Molecular dynamics of apo-adenylate kinase: a distance replica exchange method for the free energy of conformational fluctuations

Conformational dynamics of adenylate kinase in crystals

Adenylate kinase is a ubiquitous enzyme in living systems and undergoes dramatic conformational changes during its catalytic cycle. For these reasons, it is widely studied by genetic, biochemical, and biophysical methods, both experimental and theoretical. We have determined the basic crystal structures of three differently liganded states of adenylate kinase from Methanotorrus igneus, a hyperthermophilic organism whose adenylate kinase is a homotrimeric oligomer. The multiple copies of each protomer in the asymmetric unit of the crystal provide a unique opportunity to study the variation in the structure and were further analyzed using advanced crystallographic refinement methods and analysis tools to reveal conformational heterogeneity and, thus, implied dynamic behaviors in the catalytic cycle.

Applications of Molecular Dynamics Simulation in Protein Study

Molecular Dynamics (MD) Simulations is increasingly used as a powerful tool to study protein structure-related questions. Starting from the early simulation study on the photoisomerization in rhodopsin in 1976, MD Simulations has been used to study protein function, protein stability, protein-protein interaction, enzymatic reactions and drug-protein interactions, and membrane proteins. In this review, we provide a brief review for the history of MD Simulations application and the current status of MD Simulations applications in protein studies.

Recognition between CD147 and cyclophilin A deciphered by accelerated molecular dynamics simulations

CD147 functions as the receptor of extracellular cyclophilin A (CypA) in various diseases, and CD147-CypA binding ulteriorly underlies the pathological process of various viral infections including HIV-1, SARS, and SARS-CoV-2. Although CyPA has been identified as a key intermediate pro-inflammatory factor, the mechanism by which CD147 cooperates with CypA in the development of the cytokine storm remains largely unknown, and the binding profile of CD147 with CypA remains to be elucidated as well. Here, we prepared three binding models of the CD147-CypA complex, including the active site of CypA severally binding to the groove bound by the Ig1 and Ig2 domains (model-0), P180-G181 (model-1), and P211 (model-2) of CD147, as well as introducing mutations P180A-G181A and P211A individually in each model. All systems were studied using accelerated molecular dynamics simulations and the molecular mechanics generalized Born surface area (MM/GBSA) method. For model-0, CypA bound to the ectodomain of CD147 with the highest binding affinity. Moreover, mutations P180A-G181A of CD147 in model-0 decreased the binding affinity and weakened the dynamic correlation between CD147 and CypA, which resulted in CypA shifting from the initial binding location. Other residue mutations of CD147 did not significantly affect the CD147-CypA binding, as reflected by the energy and structural analyses. Compared with surface plasmon resonance results and nuclear magnetic resonance shift signals, CypA should tend to reciprocally bind to the groove of CD147, and the binding process might be modulated by P180-G181 rather than P211. Besides, residue R201 of CD147 is critical for CD147-CypA binding and needs further experimental verification. These findings further our understanding of the recruitment between CD147 and CypA and its potential role in the development of inflammation and viral infection.

TAB1 binding induced p38α conformation change: an accelerated molecular dynamics simulation study

p38α mitogen-activated protein kinase (MAPK) undergoes autophosphorylation induced by the binding of TGFβ-activated kinase 1 binding protein 1 (TAB1) in myocardial ischemia. Investigation of the conformational transformations in p38α triggered by TAB1 binding is motivated by the need to find selective p38α activation inhibitors to treat myocardial ischemia. Herein, the conformational transformations of p38α were studied via all-atom accelerated molecular dynamics simulations and principal component analysis. With the binding of TAB1, the conformational changes of p38α auto-activation were characterized by the movement of the activation loop (A-loop) away from the αG helix toward the αF, αE helixes and L16-loop. In addition, a diverse intermediate state with an extensional and phosphorylated A-loop different from the transition intermediate state was explored. The conformational changes, including the A-loop alpha-structure breaking and the stronger hydrogen bond network formation, are accompanied by the extension of the A-loop and more intramolecular interactions in p38α. TAB1 correlates with other regions of p38α that are distal from the TAB1-binding site, including the A-loop, αC helix, and L16-loop, which regulates the intramolecular correlation of p38α. And, the phosphorylation further enhances the correlations between the A-loop and the other regions of p38α. The correlation results imply the regulation process of p38α conformational transformations. These findings will improve our understanding of the autophosphorylation of kinase and facilitate the development of selective inhibitors for the treatment of ischemic injury.

