On the roles of substrate binding and hinge unfolding in conformational changes of adenylate kinase

Trajectory Statistical Learning of the Potential Mean of Force and Diffusion Coefficient from Molecular Dynamics Simulations

Central to studying the conformational changes of a complex protein is understanding the dynamics and energetics involved. Phenomenologically, structural dynamics can be formulated using an overdamped Langevin model along an observable, e.g., the distance between two residues in the protein. The Langevin model is specified by the deterministic force (the potential of mean force, PMF) and stochastic force (characterized by the diffusion coefficient, D). It is therefore of great interest to be able to extract both PMF and D from an observable time series but under the same computational framework. Here, we approach this challenge in molecular dynamics (MD) simulations by treating it as a missing-data Bayesian estimation problem. An important distinction in our methodology is that the entire MD trajectory, as opposed to the individual data elements, is used as the statistical variable in Bayesian imputation. This idea is implemented through an eigen-decomposition procedure for a time-symmetrized Fokker-Planck equation, followed by maximizing the likelihood for parameter estimation. The mathematical expressions for the functional derivatives used in learning PMF and D also provide new physical insights for the manner by which the information on both the deterministic and stochastic forces is encoded in the dynamics data. An all-atom MD simulation of a nontrivial biomolecule case is used to illustrate the application of this approach. We show that, interestingly, the results of trajectory statistical learning can motivate new order parameters for an improved description of the kinetic bottlenecks in conformational changes. Complementing purely data-driven or black-box methods, this work underscores the advantages of physics-based machine learning in gaining chemical insights from quantitative parameter estimation.

Role of Repeated Conformational Transitions in Substrate Binding of Adenylate Kinase

The catalytic cycle of the enzyme adenylate kinase involves large conformational motions between open and closed states. A previous single-molecule experiment showed that substrate binding tends to accelerate both the opening and the closing rates and that a single turnover event often involves multiple rounds of conformational switching. In this work, we showed that the repeated conformational transitions of adenylate kinase are essential for the relaxation of incorrectly bound substrates into the catalytically competent conformation by combining all-atom and coarse-grained molecular simulations. In addition, free energy calculations based on all-atom and coarse-grained models demonstrated that the enzyme with incorrectly bound substrates has much a lower free energy barrier for domain opening compared to that with the correct substrate conformation, which may explain the the acceleration of the domain opening rate by substrate binding. The results of this work provide mechanistic understanding to previous experimental observations and shed light onto the interplay between conformational dynamics and enzyme catalysis.

Integration of Adenylate Kinase 1 with Its Peptide Conformational Imprint

In the present study, molecularly imprinted polymers (MIPs) were used as a tool to grasp a targeted α-helix or β-sheet of protein. During the fabrication of the hinge-mediated MIPs, elegant cavities took shape in a special solvent on quartz crystal microbalance (QCM) chips. The cavities, which were complementary to the protein secondary structure, acted as a peptide conformational imprint (PCI) for adenylate kinase 1 (AK1). We established a promising strategy to examine the binding affinities of human AK1 in conformational dynamics using the peptide-imprinting method. Moreover, when bound to AK1, PCIs are able to gain stability and tend to maintain higher catalytic activities than free AK1. Such designed fixations not only act on hinges as accelerators; some are also inhibitors. One example of PCI inhibition of AK1 catalytic activity takes place when PCI integrates with an AK1_9-23 β-sheet. In addition, conformation ties, a general MIP method derived from random-coil AK1_133-144 in buffer/acetonitrile, are also inhibitors. The inhibition may be due to the need for this peptide to execute conformational transition during catalysis.

Structure-mechanics statistical learning uncovers mechanical relay in proteins

A protein's adaptive response to its substrates is one of the key questions driving molecular physics and physical chemistry. This work employs the recently developed structure-mechanics statistical learning method to establish a mechanical perspective. Specifically, by mapping all-atom molecular dynamics simulations onto the spring parameters of a backbone-side-chain elastic network model, the chemical moiety specific force constants (or mechanical rigidity) are used to assemble the rigidity graph, which is the matrix of inter-residue coupling strength. Using the S1A protease and the PDZ3 signaling domain as examples, chains of spatially contiguous residues are found to exhibit prominent changes in their mechanical rigidity upon substrate binding or dissociation. Such a mechanical-relay picture thus provides a mechanistic underpinning for conformational changes, long-range communication, and inter-domain allostery in both proteins, where the responsive mechanical hotspots are mostly residues having important biological functions or significant mutation sensitivity.

Protein residues exhibit specific routes of mechanical relay as the adaptive responses to substrate binding or dissociation. On such physically contiguous connections, residues experience prominent changes in their coupling strengths.

Tracking the ATP-binding response in adenylate kinase in real time

The biological function of proteins is critically dependent on dynamics inherent to the native structure. Such structural dynamics obey a predefined order and temporal timing to execute the specific reaction. Determination of the cooperativity of key structural rearrangements requires monitoring protein reactions in real time. In this work, we used time-resolved x-ray solution scattering (TR-XSS) to visualize structural changes in the Escherichia coli adenylate kinase (AdK) enzyme upon laser-induced activation of a protected ATP substrate. A 4.3-ms transient intermediate showed partial closing of both the ATP- and AMP-binding domains, which indicates a cooperative closing mechanism. The ATP-binding domain also showed local unfolding and breaking of an Arg¹³¹-Asp¹⁴⁶ salt bridge. Nuclear magnetic resonance spectroscopy data identified similar unfolding in an Arg¹³¹Ala AdK mutant, which refolded in a closed, substrate-binding conformation. The observed structural dynamics agree with a “cracking mechanism” proposed to underlie global structural transformation, such as allostery, in proteins.

