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.     

Interactions of the pleckstrin homology domain with phosphatidylinositol phosphate and membranes: characterization via molecular dynamics simulations

The mechanism of interaction of pleckstrin homology (PH) domains with phosphatidylinositol 4,5-bisphosphate (PIP 2)-containing lipid bilayers remains uncertain. While crystallographic studies have emphasized PH-inositol 1,4,5-trisphosphate (IP 3) interactions, biophysical studies indicate a degree of less specific protein-bilayer interactions. We have used molecular dynamics simulations to characterize the interactions of the PH domain from phospholipase C-delta1 with IP 3 and with PIP 2, the latter in lipid bilayers and in detergent micelles. Simulations of the PH domain in water reveal a reduction in protein flexibility when IP 3 is bound. Simulations of the PH domain bound to PIP 2 in lipid bilayers indicate a tightening of ligand-protein interactions relative to the PH-IP 3 complex, alongside formation of H-bonds between PH side chains and lipid (PC) headgroups, and a degree of penetration of hydrophobic side chains into the core of the bilayer. Comparison with simulations of the PH-bound domain to a PC bilayer in the absence of PIP 2 suggests that the presence of PIP 2 increases the extent of PH-membrane interactions. Thus, comparative molecular dynamics simulations reveal how a PI-binding domain undergoes changes in conformational dynamics on binding to a PIP 2-containing membrane and how interactions additional to those with the PI headgroup are formed.     

Adaptive conformational sampling based on replicas

Computer simulations of biomolecules such as molecular dynamics simulations are limited by the time scale of conformational rearrangements. Several sampling techniques are available to search the multi-minima free energy landscape but most efficient, time-dependent methods do generally not produce a canonical ensemble. A sampling algorithm based on a self-regulating ladder of searching copies in the dihedral subspace is developped in this paper. The learning process using short- and long-term memory functions allows an efficient search in phase space while combining a deterministic dynamics and stochastic swaps with the searching copies conserves a canonical limit. The sampling efficiency and accuracy are indicated by comparing the ansatz with conventional molecular dynamics and replica exchange simulations.     

Conformational fluctuations of the AXH monomer of Ataxin‐1

In this paper, we report the results of molecular dynamics simulations of AXH monomer of Ataxin‐1. The AXH domain plays a crucial role in Ataxin‐1 aggregation, which accompanies the initiation and progression of Spinocerebellar ataxia type 1. Our simulations involving both classical and replica exchange molecular dynamics, followed by principal component analysis of the trajectories obtained, reveal substantial conformational fluctuations of the protein structure, especially in the N‐terminal region. We show that these fluctuations can be generated by thermal noise since the free energy barriers between conformations are small enough for thermally stimulated transitions. In agreement with the previous experimental findings, our results can be considered as a basis for a future design of ataxin aggregation inhibitors that will require several key conformations identified in the present study as molecular targets for ligand binding. Proteins 2016; 84:52–59. © 2015 Wiley Periodicals, Inc.     

Enhanced sampling of molecular dynamics simulation of peptides and proteins by double coupling to thermal bath

Low sampling efficiency in conformational space is the well-known problem for conventional molecular dynamics. It greatly increases the difficulty for molecules to find the transition path to native state, and costs amount of CPU time. To accelerate the sampling, in this paper, we re-couple the critical degrees of freedom in the molecule to environment temperature, like dihedrals in generalized coordinates or nonhydrogen atoms in Cartesian coordinate. After applying to ALA dipeptide model, we find that this modified molecular dynamics greatly enhances the sampling behavior in the conformational space and provides more information about the state-to-state transition, while conventional molecular dynamics fails to do so. Moreover, from the results of 16 independent 100?ns simulations by the new method, it shows that trpzip2 has one-half chances to reach the naive state in all the trajectories, which is greatly higher than conventional molecular dynamics. Such an improvement would provide a potential way for searching the conformational space or predicting the most stable states of peptides and proteins.     

