Escherichia coli adenylate kinase dynamics: comparison of elastic network model modes with mode-coupling (15)N-NMR relaxation data

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.

Protein Dynamics to Define and Refine Disordered Protein Ensembles

Intrinsically disordered proteins and unfolded proteins have fluctuating conformational ensembles that are fundamental to their biological function and impact protein folding, stability, and misfolding. Despite the importance of protein dynamics and conformational sampling, time-dependent data types are not fully exploited when defining and refining disordered protein ensembles. Here we introduce a computational framework using an elastic network model and normal-mode displacements to generate a dynamic disordered ensemble consistent with NMR-derived dynamics parameters, including transverse R₂ relaxation rates and Lipari-Szabo order parameters (S² values). We illustrate our approach using the unfolded state of the drkN SH3 domain to show that the dynamical ensembles give better agreement than a static ensemble for a wide range of experimental validation data including NMR chemical shifts, J-couplings, nuclear Overhauser effects, paramagnetic relaxation enhancements, residual dipolar couplings, hydrodynamic radii, single-molecule fluorescence Förster resonance energy transfer, and small-angle X-ray scattering.

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.

Identification of key sites controlling protein functional motions by using elastic network model combined with internal coordinates

The elastic network model (ENM) is an effective method to extract the intrinsic dynamical properties encoded in protein tertiary structures. We have proposed a new ENM-based analysis method to reveal the motion modes directly responsible for a specific protein function, in which an internal coordinate related to the specific function was introduced to construct the internal/Cartesian hybrid coordinate space. In the present work, the function-related internal coordinates combined with a linear perturbation method were applied to identify the key sites controlling specific protein functional motions. The change in the fluctuations of the internal coordinate in response to residue perturbation was calculated in the hybrid coordinate space by using the linear response theory. The residues with the large fluctuation changes were identified to be the key sites that allosterically control the specific protein function. Two proteins, i.e., human DNA polymerase β and the chaperonin from Methanococcus maripaludis, were investigated as case studies, in which several collective and local internal coordinates were applied to identify the functionally key residues of these two studied proteins. The calculation results are consistent with the experimental observations. It is found that different collective internal coordinates lead to similar results, where the predicted functionally key sites are located at similar positions in the protein structure. While for the local internal coordinates, the predicted key sites tend to be situated at the region near to the coordinate-involving residues. Our studies provide a starting point for further exploring other function-related internal coordinates for other interesting proteins.

Allostery in Its Many Disguises: From Theory to Applications

Allosteric regulation plays an important role in many biological processes, such as signal transduction, transcriptional regulation, and metabolism. Allostery is rooted in the fundamental physical properties of macromolecular systems, but its underlying mechanisms are still poorly understood. A collection of contributions to a recent interdisciplinary CECAM (Center Européen de Calcul Atomique et Moléculaire) workshop is used here to provide an overview of the progress and remaining limitations in the understanding of the mechanistic foundations of allostery gained from computational and experimental analyses of real protein systems and model systems. The main conceptual frameworks instrumental in driving the field are discussed. We illustrate the role of these frameworks in illuminating molecular mechanisms and explaining cellular processes, and describe some of their promising practical applications in engineering molecular sensors and informing drug design efforts.

Using Spectral Representation to Classify Proteins' Conformational States

Numerous proteins are molecular targets for drug action and hence are important in drug discovery. Structure-based computational drug discovery relies on detailed information regarding protein conformations for subsequent drug screening in silico. There are two key issues in analyzing protein conformations in virtual screening. The first considers the protein’s conformational change in response to physical and chemical conditions. The second is the protein’s atomic resolution reconstruction from X-ray crystallography or nuclear magnetic resonance (NMR) data. In this latter problem, information is needed regarding the sample’s position relative to the source of X-rays. Here, we introduce a new measure for classifying protein conformational states using spectral representation and Wigner’s D-functions. Predictions based on the new measure are in good agreement with conformational states of proteins. These results could also be applied to improve conformational alignment of the snapshots given by protein crystallography.