Understanding enzyme behavior in a crowded scenario through modulation in activity, conformation and dynamics

Macromolecular crowding, inside the physiological interior, modulates the energy landscape of biological macromolecules in multiple ways. Amongst these, enzymes occupy a special place and hence understanding the function of the same in the crowded interior is of utmost importance. In this study, we have investigated the manner in which the multidomain enzyme, AK3L1 (PDB ID: 1ZD8), an isoform of adenylate kinase, has its features affected in presence of commonly used crowders (PEG 8, Dextran 40, Dextran 70, and Ficoll 70). Michaelis Menten plots reveal that the crowders in general enhance the activity of the enzyme, with the K_m and V_max values showing significant variations. Ficoll 70, induced the maximum activity for AK3L1 at 100 g/L, beyond which the activity reduced. Ensemble FRET studies were performed to provide insights into the relative domain (LID and CORE) displacements in presence of the crowders. Solvation studies reveal that the protein matrix surrounding the probe CPM (7-diethylamino-3-(4-maleimido-phenyl)-4-methylcoumarin) gets restricted in presence of the crowders, with Ficoll 70 providing the maximum rigidity, the same being linked to the decrease in the activity of the enzyme. Through our multipronged approach, we have observed a distinct correlation between domain displacement, enzyme activity and associated dynamics. Thus, keeping in mind the complex nature of enzyme activity and the surrounding bath of dense soup that the biological entity remains immersed in, indeed more such approaches need to be undertaken to have a better grasp of the "enzymes in the crowd".

Coarse-Grained Modeling of Multiple Pathways in Conformational Transitions of Multi-Domain Proteins

Large-scale conformational transitions in multi-domain proteins are often essential for their functions. To investigate the transitions, it is necessary to explore multiple potential pathways, which involve different intermediate structures. Here, we present a multi-basin (MB) coarse-grained (CG) structure-based Go̅ model for describing transitions in proteins with more than two moving domains. This model is an extension of our dual-basin Go̅ model in which system-dependent parameters are determined systematically using the multistate Bennett acceptance ratio method. In the MB Go̅ model for multi-domain proteins, we assume that intermediate structures may have partial inter-domain native contacts. This approach allows us to search multiple transition pathways that involve distinct intermediate structures using the CG molecular dynamics (MD) simulations. We apply this scheme to an enzyme, adenylate kinase (AdK), which has three major domains and can move along two different pathways. Using the optimized mixing parameters for each pathway, AdK shows frequent transitions between the Open, Closed, and the intermediate basins and samples a wide variety of conformations within each basin. The explored multiple transition pathways could be compared with experimental data and examined in more detail by atomistic MD simulations.

Integrating Rigidity Analysis into the Exploration of Protein Conformational Pathways Using RRT* and MC

To understand how proteins function on a cellular level, it is of paramount importance to understand their structures and dynamics, including the conformational changes they undergo to carry out their function. For the aforementioned reasons, the study of large conformational changes in proteins has been an interest to researchers for years. However, since some proteins experience rapid and transient conformational changes, it is hard to experimentally capture the intermediate structures. Additionally, computational brute force methods are computationally intractable, which makes it impossible to find these pathways which require a search in a high-dimensional, complex space. In our previous work, we implemented a hybrid algorithm that combines Monte-Carlo (MC) sampling and RRT*, a version of the Rapidly Exploring Random Trees (RRT) robotics-based method, to make the conformational exploration more accurate and efficient, and produce smooth conformational pathways. In this work, we integrated the rigidity analysis of proteins into our algorithm to guide the search to explore flexible regions. We demonstrate that rigidity analysis dramatically reduces the run time and accelerates convergence.

Increasing the Sampling Efficiency of Protein Conformational Change by Combining a Modified Replica Exchange Molecular Dynamics and Normal Mode Analysis

Understanding conformational change at an atomic level is significant when determining a protein functional mechanism. Replica exchange molecular dynamics (REMD) is a widely used enhanced sampling method to explore protein conformational space. However, REMD with an explicit solvent model requires huge computational resources, immensely limiting its application. In this study, a variation of parallel tempering metadynamics (PTMetaD) with the omission of solvent-solvent interactions in exchange attempts and the use of low-frequency modes calculated by normal-mode analysis (NMA) as collective variables (CVs), namely ossPTMetaD, is proposed with the aim to accelerate MD simulations simultaneously in temperature and geometrical spaces. For testing the performance of ossPTMetaD, five protein systems with diverse biological functions and motion patterns were selected, including large-scale domain motion (AdK), flap movement (HIV-1 protease and BACE1), and DFG-motif flip in kinases (p38α and c-Abl). The simulation results showed that ossPTMetaD requires much fewer numbers of replicas than temperature REMD (T-REMD) with a reduction of ∼70% to achieve a similar exchange ratio. Although it does not obey the detailed balance condition, ossPTMetaD provides consistent results with T-REMD and experimental data. The high accessibility of the large conformational change of protein systems by ossPTMetaD, especially in simulating the very challenging DFG-motif flip of protein kinases, demonstrated its high efficiency and robustness in the characterization of the large-scale protein conformational change pathway and associated free energy profile.

A Two-Ended Data-Driven Accelerated Sampling Method for Exploring the Transition Pathways between Two Known States of Protein

Conformational transitions of protein between different states are often associated with their biological functions. These dynamic processes, however, are usually not easy to be well characterized by experimental measurements, mainly because of inadequate temporal and spatial resolution. Meantime, sampling of configuration space with molecular dynamics (MD) simulations is still a challenge. Here we proposed a robust two-ended data-driven accelerated (teDA2) conformational sampling method, which drives the structural change in an adaptively updated feature space without introducing a bias potential. teDA2 was applied to explore adenylate kinase (ADK), a model with well characterized "open" and "closed" states. A single conformational transition event of ADK could be achieved within only a few or tens of nanoseconds sampled with teDA2. By analyzing hundreds of transition events, we reproduced different mechanisms and the associated pathways for domain motion of ADK reported in the literature. The multiroute characteristic of ADK was confirmed by the fact that some metastable states identified with teDA2 resemble available crystal structures determined at different conditions. This feature was further validated with Markov state modeling with independent MD simulations. Therefore, our work provides strong evidence for the conformational plasticity of protein, which is mainly due to the inherent degree of flexibility. As a reliable and efficient enhanced sampling protocol, teDA2 could be used to study the dynamics between functional states of various biomolecular machines.

