation of ATP, the populations of open state become dominant in the binary models, which agrees well with the conclusion from Li et al. that loop 3 moves away from the active center upon the binding of MgATP analogue to achieve a wider opening posture in the PDB 1EQ0 and 2F65.34 It is worthy noting that the similar phenomenon of ATP binding was found in previous theoretical studies.17,18 We propose that the ATP binding is responsible for initiating the opening transition, in which loop 3 acts as a lid or the gate of the entrance. Compared to Figure 3, in a recent simulation study of HPPK from Kaifu et al.,3 the functional landscape based on available structural information was sufficiently sampled by our coarse-grained model. This E

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This is consistent with the reported bisubstrate analogue inhibitors in the experiments.20,21 We next investigate the effect of ligand concentration on the population distribution of HPPK (Figure 7). It is shown that

allows us to explicitly characterize the conformational change mechanism of HPPK, with and without ligand binding. Effects of Ligand Binding. It is shown that the conformational dynamics of HPPK is a two-state equilibrium in apo and binary systems. Furthermore, the increase of the open peak is from the interactions between HPPK and the first ligand, ATP. The holo state appears only in the ternary system when the second ligand HP is bound (Figure 5). Therefore, we first investigate the affinity between ligands and their target enzyme HPPK by varying the ligand-binding strengths (εATP and εHP). The results are illustrated in Figure 6. We can see

Figure 7. Relationship between the ligand concentration and population distributions of HPPK. Using a wall potential to control the movement of ligands (see definition in Supporting Information), we can determine the concentrations through the volume of the reaction container for systems in the simulation by setting RATP between 40.0 and 3.0 nm, corresponding to concentrations between 6 μM and 14.7 mM. The error bar is the standard deviation.

the population of the open state increases slowly, and that of the holo state increases from 9.3 to 15.9% as the concentration of ATP increases. We can conclude that the more concentrated ATP will lead to the more open state. As a result, the activated holo state follows to increase significantly. We also test another binding order with HP to be bound first. But we found that it is hard for ATP to reach the native position in the final active center under the presence of HP. The population of bound ATP declined 13.5% as we increased the parameter εHP from 0.1 to 1.5. And the binding of HP failed to solely lead to the holo basin, even with considerable εHP (Figure S2). It seems that the binding of HP involving both loop 2 and loop 3 will hamper ATP from finding its native binding pose. Thus, the binding order for the enzymatic reaction supported that the ATP binds first and was followed by HP binding. Major Induced Fit and Minor Population Shift Pathways Coexist. We further explore the detailed mechanism by which the ligand binding and conformational changes of HPPK are coupled (Figure 1). Induced fit and population shift are two essential mechanisms that have been suggested to describe the conformational change of protein upon ligand binding. In the “induced fit” mechanism, it means that the ligand binding drives a ligand-free (usually open or apo) enzyme toward the activated conformation (usually closed). In the “population shift” mechanism, it refers to that the unbound protein takes on multiple functional states (including the activated bound conformation), subsequently, and ligand binding selectively stabilizes the pre-existing bound conformation. These two paradigms can be distinguished by whether the conformational change occurs before or after the binding. However, the actual mechanism may reside between the two extremes, considering that the induced fit can be regarded as a special case of population shift that the ligand selectively binds to the pre-existing inactive conformation

Figure 6. The dependence of populations of states on the ligandbinding strengths. (a) The first ligand, ATP, promotes the population of open state, while it has little effect on that of the holo state. (b) After calibrating εATP to match the experimental disassociation constant, the probability of holo state increases markedly with the increase of strength εHP.

clearly that the population of the open state increases as the strength of ATP binding (εATP) increases, while that of the apo state decreases in unison. At the same time, the holo state stays at very low probability in the binary−ATP systems. After calibration of εATP based on the observed disassociation constant in experiments, we then consider the response of population distribution of HPPK to the variation of εHP. From Figure 6b, we find that the open state retains a stable population around 50%, and the probability of holo state increases significantly with the increase of strength εHP. It can be expected that HPPK will be fully locked in the holo state with both high ligand-binding strengths. In other words, the ligand-binding interactions play an important role of closing the pocket of the active center and redistributing the populations. F