A probabilistic network model for structural transitions in biomolecules

Biological macromolecules often undergo large conformational rearrangements during a functional cycle. To simulate these structural transitions with full atomic detail typically demands extensive computational resources. Moreover, it is unclear how to incorporate, in a principled way, additional experimental information that could guide the structural transition. This article develops a probabilistic model for conformational transitions in biomolecules. The model can be viewed as a network of anharmonic springs that break, if the experimental data support the rupture of bonds. Hamiltonian Monte Carlo in internal coordinates is used to infer structural transitions from experimental data, thereby sampling large conformational transitions without distorting the structure. The model is benchmarked on a large set of conformational transitions. Moreover, we demonstrate the use of the probabilistic network model for integrative modeling of macromolecular complexes based on data from crosslinking followed by mass spectrometry.

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.

Choreography of the Reductase and P450BM3 Domains Toward Electron Transfer Is Instigated by the Substrate

The driving force for the electron transfer (ET) step in the catalytic cycle of cytochrome P450_BM3 is investigated using three sets of 1 μs molecular dynamic simulations for the resting state of P450 in complex with the flavin (FMN) in the reductase domain. These sets involve the following: (i) substrate-free (SF), (ii) substrate (N-palmitoyl glycine, i.e., NPG)-bound (SB), and (iii) SB with the semiquinone radical anion (SQ^-) of FMN. Starting from the X-ray structure of the SF heme domain, we observe that the α1-helix (of the reductase) and the C-helix (of the heme) undergo reorientation to a parallel orientation, which is the thermochemically stable form. The reorientation of the helices pushes away the FMN to a distance of 18.4 Å from the heme's center. When the substrate binds it causes the I-helix of the heme domain to kink and push the C-helix toward the α1-helix, thereby locking the latter two into a stabilized perpendicular conformation, wherein the FMN-heme distance is 12 Å. The distance drops further in the SQ^- form, and upon QM/MM geometry optimization the two moieties approach 8.8 Å, which enhances the ET rate (by 10⁴-10⁶ fold) to the heme's Fe³⁺ ion. These motions are driven by hydrogen bond strengthening between the C- and the α1-helices. Finally, substrate binding leads to formation of an organized water chain connecting the FMN and heme moieties. The water channel assists the ET and couples it to the proton transfer steps that should activate O₂ and create the oxo-iron active species.

A new algorithm for construction of coarse-grained sites of large biomolecules

The development of coarse-grained (CG) models for large biomolecules remains a challenge in multiscale simulations, including a rigorous definition of CG representations for them. In this work, we proposed a new stepwise optimization imposed with the boundary-constraint (SOBC) algorithm to construct the CG sites of large biomolecules, based on the s cheme of essential dynamics CG. By means of SOBC, we can rigorously derive the CG representations of biomolecules with less computational cost. The SOBC is particularly efficient for the CG definition of large systems with thousands of residues. The resulted CG sites can be parameterized as a CG model using the normal mode analysis based fluctuation matching method. Through normal mode analysis, the obtained modes of CG model can accurately reflect the functionally related slow motions of biomolecules. The SOBC algorithm can be used for the construction of CG sites of large biomolecules such as F-actin and for the study of mechanical properties of biomaterials.

Oncogenic mutations weaken the interactions that stabilize the p110α-p85α heterodimer in phosphatidylinositol 3-kinase α

Phosphatidylinositol 3-kinase (PI3K) α is a heterodimeric lipid kinase that catalyzes the conversion of phosphoinositol-4,5-bisphosphate to phosphoinositol-3,4,5-trisphosphate. The PI3Kα signaling pathway plays an important role in cell growth, proliferation, and survival. This pathway is activated in numerous cancers, where the PI3KCA gene, which encodes for the p110α PI3Kα subunit, is mutated. Its mutation often results in gain of enzymatic activity; however, the mechanism of activation by oncogenic mutations remains unknown. Here, using computational methods, we show that oncogenic mutations that are far from the catalytic site and increase the enzymatic affinity destabilize the p110α-p85α dimer. By affecting the dynamics of the protein, these mutations favor the conformations that reduce the autoinhibitory effect of the p85α nSH2 domain. For example, we determined that, in all of the mutants, the nSH2 domain shows increased positional heterogeneity as compared with the wild-type, as demonstrated by changes in the fluctuation profiles computed by normal mode analysis of coarse-grained elastic network models. Analysis of the interdomain interactions of the wild-type and mutants at the p110α-p85α interface obtained with molecular dynamics simulations suggest that all of the tumor-associated mutations effectively weaken the interactions between p110α and p85α by disrupting key stabilizing interactions. These findings have important implications for understanding how oncogenic mutations change the conformational multiplicity of PI3Kα and lead to increased enzymatic activity. This mechanism may apply to other enzymes and/or macromolecular complexes that play a key role in cell signaling.