Exploring Conformational Change of Adenylate Kinase by Replica Exchange Molecular Dynamic Simulation

Replica exchange molecular dynamics (REMD) simulation is a popular enhanced sampling method that is widely used for exploring the atomic mechanism of protein conformational change. However, the requirement of huge computational resources for REMD, especially with the explicit solvent model, largely limits its application. In this study, the availability and efficiency of a variant of velocity-scaling REMD (vsREMD) was assessed with adenylate kinase as an example. Although vsREMD achieved results consistent with those from conventional REMD and experimental studies, the number of replicas required for vsREMD (30) was much less than that for conventional REMD (80) to achieve a similar acceptance rate (∼0.2), demonstrating high efficiency of vsREMD to characterize the protein conformational change and associated free-energy profile. Thus, vsREMD is a highly efficient approach for studying the large-scale conformational change of protein systems.

Electrostatic interactions determine entrance/release order of substrates in the catalytic cycle of adenylate kinase

Adenylate kinase is a monomeric phosphotransferase with important biological function in regulating concentration of adenosine triphosphate (ATP) in cells, by transferring the terminal phosphate group from ATP to adenosine monophosphate (AMP) and forming two adenosine diphosphate (ADP) molecules. During this reaction, the kinase may undergo a large conformational transition, forming different states with its substrates. Although many structures of the protein are available, atomic details of the whole process remain unclear. In this article, we use both conventional molecular dynamics (MD) simulation and an enhanced sampling technique called parallel cascade selection MD simulation to explore different conformational states of the Escherichia coli adenylate kinase. Based on the simulation results, we propose a possible entrance/release order of substrates during the catalytic cycle. The substrate-free protein prefers an open conformation, but changes to a closed state once ATP·Mg enters into its binding pocket first and then AMP does. After the reaction of ATP transferring the terminal phosphate group to AMP, ADP·Mg and ADP are released sequentially, and finally the whole catalyze cycle is completed. Detailed contact and distance analysis reveals that the entrance/release order of substrates may be largely controlled by electrostatic interactions between the protein and the substrates.

Multiple Pathways and Time Scales for Conformational Transitions in apo-Adenylate Kinase

The open/close transition in adenylate kinase (AK) is regarded as a representative example for large-scale conformational transition in proteins, yet its mechanism remains unclear despite numerous experimental and computational studies. Using extensive (∼50 μs) explicit solvent atomistic simulations and Markov state analysis, we shed new lights on the mechanism of this transition in the apo form of AK. The closed basin of apo AK features an open NMP domain while the LID domain closes and rotates toward it. Therefore, although the computed structural properties of the closed ensemble are consistent with previously reported FRET and PRE measurements, our simulations suggest that NMP closure is likely to follow AMP binding, in contrast to the previous interpretation of FRET and PRE data that the apo state was able to sample the fully closed conformation for "ligand selection". The closed state ensemble is found to be kinetically heterogeneous; multiple pathways and time scales are associated with the open/close transition, providing new clues to the disparate time scales observed in different experiments. Besides interdomain interactions, a novel mutual information analysis identifies specific intradomain interactions that correlate strongly to transition kinetics, supporting observations from previous chimera experiments. While our results underscore the role of internal domain properties in determining the kinetics of open/close transition in apo AK, no evidence is observed for any significant degree of local unfolding during the transition. These observations about AK have general implications to our view of conformational states, transition pathways, and time scales of conformational changes in proteins. The key features and time scales of observed transition pathways are robust and similar from simulations using two popular fixed charge force fields.

Structural basis for ligand binding to an enzyme by a conformational selection pathway

Proteins can bind target molecules through either induced fit or conformational selection pathways. In the conformational selection model, a protein samples a scarcely populated high-energy state that resembles a target-bound conformation. In enzymatic catalysis, such high-energy states have been identified as crucial entities for activity and the dynamic interconversion between ground states and high-energy states can constitute the rate-limiting step for catalytic turnover. The transient nature of these states has precluded direct observation of their properties. Here, we present a molecular description of a high-energy enzyme state in a conformational selection pathway by an experimental strategy centered on NMR spectroscopy, protein engineering, and X-ray crystallography. Through the introduction of a disulfide bond, we succeeded in arresting the enzyme adenylate kinase in a closed high-energy conformation that is on-pathway for catalysis. A 1.9-Å X-ray structure of the arrested enzyme in complex with a transition state analog shows that catalytic sidechains are properly aligned for catalysis. We discovered that the structural sampling of the substrate free enzyme corresponds to the complete amplitude that is associated with formation of the closed and catalytically active state. In addition, we found that the trapped high-energy state displayed improved ligand binding affinity, compared with the wild-type enzyme, demonstrating that substrate binding to the high-energy state is not occluded by steric hindrance. Finally, we show that quenching of fast time scale motions observed upon ligand binding to adenylate kinase is dominated by enzyme-substrate interactions and not by intramolecular interactions resulting from the conformational change.

Substrate Binding Specifically Modulates Domain Arrangements in Adenylate Kinase

The enzyme adenylate kinase (ADK) features two substrate binding domains that undergo large-scale motions during catalysis. In the apo state, the enzyme preferentially adopts a globally open state with accessible binding sites. Binding of two substrate molecules (AMP + ATP or ADP + ADP) results in a closed domain conformation, allowing efficient phosphoryl-transfer catalysis. We employed molecular dynamics simulations to systematically investigate how the individual domain motions are modulated by the binding of substrates. Two-dimensional free-energy landscapes were calculated along the opening of the two flexible lid domains for apo and holo ADK as well as for all single natural substrates bound to one of the two binding sites of ADK. The simulations reveal a strong dependence of the conformational ensembles on type and binding position of the bound substrates and a nonsymmetric behavior of the lid domains. Altogether, the ensembles suggest that, upon initial substrate binding to the corresponding lid site, the opposing lid is maintained open and accessible for subsequent substrate binding. In contrast, ATP binding to the AMP-lid induces global domain closing, preventing further substrate binding to the ATP-lid site. This might constitute a mechanism by which the enzyme avoids the formation of a stable but enzymatically unproductive state.