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Figure 8. Influence of ligand binding on transition rate constants and the kinetic mechanism. Transition rate constants kAO, kAH, and kOH change with the strength of ligand binding. kAH increases sharply as the ligand binding strengths increase. kAO becomes faster with moderate εATP and finally slows down responding to the increase of the first ligand, ATP (a), however, it increases slightly as the strength of second ligand HP increases (b). Meanwhile, kOH almost remains unchanged. This supports that HPPK can switch to the activation state more directly when the conformational transitions between the apo and holo basins are faster. The induced fit pathway ( f I) is the predominant route of the HPPK system, and changing the ligand-binding interactions has hardly had any effect on the pathway weights (c).

transitions from A to B, PA is the probability of HPPK in basin A, and Ttot is the total duration of trajectory. The rate constant is in a unit of ns−1.

(population shift can also be classified as a special case of induced fit). For the case of HPPK responding to ligand binding, our results suggest a mixed mechanism that the induced fit and population shift coexist. The free HPPK exhibits wide fluctuations spreading the apo and open conformations, and the first ligand, ATP, prefers to bind to the open conformations. This deepens the open basin. It indicates a population shift mechanism. In contrast, the activated holo state occurs only after the binding interactions of the second ligand HP are formed. This process falls into the scope of a typical induced fit scenario. Therefore, our analyses have shown that the mechanism of conformational change of HPPK upon ligand binding is a mixture of population shift and induced fit. We next measure the relative weight of the two activation pathways in a quantitative way. There are two possible kinetic routes: (1) the induced fit (IF) route, where the predominant apo state of HPPK changes into holo form directly, that is, A→ H; and (2) the population shift (PS) route, where HPPK arrives at holo basin through the open basin, that is, A→O→H. The entire conformational dynamics of the HPPK system is characterized by the interbasin transitions. We construct a reduced kinetic motif by only considering the transitions among the native basins.35,36 The transition rate constants are calculated as the ratio of transition numbers to the total residence time in the former basin. NA→B is the number of

kA → B =

NA → B PA*Ttot

(1)

We considered all of the interbasin transition rate constants upon the changes in ligand binding (Figures S3 and S4 in Supporting Information). In Figure 8a,b, we find that the transition rate constant, kAH, increases sharply as the ligandbinding strengths increase. However, kAO becomes faster with moderate εATP and finally slows down responding to the increase of the first ligand, ATP, moreover, it increases slightly as the strength of second ligand HP increases. Meanwhile, kOH almost remains unchanged. It can be understood that when the conformational transitions between the apo and the holo basins are faster, HPPK will switch to the activation state more directly. It is worth noting that the interbasin transitions in our model are significantly faster than the realistic time scale due to the coarse-grained nature and consideration of implicit solvent. However, the trend and the influence of ligand binding on the conformational dynamics of HPPK are robust, considering the many agreements with earlier theoretical and experimental findings. Furthermore, we calculate the reactive flux through the two possible kinetic routes by applying the method suggested by G

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Figure 9. The comparison of contact probability maps of apo to open transition and apo to holo transition. The upper triangle (lower triangle) corresponds to the native state-specific contact probability map of the AO (AH) transition ensemble. For clarity, the open state-specific mapped structure and holo state-specific mapped structure are shown on the top. The condensed regions of specific interactions are highlighted both in the structures and contact map. The corresponding probability for a particular residual pair forming native contact is illustrated according to the side color bar, in which light colors mean low formation probability and dark colors mean high formation probability.