Role of conformational heterogeneity in domain swapping and adapter function of the Cks proteins

Cks proteins are adapter molecules that coordinate the assembly of multiprotein complexes. They share the ability to domain swap by exchanging a beta-strand, beta4. Here we use NMR spectroscopy and molecular dynamics simulations to investigate the dynamic properties of human Cks1 and its response on assembly with components of the SCF(Skp2) ubiquitin ligation machinery. In the NMR experiment with the free form of Cks1, a subset of residues displayed elevated R2 values and the cross-peaks of neighboring residues were missing from the spectrum, indicating a substantial conformational exchange contribution on the microsecond to millisecond time scale. Strikingly the region of greatest conformational variability was the beta4-strand that domain swaps to form the dimer. Binding of the ligand common to all Cks proteins, Cdk2, suppressed the conformational heterogeneity. This response was specific to Cdk2 binding; in contrast, binding of Skp2, a ligand unique to human Cks1, did not alter the dynamic behavior. Short time (<5 ns) molecular dynamics simulations indicate that residues of Cks1 that form the binding site for phosphorylated ligands are considerably more flexible in the free form of Cks1 than they are in the Cdk2-Cks1 complex. A cooperative interaction between Cdk2 and Cks1 is suggested, which reduces the configurational entropy of Cks1 and therefore facilitates phosphoprotein binding. Indications of an unusual dynamic behavior of strand beta4 in the free form of Cks1 were obtained from longer time scale (50 ns) dynamics simulations. A spontaneous reversible unzipping of hydrogen bonds between beta4 and beta2 was observed, suggesting an early intermediate structure for unfolding and/or domain swapping. We propose that the dynamic properties of the beta-sheet and its modification upon ligand binding underlie the domain swapping ability and the adapter function of Cks proteins.     

Mass-weighted molecular dynamics simulation and conformational analysis of polypeptide.

Atomic motions in protein molecules have been studied by molecular dynamics (MD) simulations; dynamics simulation methods have also been employed in conformational studies of polypeptide molecules. It was found that when atomic masses are weighted, the molecular dynamics method can significantly increase the sampling of dihedral conformation space in such studies, compared to a conventional MD simulation of the same total simulation time length. Herein the theoretical study of molecular conformation sampling by the molecular dynamics-based simulation method in which atomic masses are weighted is reported in detail; moreover, a numerical scheme for analyzing the extensive conformational sampling in the simulation of a tetrapeptide amide molecule is presented. From numerical analyses of the mass-weighted molecular dynamics trajectories of backbone dihedral angles, low-resolution structures covering the entire backbone dihedral conformation space of the molecule were determined, and the distribution of rotationally stable conformations in this space were analyzed quantitatively. The theoretical analyses based on the computer simulation and numerical analytical methods suggest that distinctive regimes in the conformational space of the peptide molecule can be identified.     

Nucleotide-dependent conformational changes in HisP: molecular dynamics simulations of an ABC transporter nucleotide-binding domain

ATP-binding cassette (ABC) transporters mediate the movement of molecules across cell membranes in both prokaryotes and eukaryotes. In ABC transporters, solute translocation occurs after ATP is either bound or hydrolyzed at the intracellular nucleotide-binding domains (NBDs). Molecular dynamics (MD) simulations have been employed to study the interactions of nucleotide with NBD. The results of extended (approximately 20 ns) MD simulations of HisP (total simulation time approximately 80 ns), the NBD of the histidine transporter HisQMP2J from Salmonella typhimurium, are presented. Analysis of the MD trajectories reveals conformational changes within HisP that are dependent on the presence of ATP in the binding pocket of the protein, and are sensitive to the presence/absence of Mg ions bound to the ATP. These changes are predominantly confined to the alpha-helical subdomain of HisP. Specifically there is a rotation of three alpha-helices within the subdomain, and a movement of the signature sequence toward the bound nucleotide. In addition, there is considerable conformational flexibility in a conserved glutamine-containing loop, which is situated at the interface between the alpha-helical subdomain and the F1-like subdomain. These results support the mechanism for ATP-induced conformational transitions derived from the crystal structures of other NBDs.     