Encompassing receptor flexibility in virtual screening using ensemble docking-based hybrid QSAR: discovery of novel phytochemicals for BACE1 inhibition

Mimicking receptor flexibility during receptor-ligand binding is a challenging task in computational drug design since it is associated with a large increase in the conformational search space. In the present study, we have devised an in silico design strategy incorporating receptor flexibility in virtual screening to identify potential lead compounds as inhibitors for flexible proteins. We have considered BACE1 (β-secretase), a key target protease from a therapeutic perspective for Alzheimer's disease, as the highly flexible receptor. The protein undergoes significant conformational transitions from open to closed form upon ligand binding, which makes it a difficult target for inhibitor design. We have designed a hybrid structure-activity model containing both ligand based descriptors and energetic descriptors obtained from molecular docking based on a dataset of structurally diverse BACE1 inhibitors. An ensemble of receptor conformations have been used in the docking study, further improving the prediction ability of the model. The designed model that shows significant prediction ability judged by several statistical parameters has been used to screen an in house developed 3-D structural library of 731 phytochemicals. 24 highly potent, novel BACE1 inhibitors with predicted activity (Ki) ≤ 50 nM have been identified. Detailed analysis reveals pharmacophoric features of these novel inhibitors required to inhibit BACE1.

Protein unfolding from free-energy calculations: integration of the Gaussian network model with bond binding energies

Motivated by single molecule experiments, we study thermal unfolding pathways of four proteins, chymotrypsin inhibitor, barnase, ubiquitin, and adenylate kinase, using bond network models that combine bond energies and elasticity. The protein elasticity is described by the Gaussian network model (GNM), to which we add prescribed bond binding energies that are assigned to all (nonbackbone) connecting bonds in the GNM of native state and assumed identical for simplicity. Using exact calculation of the Helmholtz free energy for this model, we consider bond rupture single events. The bond designated for rupture is chosen by minimizing the free-energy difference for the process, over all (nonbackbone) bonds in the network. Plotting the free-energy profile along this pathway at different temperatures, we observe a few major partial unfolding, metastable or stable, states, that are separated by free-energy barriers and change role as the temperature is raised. In particular, for adenylate kinase we find three major partial unfolding states, which is consistent with single molecule FRET experiments [Pirchi et al., Nat. Commun. 2, 493 (2011)] for which hidden Markov analysis reveals between three and five such states. Such states can play a major role in enzymatic activity.

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.

Aligning experimental and theoretical anisotropic B-factors: water models, normal-mode analysis methods, and metrics

The strength of X-ray crystallography in providing the information for protein dynamics has been under appreciated. The anisotropic B-factors (ADPs) from high-resolution structures are invaluable in studying the relationship among structure, dynamics, and function. Here, starting from an in-depth evaluation of the metrics used for comparing the overlap between two ellipsoids, we applied normal-mode analysis (NMA) to predict the theoretical ADPs and then align them with experimental results. Adding an extra layer of explicitly treated water on protein surface significantly improved the energy minimization results and better reproduced the anisotropy of experimental ADPs. In comparing experimental and theoretical ADPs, we focused on the overlap in shape, the alignment of dominant directions, and the similarity in magnitude. The choices of water molecules, NMA methods, and the metrics for evaluating the overlap of ADPs determined final results. This study provides useful information for exploring the physical basis and the application potential of experimental ADPs.