ensembles. We located the transition state by finding the extremum between the minima of the free energy profile as the saddle point of the free energy landscape. We identified the transitions between A, O, and H basins from the thermodynamic free energy profile projected onto the functional Qa and Qh. The functional Qx (X can be A, O, and H) is the order parameters representing the fraction of state-specific native contacts relative to apo, holo, or open state, and is used to monitor the closeness to the respective states. In Figure 9, we show the contact probability maps for AO and AH transition ensembles. Only the state-specific contact pairs are illustrated in this map to compare the two typical transitions. Clearly, we can see a red point in the C region. It tells us that the contact pair, R92-D95, was almost formed in the transition state between apo and holo basins, while this was not found in the AO transition. This theoretical prediction agreed well with many experiments that R92 is a key residue in the process of closing loop 3, and the charged contact pair, R92-D95, triggers the final closure of loop 3 in apo directly to holo transition.37,38 Another obvious region with different contact probability is region E, in which we can find a much higher probability formed in AH transition. It indicates that contacts between loop 2 and loop 3 become more compact in the AH transition than in the AO transition. There are two open state-specific contacts (region B) between loop 1 and loop 2 in the AO transition. It shows that loop 1 moves toward loop 2 at the beginning of AO transition, and this movement of loop 1, which cannot be seen in the AH transition, plays an important role in leading apo to open conformational

Hammes et al.36 Only the A→H transition flux (FIF) and A→ O→H transition flux (FPS) are computed to analyze the conformational transition mechanisms. Instead of the absolute flux, we used the fractional flux, which is equal to the ratio of flux from A to B to the total flux. As shown in Figure S5, the symmetry that the forward fluxes approximate that of the reverse direction for all possible paths between adjacent basins implies the sufficient sampling and equilibrium of the HPPK system. The fractional flux, f I and f P, can be calculated as follows: fI =

FIF NA→H = FIF + FPS NA →H +NA →O →H

(2)

fP =

FPS = 1 − fI FIF + FPS

(3)

The relationship between the fractional flux and ligand binding is shown in Figure 8c. We can see clearly that the induced fit pathway is the predominant route of the HPPK system, and changing the ligand-binding interactions hardly affected the pathway weights. Thus, our results reveal an underlying mechanism, whereby major induced fit and minor population shift coexist. The ligands play a significant role in modulating the population of basins. However, they do not change the mechanism of conformational transitions at the present temperature. Contact Map of Transition States. Besides the above kinetic properties of the conformational transitions, we also describe the structural characterization in the transition state H

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Figure 10. Functional Φ values analysis of transition states between A, O, and H basins. The functional Φ values are not calculated for the residues in which the difference between ⟨Qi⟩A and ⟨Qi⟩B is less than a certain cutoff value (using 0.8 in this article). (a,c,e) Functional ΦAO, ΦAH, and ΦOH as a function of residue index. The colored segments labeled in the X-axis correspond to loop1 (red), loop2 (green), and loop3 (yellow). (b,d,f) Functional ΦAO, ΦAH, and ΦOH mapped onto the crystal structures. The residues with Φ values are represented by spheres with different colors according to the right color bar, in which red means high value and blue means low value. In addition, the residue will be colored yellow if the Φ value is larger than 1.

We calculate the functional Φ values for residues in the transition states between A, O, and H basins. The functional Φ values can be expressed through the following equation:

transition. HPPK needs to seal the active center for catalysis reaction, and loop 3 acts as the main lid. When loop 3 moves close to loop 2 and aggregates the three loops (region F shows that the contacts between loop 3 and loop 1 emerge in AH transition), holo-closed state starts to form, and this prepares the site for catalytic reactions. The contacts between loop 3 and the rigid core of enzyme in region D indicate the final closeness of loop 3. In contrast, we can achieve an open state with loop 3 opening up and loop 1 moving close to loop 2. The three flexible loops control the conformational dynamics, as well as ligand binding.