Active-Loop Dynamics within the Michaelis Complex of Lactate Dehydrogenase from Bacillus stearothermophilus

Laser-induced temperature-jump relaxation spectroscopy was used to study the active site mobile-loop dynamics found in the binding of the NADH nucleotide cofactor and oxamate substrate mimic to lactate dehydrogenase in Bacillus stearothermophilus thermophilic bacteria (bsLDH). The kinetic data can be best described by a model in which NADH can bind only to the open-loop apoenzyme, oxamate can bind only to the bsLDH·NADH binary complex in the open-loop conformation, and oxamate binding is followed by closing of the active site loop preventing oxamate unbinding. The open and closed states of the loop are in dynamic equilibrium and interconvert on the submillisecond time scale. This interconversion strongly accelerates with an increase in temperature because of significant enthalpy barriers. Binding of NADH to bsLDH results in minor changes of the loop dynamics and does not shift the open-closed equilibrium, but binding of the oxamate substrate mimic shifts this equilibrium to the closed state. At high excess oxamate concentrations where all active sites are nearly saturated with the substrate mimic, all active site mobile loops are mainly closed. The observed active-loop dynamics for bsLDH is very similar to that previously observed for pig heart LDH.

Mapping the Dynamics Landscape of Conformational Transitions in Enzyme: The Adenylate Kinase Case

Conformational transition describes the essential dynamics and mechanism of enzymes in pursuing their various functions. The fundamental and practical challenge to researchers is to quantitatively describe the roles of large-scale dynamic transitions for regulating the catalytic processes. In this study, we tackled this challenge by exploring the pathways and free energy landscape of conformational changes in adenylate kinase (AdK), a key ubiquitous enzyme for cellular energy homeostasis. Using explicit long-timescale (up to microseconds) molecular dynamics and bias-exchange metadynamics simulations, we determined at the atomistic level the intermediate conformational states and mapped the transition pathways of AdK in the presence and absence of ligands. There is clearly chronological operation of the functional domains of AdK. Specifically in the ligand-free AdK, there is no significant energy barrier in the free energy landscape separating the open and closed states. Instead there are multiple intermediate conformational states, which facilitate the rapid transitions of AdK. In the ligand-bound AdK, the closed conformation is energetically most favored with a large energy barrier to open it up, and the conformational population prefers to shift to the closed form coupled with transitions. The results suggest a perspective for a hybrid of conformational selection and induced fit operations of ligand binding to AdK. These observations, depicted in the most comprehensive and quantitative way to date, to our knowledge, emphasize the underlying intrinsic dynamics of AdK and reveal the sophisticated conformational transitions of AdK in fulfilling its enzymatic functions. The developed methodology can also apply to other proteins and biomolecular systems.

Structural basis for catalytically restrictive dynamics of a high-energy enzyme state

An emerging paradigm in enzymology is that transient high-energy structural states play crucial roles in enzymatic reaction cycles. Generally, these high-energy or ‘invisible' states cannot be studied directly at atomic resolution using existing structural and spectroscopic techniques owing to their low populations or short residence times. Here we report the direct NMR-based detection of the molecular topology and conformational dynamics of a catalytically indispensable high-energy state of an adenylate kinase variant. On the basis of matching energy barriers for conformational dynamics and catalytic turnover, it was found that the enzyme's catalytic activity is governed by its dynamic interconversion between the high-energy state and a ground state structure that was determined by X-ray crystallography. Our results show that it is possible to rationally tune enzymes' conformational dynamics and hence their catalytic power—a key aspect in rational design of enzymes catalysing novel reactions.

Adenylate kinase (AdK) plays a key role in cellular energy homeostasis by catalysing the reversible magnesium-dependent formation of ADP from AMP and ATP. Here the authors present a detailed analysis of adenylate kinase's conformational dynamics and characterize a high-energy state of AdK indispensable for catalysis.

The Atomistic Mechanism of Conformational Transition of Adenylate Kinase Investigated by Lorentzian Structure-Based Potential

We present a new all-atom structure-based method to study protein conformational transitions using Lorentzian attractive interactions based on native structures. The variability of each native contact is estimated based on evolutionary information using a machine learning method. To test the validity of this approach, we have investigated the conformational transition of adenylate kinase (ADK). The intrinsic boundedness of the Lorentzian attractive interactions facilitated frequent conformational transitions, and consequently we were able to observe more than 1000 structural interconversions between the open and closed states of ADK out of a total of 6 μs MD simulations. ADK has three domains: the nucleoside monophosphate (NMP) binding domain, the LID-domain, and the CORE domain, which catalyze the interconversion between ATP and ADP. We identified two transition states: a more frequent LID-closed-NMP-open (TS1) state and a less frequent LID-open-NMP-closed (TS2) state. The transition was found to be symmetric in both directions via TS1. We also obtained an off-pathway metastable state that was previously observed with physics-based all-atom simulations but not with coarse-grained models. In the metastable state, the LID domain was slightly twisted and formed contacts with the NMP domain. Our model correctly identified a total of 14 out of the top 16 residues with highest fluctuation by NMR experiment, thus showing excellent agreement with experimental NMR relaxation data and overwhelmingly better results than existing models.

WEBnm@ v2.0: Web server and services for comparing protein flexibility

BACKGROUND

Normal mode analysis (NMA) using elastic network models is a reliable and cost-effective computational method to characterise protein flexibility and by extension, their dynamics. Further insight into the dynamics-function relationship can be gained by comparing protein motions between protein homologs and functional classifications. This can be achieved by comparing normal modes obtained from sets of evolutionary related proteins.

RESULTS

We have developed an automated tool for comparative NMA of a set of pre-aligned protein structures. The user can submit a sequence alignment in the FASTA format and the corresponding coordinate files in the Protein Data Bank (PDB) format. The computed normalised squared atomic fluctuations and atomic deformation energies of the submitted structures can be easily compared on graphs provided by the web user interface. The web server provides pairwise comparison of the dynamics of all proteins included in the submitted set using two measures: the Root Mean Squared Inner Product and the Bhattacharyya Coefficient. The Comparative Analysis has been implemented on our web server for NMA, WEBnm@, which also provides recently upgraded functionality for NMA of single protein structures. This includes new visualisations of protein motion, visualisation of inter-residue correlations and the analysis of conformational change using the overlap analysis. In addition, programmatic access to WEBnm@ is now available through a SOAP-based web service. Webnm@ is available at http://apps.cbu.uib.no/webnma .

