ABSTRACT: To clarify the extent structure plays in determining protein dynamics, a comparative study is made using three models that characterize native state dynamics of single domain proteins starting from known structures taken from four distinct SCOP classifications. A geometrical simulation using the framework rigidity optimized dynamics algorithm (FRODA) based on rigid cluster decomposition is compared to the commonly employed elastic network model (specifically the Anisotropic Network Model ANM) and molecular dynamics (MD) simulation. The essential dynamics are quantified by a mode subspace constructed from ANM and a principal component analysis (PCA) on FRODA and MD trajectories. Aggregate conformational ensembles are constructed to provide a basis for quantitative comparisons between FRODA runs using different parameter settings to critically assess how the predictions of essential dynamics depend on a priori arbitrary user-defined distance constraint rules. We established a range of physicality for these parameters. Surprisingly, FRODA maintains greater intra-consistent results than obtained from MD trajectories, comparable to ANM. Additionally, a mode subspace is constructed from PCA on an exemplar set of myoglobin structures from the Protein Data Bank. Significant overlap across the three model subspaces and the experimentally derived subspace is found. While FRODA provides the most robust sampling and characterization of the native basin, all three models give similar dynamical information of a native state, further demonstrating that structure is the key determinant of dynamics.
Project description:Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.
Project description:By examining the molecular dynamics (MD) of protein folding trajectories, generated with the coarse-grained UNRES force field, for the B-domain of staphylococcal protein A and the triple ?-strand WW domain from the Formin binding protein 28 (FBP), by principal component analysis (PCA), it is demonstrated how different free energy landscapes (FELs) and folding pathways of trajectories can be, even though they appear to be very similar by visual inspection of the time-dependence of the root-mean-square deviation (rmsd). Approaches to determine the minimal dimensionality of FELs for a correct description of protein folding dynamics are discussed. The correlation between the amplitude of the fluctuations of proteins and the dimensionality of the FELs is shown. The advantage of internal coordinate PCA over Cartesian PCA for small proteins is also illustrated.
Project description:The Anton supercomputing technology recently developed for efficient molecular dynamics simulations permits us to examine micro- to milli-second events at full atomic resolution for proteins in explicit water and lipid bilayer. It also permits us to investigate to what extent the collective motions predicted by network models (that have found broad use in molecular biophysics) agree with those exhibited by full-atomic long simulations. The present study focuses on Anton trajectories generated for two systems: the bovine pancreatic trypsin inhibitor, and an archaeal aspartate transporter, GltPh. The former, a thoroughly studied system, helps benchmark the method of comparative analysis, and the latter provides new insights into the mechanism of function of glutamate transporters. The principal modes of motion derived from both simulations closely overlap with those predicted for each system by the anisotropic network model (ANM). Notably, the ANM modes define the collective mechanisms, or the pathways on conformational energy landscape, that underlie the passage between the crystal structure and substates visited in simulations. In particular, the lowest frequency ANM modes facilitate the conversion between the most probable substates, lending support to the view that easy access to functional substates is a robust determinant of evolutionarily selected native contact topology.
Project description:A multivariate statistical theory, local feature analysis (LFA), extracts functionally relevant domains from molecular dynamics (MD) trajectories. The LFA representations, like those of principal component analysis (PCA), are low dimensional and provide a reduced basis set for collective motions of simulated proteins, but the local features are sparsely distributed and spatially localized, in contrast to global PCA modes. One key problem in the assignment of local features is the coarse-graining of redundant LFA output functions by means of seed atoms. One can solve the combinatorial problem by adding seed atoms one after another to a growing set, minimizing a reconstruction error at each addition. This allows for an efficient implementation, but the sequential algorithm does not guarantee the optimal mutual correlation of the sequentially assigned features. Here, we present a novel coarse-graining algorithm for proteins that directly minimizes the mutual correlation of seed atoms by Monte Carlo (MC) simulations. Tests on MD trajectories of two biological systems, bacteriophage T4 lysozyme and myosin II motor domain S1, demonstrate that the new algorithm provides statistically reproducible results and describes functionally relevant dynamics. The well-known undersampling of large-scale motion by short MD simulations is apparent also in our model, but the new coarse-graining offers a major advantage over PCA; converged features are invariant across multiple windows of the trajectory, dividing the protein into converged regions and a smaller number of localized, undersampled regions. In addition to its use in structure classification, the proposed coarse-graining thus provides a localized measure of MD sampling efficiency.
Project description:It is of interest to know whether local fluctuations in a polypeptide chain play any role in the mechanism by which the chain folds to the native structure of a protein. This question is addressed by analyzing folding and non-folding trajectories of a protein; as an example, the analysis is applied to the 37-residue triple ?-strand WW domain from the Formin binding protein 28 (FBP28) (PDB ID: 1E0L). Molecular dynamics (MD) trajectories were generated with the coarse-grained united-residue force field, and one- and two-dimensional free-energy landscapes (FELs) along the backbone virtual-bond angle ? and backbone virtual-bond-dihedral angle ? of each residue, and principal components, respectively, were analyzed. The key residues involved in the folding of the FBP28 WW domain are elucidated by this analysis. The correlations between local and global motions are found. It is shown that most of the residues in the folding trajectories of the system studied here move in a concerted fashion, following the dynamics of the whole system. This demonstrates how the choice of a pathway has to involve concerted movements in order for this protein to fold. This finding also sheds light on the effectiveness of principal component analysis (PCA) for the description of the folding dynamics of the system studied. It is demonstrated that the FEL along the PCs, computed by considering only several critically-placed residues, can correctly describe the folding dynamics.