Φ AB =

⟨Q i⟩TS − ⟨Q i⟩A ⟨Q i⟩B − ⟨Q i⟩A

(4)

where ⟨Qi⟩ is the thermal mean value of the number of twobody interaction contacts for residue i over all the corresponding states, and the TS subscript represents the transition state from A to B state. A and B subscripts represent any two of the apo, open, and holo states, respectively. It is I

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Figure 11. Temperature dependence of populations of states, pathways, and mean passage times. (a) Increasing the temperature results in different changes in the populations of three native states. (b) Increasing the temperature encourages HPPK to follow the more population shift pathway, while the induced fit pathway is always the predominant activation route of HPPK system. (c) Higher temperature can accelerate the interbasin transitions, especially the PS pathway (A→O→H). However, the MPT of IF pathway (A→H) has no response to the temperature, and it keeps faster than that of PS pathway in the range of the simulation temperature.

worthwhile to note that their functional Φ values are not calculated for the residues in which the difference between ⟨Qi⟩A and ⟨Qi⟩B is less than a certain cutoff value (using 0.8 in this article). When Φ is near 1, the residue is important for the transition, since the residue is already in its product conformation. However, when Φ is near 0, it means that the residue is not important for the transition from the reactant to product state or close to the reactant state at the transition state. It shows that residue Y53 on loop 2 and R84 on loop 3, which are both located near the connection of the loop and core region, play a key role in driving the transition from apo to open state (Φ AO > 0.7 in Figure 10a). There are more key residues from all of the three flexible loops participating in the AH transition in Figure 10b. They make up the lids to seal the active center. Interestingly, we found that ΦOH value of E87 is larger than 1 as ⟨Qi⟩TS is out of the range of ⟨Qi⟩A and ⟨Qi⟩B. E87 is located in the middle region of loop 3, and we propose that the abnormal ΦOH value is most likely coming from the flexibility of loop 3. The movement of loop 3, which has the most degree of freedom among the loops, is not completely coupled to the rigid core region of the enzyme. Our predictions can give guidance for future experimental explorations of conformational change and catalytic reactions of HPPK. Temperature Regulates the Conformational Dynamics of HPPK upon Ligand Binding. Mounting evidence suggests that the efficiency of enzymatic catalysis is very

sensitive to the environment, such as salts, pH, ligand concentration, and also temperature. In this section, we investigate the dependence of conformational distribution on temperature. We would like to emphasize that the temperature here cannot be exactly the same in value as the temperature of the typical experimental studies of HPPK, considering the coarse-grained feature of our model. We chose the temperatures, at which the populations of the two native basins (apo and open states) in the ligand-free model are similar, to guarantee sufficient sampling of conformational transitions. In Figure 11a, it is clearly shown that the populations of open and holo states decrease when increasing the temperature. At the same time, the apo state progressively becomes the majority. In addition, we reveal the influence of the temperatures on the mechanism of conformational changes by displaying the pathway weights as a function of the simulation temperatures (Figure 11b). The correlation between the pathways and temperatures indicates that increasing the temperature encourages the HPPK to follow a population shift route (Figures S6 and S7). Intriguingly, the population of the IF pathway is always larger than the PS pathway in the whole range of our simulation temperatures. This strongly supports the view that the IF pathway is the predominant activation route of HPPK system. On the other hand, we calculated the mean passage time39,40 to describe the kinetics of the conformational transitions between the native states. In Figure 11c, we can see that increasing the temperature mostly J