Locally accessible conformations of proteins: multiple molecular dynamics simulations of crambin.

Multiple molecular dynamics (MD) simulations of crambin with different initial atomic velocities are used to sample conformations in the vicinity of the native structure. Individual trajectories of length up to 5 ns sample only a fraction of the conformational distribution generated by ten independent 120 ps trajectories at 300 K. The backbone atom conformational space distribution is analyzed using principal components analysis (PCA). Four different major conformational regions are found. In general, a trajectory samples only one region and few transitions between the regions are observed. Consequently, the averages of structural and dynamic properties over the ten trajectories differ significantly from those obtained from individual trajectories. The nature of the conformational sampling has important consequences for the utilization of MD simulations for a wide range of problems, such as comparisons with X-ray or NMR data. The overall average structure is significantly closer to the X-ray structure than any of the individual trajectory average structures. The high frequency (less than 10 ps) atomic fluctuations from the ten trajectories tend to be similar, but the lower frequency (100 ps) motions are different. To improve conformational sampling in molecular dynamics simulations of proteins, as in nucleic acids, multiple trajectories with different initial conditions should be used rather than a single long trajectory.     

CD4 binding partially locks the bridging sheet in gp120 but leaves the beta2/3 strands flexible

The structure of the free form HIV gp120, critical for therapeutic agent development, is unavailable due to its high flexibility. Previous thermodynamic data, structural analysis and simulation results have suggested a large conformational change in the core domain upon CD4 binding. The bridging sheet, which consists of four beta-strands with beta20/21 nestling against the inner/outer domains and beta2/3 facing outward, more exposed to the solvent, was proposed to be unfolded in the native state. In order to test this proposition and to characterize the native conformations, we performed potential mean force (PMF) molecular dynamics (MD) simulations on the CD4-bound crystal structure. We pushed the bridging sheet away from the inner and outer domain to explore the accessible conformational space for the bridging sheet. In addition, we performed conventional MD simulations on structures with the bridging sheet partially unfolded to investigate the stability of the association between the inner and outer domains. Based on the free energy profiles, we find that the whole bridging sheet is unlikely to unfold without other concurrent conformational changes. On the other hand, the partial bridging sheet, beta strands 2/3, can switch its conformation from the folded to the unfolded state. Furthermore, relaxation of conformation with partially unfolded bridging sheet through MD simulations leads to a conformation with beta strands 20/21 quickly re-anchoring against the inner and outer domains. Such a conformation, although lacking some of the hydrophobic interactions present in the CD4-bound structure, displayed high stability as further indicated by other restrained MD simulations. The relevance of this conformation to the free form structure and the pathway for conformational change from the free form to the CD4-bound structure is discussed in detail in light of the available unliganded SIV gp120 crystal structure.     

Internal Dynamics of Dynactin CAP-Gly Is Regulated by Microtubules and Plus End Tracking Protein EB1

CAP-Gly domain of dynactin, a microtubule-associated activator of dynein motor, participates in multiple cellular processes, and its point mutations are associated with neurodegenerative diseases. Recently, we have demonstrated that conformational plasticity is an intrinsic property of CAP-Gly. To understand its origin, we addressed internal dynamics of CAP-Gly assembled on polymeric microtubules, bound to end-binding protein EB1 and free, by magic angle spinning NMR and molecular dynamics simulations. The analysis of residue-specific dynamics of CAP-Gly on time scales spanning nano- through milliseconds reveals its unusually high mobility, both free and assembled on polymeric microtubules. On the contrary, CAP-Gly bound to EB1 is significantly more rigid. Molecular dynamics simulations indicate that these motions are strongly temperature-dependent, and loop regions are surprisingly mobile. These findings establish the connection between conformational plasticity and internal dynamics in CAP-Gly, which is essential for the biological functions of CAP-Gly and its ability to bind to polymeric microtubules and multiple binding partners. In this work, we establish an approach, for the first time, to probe atomic resolution dynamic profiles of a microtubule-associated protein assembled on polymeric microtubules. More broadly, the methodology established here can be applied for atomic resolution analysis of dynamics in other microtubule-associated protein assemblies, including but not limited to dynactin, dynein, and kinesin motors assembled on microtubules.     