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".

Identification of Alternative Allosteric Sites in Glycolytic Enzymes for Potential Use as Species-Specific Drug Targets

Three allosteric glycolytic enzymes, phosphofructokinase, glyceraldehyde-3 phosphate dehydrogenase and pyruvate kinase, associated with bacterial, parasitic and human species, were explored to identify potential allosteric sites that would be used as prime targets for species-specific drug design purposes using a newly developed approach which incorporates solvent mapping, elastic network modeling, sequence and structural alignments. The majority of binding sites detected by solvent mapping overlapped with the interface regions connecting the subunits, thus appeared as promising target sites for allosteric regulation. Each binding site was then evaluated by its ability to alter the global dynamics of the receptor defined by the percentage change in the frequencies of the lowest-frequency modes most significantly and as anticipated, the most effective ones were detected in the vicinity of the well-reported catalytic and allosteric sites. Furthermore, some of our proposed regions intersected with experimentally resolved sites which are known to be critical for activity regulation, which further validated our approach. Despite the high degree of structural conservation encountered between bacterial/parasitic and human glycolytic enzymes, the majority of the newly presented allosteric sites exhibited a low degree of sequence conservation which further increased their likelihood to be used as species-specific target regions for drug design studies.

Protein structure predictions by enhanced conformational sampling methods

In this Special Festschrift Issue for the celebration of Professor Nobuhiro Gō's 80th birthday, we review enhanced conformational sampling methods for protein structure predictions. We present several generalized-ensemble algorithms such as multicanonical algorithm, replica-exchange method, etc. and parallel Monte Carlo or molecular dynamics method with genetic crossover. Examples of the results of these methods applied to the predictions of protein tertiary structures are also presented.

REVO: Resampling of ensembles by variation optimization

Conventional molecular dynamics simulations are incapable of sampling many important interactions in biomolecular systems due to their high dimensionality and rough energy landscapes. To observe rare events and calculate transition rates in these systems, enhanced sampling is a necessity. In particular, the study of ligand-protein interactions necessitates a diverse ensemble of protein conformations and transition states, and for many systems, this occurs on prohibitively long time scales. Previous strategies such as WExplore that can be used to determine these types of ensembles are hindered by problems related to the regioning of conformational space. Here, we propose a novel, regionless, enhanced sampling method that is based on the weighted ensemble framework. In this method, a value referred to as "trajectory variation" is optimized after each cycle through cloning and merging operations. This method allows for a more consistent measurement of observables and broader sampling resulting in the efficient exploration of previously unexplored conformations. We demonstrate the performance of this algorithm with the N-dimensional random walk and the unbinding of the trypsin-benzamidine system. The system is analyzed using conformation space networks, the residence time of benzamidine is confirmed, and a new unbinding pathway for the trypsin-benzamidine system is found. We expect that resampling of ensembles by variation optimization will be a useful general tool to broadly explore free energy landscapes.

Evaluation of Predicted Protein-Protein Complexes by Binding Free Energy Simulations

The accurate prediction of protein-protein complex geometries is of major importance to ultimately model the complete interactome of interacting proteins in a cell. A major bottleneck is the realistic free energy evaluation of predicted docked structures. Typically, simple scoring functions applied to single-complex structures are employed that neglect conformational entropy and often solvent effects completely. The binding free energy of a predicted protein-protein complex can, however, be calculated using umbrella sampling (US) along a predefined dissociation/association coordinate of a complex. We employed atomistic US-molecular dynamics simulations including appropriate conformational and axial restraints and an implicit generalized Born solvent model to calculate binding free energies of a large set of docked decoys for 20 different complexes. Free energies associated with the restraints were calculated separately. In principle, the approach includes all energetic and entropic contributions to the binding process. The evaluation of docked complexes based on binding free energy calculation was in better agreement with experiment compared to a simple scoring based on energy minimization or MD refinement using exactly the same force field description. Even calculated absolute binding free energies of structures close to the native binding geometry showed a reasonable correlation to experiment. However, still for a number of complexes docked decoys of lower free energy than near-native geometries were found indicating inaccuracies in the force field or the implicit solvent model. Although time consuming the approach may open up a new route for realistic ranking of predicted geometries based on calculated free energy of binding.