A conformational intermediate in glutamate receptor activation

Ionotropic glutamate receptors (iGluRs) transduce the chemical signal of neurotransmitter release into membrane depolarization at excitatory synapses in the brain. The opening of the transmembrane ion channel of these ligand-gated receptors is driven by conformational transitions that are induced by the association of glutamate molecules to the ligand-binding domains (LBDs). Here, we describe the crystal structure of a GluA2 LBD tetramer in a configuration that involves an ∼30° rotation of the LBD dimers relative to the crystal structure of the full-length receptor. The configuration is stabilized by an engineered disulfide crosslink. Biochemical and electrophysiological studies on full-length receptors incorporating either this crosslink or an engineered metal bridge show that this LBD configuration corresponds to an intermediate state of receptor activation. GluA2 activation therefore involves a combination of both intra-LBD (cleft closure) and inter-LBD dimer conformational transitions. Overall, these results provide a comprehensive structural characterization of an iGluR intermediate state.

The interplay of structure and dynamics: insights from a survey of HIV-1 reverse transcriptase crystal structures

HIV-1 reverse transcriptase (RT) is a critical drug target for HIV treatment, and understanding the exact mechanisms of its function and inhibition would significantly accelerate the development of new anti-HIV drugs. It is well known that structure plays a critical role in protein function, but for RT, structural information has proven to be insufficient-despite enormous effort-to explain the mechanism of inhibition and drug resistance of non-nucleoside RT inhibitors. We hypothesize that the missing link is dynamics, information about the motions of the system. However, many of the techniques that give the best information about dynamics, such as solution nuclear magnetic resonance and molecular dynamics simulations, cannot be easily applied to a protein as large as RT. As an alternative, we combine elastic network modeling with simultaneous hierarchical clustering of structural and dynamic data. We present an extensive survey of the dynamics of RT bound to a variety of ligands and with a number of mutations, revealing a novel mechanism for drug resistance to non-nucleoside RT inhibitors. Hydrophobic core mutations restore active-state motion to multiple functionally significant regions of HIV-1 RT. This model arises out of a combination of structural and dynamic information, rather than exclusively from one or the other.

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.

Cooperativity in thermal and force-induced protein unfolding: integration of crack propagation and network elasticity models

We investigate force-induced and temperature-induced unfolding of proteins using the combination of a gaussian network model and a crack propagation model based on "bond"-breaking independent events. We assume the existence of threshold values for the mean strain and strain fluctuations that dictate bond rupture. Surprisingly, we find that this stepwise process usually leads to a few cooperative, first-order-like, transitions in which several bonds break simultaneously, reminiscent of the "avalanches" seen in disordered networks.

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.

Dynamics of endoglucanase catalytic domains: implications towards thermostability

Thermostable endoglucanases play a crucial role in the production of biofuels to breakdown plant cellulose. Analyzing their structure-dynamics relationship can inform about the origins of their thermostability. Although tertiary structures of many endoglucanase proteins are available, the relationship between thermostability, structure, and dynamics is not explored fully. We have generated elastic network models for thermostable and mesostable endoglucanases with the (αβ)₈ fold in substrate bound and unbound states. The comparative analyses shed light on the relation between protein dynamics, thermostability, and substrate binding. We observed specific differences in the dynamic behavior of catalytic residues in slow modes: while both the nucleophile and the acid/base donor residues show positively correlated motions in the thermophile, their dynamics is uncoupled in the mesophile. Our proof-of-concept comparison study suggests that global dynamics can be harnessed to further our understanding of thermostability.

An adaptive weighted ensemble procedure for efficient computation of free energies and first passage rates

We introduce an adaptive weighted-ensemble procedure (aWEP) for efficient and accurate evaluation of first-passage rates between states for two-state systems. The basic idea that distinguishes aWEP from conventional weighted-ensemble (WE) methodology is the division of the configuration space into smaller regions and equilibration of the trajectories within each region upon adaptive partitioning of the regions themselves into small grids. The equilibrated conditional∕transition probabilities between each pair of regions lead to the determination of populations of the regions and the first-passage times between regions, which in turn are combined to evaluate the first passage times for the forward and backward transitions between the two states. The application of the procedure to a non-trivial coarse-grained model of a 70-residue calcium binding domain of calmodulin is shown to efficiently yield information on the equilibrium probabilities of the two states as well as their first passage times. Notably, the new procedure is significantly more efficient than the canonical implementation of the WE procedure, and this improvement becomes even more significant at low temperatures.

