Simulation of protein conformational freedom as a function of pH: constant-pH molecular dynamics using implicit titration

Solution pH is a determinant parameter on protein function and stability, and its inclusion in molecular dynamics simulations is attractive for studies at the molecular level. Current molecular dynamics simulations can consider pH only in a very limited way, through a somewhat arbitrary choice of a set of fixed charges on the titrable sites. Conversely, continuum electrostatic methods that explicitly treat pH effects assume a single protein conformation whose choice is not clearly defined. In this paper we describe a general method that combines both titration and conformational freedom. The method is based on a potential of mean force for implicit titration and combines both usual molecular dynamics and pH-dependent calculations based on continuum methods. A simple implementation of the method, using a mean field approximation, is presented and applied to the bovine pancreatic trypsin inhibitor. We believe that this constant-pH molecular dynamics method, by correctly sampling both charges and conformation, can become a valuable help in the understanding of the dependence of protein function and stability on pH. © 1997 Wiley-Liss Inc.     

Methods for molecular dynamics simulations of protein folding/unfolding in solution

All atom molecular dynamics simulations have become a standard method for mapping equilibrium protein dynamics and non-equilibrium events like folding and unfolding. Here, we present detailed methods for performing such simulations. Generic protocols for minimization, solvation, simulation, and analysis derived from previous studies are also presented. As a measure of validation, our water model is compared with experiment. An example of current applications of these methods, simulations of the ultrafast folding protein Engrailed Homeodomain are presented including the experimental evidence used to verify their results. Ultrafast folders are an invaluable tool for studying protein behavior as folding and unfolding events measured by experiment occur on timescales accessible with the high-resolution molecular dynamics methods we describe. Finally, to demonstrate the prospect of these methods for folding proteins, a temperature quench simulation of a thermal unfolding intermediate of the Engrailed Homeodomain is described.     

High-Performance Drug Discovery: Computational Screening by Combining Docking and Molecular Dynamics Simulations

Virtual compound screening using molecular docking is widely used in the discovery of new lead compounds for drug design. However, this method is not completely reliable and therefore unsatisfactory. In this study, we used massive molecular dynamics simulations of protein-ligand conformations obtained by molecular docking in order to improve the enrichment performance of molecular docking. Our screening approach employed the molecular mechanics/Poisson-Boltzmann and surface area method to estimate the binding free energies. For the top-ranking 1,000 compounds obtained by docking to a target protein, approximately 6,000 molecular dynamics simulations were performed using multiple docking poses in about a week. As a result, the enrichment performance of the top 100 compounds by our approach was improved by 1.6–4.0 times that of the enrichment performance of molecular dockings. This result indicates that the application of molecular dynamics simulations to virtual screening for lead discovery is both effective and practical. However, further optimization of the computational protocols is required for screening various target proteins.     

Revealing Atomic-Level Mechanisms of Protein Allostery with Molecular Dynamics Simulations

Molecular dynamics (MD) simulations have become a powerful and popular method for the study of protein allostery, the widespread phenomenon in which a stimulus at one site on a protein influences the properties of another site on the protein. By capturing the motions of a protein’s constituent atoms, simulations can enable the discovery of allosteric binding sites and the determination of the mechanistic basis for allostery. These results can provide a foundation for applications including rational drug design and protein engineering. Here, we provide an introduction to the investigation of protein allostery using molecular dynamics simulation. We emphasize the importance of designing simulations that include appropriate perturbations to the molecular system, such as the addition or removal of ligands or the application of mechanical force. We also demonstrate how the bidirectional nature of allostery—the fact that the two sites involved influence one another in a symmetrical manner—can facilitate such investigations. Through a series of case studies, we illustrate how these concepts have been used to reveal the structural basis for allostery in several proteins and protein complexes of biological and pharmaceutical interest.     