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.

Network of Conformational Transitions Revealed by Molecular Dynamics Simulations of the Carbonic Anhydrase II Apo-Enzyme

Human carbonic anhydrase II (HCA II) is an enzyme that catalyzes the reversible hydration of CO2 into bicarbonate (HCO3-) and a proton (H+) as well as other reactions at an extremely high rate. This enzyme plays fundamental roles in human physiology/pathology, such as controlling the pH level in cells and so on. However, the binding mechanism between apo-HCA II and CO2 or other ligands as well as related conformational changes remains poorly understood, and atomic investigation into it could promote our understanding of related internal physiological/pathological mechanisms. In this study, long-time atomic molecular dynamics simulations as well as the clustering and free-energy analysis were performed to reveal the dynamics of apo-HCA II as well as the mechanism upon ligand binding. Our simulations indicate that the crystallographic B-factors considerably underestimate the loop dynamics: multiple conformations can be adopted by loops 1 and 2, especially for loop 1 because loop 1 is one side of the binding pocket, and its left-to-right movement can compress or extend the binding pocket, leading to one inactive (closed) state, three intermediate (semiopen) states, and one active (open) state; CO2 cannot get into the binding pocket of the inactive state but can get into those of intermediate and active states. The coexistence of multiple conformational states proposes a possible conformational selection model for the binding mechanism between apo-HCA II and CO2 or other ligands, revising our previous view of its functional mechanism of conformational change upon ligand binding and offering valuable structural insights into the workings of HCA II.

Hybrid All-Atom/Coarse-Grained Simulations of Proteins by Direct Coupling of CHARMM and PRIMO Force Fields

Hybrid all-atom/coarse-grained (AA/CG) simulations of proteins offer a computationally efficient compromise where atomistic details are only applied to biologically relevant regions while benefiting from the speedup of treating the remaining parts of a given system at the CG level. The recently developed CG model, PRIMO, allows a direct coupling with an atomistic force field with no additional modifications or coupling terms and the ability to carry out dynamic simulations without any restraints on secondary or tertiary structures. A hybrid AA/CG scheme based on combining all-atom CHARMM and coarse-grained PRIMO representations was validated via molecular dynamics and replica exchange simulations of soluble and membrane proteins. The AA/CG scheme was also tested in the calculation of the free energy profile for the transition from the closed to the open state of adenylate kinase via umbrella sampling molecular dynamics method. The overall finding is that the AA/CG scheme generates dynamics and energetics that are qualitatively and quantitatively comparable to AA simulations while offering the computational advantages of coarse-graining. This model opens the door to challenging applications where high accuracy is required only in parts of large biomolecular complexes.

A Network of Conformational Transitions in the Apo Form of NDM-1 Enzyme Revealed by MD Simulation and a Markov State Model

New Delhi metallo-β-lactamase-1 (NDM-1) is a novel β-lactamase enzyme that confers enteric bacteria with nearly complete resistance to all β-lactam antibiotics, so it raises a formidable and global threat to human health. However, the binding mechanism between apo-NDM-1 and antibiotics as well as related conformational changes remains poorly understood, which largely hinders the overcoming of its antibiotic resistance. In our study, long-time conventional molecular dynamics simulation and Markov state models were applied to reveal both the dynamical and conformational landscape of apo-NDM-1: the MD simulation demonstrates that loop L3, which is responsible for antibiotic binding, is the most flexible and undergoes dramatic conformational changes; moreover, the Markov state model built from the simulation maps four metastable states including open, semiopen, and closed conformations of loop L3 as well as frequent transitions between the states. Our findings propose a possible conformational selection model for the binding mechanism between apo-NDM-1 and antibiotics, which facilitates the design of novel inhibitors and antibiotics.

Consistent Principal Component Modes from Molecular Dynamics Simulations of Proteins

Principal component analysis is a technique widely used for studying the movements of proteins using data collected from molecular dynamics simulations. In spite of its extensive use, the technique has a serious drawback: equivalent simulations do not afford the same PC-modes. In this article, we show that concatenating equivalent trajectories and calculating the PC-modes from the concatenated one significantly enhances the reproducibility of the results. Moreover, the consistency of the modes can be systematically improved by adding more individual trajectories to the concatenated one.