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.

Pre-existing soft modes of motion uniquely defined by native contact topology facilitate ligand binding to proteins

Modeling protein flexibility constitutes a major challenge in accurate prediction of protein-ligand and protein-protein interactions in docking simulations. The lack of a reliable method for predicting the conformational changes relevant to substrate binding prevents the productive application of computational docking to proteins that undergo large structural rearrangements. Here, we examine how coarse-grained normal mode analysis has been advantageously applied to modeling protein flexibility associated with ligand binding. First, we highlight recent studies that have shown that there is a close agreement between the large-scale collective motions of proteins predicted by elastic network models and the structural changes experimentally observed upon ligand binding. Then, we discuss studies that have exploited the predicted soft modes in docking simulations. Two general strategies are noted: pregeneration of conformational ensembles that are then utilized as input for standard fixed-backbone docking and protein structure deformation along normal modes concurrent to docking. These studies show that the structural changes apparently "induced" upon ligand binding occur selectively along the soft modes accessible to the protein prior to ligand binding. They further suggest that proteins offer suitable means of accommodating/facilitating the recognition and binding of their ligand, presumably acquired by evolutionary selection of the suitable three-dimensional structure.

A normal mode-based geometric simulation approach for exploring biologically relevant conformational transitions in proteins

A three-step approach for multiscale modeling of protein conformational changes is presented that incorporates information about preferred directions of protein motions into a geometric simulation algorithm. The first two steps are based on a rigid cluster normal-mode analysis (RCNMA). Low-frequency normal modes are used in the third step (NMSim) to extend the recently introduced idea of constrained geometric simulations of diffusive motions in proteins by biasing backbone motions of the protein, whereas side-chain motions are biased toward favorable rotamer states. The generated structures are iteratively corrected regarding steric clashes and stereochemical constraint violations. The approach allows performing three simulation types: unbiased exploration of conformational space; pathway generation by a targeted simulation; and radius of gyration-guided simulation. When applied to a data set of proteins with experimentally observed conformational changes, conformational variabilities are reproduced very well for 4 out of 5 proteins that show domain motions, with correlation coefficients r > 0.70 and as high as r = 0.92 in the case of adenylate kinase. In 7 out of 8 cases, NMSim simulations starting from unbound structures are able to sample conformations that are similar (root-mean-square deviation = 1.0-3.1 Å) to ligand bound conformations. An NMSim generated pathway of conformational change of adenylate kinase correctly describes the sequence of domain closing. The NMSim approach is a computationally efficient alternative to molecular dynamics simulations for conformational sampling of proteins. The generated conformations and pathways of conformational transitions can serve as input to docking approaches or as starting points for more sophisticated sampling techniques.

Role of loop dynamics in thermal stability of mesophilic and thermophilic adenylosuccinate synthetase: a molecular dynamics and normal mode analysis study

Enzymes from thermophiles are poorly active at temperatures at which their mesophilic homologs exhibit high activity and attain corresponding active states at high temperatures. In this study, comparative molecular dynamics (MD) simulations, supplemented by normal mode analysis, have been performed on an enzyme Adenylosuccinate synthetase (AdSS) from E. coli (mesophilic) and P. horikoshii (thermophilic) systems to understand the effects of loop dynamics on thermal stability of AdSS. In mesophilic AdSS, both ligand binding and catalysis are facilitated through the coordinated movement of five loops on the protein. The simulation results suggest that thermophilic P. horikoshii preserves structure and catalytic function at high temperatures by using the movement of only a subset of loops (two out of five) for ligand binding and catalysis unlike its mesophilic counterpart in E. coli. The pre-arrangement of the catalytic residues in P. horikoshii is well-preserved and salt bridges remain stable at high temperature (363K). The simulations suggest a general mechanism (including pre-arrangement of catalytic residues, increased polar residue content, stable salt bridges, increased rigidity, and fewer loop movements) used by thermophilic enzymes to preserve structure and be catalytically active at elevated temperatures.