Multi‐scale characterization of the energy landscape of proteins with application to the C3D/Efb‐C complex

We present a novel multi‐level methodology to explore and characterize the low energy landscape and the thermodynamics of proteins. Traditional conformational search methods typically explore only a small portion of the conformational space of proteins and are hard to apply to large proteins due to the large amount of calculations required. In our multi‐scale approach, we first provide an initial characterization of the equilibrium state ensemble of a protein using an efficient computational conformational sampling method. We then enrich the obtained ensemble by performing short Molecular Dynamics (MD) simulations on selected conformations from the ensembles as starting points. To facilitate the analysis of the results, we project the resulting conformations on a low‐dimensional landscape to efficiently focus on important interactions and examine low energy regions. This methodology provides a more extensive sampling of the low energy landscape than an MD simulation starting from a single crystal structure as it explores multiple trajectories of the protein. This enables us to obtain a broader view of the dynamics of proteins and it can help in understanding complex binding, improving docking results and more. In this work, we apply the methodology to provide an extensive characterization of the bound complexes of the C3d fragment of human Complement component C3 and one of its powerful bacterial inhibitors, the inhibitory domain of Staphylococcus aureus extra‐cellular fibrinogen‐binding domain (Efb‐C) and two of its mutants. We characterize several important interactions along the binding interface and define low free energy regions in the three complexes. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

NMR relaxation unravels interdomain crosstalk of the two domain prolyl isomerase and chaperone SlyD

The dynamics of the two domain prolyl-peptidyl cis/trans isomerase and chaperone SlyD was studied on a ps-to-ns time scale to correlate dynamic changes with the catalytic function. (15)N transversal and longitudinal relaxation rates as well as heteronuclear Overhauser effects were determined at different temperatures for Escherichia coli SlyD (EcSlyD) and for Thermus thermophilus SlyD (TtSlyD). With the well established extended Lipari-Szabo approach, the order parameter, S(2), the internal correlation time, τ(e), the exchange rate, R(ex), of the backbone amide protons, and the overall molecular tumbling time, τ(m), were determined. The study was extended to a relaxation analysis of the peptide bound state for both SlyD species. We found highly different relaxation and dynamic behavior of the two domains for free SlyD. Surprisingly, in the presence of a substrate for the chaperone domain, the ps-to-ns dynamics in the remote center of the prolyl-peptidyl cis/trans isomerization domain increases. We observed this crosstalk between the two domains for both EcSlyD and TtSlyD.     

Conformational flexibility and binding interactions of the G protein βγ heterodimer

Previous NMR experiments on unbound G protein βγ heterodimer suggested that particular residues in the binding interface are mobile on the nanosecond timescale. In this work we performed nanosecond‐timescale molecular dynamics simulations to investigate conformational changes and dynamics of Gβγ in the presence of several binding partners: a high‐affinity peptide (SIGK), phosducin, and the GDP‐bound α subunit. In these simulations, the high mobility of GβW99 was reduced by SIGK, and it appeared that a tyrosine might stabilize GβW99 by hydrophobic or aromatic stacking interactions in addition to hydrogen bonds. Simulations of the phosducin‐Gβγ complex showed that the mobility of GβW99 was restricted, consistent with inferences from NMR. However, large‐scale conformational changes of Gβγ due to binding, which were hypothesized in the NMR study, were not observed in the simulations, most likely due to their short (nanosecond) duration. A pocket consisting of hydrophobic amino acids on Gα appears to restrict GβW99 mobility in the crystal structure of the Gαβγ? heterotrimer. The simulation trajectories are consistent with this idea. However, local conformational changes of residues GβW63, GβW211, GβW297, GβW332, and GβW339 were detected during the MD simulations. As expected, the magnitude of atomic fluctuations observed in simulations was greater for α than for the βγ subunits, suggesting that α has greater flexibility. These observations support the notion that to maintain the high mobility of GβW99 observed by solution NMR requires that the Gβ–α interface must open up on time scale longer than can be observed in nanosecond scale simulations. Proteins 2011. © 2010 Wiley‐Liss, Inc.     