A Network of Conformational Transitions Revealed by Molecular Dynamics Simulations of the Binary Complex of Escherichia coli 6-Hydroxymethyl-7,8-dihydropterin Pyrophosphokinase with MgATP

6-Hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) catalyzes the first reaction in the folate biosynthetic pathway. Comparison of its X-ray and nuclear magnetic resonance structures suggests that the enzyme undergoes significant conformational change upon binding to its substrates, especially in three catalytic loops. Experimental research has shown that, in its binary form, even bound by analogues of MgATP, loops 2 and 3 remain rather flexible; this raises questions about the putative large-scale induced-fit conformational change of the HPPK-MgATP binary complex. In this work, long-time all-atomic molecular dynamics simulations were conducted to investigate the loop dynamics in this complex. Our simulations show that, with loop 3 closed, multiple conformations of loop 2, including the open, semiopen, and closed forms, are all accessible to the binary complex. These results provide valuable structural insights into the details of conformational changes upon 6-hydroxymethyl-7,8-dihydropterin (HP) binding and biological activities of HPPK. Conformational network analysis and principal component analysis related to the loops are also discussed.

ClustENM: ENM-Based Sampling of Essential Conformational Space at Full Atomic Resolution

Accurate sampling of conformational space and, in particular, the transitions between functional substates has been a challenge in molecular dynamic (MD) simulations of large biomolecular systems. We developed an Elastic Network Model (ENM)-based computational method, ClustENM, for sampling large conformational changes of biomolecules with various sizes and oligomerization states. ClustENM is an iterative method that combines ENM with energy minimization and clustering steps. It is an unbiased technique, which requires only an initial structure as input, and no information about the target conformation. To test the performance of ClustENM, we applied it to six biomolecular systems: adenylate kinase (AK), calmodulin, p38 MAP kinase, HIV-1 reverse transcriptase (RT), triosephosphate isomerase (TIM), and the 70S ribosomal complex. The generated ensembles of conformers determined at atomic resolution show good agreement with experimental data (979 structures resolved by X-ray and/or NMR) and encompass the subspaces covered in independent MD simulations for TIM, p38, and RT. ClustENM emerges as a computationally efficient tool for characterizing the conformational space of large systems at atomic detail, in addition to generating a representative ensemble of conformers that can be advantageously used in simulating substrate/ligand-binding events.

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.

Coupled folding and binding with 2D Window-Exchange Umbrella Sampling

Intrinsically disordered regions of proteins can gain structure by binding to a partner. This process, of coupled folding and binding (CFaB), is a fundamental part of many important biological processes. Structure-based models have proven themselves capable of revealing fundamental aspects of how CFaB occurs, however, typical methods to enhance the sampling of these transitions, such as replica exchange, do not adequately sample the transition state region of this extremely rare process. Here, we use a variant of Umbrella Sampling to enforce sampling of the transition states of CFaB of HdeA monomers at neutral pH, an extremely rare process that occurs over timescales ranging from seconds to hours. Using high resolution sampling in the transition state region, we cluster states along the principal transition path to obtain a detailed description of coupled binding and folding for the HdeA dimer, revealing new insight into the ensemble of states that are accessible to client recognition. We then demonstrate that exchanges between umbrella sampling windows, as done in previous work, significantly improve relaxation in variables orthogonal to the restraints used. Altogether, these results show that Window-Exchange Umbrella Sampling is a promising approach for systems that exhibit flexible binding, and can reveal transition state ensembles of these systems in high detail. © 2015 Wiley Periodicals, Inc.

