Molecular Dynamics Simulations Of Proteins Research Articles

Structural Effects of an Atomic-Level Layer of Water Molecules around Proteins Solvated in Supra-Molecular Coarse-Grained Water

Atomistic molecular dynamics simulations of proteins in aqueous solution are still limited to the multinanosecond time scale and multinanometer range by computational cost. Combining atomic solutes with a supra-molecular solvent model in hybrid fine-grained/coarse-grained (FG/CG) simulations allows atomic detail in the region of interest while being computationally more efficient. A recent comparison of the properties of four proteins in CG water versus FG water showed the preservation of the secondary and tertiary structure with a computational speed-up of at least an order of magnitude. However, an increased occurrence of hydrogen bonds between side chains was observed due to a lack of hydrogen-bonding partners in the supra-molecular solvent. Here, the introduction of a FG water layer around the protein to recover the hydrogen-bonding pattern of the atomistic simulations is studied. Three layer thicknesses of 0.2, 0.4, and 0.8 nm are considered. A layer thickness of 0.8 nm is found sufficient to recover the behavior of the proteins in the atomistic simulations, whereas the hybrid simulation is still three times more efficient than the atomistic one and the cutoff radius for nonbonded interactions could be increased from 1.4 to 2.0 nm.

Wavelet Analysis of Protein Motion.

As high-throughput molecular dynamics simulations of proteins become more common and the databases housing the results become larger and more prevalent, more sophisticated methods to quickly and accurately mine large numbers of trajectories for relevant information will have to be developed. One such method, which is only recently gaining popularity in molecular biology, is the continuous wavelet transform, which is especially well-suited for time course data such as molecular dynamics simulations. We describe techniques for the calculation and analysis of wavelet transforms of molecular dynamics trajectories in detail and present examples of how these techniques can be useful in data mining. We demonstrate that wavelets are sensitive to structural rearrangements in proteins and that they can be used to quickly detect physically relevant events. Finally, as an example of the use of this approach, we show how wavelet data mining has led to a novel hypothesis related to the mechanism of the protein γδ resolvase.

Protein Dynamics in Organic Media at Varying Water Activity Studied by Molecular Dynamics Simulation

In nonaqueous enzymology, control of enzyme hydration is commonly approached by fixing the thermodynamic water activity of the medium. In this work, we present a strategy for evaluating the water activity in molecular dynamics simulations of proteins in water/organic solvent mixtures. The method relies on determining the water content of the bulk phase and uses a combination of Kirkwood-Buff theory and free energy calculations to determine corresponding activity coefficients. We apply the method in a molecular dynamics study of Candida antarctica lipase B in pure water and the organic solvents methanol, tert-butyl alcohol, methyl tert-butyl ether, and hexane, each mixture at five different water activities. It is shown that similar water activity yields similar enzyme hydration in the different solvents. However, both solvent and water activity are shown to have profound effects on enzyme structure and flexibility.

Potential of mean force of water–proton bath and molecular dynamic simulation of proteins at constant pH

An advanced implicit solvent model of water-proton bath for protein simulations at constant pH is presented. The implicit water-proton bath model approximates the potential of mean force of a protein in water solvent in a presence of hydrogen ions. Accurate and fast computational implementation of the implicit water-proton bath model is developed using the continuum electrostatic Poisson equation model for calculation of ionization equilibrium and the corrected MSR6 generalized Born model for calculation of the electrostatic atom-atom interactions and forces. Molecular dynamics (MD) method for protein simulation in the potential of mean force of water-proton bath is developed and tested on three proteins. The model allows to run MD simulations of proteins at constant pH, to calculate pH-dependent properties and free energies of protein conformations. The obtained results indicate that the developed implicit model of water-proton bath provides an efficient way to study thermodynamics of biomolecular systems as a function of pH, pH-dependent ionization-conformation coupling, and proton transfer events.

Will molecular dynamics simulations of proteins ever reach equilibrium?