Project description:The structural and dynamical behavior of the 41-56 beta-hairpin from the protein G B1 domain (GB1) has been studied at different temperatures using molecular dynamics (MD) simulations in an aqueous environment. The purpose of these simulations is to establish the stability of this hairpin in view of its possible role as a nucleation site for protein folding. The conformation of the peptide in the crystallographic structure of the protein GB1 (native conformation) was lost in all simulations. The new equilibrium conformations are stable for several nanoseconds at 300K (>10 ns), 350 K (>6.5 ns), and even at 450 K (up to 2.5 ns). The new structures have very similar hairpin-like conformations with properties in agreement with available experimental nuclear Overhauser effect (NOE) data. The stability of the structure in the hydrophobic core region during the simulations is consistent with the experimental data and provides further evidence for the role played by hydrophobic interactions in hairpin structures. Essential dynamics analysis shows that the dynamics of the peptide at different temperatures spans basically the same essential subspace. The main equilibrium motions in this subspace involve large fluctuations of the residues in the turn and ends regions. Of the six interchain hydrogen bonds, the inner four remain stable during the simulations. The space spanned by the first two eigenvectors, as sampled at 450 K, includes almost all of the 47 different hairpin structures found in the database. Finally, analysis of the hydration of the 300 K average conformations shows that the hydration sites observed in the native conformation are still well hydrated in the equilibrium MD ensemble.
Project description:Identifying the functional motions of membrane proteins is difficult because they range from large-scale collective dynamics to local small atomic fluctuations at different timescales that are difficult to measure experimentally due to the hydrophobic nature of these proteins. Elastic Network Models, and in particular their most widely used implementation, the Anisotropic Network Model (ANM), have proven to be useful computational methods in many recent applications to predict membrane protein dynamics. These models are based on the premise that biomolecules possess intrinsic mechanical characteristics uniquely defined by their particular architectures. In the ANM, interactions between residues in close proximity are represented by harmonic potentials with a uniform spring constant. The slow mode shapes generated by the ANM provide valuable information on the global dynamics of biomolecules that are relevant to their function. In its recent extension in the form of ANM-guided molecular dynamics (MD), this coarse-grained approach is augmented with atomic detail. The results from ANM and its extensions can be used to guide experiments and thus speedup the process of quantifying motions in membrane proteins. Testing the predictions can be accomplished through (a) direct observation of motions through studies of structure and biophysical probes, (b) perturbation of the motions by, e.g., cross-linking or site-directed mutagenesis, and (c) by studying the effects of such perturbations on protein function, typically through ligand binding and activity assays. To illustrate the applicability of the combined computational ANM-experimental testing framework to membrane proteins, we describe-alongside the general protocols-here the application of ANM to rhodopsin, a prototypical member of the pharmacologically relevant G-protein coupled receptor family.
Project description:The p38 MAP kinases play a critical role in regulating stress-activated pathways, and serve as molecular targets for controlling inflammatory diseases. Computer-aided efforts for developing p38 inhibitors have been hampered by the necessity to include the enzyme conformational flexibility in ligand docking simulations. A useful strategy in such complicated cases is to perform ensemble-docking provided that a representative set of conformers is available for the target protein either from computations or experiments. We explore here the abilities of two computational approaches, molecular dynamics (MD) simulations and anisotropic network model (ANM) normal mode analysis, for generating potential ligand-bound conformers starting from the apo state of p38, and benchmark them against the space of conformers (or the reference modes of structural changes) inferred from principal component analysis of 134 experimentally resolved p38 kinase structures. ANM-generated conformations are found to provide a significantly better coverage of the inhibitor-bound conformational space observed experimentally, compared to MD simulations performed in explicit water, suggesting that ANM-based sampling of conformations can be advantageously employed as input structural models in docking simulations.
Project description:Molecular dynamics simulation is commonly employed to explore protein dynamics. Despite the disparate timescales between functional mechanisms and molecular dynamics (MD) trajectories, functional differences are often inferred from differences in conformational ensembles between two proteins in structure-function studies that investigate the effect of mutations. A common measure to quantify differences in dynamics is the root mean square fluctuation (RMSF) about the average position of residues defined by C?-atoms. Using six MD trajectories describing three native/mutant pairs of beta-lactamase, we make comparisons with additional measures that include Jensen-Shannon, modifications of Kullback-Leibler divergence, and local p-values from 1-sample Kolmogorov-Smirnov tests. These additional measures require knowing a probability density function, which we estimate by using a nonparametric maximum entropy method that quantifies rare events well. The same measures are applied to distance fluctuations between C?-atom pairs. Results from several implementations for quantitative comparison of a pair of MD trajectories are made based on fluctuations for on-residue and residue-residue local dynamics. We conclude that there is almost always a statistically significant difference between pairs of 100 ns all-atom simulations on moderate-sized proteins as evident from extraordinarily low p-values.
Project description:Protein folding is considered here by studying the dynamics of the folding of the triple beta-strand WW domain from the Formin-binding protein 28. Starting from the unfolded state and ending either in the native or nonnative conformational states, trajectories are generated with the coarse-grained united residue (UNRES) force field. The effectiveness of principal components analysis (PCA), an already established mathematical technique for finding global, correlated motions in atomic simulations of proteins, is evaluated here for coarse-grained trajectories. The problems related to PCA and their solutions are discussed. The folding and nonfolding of proteins are examined with free-energy landscapes. Detailed analyses of many folding and nonfolding trajectories at different temperatures show that PCA is very efficient for characterizing the general folding and nonfolding features of proteins. It is shown that the first principal component captures and describes in detail the dynamics of a system. Anomalous diffusion in the folding/nonfolding dynamics is examined by the mean-square displacement (MSD) and the fractional diffusion and fractional kinetic equations. The collisionless (or ballistic) behavior of a polypeptide undergoing Brownian motion along the first few principal components is accounted for.