CONCLUSION

WEBnm@ v2.0 is an online tool offering unique capability for comparative NMA on multiple protein structures. Along with a convenient web interface, powerful computing resources, and several methods for mode analyses, WEBnm@ facilitates the assessment of protein flexibility within protein families and superfamilies. These analyses can give a good view of how the structures move and how the flexibility is conserved over the different structures.

Global transitions of proteins explored by a multiscale hybrid methodology: application to adenylate kinase

Efficient and accurate mapping of transition pathways is a challenging problem in allosteric proteins. We propose here a to our knowledge new methodology called collective molecular dynamics (coMD). coMD takes advantage of the collective modes of motions encoded by the fold, simultaneously evaluating the interactions and energetics via a full-atomic MD simulation protocol. The basic approach is to deform the structure collectively along the modes predicted by the anisotropic network model, upon selecting them via a Monte Carlo/Metropolis algorithm from among the complete pool of all accessible modes. Application to adenylate kinase, an allosteric enzyme composed of three domains, CORE, LID, and NMP, shows that both open-to-closed and closed-to-open transitions are readily sampled by coMD, with large-scale motions of the LID dominating. An energy-barrier crossing occurs during the NMP movements. The energy barrier originates from a switch between the salt bridges K136-D118 at the LID-CORE interface and K57-E170 and D33-R156 at the CORE-NMP and LID-NMP interfaces, respectively. Despite its simplicity and computing efficiency, coMD yields ensembles of transition pathways in close accord with detailed full atomic simulations, lending support to its utility as a multiscale hybrid method for efficiently exploring the allosteric transitions of multidomain or multimeric proteins.

Exploring the conformational transitions of biomolecular systems using a simple two-state anisotropic network model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.

Many biomolecules are like tiny molecular machines that need to change their shapes and visit many states to perform their biological functions. For a complete molecular understanding of a biological process, one needs to have information on the relevant stable states of the system in question, as well as the pathways by which the system travels from one state to another. We report here an efficient computational method that uses the knowledge of experimental structures of a pair of stable states in order to construct an energetically favoravle pathway between them. We adopt a simple representation of the molecular system by replacing the atoms with beads connected by springs and constructing an energy function with two minima around the end-states. We searched for the structure with highest energy that the system is most likely to visit during the transition and created two paths starting from this structure and proceeding toward the end-states. The combined result of these two paths is the minimum energy pathway between the two stable states. We apply this method to study important structural changes in one enzyme and three large proteins that transport small molecules and ions across the cell membrane.

Conformational dynamics of a ligand-free adenylate kinase

Adenylate kinase (AdK) is a phosphoryl-transfer enzyme with important physiological functions. Based on a ligand-free open structure and a ligand-bound closed structure solved by crystallography, here we use molecular dynamics simulations to examine the stability and dynamics of AdK conformations in the absence of ligands. We first perform multiple simulations starting from the open or the closed structure, and observe their free evolutions during a simulation time of 100 or 200 nanoseconds. In all seven simulations starting from the open structure, AdK remained stable near the initial conformation. The eight simulations initiated from the closed structure, in contrast, exhibited large variation in the subsequent evolutions, with most (seven) undergoing large-scale spontaneous conformational changes and approaching or reaching the open state. To characterize the thermodynamics of the transition, we propose and apply a new sampling method that employs a series of restrained simulations to calculate a one-dimensional free energy along a curved pathway in the high-dimensional conformational space. Our calculated free energy profile features a single minimum at the open conformation, and indicates that the closed state, with a high (∼13 kcal/mol) free energy, is not metastable, consistent with the observed behaviors of the unrestrained simulations. Collectively, our simulations suggest that it is energetically unfavorable for the ligand-free AdK to access the closed conformation, and imply that ligand binding may precede the closure of the enzyme.

Molecular dynamics studies on the conformational transitions of adenylate kinase: a computational evidence for the conformational selection mechanism

Escherichia coli adenylate kinase (ADK) is a monomeric phosphotransferase enzyme that catalyzes reversible transfer of phosphoryl group from ATP to AMP with a large-scale domain motion. The detailed mechanism for this conformational transition remains unknown. In the current study, we performed long time-scale molecular dynamics simulations on both open and closed states of ADK. Based on the structural analyses of the simulation trajectories, we detected over 20 times conformational transitions between the open and closed states of ADK and identified two novel conformations as intermediate states in the catalytic processes. With these findings, we proposed a possible mechanism for the large-scale domain motion of Escherichia coli ADK and its catalytic process: (1) the substrate free ADK adopted an open conformation; (2) ATP bound with LID domain closure; (3) AMP bound with NMP domain closure; (4) phosphoryl transfer occurred with ATP, and AMP converted into two ADPs, and no conformational transition was detected in the enzyme; (5) LID domain opened with one ADP released; (6) another ADP released with NMP domain open. As both open and closed states sampled a wide range of conformation transitions, our simulation strongly supported the conformational selection mechanism for Escherichia coli ADK.

Transitions to catalytically inactive conformations in EGFR kinase

The epidermal growth factor receptor (EGFR) is a key protein in cellular signaling, and its kinase domain (EGFR kinase) is an intensely pursued target of small-molecule drugs. Although both catalytically active and inactive conformations of EGFR kinase have been resolved crystallographically, experimental characterization of the transitions between these conformations remains difficult. Using unbiased, all-atom molecular dynamics simulations, we observed EGFR kinase spontaneously transition from the active to the so-called "Src-like inactive" conformation by way of two sets of intermediate conformations: One corresponds to a previously identified locally disordered state and the other to previously undescribed "extended" conformations, marked by the opening of the ATP-binding site between the two lobes of the kinase domain. We also simulated the protonation-dependent transition of EGFR kinase to another ["Asp-Phe-Gly-out" ("DFG-out")] inactive conformation and observed similar intermediate conformations. A key element observed in the simulated transitions is local unfolding, or "cracking," which supports a prediction of energy landscape theory. We used hydrogen-deuterium (H/D) exchange measurements to corroborate our simulations and found that the simulated intermediate conformations correlate better with the H/D exchange data than existing active or inactive EGFR kinase crystal structures. The intermediate conformations revealed by our simulations of the transition process differ significantly from the existing crystal structures and may provide unique possibilities for structure-based drug discovery.