We show that conformational entropies calculated for five proteins and protein-ligand complexes with dihedral-distribution histogramming, the von Mises approach, or quasi-harmonic analysis do not converge to any useful precision even if molecular dynamics (MD) simulations of 380-500 ns length are employed (the uncertainty is 12-89 kJ mol(-1)). To explain this, we suggest a simple protein model involving dihedrals with effective barriers forming a uniform distribution and show that for such a model, the entropy increases logarithmically with time until all significantly populated dihedral states have been sampled, in agreement with the simulations (during the simulations, 52-70% of the available dihedral phase space has been visited). This is also confirmed by the analysis of the trajectories of a 1 ms simulation of bovine pancreatic trypsin inhibitor (31 kJ mol(-1) difference in the entropy between the first and second part of the simulation). Strictly speaking, this means that it is practically impossible to equilibrate MD simulations of proteins. We discuss the implications of such a lack of strict equilibration of protein MD simulations and show that ligand-binding free energies estimated with the MM/GBSA method (molecular mechanics with generalised Born and surface-area solvation) vary by 3-15 kJ mol(-1) during a 500 ns simulation (the higher estimate is caused by rare conformational changes), although they involve a questionable but well-converged normal-mode entropy estimate, whereas free energies estimated by free-energy perturbation vary by less than 0.6 kJ mol(-1) for the same simulation.

Denaturation of proteins near polar surfaces

All-atom molecular dynamics simulations for proteins placed near a model mica surface indicate existence of two types of evolution. One type leads to the surface-induced unfolding and the other just to a deformation. The two behaviors are characterized by distinct properties of the radius of gyration and of a novel distortion parameter that distinguishes between elongated, globular, and planar shapes. They also differ in the nature of their single site diffusion and two-site distance fluctuations. The four proteins chosen for the studies, the tryptophan cage, protein G, hydrophobin and lyzozyme, are small to allow for a fair determination of the forces generated by the surface as the effects of finite cutoffs in the Coulombic interactions are thus minimized. When the net charge on the surface is set to zero artificially, infliction of deformation is seen to persists but no unfolding takes place. Unfolding may also be prevented by a cluster of disulfide bonds, as we observe in simulations of hydrophobin.

Lipid models for united-atom molecular dynamics simulations of protein

AbstractMolecular dynamics (MD) simulations of biomolecules are performed at various levels of atomic detail from all-atom models to coarse grained models. United-atom models are at an intermediate level, in which non-polar hydrogen atoms are subsumed into their adjacent carbon-atom reducing the number of particles for a DPPC lipid molecule by 60%. United-atom models of the lipids DPPC, DMPC, POPC and POPG in the GROMOS96 53a6 force field were developed, that reproduced experimental properties of lipid bilayers without assumption of a constant surface area or inclusion of surface pressure. In the absence of experimental data a surface per lipid area for the negatively charged POPG of 0.700±0.007 nm2 was obtained that is higher than 0.53 to 0.56 nm2 reported in previous simulation studies in the literature. It is argued that MD simulations of anionic bilayers may have underestimated the steric requirements of sodium counter ions entering the head group region in order to compensate the negative charge. The use of the DMPC GROMOS96 53a6 model was evaluated in an MD simulation of the ErbB2 transmembrane peptide and showed closer agreement with the NMR-derived structure than the GROMOS87 force field that was most commonly used for membrane protein simulations previously. Lipid topologies and coordinates are available via LipidBook (http://lipidbook.bioch.ox.ac.uk/).