Predicting large-scale conformational changes in proteins using energy-weighted normal modes

We report the development of a method to improve the sampling of protein conformational space in molecular simulations. It is shown that a principal component analysis of energy-weighted normal modes in Cartesian coordinates can be used to extract vectors suitable for describing the dynamics of protein substructures. The method can operate with either atomistic or user-defined coarse-grained models of protein structure. An implicit reverse coarse-graining allows the dynamics of all-atoms to be recovered when a coarse-grained model is used. For an external test set of four proteins, it is shown that the new method is more successful than normal mode analysis in describing the large-scale conformational changes observed on ligand binding. The method has potential applications in protein-ligand and protein-protein docking and in biasing molecular dynamics simulations.     

Convergence of molecular dynamics simulations of membrane proteins

The central question in evaluating almost any result from a molecular dynamics simulation is whether the calculation has converged. Unfortunately, assessing the ergodicity of a single trajectory is very difficult to do. In this work, we assess the sampling of molecular dynamics simulations of the membrane protein rhodopsin by comparing the results from 26 independent trajectories, each run for 100 ns. By examining principal components and cluster populations, we show that rhodopsin's fluctuations are not well described by 100 ns of dynamics, and that the sampling is not fully converged even for individual loops. The results serve as a reminder of the caution required when interpreting molecular dynamics simulations of macromolecules.     

Translational hydration water dynamics drives the protein glass transition

Experimental and computer simulation studies have revealed the presence of a glass-like transition in the internal dynamics of hydrated proteins at approximately 200 K involving an increase of the amplitude of anharmonic dynamics. This increase in flexibility has been correlated with the onset of protein activity. Here, we determine the driving force behind the protein transition by performing molecular dynamics simulations of myoglobin surrounded by a shell of water. A dual heat bath method is used with which, in any given simulation, the protein and solvent are held at different temperatures, and sets of simulations are performed varying the temperature of the components. The results show that the protein transition is driven by a dynamical transition in the hydration water that induces increased fluctuations primarily in side chains in the external regions of the protein. The water transition involves activation of translational diffusion and occurs even in simulations where the protein atoms are held fixed.     

Collective motions in proteins: a covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations.

A method is described for identifying collective motions in proteins from molecular dynamics trajectories or normal mode simulations. The method makes use of the covariances of atomic positional fluctuations. It is illustrated by an analysis of the bovine pancreatic trypsin inhibitor. Comparison of the covariance and cross-correlation matrices shows that the relative motions have many similar features in the different simulations. Many regions of the protein, especially regions of secondary structure, move in a correlated manner. Anharmonic effects, which are included in the molecular dynamics simulations but not in the normal analysis, are of some importance in determining the larger scale collective motions, but not the more local fluctuations. Comparisons of molecular dynamics simulations in the present and absence of solvent indicate that the environment is of significance for the long-range motions.     

Novel computational biology methods and their applications to drug discovery

Computational biology methods are now firmly entrenched in the drug discovery process. These methods focus on modeling and simulations of biological systems to complement and direct conventional experimental approaches. Two important branches of computational biology include protein homology modeling and the computational biophysics method of molecular dynamics. Protein modeling methods attempt to accurately predict three-dimensional (3D) structures of uncrystallized proteins for subsequent structure-based drug design applications. Molecular dynamics methods aim to elucidate the molecular motions of the static representations of crystallized protein structures. In this review we highlight recent novel methodologies in the field of homology modeling and molecular dynamics. Selected drug discovery applications using these methods conclude the review.     

The MUMO (minimal under-restraining minimal over-restraining) method for the determination of native state ensembles of proteins

While reliable procedures for determining the conformations of proteins are available, methods for generating ensembles of structures that also reflect their flexibility are much less well established. Here we present a systematic assessment of the ability of ensemble-averaged molecular dynamics simulations with ensemble-averaged NMR restraints to simultaneously reproduce the average structure of proteins and their associated dynamics. We discuss the effects that under-restraining (overfitting) and over-restraining (underfitting) have on the structures generated in ensemble-averaged molecular simulations. We then introduce the MUMO (minimal under-restraining minimal over-restraining) method, a procedure in which different observables are averaged over a different number of molecules. As both over-restraining and under-restraining are significantly reduced in the MUMO method, it is possible to generate ensembles of conformations that accurately characterize both the structure and the dynamics of native states of proteins. The application of the MUMO method to the protein ubiquitin yields a high-resolution structural ensemble with an RDC Q-factor of 0.19.     