Allosteric activation transitions in enzymes and biomolecular motors: insights from atomistic and coarse-grained simulations

The chemical step in enzymes is usually preceded by a kinetically distinct activation step that involves large-scale conformational transitions. In "simple" enzymes this step corresponds to the closure of the active site; in more complex enzymes, such as biomolecular motors, the activation step is more complex and may involve interactions with other biomolecules. These activation transitions are essential to the function of enzymes and perturbations in the scale and/or rate of these transitions are implicated in various serious human diseases; incorporating key flexibilities into engineered enzymes is also considered a major remaining challenge in rational enzyme design. Therefore it is important to understand the underlying mechanism of these transitions. This is a significant challenge to both experimental and computational studies because of the allosteric and multi-scale nature of such transitions. Using our recent studies of two enzyme systems, myosin and adenylate kinase (AK), we discuss how atomistic and coarse-grained simulations can be used to provide insights into the mechanism of activation transitions in realistic systems. Collectively, the results suggest that although many allosteric transitions can be viewed as domain displacements mediated by flexible hinges, there are additional complexities and various deviations. For example, although our studies do not find any evidence for "cracking" in AK, our results do underline the contribution of intra-domain properties (e.g., dihedral flexibility) to the rate of the transition. The study of mechanochemical coupling in myosin highlights that local changes important to chemistry require stabilization from more extensive structural changes; in this sense, more global structural transitions are needed to activate the chemistry in the active site. These discussions further emphasize the importance of better understanding factors that control the degree of co-operativity for allosteric transitions, again hinting at the intimate connection between protein stability and functional flexibility. Finally, a number of topics of considerable future interest are briefly discussed.

Exploring the Dynamic Functional Landscape of Adenylate Kinase Modulated by Substrates

Adenylate kinase (ADK) has been explored widely, through both experimental and theoretical studies. However, still less is known about how the functional dynamics of ADK is modulated explicitly by its natural substrates. Here, we report a quantitative study of the dynamic energy landscape for ADK responding to the substrate binding by integrating both experimental investigations and theoretical modeling. We make theoretical predictions which are in remarkable agreement with the single molecule experiments on the substrate-bound complex. With our combined models of ADK in its apo form, in the presence of AMP or ATP, and in complex with both substrates, we specifically address the following key questions: (1) Are there intermediate state(s) during their catalytic cycle and if so how many? (2) How many pathways are there along the open-to-closed transitions and what are their corresponding weights? (3) How do substrates influence the pathway weights and the stability of the intermediates? (4) Which lid's motion is rate-limiting along the turnover cycle, the NMP or the LID domain? Our models predict two major parallel stepwise pathways and two on-pathway intermediates which are denoted as IN (NMP domain open while LID domain closed) and IL (LID domain open and NMP domain closed), respectively. Further investigation of temperature effects suggests that the IN pathway is dominant at room temperature, but the IL pathway is dominant at the optimal temperature. This leads us to propose that the IL pathway is more dominant by entropy and IN pathway by enthalpy. Remarkably, our results show that even with maximum concentrations of natural substrates, ADK still fluctuates between multiple functional states, reflecting an intrinsic capability of large-scale conformational fluctuations which may be essential to its biological function. The results based on the dual-ligands model provide the theoretical validation of random bisubstrate biproducts (Bi-Bi) mechanism for the enzymatic reaction of ADK. Additionally, the pathway flux analysis strongly suggests that the motion of the NMP domain is the rate-determining step for the conformational cycle (opening and closing).

Modulation of a pre-existing conformational equilibrium tunes adenylate kinase activity

Structural plasticity is often required for distinct microscopic steps during enzymatic reaction cycles. Adenylate kinase from Escherichia coli (AK(eco)) populates two major conformations in solution; the open (inactive) and closed (active) state, and the overall turnover rate is inversely proportional to the lifetime of the active conformation. Therefore, structural plasticity is intimately coupled to enzymatic turnover in AK(eco). Here, we probe the open to closed conformational equilibrium in the absence of bound substrate with NMR spectroscopy and molecular dynamics simulations. The conformational equilibrium in absence of substrate and, in turn, the turnover number can be modulated with mutational- and osmolyte-driven perturbations. Removal of one hydrogen bond between the ATP and AMP binding subdomains results in a population shift toward the open conformation and a resulting increase of k(cat). Addition of the osmolyte TMAO to AK(eco) results in population shift toward the closed conformation and a significant reduction of k(cat). The Michaelis constants (K(M)) scale with the change in k(cat), which follows from the influence of the population of the closed conformation for substrate binding affinity. Hence, k(cat) and K(M) are mutually dependent, and in the case of AK(eco), any perturbation that modulates k(cat) is mirrored with a proportional response in K(M). Thus, our results demonstrate that the equilibrium constant of a pre-existing conformational equilibrium directly affects enzymatic catalysis. From an evolutionary perspective, our findings suggest that, for AK(eco), there exists ample flexibility to obtain a specificity constant (k(cat)/K(M)) that commensurate with the exerted cellular selective pressure.

Event detection and sub-state discovery from biomolecular simulations using higher-order statistics: application to enzyme adenylate kinase

Biomolecular simulations at millisecond and longer time-scales can provide vital insights into functional mechanisms. Because post-simulation analyses of such large trajectory datasets can be a limiting factor in obtaining biological insights, there is an emerging need to identify key dynamical events and relating these events to the biological function online, that is, as simulations are progressing. Recently, we have introduced a novel computational technique, quasi-anharmonic analysis (QAA) (Ramanathan et al., PLoS One 2011;6:e15827), for partitioning the conformational landscape into a hierarchy of functionally relevant sub-states. The unique capabilities of QAA are enabled by exploiting anharmonicity in the form of fourth-order statistics for characterizing atomic fluctuations. In this article, we extend QAA for analyzing long time-scale simulations online. In particular, we present HOST4MD--a higher-order statistical toolbox for molecular dynamics simulations, which (1) identifies key dynamical events as simulations are in progress, (2) explores potential sub-states, and (3) identifies conformational transitions that enable the protein to access those sub-states. We demonstrate HOST4MD on microsecond timescale simulations of the enzyme adenylate kinase in its apo state. HOST4MD identifies several conformational events in these simulations, revealing how the intrinsic coupling between the three subdomains (LID, CORE, and NMP) changes during the simulations. Further, it also identifies an inherent asymmetry in the opening/closing of the two binding sites. We anticipate that HOST4MD will provide a powerful and extensible framework for detecting biophysically relevant conformational coordinates from long time-scale simulations.