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The Journal of Physical Chemistry B

the SI for greater detail). The coarse-graining process is similar to the webtool SMOG.41 To include side-chain dynamics to the conformational change of protein, we used a coarse-grained model in which each amino acid in HPPK is represented by one or two beads depending on their location and properties. One bead (named CA in our model), representing the backbone, is located on the Cα atom, and one bead (named CB), representing the side chain, is located on the center of mass or the farthest heavy atom of the side chain, depending on its residual characterization. In addition, the ligand-related Hamiltonian is also included, and the ligand−protein contacts are extracted from the holo structure (PDB: 1Q0N). We employed the wall potential as a function of the distance between the center of mass of the protein and ligands to control their concentrations. Considering the charged interactions in conformational dynamics and ligand binding, we use Debye−Hückel potential to describe the electrostatic interactions. Water and ions were incorporated implicitly into our model as the dielectric constant and Debye screening length. Simulations were carried out with Gromacs 4.5.4 package.42 Reduced units were used for all calculations. The time step is 0.0005 time unit (ps) and the simulation was coupled to a temperature bath via Langevin dynamics with a coupling time of 1.0. To ensure that the simulation is converged and the statistical errors are small enough, we simultaneously run several independent simulations using the same parameter set.

accelerates the interbasin transitions. The MPT of the population shift pathway (A→O→H) dramatically decreases as the temperature increases, however, that of the induced fit pathway (A→H) has no response to the temperature, and always keeps faster than the PS pathway. These results also give strong support that the mechanism of conformational transitions of HPPK is dominated by “induced fit”, and the higher temperatures prefer the population shift pathway more.

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DISCUSSION Understanding the role of multistate conformational dynamics of HPPK is the key to elucidate the relationship between enzyme catalysis and ligand binding. In this work, we developed a coarse-grained triple-basin structure-based model with explicit consideration of the two ligands to explore the conformational changes of HPPK. We performed thermodynamic and kinetic simulations of conformational transitions between the three native states of HPPK, and obtained thousands of transitions which can give us statistical reliability. It provided us a detailed description of the dynamical processes of the conformational transitions of HPPK upon ligand binding. The ligand-free HPPK is intrinsic to execute large-scale conformational fluctuations around the apo and open basins. When the first ligand, ATP, came in, the conformational dynamics between the two basins were not changed, that is, the two-state fluctuations spreading the apo and open conformations remained steady. ATP preferred to bind to the open conformations and promoted the population of the open state. After calibrating εATP to match the experimental disassociation constant, we investigated the detailed effects of HP binding on the multistate conformational transition system. We found that only when both ligands are bound, can the conformational transitions among all of the three native states emerge. We have also shown that the binding order must be ATP first, due to the failure of achieving the holo state with the reverse order. By quantitative flux analysis, our model allowed us to determine that the induced fit pathway is the predominant route of the conformational changes of HPPK system. The mechanism of conformational transitions of HPPK is relatively robust to the binding affinity of both ligands. In contrast, it is very sensitive to the temperature. Increasing the simulation temperature will certainly promote the ratio of the population shift pathway, but still no more than that of the induced fit pathway. In addition, we also pointed out the structural correlations to the conformational changes and identified the key residues as well as contact interactions. We provided rich information on the microscopic origin for the conformational change at single molecule level. As a consequence, we propose that HPPK has the ability to sample the large conformational space spreading the apo and open states without the natural substrates. Furthermore, HPPK can switch to the activated holo state with the ordered binding of the first ligand, ATP, and second ligand, HP, via a mixed pathway whereby major induced fit and minor population shift coexist.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b12562. Model and simulation details and estimation of the disassociation constant (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Lingci Zhao: 0000-0001-7531-5224 H. Peter Lu: 0000-0003-2027-428X Jin Wang: 0000-0002-2841-4913 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS L.Z. and J.W. are thankful for support from National Science Foundation of China Grant 91430217 and Ministry of Science and Technology, China, Grants 2016YFA0203200 and 2013YQ170585. J.W. gives thanks for the support in part from National Science Foundation Grant NSF-PHY-76066. H.P.L. acknowledges support from the National Institutes of Health National Institute of General Medicine Science and the Ohio Eminent Scholar Endowment.

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METHODS The structure-based models have been proven to be successful at combining the energy landscape theory of protein folding/ binding with an efficient molecular simulation. To extend the structure-based model to systems with multiple basins upon ligand binding, we modified the Hamiltonian energy by integrating structural information on three native states (see

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