Molecular dynamics simulations of biological membranes and membrane proteins using enhanced conformational sampling algorithms

This paper reviews various enhanced conformational sampling methods and explicit/implicit solvent/membrane models, as well as their recent applications to the exploration of the structure and dynamics of membranes and membrane proteins. Molecular dynamics simulations have become an essential tool to investigate biological problems, and their success relies on proper molecular models together with efficient conformational sampling methods. The implicit representation of solvent/membrane environments is reasonable approximation to the explicit all-atom models, considering the balance between computational cost and simulation accuracy. Implicit models can be easily combined with replica-exchange molecular dynamics methods to explore a wider conformational space of a protein. Other molecular models and enhanced conformational sampling methods are also briefly discussed. As application examples, we introduce recent simulation studies of glycophorin A, phospholamban, amyloid precursor protein, and mixed lipid bilayers and discuss the accuracy and efficiency of each simulation model and method. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Molecular dynamics simulations of the Escherichia coli HPPK apo-enzyme reveal a network of conformational transitions

6-Hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) catalyzes the first reaction in the folate biosynthetic pathway. Comparison of its X-ray and nuclear magnetic resonance structures suggests that the enzyme undergoes significant conformational change upon binding to its substrates, especially in three catalytic loops. Experimental research has shown that even when confined by crystal contacts, loops 2 and 3 remain rather flexible when the enzyme is in its apo form, raising questions about the putative large-scale induced-fit conformational change of HPPK. To investigate the loop dynamics in a crystal-free environment, we performed conventional molecular dynamics simulations of the apo-enzyme at two different temperatures (300 and 350 K). Our simulations show that the crystallographic B-factors considerably underestimate the loop dynamics; multiple conformations of loops 2 and 3, including the open, semi-open, and closed conformations that an enzyme must adopt throughout its catalytic cycle, are all accessible to the apo-enzyme. These results revise our previous view of the functional mechanism of conformational change upon MgATP binding and offer valuable structural insights into the workings of HPPK. In this paper, conformational network analysis and principal component analysis related to the loops are discussed to support the presented conclusions.

Energetics and structural characterization of the large-scale functional motion of adenylate kinase

Adenylate Kinase (AK) is a signal transducing protein that regulates cellular energy homeostasis balancing between different conformations. An alteration of its activity can lead to severe pathologies such as heart failure, cancer and neurodegenerative diseases. A comprehensive elucidation of the large-scale conformational motions that rule the functional mechanism of this enzyme is of great value to guide rationally the development of new medications. Here using a metadynamics-based computational protocol we elucidate the thermodynamics and structural properties underlying the AK functional transitions. The free energy estimation of the conformational motions of the enzyme allows characterizing the sequence of events that regulate its action. We reveal the atomistic details of the most relevant enzyme states, identifying residues such as Arg119 and Lys13, which play a key role during the conformational transitions and represent druggable spots to design enzyme inhibitors. Our study offers tools that open new areas of investigation on large-scale motion in proteins.

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.

Variance of a potential of mean force obtained using the weighted histogram analysis method

A potential of mean force (PMF) that provides the free energy of a thermally driven system along some chosen reaction coordinate (RC) is a useful descriptor of systems characterized by complex, high dimensional potential energy surfaces. Umbrella sampling window simulations use potential energy restraints to provide more uniform sampling along a RC so that potential energy barriers that would otherwise make equilibrium sampling computationally difficult can be overcome. Combining the results from the different biased window trajectories can be accomplished using the Weighted Histogram Analysis Method (WHAM). Here, we provide an analysis of the variance of a PMF along the reaction coordinate. We assume that the potential restraints used for each window lead to Gaussian distributions for the window reaction coordinate densities and that the data sampling in each window is from an equilibrium ensemble sampled so that successive points are statistically independent. Also, we assume that neighbor window densities overlap, as required in WHAM, and that further-than-neighbor window density overlap is negligible. Then, an analytic expression for the variance of the PMF along the reaction coordinate at a desired level of spatial resolution can be generated. The variance separates into a sum over all windows with two kinds of contributions: One from the variance of the biased window density normalized by the total biased window density and the other from the variance of the local (for each window's coordinate range) PMF. Based on the desired spatial resolution of the PMF, the former variance can be minimized relative to that from the latter. The method is applied to a model system that has features of a complex energy landscape evocative of a protein with two conformational states separated by a free energy barrier along a collective reaction coordinate. The variance can be constructed from data that is already available from the WHAM PMF construction.

Elucidating the ensemble of functionally-relevant transitions in protein systems with a robotics-inspired method

Background

Many proteins tune their biological function by transitioning between different functional states, effectively acting as dynamic molecular machines. Detailed structural characterization of transition trajectories is central to understanding the relationship between protein dynamics and function. Computational approaches that build on the Molecular Dynamics framework are in principle able to model transition trajectories at great detail but also at considerable computational cost. Methods that delay consideration of dynamics and focus instead on elucidating energetically-credible conformational paths connecting two functionally-relevant structures provide a complementary approach. Effective sampling-based path planning methods originating in robotics have been recently proposed to produce conformational paths. These methods largely model short peptides or address large proteins by simplifying conformational space.