Conformation spaces of proteins

We report a simple method for measuring the accessible conformational space explored by an ensemble of protein structures. The method is useful for diverse ensembles derived from molecular dynamics trajectories, molecular modeling, and molecular structure determinations. It can be used to examine a wide range of time scales. The central tactic we use, which has been previously employed, is to replace the true mechanical degrees of freedom of a molecular system with the conformationally effective degrees of freedom as measured by the root-mean squared cartesian distances among all pairs of conformations. Each protein conformation is treated as a point in a high dimensional euclidean space. In this article, we model this space in a novel way by representing it as an N-dimensional hypercube, describable with only two parameters: the number of dimensions and the edge length. To validate this approach, we provide a number of elementary test cases and then use the N-cube method for measuring the size and shape of conformational space covered by molecular dynamics trajectories spanning 10 orders of magnitude in time. These calculations were performed on a small protein, the villin headpiece subdomain, exploring both the native state and the misfolded/folding regime. Distinct features include single, vibrationally averaged, substate minima on the 0.1-1-ps time scale, thermally averaged conformational states that persist for 1-100 ps and transitions between these local minima on nanosecond time scales. Large-scale refolding modes appear to become uncorrelated on the microsecond time scale. Associated length scales for these events are 0.2 A for the vibrational minima; 0.5 A for the conformational minima; and 1-2 A for the nanosecond events. We find that the conformational space that is dynamically accessible during folding of villin has enough volume for approximately 10(9) minima of the variety that persist for picoseconds. Molecular dynamics trajectories of the native protein and experimentally derived solution ensembles suggest the native state to be composed of approximately 10(2) of these thermally accessible minima. Thus, based on random exploration of accessible folding space alone, protein folding for a small protein is predicted to be a milliseconds time scale event. This time can be compared with the experimental folding time for villin of 10-100 micros. One possible explanation for the 10-100-fold discrepancy is that the slope of the "folding funnel" increases the rate 1-2 orders of magnitude above random exploration of substates.     

Activation of the edema factor of Bacillus anthracis by calmodulin: evidence of an interplay between the EF-calmodulin interaction and calcium binding

Calmodulin (CaM) is a remarkably flexible protein which can bind multiple targets in response to changes in intracellular calcium concentration. It contains four calcium-binding sites, arranged in two globular domains. The calcium affinity of CaM N-terminal domain (N-CaM) is dramatically reduced when the complex with the edema factor (EF) of Bacillus anthracis is formed. Here, an atomic explanation for this reduced affinity is proposed through molecular dynamics simulations and free energy perturbation calculations of the EF-CaM complex starting from different crystallographic models. The simulations show that electrostatic interactions between CaM and EF disfavor the opening of N-CaM domains usually induced by calcium binding. Relative calcium affinities of the N-CaM binding sites are probed by free energy perturbation, and dissociation probabilities are evaluated with locally enhanced sampling simulations. We show that EF impairs calcium binding on N-CaM through a direct conformational restraint on Site 1, by an indirect destabilization of Site 2, and by reducing the cooperativity between the two sites.     