A molecular dynamics study and free energy analysis of complexes between the Mlc1p protein and two IQ motif peptides

The Mlc1p protein from the budding yeast Saccharomyces cerevisiae is a Calmodulin-like protein, which interacts with IQ-motif peptides located at the yeast's myosin neck. In this study, we report a molecular dynamics study of the Mlc1p-IQ2 protein-peptide complex, starting with its crystal structure, and investigate its dynamics in an aqueous solution. The results are compared with those obtained by a previous study, where we followed the solution structure of the Mlc1p-IQ4 protein-peptide complex by molecular dynamics simulations. After the simulations, we performed an interaction free-energy analysis using the molecular mechanics Poisson-Boltzmann surface area approach. Based on the dynamics of the Mlc1p-IQ protein-peptide complexes, the structure of the light-chain-binding domain of myosin V from the yeast S. cerevisiae is discussed.     

Flexible fitting of atomic structures into electron microscopy maps using molecular dynamics

A novel method to flexibly fit atomic structures into electron microscopy (EM) maps using molecular dynamics simulations is presented. The simulations incorporate the EM data as an external potential added to the molecular dynamics force field, allowing all internal features present in the EM map to be used in the fitting process, while the model remains fully flexible and stereochemically correct. The molecular dynamics flexible fitting (MDFF) method is validated for available crystal structures of protein and RNA in different conformations; measures to assess and monitor the fitting process are introduced. The MDFF method is then used to obtain high-resolution structures of the E. coli ribosome in different functional states imaged by cryo-EM.     

Projection of Monte Carlo and molecular dynamics trajectories onto the normal mode axes: human lysozyme

A method is presented to describe the internal motions of proteins obtained from molecular dynamics or Monte Carlo simulations as motions of normal mode variables. This method calculates normal mode variables by projecting trajectories of these simulations onto the axes of normal modes and expresses the trajectories as a linear combination of normal mode variables. This method is applied to the result of the molecular dynamics and the Monte Carlo simulations of human lysozyme. The motion of the lowest frequency mode extracted from the simulations represents the hinge bending motion very faithfully. Analysis of the obtained motions of the normal mode variables provides an explanation of the anharmonic aspects of protein dynamics as due first to the anharmonicity of the actual potential energy surface near a minimum and second to trans-minimum conformational changes.     

Segmented Transition Pathway of the Signaling Protein Nitrogen Regulatory Protein C

Recent advances in experimental methods provide increasing evidence that proteins sample the conformational substates that are important for function in the absence of their ligands. An example is the receiver domain of nitrogen regulatory protein C, a member of the phosphorylation-mediated signaling family of “two-component systems.” The receiver domain of nitrogen regulatory protein C samples both inactive conformation and the active conformation before phosphorylation. Here we determine a possible pathway of interconversion between the active state and the inactive state by targeted molecular dynamics simulations and quasi-harmonic analysis; these methods are used because the experimental conversion rate is in the high microsecond range, longer than those that are easily accessible to atomistic molecular dynamics simulations. The calculated pathway is found to be composed of four consecutive stages described by different progress variables. The lowest quasi-harmonic principal components from unbiased molecular dynamics simulations on the active state correspond to the first stage, but not to the subsequent stages of the transition. The targeted molecular dynamics pathway suggests that several transient nonnative hydrogen bonds may facilitate the transition.     

Molecular dynamics of myoglobin at 298 degrees K. Results from a 300-ps computer simulation.

We have carried out a very long (300 ps) molecular dynamics simulation of the protein myoglobin. This trajectory is approximately three times longer than the longest previous molecular dynamics simulation of a protein, and ten times longer than protein simulations of comparable size (1,423 atoms in our model). Here we report results from this long simulation concerning the average structure, the mean square fluctuations of atoms about the average structure, and the nuclear magnetic resonance order parameters for various groups in myoglobin. The results demonstrate that the average coordinates change very slowly during the simulation. The relative atomic mobilities are well described by the simulation. For both the mean square atomic fluctuations and the order parameters, however, there are significant quantitative differences when values calculated using shorter portions of the trajectory are compared with results obtained for the entire 300-ps simulation. The implications of this result for obtaining converged properties from protein molecular dynamics simulations for comparison with experiment are discussed.     