Methods

We propose a robotics-inspired method that connects two given structures of a protein by sampling conformational paths. The method focuses on small- to medium-size proteins, efficiently modeling structural deformations through the use of the molecular fragment replacement technique. In particular, the method grows a tree in conformational space rooted at the start structure, steering the tree to a goal region defined around the goal structure. We investigate various bias schemes over a progress coordinate for balance between coverage of conformational space and progress towards the goal. A geometric projection layer promotes path diversity. A reactive temperature scheme allows sampling of rare paths that cross energy barriers.

Results and conclusions

Experiments are conducted on small- to medium-size proteins of length up to 214 amino acids and with multiple known functionally-relevant states, some of which are more than 13Å apart of each-other. Analysis reveals that the method effectively obtains conformational paths connecting structural states that are significantly different. A detailed analysis on the depth and breadth of the tree suggests that a soft global bias over the progress coordinate enhances sampling and results in higher path diversity. The explicit geometric projection layer that biases the exploration away from over-sampled regions further increases coverage, often improving proximity to the goal by forcing the exploration to find new paths. The reactive temperature scheme is shown effective in increasing path diversity, particularly in difficult structural transitions with known high-energy barriers.

Analysis of conformational motions and residue fluctuations for Escherichia coli ribose-binding protein revealed with elastic network models

The ribose-binding protein (RBP) is a sugar-binding bacterial periplasmic protein whose function is associated with a large allosteric conformational change from an open to a closed conformation upon binding to ribose. The open (ligand-free) and closed (ligand-bound) forms of RBP have been found. Here we investigate the conformational motions and residue fluctuations of the RBP by analyzing the modes of motion with two coarse-grained elastic network models, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM). The calculated B-factors in both the calculated models are in good agreement with the experimentally determined B-factors in X-ray crystal structures. The slowest mode analysis by GNM shows that both forms have the same motion hinge axes around residues Ser103, Gln235, Asp264 and the two domains of both structures have similar fluctuation range. The superposition of the first three dominant modes of ANM, consisting of the rotating, bending and twisting motions of the two forms, accounts for large rearrangement of domains from the ligand-free (open) to ligand-bound (closed) conformation and thus constitutes a critical component of the RBP's functions. By analyzing cross-correlations between residue fluctuation and the difference-distance plot, it is revealed that the conformational change can be described as a rigid rotation of the two domains with respect to each other, whereas the internal structure of the two domains remains largely intact. The results directly indicate that the dominant dynamic characteristics of protein structures can be captured from their static native state using coarse-grained models.

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.

Enhanced sampling algorithms

In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present various extensions of these three generalized-ensemble algorithms. The effectiveness of the methods is tested with short peptide and protein systems.

Minimum free energy path of ligand-induced transition in adenylate kinase

Large-scale conformational changes in proteins involve barrier-crossing transitions on the complex free energy surfaces of high-dimensional space. Such rare events cannot be efficiently captured by conventional molecular dynamics simulations. Here we show that, by combining the on-the-fly string method and the multi-state Bennett acceptance ratio (MBAR) method, the free energy profile of a conformational transition pathway in Escherichia coli adenylate kinase can be characterized in a high-dimensional space. The minimum free energy paths of the conformational transitions in adenylate kinase were explored by the on-the-fly string method in 20-dimensional space spanned by the 20 largest-amplitude principal modes, and the free energy and various kinds of average physical quantities along the pathways were successfully evaluated by the MBAR method. The influence of ligand binding on the pathways was characterized in terms of rigid-body motions of the lid-shaped ATP-binding domain (LID) and the AMP-binding (AMPbd) domains. It was found that the LID domain was able to partially close without the ligand, while the closure of the AMPbd domain required the ligand binding. The transition state ensemble of the ligand bound form was identified as those structures characterized by highly specific binding of the ligand to the AMPbd domain, and was validated by unrestrained MD simulations. It was also found that complete closure of the LID domain required the dehydration of solvents around the P-loop. These findings suggest that the interplay of the two different types of domain motion is an essential feature in the conformational transition of the enzyme.