Simulation of the activation of alpha-chymotrypsin: analysis of the pathway and role of the propeptide

Alpha-chymotrypsin undergoes a reversible conformational change from an inactive chymotrypsinogen-like structure at high pH to an active conformation at neutral pH. In order to gain insight into this process on a structural level, we applied molecular dynamics and targeted molecular dynamics simulations in aqueous environment on the activation and inactivation processes of three different types of chymotrypsin. These are the wild-type bovine chymotrypsin containing the propeptide and the bovine and rat chymotrypsin lacking the propeptide. From these simulations, the importance of the propeptide and of the sequence differences between the rat and bovine variants from the viewpoint of activation could be evaluated and compared with previous fluorescence stopped flow results. The obtained results show the unambiguous influence of the propeptide on the explored conformational space, whereas the sequence differences between bovine and rat chymotrypsin play a minor role. The main features of activation are present in both the wild type and the variant lacking the propeptide, despite the fact that different parts of the conformational space were explored. The comparison of all trajectories shows that particular amino acid residues, such as 17, 18, 19, 187, 217, 218, and 223, undergo large dihedral transitions during the activation process, suggesting a role as hinge residues during the conformational change.     

Mobility in the structure of E.coli recQ helicase upon substrate binding as seen from molecular dynamics simulations

RecQ helicases feature multiple domains in their structure, of which the helicase domain, the RecQ-Ct domain and the HRDC domains are well conserved among the SF2 helicases. The helicase domain and the RecQ-Ct domain constitute the catalytic core of the enzyme. The domain interfaces are the DNA binding sites which display significant conformational changes in our molecular dynamics simulation studies. The preferred conformational states of the DNA bound and unbound forms of RecQ appear to be quite different from each other. DNA binding induces inter-domain flexibility leading to hinge mobility between the domains. The divergence in the dynamics of the two structures is caused by changes in the interactions at the domain interface, which seems to propagate along the whole protein structure. This could be essential in ssDNA binding after strand separation, as well as aiding translocation of the RecQ protein like an inch-worm.     

A coupling of homology modeling with multiple molecular dynamics simulation for identifying representative conformation of GPCR structures: a case study on human bombesin receptor subtype-3

In this study, a computational pipeline was therefore devised to overcome homology modeling (HM) bottlenecks. The coupling of HM with molecular dynamics (MD) simulation is useful in that it tackles the sampling deficiency of dynamics simulations by providing good-quality initial guesses for the native structure. Indeed, HM also relaxes the severe requirement of force fields to explore the huge conformational space of protein structures. In this study, the interaction between the human bombesin receptor subtype-3 and MK-5046 was investigated integrating HM, molecular docking, and MD simulations. To improve conformational sampling in typical MD simulations of GPCRs, as in other biomolecules, multiple trajectories with different initial conditions can be employed rather than a single long trajectory. Multiple MD simulations of human bombesin receptor subtype-3 with different initial atomic velocities are applied to sample conformations in the vicinity of the structure generated by HM. The backbone atom conformational space distribution of replicates is analyzed employing principal components analysis. As a result, the averages of structural and dynamic properties over the twenty-one trajectories differ significantly from those obtained from individual trajectories.     

Molecular dynamics studies on free and bound targets of the bovine papillomavirus type I e2 protein: the protein binding effect on DNA and the recognition mechanism

Molecular dynamics simulations of a total duration of 30 ns in explicit solvent were carried out on the BPV-1-E2 protein complexed to a high-affinity DNA target containing the two hydrogen-bonded ACCG.CGGT half-sites separated by the noncontacted ACGT sequence. The analysis of the trajectories focuses on the DNA structure and on the dynamics. The data are compared to those issued from recent simulations made on three free targets that recognize E2 with different affinities. E2 does not drastically perturb the mechanic properties of the free DNA: the structural relationships between the BI/BII backbone substates and some helical parameters are preserved in the complex despite a severe slowing down of the phosphate group motions. The structures of both free and bound half-sites are very close to each other although the conformational space explored by these regions is narrowed when they are contacted by the protein. The enhanced plasticity found in the best free target spacers, mainly manifested through the backbone motions, allows a clear overlap between several free and bound global DNA features such as the base displacement. Furthermore, this flexibility is preserved in the complex. Our results support the hypothesis that E2 takes advantage of free predistorted structures that may minimize the DNA deformation cost. In addition, we observe that E2 is far from totally stiffening the DNA, suggesting that the entropic penalty inherent in the complex formation could be limited.