Biomolecular dynamics: order-disorder transitions and energy landscapes

While the energy landscape theory of protein folding is now a widely accepted view for understanding how relatively weak molecular interactions lead to rapid and cooperative protein folding, such a framework must be extended to describe the large-scale functional motions observed in molecular machines. In this review, we discuss (1) the development of the energy landscape theory of biomolecular folding, (2) recent advances toward establishing a consistent understanding of folding and function and (3) emerging themes in the functional motions of enzymes, biomolecular motors and other biomolecular machines. Recent theoretical, computational and experimental lines of investigation have provided a very dynamic picture of biomolecular motion. In contrast to earlier ideas, where molecular machines were thought to function similarly to macroscopic machines, with rigid components that move along a few degrees of freedom in a deterministic fashion, biomolecular complexes are only marginally stable. Since the stabilizing contribution of each atomic interaction is on the order of the thermal fluctuations in solution, the rigid body description of molecular function must be revisited. An emerging theme is that functional motions encompass order-disorder transitions and structural flexibility provides significant contributions to the free energy. In this review, we describe the biological importance of order-disorder transitions and discuss the statistical-mechanical foundation of theoretical approaches that can characterize such transitions.

Structural distributions from single-molecule measurements as a tool for molecular mechanics

A mechanical view provides an attractive alternative for predicting the behavior of complex systems since it circumvents the resource-intensive requirements of atomistic models; however, it remains extremely challenging to characterize the mechanical responses of a system at the molecular level. Here, the structural distribution is proposed to be an effective means to extracting the molecular mechanical properties. End-to-end distance distributions for a series of short poly-L-proline peptides with the sequence P(n)CG(3)K-biotin (n = 8, 12, 15 and 24) were used to experimentally illustrate this new approach. High-resolution single-molecule Förster-type resonance energy transfer (FRET) experiments were carried out and the conformation-resolving power was characterized and discussed in the context of the conventional constant-time binning procedure for FRET data analysis. It was shown that the commonly adopted theoretical polymer models-including the worm-like chain, the freely jointed chain, and the self-avoiding chain-could not be distinguished by the averaged end-to-end distances, but could be ruled out using the molecular details gained by conformational distribution analysis because similar polymers of different sizes could respond to external forces differently. Specifically, by fitting the molecular conformational distribution to a semi-flexible polymer model, the effective persistence lengths for the series of short poly-L-proline peptides were found to be size-dependent with values of ~190 Å, ~67 Å, ~51 Å, and ~76 Å for n = 8, 12, 15, and 24, respectively. A comprehensive computational modeling was carried out to gain further insights for this surprising discovery. It was found that P(8) exists as the extended all-trans isomaer whereas P(12) and P(15) predominantly contained one proline residue in the cis conformation. P(24) exists as a mixture of one-cis (75%) and two-cis (25%) isomers where each isomer contributes to an experimentally resolvable conformational mode. This work demonstrates the resolving power of the distribution-based approach, and the capacity of integrating high-resolution single-molecule FRET experiments with molecular modeling to reveal detailed structural information about the conformation of molecules on the length scales relevant to the study of biological molecules.

Large-scale motions in the adenylate kinase solution ensemble: coarse-grained simulations and comparison with solution X-ray scattering

While coarse-grained (CG) simulations provide an efficient approach to identify small- and large-scale motions important to protein conformational transitions, coupling with appropriate experimental validation is essential. Here, by comparing small-angle X-ray scattering (SAXS) predictions from CG simulation ensembles of adenylate kinase (AK) with a range of energetic parameters, we demonstrate that AK is flexible in solution in the absence of ligand and that a small population of the closed form exists without ligand. In addition, by analyzing variation of scattering patterns within CG simulation ensembles, we reveal that rigid-body motion of the LID domain corresponds to a dominant scattering feature. Thus, we have developed a novel approach for three-dimensional structural interpretation of SAXS data. Finally, we demonstrate that the agreement between predicted and experimental SAXS can be improved by increasing the simulation temperature or by computationally mutating selected residues to glycine, both of which perturb LID rigid-body flexibility.

Enzyme closure and nucleotide binding structurally lock guanylate kinase

We investigate the conformational dynamics and mechanical properties of guanylate kinase (GK) using a multiscale approach combining high-resolution atomistic molecular dynamics and low-resolution Brownian dynamics simulations. The GK enzyme is subject to large conformational changes, leading from an open to a closed form, which are further influenced by the presence of nucleotides. As suggested by recent work on simple coarse-grained models of apo-GK, we primarily focus on GK's closure mechanism with the aim to establish a detailed picture of the hierarchy and chronology of structural events essential for the enzymatic reaction. We have investigated open-versus-closed, apo-versus-holo, and substrate-versus-product-loaded forms of the GK enzyme. Bound ligands significantly modulate the mechanical and dynamical properties of GK and rigidity profiles of open and closed states hint at functionally important differences. Our data emphasizes the role of magnesium, highlights a water channel permitting active site hydration, and reveals a structural lock that stabilizes the closed form of the enzyme.