Identification of functional motions in the adenylate kinase (ADK) protein family by computational hybrid approaches

Based on integrative computational hybrid approaches that combined statistical coupling analysis (SCA), molecular dynamics (MD), and normal mode analysis (NMA), evolutionarily coupled residues involved in functionally relevant motion in the adenylate kinase protein family were identified. The hybrids identified four top-ranking site pairs that belong to a conserved hydrogen bond network that is involved in the enzyme's flexibility. A second group of top-ranking site pairs was identified in critical regions for functional dynamics, such as those related to enzymatic turnover. The high consistency of the results obtained by SCA with NMA (SCA.NMA) and by SCA.MD hybrid analyses suggests that suitable replacement of the matrix of cross-correlation analysis of atomic fluctuations (derived by using NMA) with those based on MD contributes to the identification of such sites by means of a fast computational calculation. The analysis presented here strongly supports the hypothesis that evolutionary forces, such as coevolution at the sequence level, have promoted functional dynamic properties of the adenylate kinase protein family. Finally, these hybrid approaches can be used to identify, at the residue level, protein motion coordination patterns not previously observed, such as in hinge regions.

Conformational transition in the substrate binding domain of β-secretase exploited by NMA and its implication in inhibitor recognition: BACE1-myricetin a case study

BACE1 is a key protease involved in the proteolysis of amyloid precursor protein (APP) that generates a toxic peptide amyloid beta (Aβ), a pathological feature of Alzheimer's disease (AD). The enzyme is believed to possess an open and a closed conformation that corresponds to its free and inhibitor-bound form respectively. Here, we study the dynamic transition of BACE1 employing normal mode analysis (NMA) using a simplified elastic network model (ENM). Estimation of the catalytic cavity volume on the structures of BACE1 encoded by the lowest frequency normal mode reveals the dynamical transition of the enzyme from the open to the closed conformer. Detailed analysis reveals that concerted movement of different loop segments in the active site of the protein, namely flap regions, 10s loop, A loop and F loop, squeeze the catalytic cavity between the N-terminal and C-terminal lobe of the substrate binding domain of BACE1. We also propose that the NMA encoded multiple receptor conformations (MRC) of BACE1 elucidate the pharmacophoric feature necessary to inhibit the enzyme by a polyphenol, myricetin. van der Waals interaction is found to be the main driving force that guides the ligand induced conformational switching to the closed conformer. We suggest that NMA derived MRC of BACE1 is an efficient way to treat the receptor flexibility in docking and thus can be further applied in virtual screening and structure based drug design.

An enhanced molecular dynamics study of HPPK-ATP conformation space exploration and ATP binding to HPPK

HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase) catalyzes the transfer of pyrophosphate from ATP to HP (6-hydroxymethyl-7,8-dihydropterin). This first reaction in the folate biosynthetic pathway is an important target for potential antimicrobial agents. In this work, the mechanism by which HPPK traps and binds ATP is studied by molecular dynamics (MD)-based methods. Based on the ternary crystal structure of HPPK with an ATP mimic and HP, a complex of ATPMg(2) and HPPK is simulated and found to undergo small conformational changes with conventional MD, as does also conventional MD when started from the apo crystal structure. The introduction of restraints in the MD that serve to move HPPK-ATP from its ternary complex (closed) to apo-like (open) forms shows that throughout the restraint path ATP remains bound to HPPK. That ATP remains bound suggests that there is an ensemble of conformations with ATP bound to HPPK that span the apo to more ligand-bound-like conformations, consistent with the pre-existing equilibrium hypothesis of ligand binding, whereby a ligand can select from and bind to a broad range of protein conformations. In the apo-like conformations, ATPMg(2) remains bound to HPPK through a number of mainly salt-bridge-like interactions between several negatively charged residues and the two magnesium cations. The introduction of a reweight method that enhances the sampling of MD by targeting explicit terms in the force field helps define the interactions that bind ATP to HPPK. Using the reweight method, conformational and center of mass motions of ATP, driven by the breaking and making of hydrogen bonds and salt bridges, are identified that lead to ATP separating from HPPK. An elastic normal mode (ENM) approach to opening the ternary complex and closing the apo crystal structures was carried out. The ENM analysis of the apo structure analysis shows one mode that does have a closing motion of HPPK loops, but the direction does not correlate strongly with the loop motions that are required for forming the ternary complex.