Lipid models for united-atom molecular dynamics simulations of protein

Molecular dynamics (MD) simulations of biomolecules are performed at various levels of atomic detail from all-atom models to coarse grained models. United-atom models are at an intermediate level, in which non-polar hydrogen atoms are subsumed into their adjacent carbon-atom reducing the number of particles for a DPPC lipid molecule by 60%. United-atom models of the lipids DPPC, DMPC, POPC and POPG in the GROMOS96 53a6 force field were developed, that reproduced experimental properties of lipid bilayers without assumption of a constant surface area or inclusion of surface pressure. In the absence of experimental data a surface per lipid area for the negatively charged POPG of 0.700±0.007 nm2 was obtained that is higher than 0.53 to 0.56 nm2 reported in previous simulation studies in the literature. It is argued that MD simulations of anionic bilayers may have underestimated the steric requirements of sodium counter ions entering the head group region in order to compensate the negative charge. The use of the DMPC GROMOS96 53a6 model was evaluated in an MD simulation of the ErbB2 transmembrane peptide and showed closer agreement with the NMR-derived structure than the GROMOS87 force field that was most commonly used for membrane protein simulations previously. Lipid topologies and coordinates are available via LipidBook (http://lipidbook.bioch.ox.ac.uk/).

Protein Dynamics: Moore's Law in Molecular Biology

The millisecond barrier has been broken in molecular dynamics simulations ofproteins. Such simulations are increasingly revealing the inner workings of biological systems by generating atomic-level descriptions of their behaviour that make testable predictions about key molecular processes.

Analysis of motion features for molecular dynamics simulation of proteins

Recently, a new method for time series analysis using the wavelet transformation has been proposed by Sakurai et al. We apply it to molecular dynamics simulation of Thermomyces lanuginosa lipase (TLL). Introducing indexes to characterize collective motion of the protein, we have obtained the following two results. First, time evolution of the collective motion involves not only the dynamics within a single potential well but also takes place wandering around multiple conformations. Second, correlation of the collective motion between secondary structures shows that collective motion exists involving multiple secondary structures. We discuss future prospects of our study involving ‘disordered proteins’.

Using NMR Chemical Shifts as Structural Restraints in Molecular Dynamics Simulations of Proteins

We introduce a procedure to determine the structures of proteins by incorporating NMR chemical shifts as structural restraints in molecular dynamics simulations. In this approach, the chemical shifts are expressed as differentiable functions of the atomic coordinates and used to compute forces to generate trajectories that lead to the reduction of the differences between experimental and calculated chemical shifts. We show that this strategy enables the folding of a set of proteins with representative topologies starting from partially denatured initial conformations without the use of additional experimental information. This method also enables the straightforward combination of chemical shifts with other standard NMR restraints, including those derived from NOE, J-coupling, and residual dipolar coupling measurements. We illustrate this aspect by calculating the structure of a transiently populated excited state conformation from chemical shift and residual dipolar coupling data measured by relaxation dispersion NMR experiments.

Membrane Diffusion of PH Domain-PIP3 Complexes: the Effects of Target Lipid Stoichiometry on Diffusion Constant Probed Using Single-Molecule Fluorescence Microscopy

Pleckstrin homology (PH) domains are recruited to specific membrane surfaces during a variety of cell signaling events, including those occurring at the leading edge of chemotaxing cells. This recruitment is often driven by molecular recognition of specific phosphatidylinositol phosphate lipids, such as phosphatidylinositol-(3,4,5)-trisphosphate (PIP3). Using single-molecule fluorescence microscopy, we have recently shown that when bound to PIP3 on the surface of a supported lipid bilayer, the PH domain of GRP1 diffuses at the same rate as an individual phospholipid molecule diffusing in the same type of bilayer. More generally, we hypothesize that protein lateral diffusion constant will decrease as the number of lipid molecules tightly bound to the protein increases. Here, we probe the effects of PIP3 stoichiometry on the diffusion constants of constructs containing one, two, or three GRP1 PH domains coupled by flexible linkers. To a first approximation, we find that the lateral diffusion constants of these engineered PH domain constructs are inversely proportional to the number of bound PIP3 molecules. This observation suggests that the frictional contributions of multiple, tightly bound lipids are additive, at least when the binding sites are located on separate domains. At the meeting we will present our latest diffusion constant measurements, which will shed light on the mechanisms of peripheral membrane protein diffusion, and will provide useful calibration points in molecular dynamics simulations of proteins docked to membranes. Overall, single molecule diffusion methods provide a new, much needed window into the lipid interactions of membrane targeting proteins.