Interconversion of functional motions between mesophilic and thermophilic adenylate kinases

Dynamic properties are functionally important in many proteins, including the enzyme adenylate kinase (AK), for which the open/closed transition limits the rate of catalytic turnover. Here, we compare our previously published coarse-grained (double-well Gō) simulation of mesophilic AK from E. coli (AKmeso) to simulations of thermophilic AK from Aquifex aeolicus (AKthermo). In AKthermo, as with AKmeso, the LID domain prefers to close before the NMP domain in the presence of ligand, but LID rigid-body flexibility in the open (O) ensemble decreases significantly. Backbone foldedness in O and/or transition state (TS) ensembles increases significantly relative to AKmeso in some interdomain backbone hinges and within LID. In contact space, the TS of AKthermo has fewer contacts at the CORE-LID interface but a stronger contact network surrounding the CORE-NMP interface than the TS of AKmeso. A “heated” simulation of AKthermo at 375K slightly increases LID rigid-body flexibility in accordance with the “corresponding states” hypothesis. Furthermore, while computational mutation of 7 prolines in AKthermo to their AKmeso counterparts produces similar small perturbations, mutation of these sites, especially positions 8 and 155, to glycine is required to achieve LID rigid-body flexibility and hinge flexibilities comparable to AKmeso. Mutating the 7 sites to proline in AKmeso reduces some hinges' flexibilities, especially hinge 2, but does not reduce LID rigid-body flexibility, suggesting that these two types of motion are decoupled in AKmeso. In conclusion, our results suggest that hinge flexibility and global functional motions alike are correlated with but not exclusively determined by the hinge residues. This mutational framework can inform the rational design of functionally important flexibility and allostery in other proteins toward engineering novel biochemical pathways.

Dynamic properties are functionally important in many proteins, including the enzyme adenylate kinase (AK), which undergoes chemically rate-limiting domain motions coupled to substrate binding. Since mesophiles and thermophiles often differ in functionally important motions, we compare coarse-grained simulations of AKmeso and AKthermo as well as several proline and glycine mutational variants designed to interconvert the dynamics. As might be expected, both domain motions and local unfolding motions are reduced in AKthermo relative to AKmeso. In AKthermo, both of these types of motions can be partially shifted toward more flexible AKmeso by heating or by mutating hinge prolines. However, only mutation to highly flexible glycine produces motions like those of AKmeso. Thus, the rate-limiting global transition likely depends on a combination of hinge flexibility and stability within the LID and NMP domains. Finally, this mutagenic framework can inform the rational design of flexibility and allostery in other proteins toward engineering novel biological control systems.

"Fluctuograms" reveal the intermittent intra-protein communication in subtilisin Carlsberg and correlate mechanical coupling with co-evolution

The mechanism of intra-protein communication and allosteric coupling is key to understanding the structure-property relationship of protein function. For subtilisin Carlsberg, the Ca²⁺-binding loop is distal to substrate-binding and active sites, yet the serine protease function depends on Ca²⁺ binding. The atomic molecular dynamics (MD) simulations of apo and Ca²⁺-bound subtilisin show similar structures and there is no direct evidence that subtilisin has alternative conformations. To model the intra-protein communication due to Ca²⁺ binding, we transform the sequential segments of an atomic MD trajectory into separate elastic network models to represent anharmonicity and nonlinearity effectively as the temporal and spatial variation of the mechanical coupling network. In analogy to the spectrogram of sound waves, this transformation is termed the “fluctuogram” of protein dynamics. We illustrate that the Ca²⁺-bound and apo states of subtilisin have different fluctuograms and that intra-protein communication proceeds intermittently both in space and in time. We found that residues with large mechanical coupling variation due to Ca²⁺ binding correlate with the reported mutation sites selected by directed evolution for improving the stability of subtilisin and its activity in a non-aqueous environment. Furthermore, we utilize the fluctuograms calculated from MD to capture the highly correlated residues in a multiple sequence alignment. We show that in addition to the magnitude, the variance of coupling strength is also an indicative property for the sequence correlation observed in a statistical coupling analysis. The results of this work illustrate that the mechanical coupling networks calculated from atomic details can be used to correlate with functionally important mutation sites and co-evolution.

A hallmark of protein molecules is their machine-like behaviors while carrying out biological functions. At the molecular level, molecular signals such as binding a metal ion at an action site can cause long-range effects and alter protein function. Such phenomena are often referred to as intra-protein communication or allosteric coupling. Elucidating the underlying mechanisms could lead to novel discovery of molecular modulators to regulate protein function in a more specific and effective manner. A long-standing puzzle is the roles of the anharmonicity and nonlinearity in protein dynamics. To incorporate these characters in modeling intra-protein communication, we devise a “fluctuogram” analysis to record the choreography of allosteric coupling in an atomic molecular dynamics simulation. We show that fluctuogram analysis can bridge the results of physics-based simulation and sequence alignment in bioinformatics by capturing the residues that exhibit high correlation in a multiple sequence alignment. We also show that the fluctuograms calculated from atomic details have the potential to be applied as a tool to select mutation sites for modulating protein function.

Allostery in the ferredoxin protein motif does not involve a conformational switch

Regulation of protein function via cracking, or local unfolding and refolding of substructures, is becoming a widely recognized mechanism of functional control. Oftentimes, cracking events are localized to secondary and tertiary structure interactions between domains that control the optimal position for catalysis and/or the formation of protein complexes. Small changes in free energy associated with ligand binding, phosphorylation, etc., can tip the balance and provide a regulatory functional switch. However, understanding the factors controlling function in single-domain proteins is still a significant challenge to structural biologists. We investigated the functional landscape of a single-domain plant-type ferredoxin protein and the effect of a distal loop on the electron-transfer center. We find the global stability and structure are minimally perturbed with mutation, whereas the functional properties are altered. Specifically, truncating the L1,2 loop does not lead to large-scale changes in the structure, determined via X-ray crystallography. Further, the overall thermal stability of the protein is only marginally perturbed by the mutation. However, even though the mutation is distal to the iron-sulfur cluster (∼20 Å), it leads to a significant change in the redox potential of the iron-sulfur cluster (57 mV). Structure-based all-atom simulations indicate correlated dynamical changes between the surface-exposed loop and the iron-sulfur cluster-binding region. Our results suggest intrinsic communication channels within the ferredoxin fold, composed of many short-range interactions, lead to the propagation of long-range signals. Accordingly, protein interface interactions that involve L1,2 could potentially signal functional changes in distal regions, similar to what is observed in other allosteric systems.