Tracing conformational changes in proteins

Background

Many proteins undergo extensive conformational changes as part of their functionality. Tracing these changes is important for understanding the way these proteins function. Traditional biophysics-based conformational search methods require a large number of calculations and are hard to apply to large-scale conformational motions.

Results

In this work we investigate the application of a robotics-inspired method, using backbone and limited side chain representation and a coarse grained energy function to trace large-scale conformational motions. We tested the algorithm on four well known medium to large proteins and we show that even with relatively little information we are able to trace low-energy conformational pathways efficiently. The conformational pathways produced by our methods can be further filtered and refined to produce more useful information on the way proteins function under physiological conditions.

Conclusions

The proposed method effectively captures large-scale conformational changes and produces pathways that are consistent with experimental data and other computational studies. The method represents an important first step towards a larger scale modeling of more complex biological systems.

Allosteric Conformational Transition in Adenylate Kinase: Dynamic Correlations and Implication for Allostery

An essential aspect of protein science is to determine the deductive relationship between structure, dynamics, and various sets of functions. The role of dynamics is currently challenging our understanding of protein functions, both experimentally and theoretically. To verify the internal fluctuations and dynamics correlations in an enzyme protein undergoing conformational transitions, we have applied a coarse-grained dynamics algorithm using the elastic network model for adenylate kinase. Normal mode analysis reveals possible dynamical and allosteric pathways for the transition between the open and the closed states of adenylate kinase. As the ligands binding induces significant flexibility changes of the nucleotides monophosphate (NMP) domain and adenosine triphosphate (ATP) domain, the diagonalized correlation between different structural transition states shows that most correlated motions occur between the NMP domain and the helices surrounding the ATP domain. The simultaneous existence of positive and negative correlations indicates that the conformational changes of adenylate kinase take place in an allosteric manner. Analyses of the cumulated normal mode overlap coefficients and long-range correlated motion provide new insights of operating mechanisms and dynamics of adenylate kinase. They also suggest a quantitative dynamics criterion for determining the allosteric cooperativity, which may be applicable to other proteins.

Zipping and unzipping of adenylate kinase: atomistic insights into the ensemble of open<-->closed transitions

Adenylate kinase (AdK), a phosphotransferase enzyme, plays an important role in cellular energy homeostasis. It undergoes a large conformational change between an open and a closed state, even in the absence of substrate. We investigate the apo-AdK transition at the atomic level both with free-energy calculations and with our new dynamic importance sampling (DIMS) molecular dynamics method. DIMS is shown to sample biologically relevant conformations as verified by comparing an ensemble of hundreds of DIMS transitions to AdK crystal structure intermediates. The simulations reveal in atomic detail how hinge regions partially and intermittently unfold during the transition. Conserved salt bridges are seen to have important structural and dynamic roles; in particular, four ionic bonds that open in a sequential, zipper-like fashion and, thus, dominate the free-energy landscape of the transition are identified. Transitions between the closed and open conformations only have to overcome moderate free-energy barriers. Unexpectedly, the closed state and the open state encompass broad free-energy basins that contain conformations differing in domain hinge motions by up to 40 degrees . The significance of these extended states is discussed in relation to recent experimental Förster resonance energy transfer measurements. Taken together, these results demonstrate how a small number of cooperative key interactions can shape the overall dynamics of an enzyme and suggest an "all-or-nothing" mechanism for the opening and closing of AdK. Our efficient DIMS molecular dynamics computer simulation approach can provide a detailed picture of a functionally important macromolecular transition and thus help to interpret and suggest experiments to probe the conformational landscape of dynamic proteins such as AdK.