Two coarse-graining studies of stochastic models in molecular biology

We examine stochastic coarse-graining strategies for two biomolecular systems. First, we compute the large-scale transport properties of the basic flashing ratchet mathematical model for (Brownian) molecular motors and consider in this light whether the underlying continuous-space, continuous-time Markovian model can be coarse-grained as a discrete-state, continuous-time Markovian random walk model. Through careful computation of associated statistical signatures of Markovianity, we find that such a discrete coarse-graining is an excellent approximation over much but not all of the parameter regime. In particular, for the parameter values associated with the fastest transport by the flashing ratchet, the discretized model displays non-Markovian features such as waiting times between jumps which are not exponentially distributed. We provide a theoretical framework for understanding the conditions under which Markovianity is to be expected in the discretized model and two mechanisms by which the flashing ratchet model coarse-grains to a non-Markovian discretized model. Next we turn to a basic question of how the dynamics of water molecules near the surface of a solute can be represented by a simple drift-diffusion stochastic model. This question is of most interest for the purpose of accelerating molecular dynamics simulations of proteins, but for simplicity, we here examine the simple case where the solute is a C60 buckyball, which has a homogenous, roughly isotropic form. We compare the mathematical drift-diffusion framework with a statistical quantification of water dynamics near a solute discussed in the biophysical literature. A key concern is the choice of time interval on which to sample the molecular dynamics data to generate estimators for the drift and diffusivity. We use a simple mathematical toy model to establish insight and a strategy, but find for the actual molecular dynamics data, that the sampling times which produce the most faithful drift coefficient and the sampling times which produce the most faithful diffusion coefficient do not overlap, so that sacrifice of quality in one or the other parameter appears necessary.

Microcanonical replica exchange molecular dynamics simulation of proteins

We present microcanonical replica exchange molecular dynamics simulations as an alternative to canonical ones. Its advantage is the easily tunable high acceptance rate for replica exchange. We present the theory, comment on its actual implementation, and demonstrate its application for a common test case, the trp-cage protein.

Interactive Visualization of Molecular Surface Dynamics

Molecular dynamics simulations of proteins play a growing role in various fields such as pharmaceutical, biochemical and medical research. Accordingly, the need for high quality visualization of these protein systems raises. Highly interactive visualization techniques are especially needed for the analysis of time-dependent molecular simulations. Beside various other molecular representations the surface representations are of high importance for these applications. So far, users had to accept a trade-off between rendering quality and performance--particularly when visualizing trajectories of time-dependent protein data. We present a new approach for visualizing the Solvent Excluded Surface of proteins using a GPU ray casting technique and thus achieving interactive frame rates even for long protein trajectories where conventional methods based on precomputation are not applicable. Furthermore, we propose a semantic simplification of the raw protein data to reduce the visual complexity of the surface and thereby accelerate the rendering without impeding perception of the protein's basic shape. We also demonstrate the application of our Solvent Excluded Surface method to visualize the spatial probability density for the protein atoms over the whole period of the trajectory in one frame, providing a qualitative analysis of the protein flexibility.

Characterizing rare-event property distributions via replicate molecular dynamics simulations of proteins

As computational resources increase, molecular dynamics simulations of biomolecules are becoming an increasingly informative complement to experimental studies. In particular, it has now become feasible to use multiple initial molecular configurations to generate an ensemble of replicate production-run simulations that allows for more complete characterization of rare events such as ligand-receptor unbinding. However, there are currently no explicit guidelines for selecting an ensemble of initial configurations for replicate simulations. Here, we use clustering analysis and steered molecular dynamics simulations to demonstrate that the configurational changes accessible in molecular dynamics simulations of biomolecules do not necessarily correlate with observed rare-event properties. This informs selection of a representative set of initial configurations. We also employ statistical analysis to identify the minimum number of replicate simulations required to sufficiently sample a given biomolecular property distribution. Together, these results suggest a general procedure for generating an ensemble of replicate simulations that will maximize accurate characterization of rare-event property distributions in biomolecules.