Simulations of temperature and salt concentration effects on bZIP, a basic region leucine zipper

Basic region leucine zipper (bZIP) transcription factors are dimeric proteins that recognize DNA. The monomers consist of a leucine zipper subdomain responsible for dimerization and a highly basic DNA recognition subdomain. Twelve explicit solvent molecular dynamics (MD) trajectories were run on the GCN4 bZIP transcriptional factor in the absence of DNA at three temperatures and two ion concentrations (0 mM with Cl(-) ions to neutralize the bZIP and 200 mM with additional Na(+) and Cl(-) ions) to probe the conformational ensemble that the basic region samples. In most trajectories, the basic region exhibits an alligator-jaw-like opening and closing (only one monomer moves), versus scissor-like motion, by a mainly rigid body, hinge motion centered on three "fork" residues that span the basic region to the coiled coil. In this motion, the α-helical character of the basic region monomers is mostly maintained. A broad range of distances is accessed, consistent with the absence of particular interactions for the basic region monomers. In two of the trajectories, the basic region monomers "collapse" to form a stable state. The coiled coil, leucine zipper subdomain is very stable for all of the trajectories. Ion solvation of the charged residue side chains is transient, on the scale of a few picoseconds. There is no evidence for persistent specific ion salt bridges to charged residues. For 0 mM, only certain basic region positively charged residues are substantially Cl(-) ion salt bridged. For 200 mM, in addition, some basic region negatively (positively) charged residues are salt bridged to Na(+) (Cl(-)) ions. The different ion solvation patterns at the two ion concentrations are not greatly temperature sensitive, and the conformational sampling found in the MD is remarkably unperturbed by ion concentration and/or temperature.

Predicting flexible loop regions that interact with ligands: the challenge of accurate scoring

Flexible loop regions play a critical role in the biological function of many proteins and have been shown to be involved in ligand binding. In the context of structure-based drug design, using or predicting an incorrect loop configuration can be detrimental to the study if the loop is capable of interacting with the ligand. Three protein systems, each with at least one flexible loop region in close proximity to the known binding site, were selected for loop prediction using the CorLps program; a six residue loop region from phosphoribosylglycinamide formyltransferase (GART), two nine residue loop regions from cytochrome P450 (CYP) 119, and an 11 residue loop region from enolase were selected for loop prediction. The results of this study indicate that the statistically based DFIRE scoring function implemented in the CorLps program did not accurately rank native-like predicted loop configurations in any protein system. In an attempt to improve the ranking of the native-like predicted loop configurations, the MM/GBSA and the optimized MM/GBSA-dsr scoring functions were used to re-rank the predicted loops with and without bound ligand. In general, single snapshot MM/GBSA scoring provided the best ranking of native-like loop configurations. Based on the scoring function analyses presented, the optimal ranking of native-like loop configurations is still a difficult challenge and the choice of the "best" scoring function appears to be system dependent.

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.

Efficient incorporation of protein flexibility and dynamics into molecular docking simulations

Flexibility and dynamics are protein characteristics that are essential for the process of molecular recognition. Conformational changes in the protein that are coupled to ligand binding are described by the biophysical models of induced fit and conformational selection. Different concepts that incorporate protein flexibility into protein-ligand docking within the context of these two models are reviewed. Several computational studies that discuss the validity and possible limitations of such approaches will be presented. Finally, different approaches that incorporate protein dynamics, e.g., configurational entropy, and solvation effects into docking will be highlighted.

Free energy of conformational transition paths in biomolecules: the string method and its application to myosin VI

A set of techniques developed under the umbrella of the string method is used in combination with all-atom molecular dynamics simulations to analyze the conformation change between the prepowerstroke (PPS) and rigor (R) structures of the converter domain of myosin VI. The challenges specific to the application of these techniques to such a large and complex biomolecule are addressed in detail. These challenges include (i) identifying a proper set of collective variables to apply the string method, (ii) finding a suitable initial string, (iii) obtaining converged profiles of the free energy along the transition path, (iv) validating and interpreting the free energy profiles, and (v) computing the mean first passage time of the transition. A detailed description of the PPS↔R transition in the converter domain of myosin VI is obtained, including the transition path, the free energy along the path, and the rates of interconversion. The methodology developed here is expected to be useful more generally in studies of conformational transitions in complex biomolecules.