Visualization of energetics and conformations from molecular computer simulations

The quantity of data generated from molecular dynamics simulations and energy minimizations of macromolecules is overwhelming. It is an arduous task to extract the relevant and interesting information from the numerous coordinate sets produced. To help solve this problem, the authors have developed a method to aid the visualization of the relevant information from the simulations. This approach combines animation of the results on a high performance graphics device, such as the PS300, with colour-coded atoms based on changes in energy or conformation. The method will be illustrated using as examples: the molecular mechanics minimization of a nonapeptide, the molecular dynamics simulation of the protein myoglobin, including the analysis of the motion of helices during a 300ps trajectory, and changes in sugar puckering that occur during the molecular dynamics simulation of a DNA oligomer. The method is also applicable for analysing energy components and conformational properties of a fixed conformation.     

GRID-MD-A tool for massive simulation of protein channels

We present here a fast method for the exploration of channels in proteins based on molecular dynamics simulations of probe particles in a discrete grid space defined by an ensemble of protein conformations obtained either experimentally or by out-of-the-grid atomistic molecular dynamics simulations. The method is able to provide millisecond-long trajectories with a small computational effort, requires no human intervention in defining possible exit pathways and can detect both major and minor channels, giving a correct balance to the relative flux between them. The Grid-Molecular-Dynamics approach is then a suitable method for massive exploration of channels in proteins, even of those with unknown functional annotation.     

A topological data analytic approach for discovering biophysical signatures in protein dynamics

Identifying structural differences among proteins can be a non-trivial task. When contrasting ensembles of protein structures obtained from molecular dynamics simulations, biologically-relevant features can be easily overshadowed by spurious fluctuations. Here, we present SINATRA Pro, a computational pipeline designed to robustly identify topological differences between two sets of protein structures. Algorithmically, SINATRA Pro works by first taking in the 3D atomic coordinates for each protein snapshot and summarizing them according to their underlying topology. Statistically significant topological features are then projected back onto a user-selected representative protein structure, thus facilitating the visual identification of biophysical signatures of different protein ensembles. We assess the ability of SINATRA Pro to detect minute conformational changes in five independent protein systems of varying complexities. In all test cases, SINATRA Pro identifies known structural features that have been validated by previous experimental and computational studies, as well as novel features that are also likely to be biologically-relevant according to the literature. These results highlight SINATRA Pro as a promising method for facilitating the non-trivial task of pattern recognition in trajectories resulting from molecular dynamics simulations, with substantially increased resolution.     

Advances in biomolecular simulations: methodology and recent applications

Molecular dynamics simulations are widely used today to tackle problems in biochemistry and molecular biology. In the 25 years since the first simulation of a protein computers have become faster by many orders of magnitude, algorithms and force fields have been improved, and simulations can now be applied to very large systems, such as protein-nucleic acid complexes and multimeric proteins in aqueous solution. In this review we give a general background about molecular dynamics simulations, and then focus on some recent technical advances, with applications to biologically relevant problems.     

Protein-Folding Analysis Using Features Obtained by Persistent Homology

Understanding the protein-folding process is an outstanding issue in biophysics; recent developments in molecular dynamics simulation have provided insights into this phenomenon. However, the large freedom of atomic motion hinders the understanding of this process. In this study, we applied persistent homology, an emerging method to analyze topological features in a data set, to reveal protein-folding dynamics. We developed a new, to our knowledge, method to characterize the protein structure based on persistent homology and applied this method to molecular dynamics simulations of chignolin. Using principle component analysis or nonnegative matrix factorization, our analysis method revealed two stable states and one saddle state, corresponding to the native, misfolded, and transition states, respectively. We also identified an unfolded state with slow dynamics in the reduced space. Our method serves as a promising tool to understand the protein-folding process.