Substrate induced structural and dynamics changes in human phosphomevalonate kinase and implications for mechanism

Phosphomevalonate kinase (PMK) catalyzes an essential step in the mevalonate pathway, which is the only pathway for synthesis of isoprenoids and steroids in humans. PMK catalyzes transfer of the gamma-phosphate of ATP to mevalonate 5-phosphate (M5P) to form mevalonate 5-diphosphate. Bringing these phosphate groups in proximity to react is especially challenging, given the high negative charge density on the four phosphate groups in the active site. As such, conformational and dynamics changes needed to form the Michaelis complex are of mechanistic interest. Herein, we report the characterization of substrate induced changes (Mg-ADP, M5P, and the ternary complex) in PMK using NMR-based dynamics and chemical shift perturbation measurements. Mg-ADP and M5P K(d)'s were 6-60 microM in all complexes, consistent with there being little binding synergy. Binding of M5P causes the PMK structure to compress (tau(c) = 13.5 nsec), whereas subsequent binding of Mg-ADP opens the structure up (tau(c) = 15.6 nsec). The overall complex seems to stay very rigid on the psec-nsec timescale with an average NMR order parameter of S(2) approximately 0.88. Data are consistent with addition of M5P causing movement around a hinge region to permit domain closure, which would bring the M5P domain close to ATP to permit catalysis. Dynamics data identify potential hinge residues as H55 and R93, based on their low order parameters and their location in extended regions that connect the M5P and ATP domains in the PMK homology model. Likewise, D163 may be a hinge residue for the lid region that is homologous to the adenylate kinase lid, covering the "Walker-A" catalytic loop. Binding of ATP or ADP appears to cause similar conformational changes; however, these observations do not indicate an obvious role for gamma-phosphate binding interactions. Indeed, the role of gamma-phosphate interactions may be more subtle than suggested by ATP/ADP comparisons, because the conservative O to NH substitution in the beta-gamma bridge of ATP causes a dramatic decrease in affinity and induces few chemical shift perturbations. In terms of positioning of catalytic residues, binding of M5P induces a rigidification of Gly21 (adjacent to the catalytically important Lys22), although exchange broadening in the ternary complex suggests some motion on a slower timescale does still occur. Finally, the first nine residues of the N-terminus are highly disordered, suggesting that they may be part of a cleavable signal or regulatory peptide sequence.

Apo adenylate kinase encodes its holo form: a principal component and varimax analysis

Adenylate kinase undergoes large-scale motions of its LID and AMP-binding (AMPbd) domains when its apo, open form closes over its substrates, AMP and Mg2+-ATP. It may be an example of an enzyme that provides an ensemble of conformations in its apo state from which its substrates can select and bind to produce catalytically competent conformations. In this work, the fluctuations of the enzyme apo Escherichia coli adenylate kinase (AKE) are obtained with molecular dynamics. The resulting trajectory is analyzed with principal component analysis (PCA) that decomposes the atom motions into orthogonal modes ordered by their decreasing contributions to the total protein fluctuation. In apo AKE, a small set of the PCA modes describes the bulk of the fluctuations. Identification of the atom motions that are important contributors to these modes is improved with the use of a varimax rotation method that rotates the PCA modes to a new mode set that concentrates the atom contributions to a smaller set of atoms in these new modes. In this way, the nature of the important motions of the LID and AMPbd domains are clarified. The dominant PCA modes are used to investigate if apo AKE can fluctuate to conformations that are holo-like, even though the apo trajectory is mainly confined to a region around the initial apo structure. This is accomplished by expressing the difference between the protein coordinates, obtained from the holo and apo crystal structures, using as a basis the PCA modes from the apo AKE trajectory. The coherent motion described by a small set of the apo PCA modes is shown to be able to produce protein conformations that are quite similar to the holo conformation of the protein. In this sense, apo AKE does encode in its fluctuations information about holo-like conformations.