A hamiltonian replica exchange method for building protein-protein interfaces applied to a leucine zipper

Leucine zippers consist of alpha helical monomers dimerized (or oligomerized) into alpha superhelical structures known as coiled coils. Forming the correct interface of a dimer from its monomers requires an exploration of configuration space focused on the side chains of one monomer that must interdigitate with sites on the other monomer. The aim of this work is to generate good interfaces in short simulations starting from separated monomers. Methods are developed to accomplish this goal based on an extension of a previously introduced [Su and Cukier, J. Phys. Chem. B 113, 9595, (2009)] hamiltonian temperature replica exchange method (HTREM), which scales the hamiltonian in both potential and kinetic energies that was used for the simulation of dimer melting curves. The new method, HTREM_MS (MS designates mean square), focused on interface formation, adds restraints to the hamiltonians for all but the physical system, which is characterized by the normal molecular dynamics force field at the desired temperature. The restraints in the nonphysical systems serve to prevent the monomers from separating too far, and have the dual aims of enhancing the sampling of close in configurations and breaking unwanted correlations in the restrained systems. The method is applied to a 31-residue truncation of the 33-residue leucine zipper (GCN4-p1) of the yeast transcriptional activator GCN4. The monomers are initially separated by a distance that is beyond their capture length. HTREM simulations show that the monomers oscillate between dimerlike and monomerlike configurations, but do not form a stable interface. HTREM_MS simulations result in the dimer interface being faithfully reconstructed on a 2 ns time scale. A small number of systems (one physical and two restrained with modified potentials and higher effective temperatures) are sufficient. An in silico mutant that should not dimerize because it lacks charged residues that provide electrostatic stabilization of the dimer does not with HTREM_MS, giving confidence in the method. The interface formation time scale is sufficiently short that using HTREM_MS as a screening tool to validate leucine zipper design methods may be feasible.

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

We characterized the conformational change of adenylate kinase (AK) between open and closed forms by conducting five all-atom molecular-dynamics simulations, each of 100 ns duration. Different initial structures and substrate binding configurations were used to probe the pathways of AK conformational change in explicit solvent, and no bias potential was applied. A complete closed-to-open and a partial open-to-closed transition were observed, demonstrating the direct impact of substrate-mediated interactions on shifting protein conformation. The sampled configurations suggest two possible pathways for connecting the open and closed structures of AK, affirming the prediction made based on available x-ray structures and earlier works of coarse-grained modeling. The trajectories of the all-atom molecular-dynamics simulations revealed the complexity of protein dynamics and the coupling between different domains during conformational change. Calculations of solvent density and density fluctuations surrounding AK did not show prominent variation during the transition between closed and open forms. Finally, we characterized the effects of local unfolding of an important hinge near Pro(177) on the closed-to-open transition of AK and identified a novel mechanism by which hinge unfolding modulates protein conformational change. The local unfolding of Pro(177) hinge induces alternative tertiary contacts that stabilize the closed structure and prevent the opening transition.

Conformational coupling, bridge helix dynamics and active site dehydration in catalysis by RNA polymerase

Molecular dynamics simulation of Thermus thermophilus (Tt) RNA polymerase (RNAP) in a catalytic conformation demonstrates that the active site dNMP-NTP base pair must be substantially dehydrated to support full active site closing and optimum conditions for phosphodiester bond synthesis. In silico mutant beta R428A RNAP, which was designed based on substitutions at the homologous position (Rpb2 R512) of Saccharomyces cerevisiae (Sc) RNAP II, was used as a reference structure to compare to Tt RNAP in simulations. Long range conformational coupling linking a dynamic segment of the bridge alpha-helix, the extended fork loop, the active site, and the trigger loop-trigger helix is apparent and adversely affected in beta R428A RNAP. Furthermore, bridge helix bending is detected in the catalytic structure, indicating that bridge helix dynamics may regulate phosphodiester bond synthesis as well as translocation. An active site "latch" assembly that includes a key trigger helix residue Tt beta' H1242 and highly conserved active site residues beta E445 and R557 appears to help regulate active site hydration/dehydration. The potential relevance of these observations in understanding RNAP and DNAP induced fit and fidelity is discussed.