Refinement of the primary hydration shell model for molecular dynamics simulations of large proteins

A realistic representation of water molecules is important in molecular dynamics simulation of proteins. However, the standard method of solvating biomolecules, that is, immersing them in a box of water with periodic boundary conditions, is computationally expensive. The primary hydration shell (PHS) method, developed more than a decade ago and implemented in CHARMM, uses only a thin shell of water around the system of interest, and so greatly reduces the computational cost of simulations. Applying the PHS method, especially to larger proteins, revealed that further optimization and a partial reworking was required and here we present several improvements to its performance. The model is applied to systems with different sizes, and both water and protein behaviors are compared with those observed in standard simulations with periodic boundary conditions and, in some cases, with experimental data. The advantages of the modified PHS method over its original implementation are clearly apparent when it is applied to simulating the 82 kDa protein Malate Synthase G.

A coarse‐grained potential for fold recognition and molecular dynamics simulations of proteins

A coarse-grained potential for protein simulations and fold ranking is presented. The potential is based on a two-point model of individual amino acids and a specific implementation of hydrogen bonding. Parameters are determined for distance dependent pair interactions, pseudo bonds, angles, and torsions. A scaling factor for a hydrogen bonding term is also determined. Iterative sampling for 4867 proteins reproduces distributions of internal coordinates and distances observed in the Protein Data Bank. The adjustment of the potential and resampling are in the spirit of the generalized ensemble approach. No native structure information (e.g., secondary structure) is used in the calculation of the potential or in the simulation of a particular protein. The potential is subject to two tests as follows: (i) simulations of 956 globular proteins in the neighborhood of their native folds (these proteins were not used in the training set) and (ii) discrimination between native and decoy structures for 2470 proteins with 305,000 decoys and the "Decoys 'R' Us" dataset. In the first test, 58% of tested proteins stay within 5 A from the native fold in Molecular Dynamics simulations of more than 20 nanoseconds using the new potential. The potential is also useful in differentiating between correct and approximate folds providing significant signal for structure prediction algorithms. Sampling with the potential consistently regenerates the distribution of distances and internal coordinates it learned. Nevertheless, during Molecular Dynamics simulations structures are found that reproduce the learned distributions but are far from the native fold.

A Modified Primary Hydration Shell (PHS) Method Allows Up To Two Orders Of Magnitude Time Saving In Molecular Dynamics Simulations: Application To Large Systems And Lipid Bilayers

A realistic representation of water molecules is essential in molecular dynamics simulation of proteins. However, the standard method of solvating biomolecules, i.e. immersing them in a box of water with periodic boundary conditions, is computationally very expensive. The primary hydration shell (PHS) method, developed more than a decade ago [1], uses only a thin shell of water around the system of interest, and so greatly reduces the computational power needed for simulations [2]. The method, however, was not perfect especially when large proteins are concerned. We have modified the PHS method in several ways to improve its performance when large systems are simulated [3]. The model is applied to several systems with different sizes, and both water and protein behaviors are compared with those obtained from standard simulations with periodic boundary conditions and with experimental data. Specifically, Lipari-Szabo order parameters for the proteins of interest are shown to be in good agreement with those derived from standard simulations and NMR relaxation measurements. Finally, the results of the application of the modified PHS method to simulating the cytoplasmic region of the transmembrane protein Plexin B1, and its interaction with the membrane are discussed.[1] Beglov, D., and Roux B. 1994, Biopolymers. 35:171-178.[2] Hamaneh, M. B., and Buck M. 2007, Biophysical Journal 92:L49-L51.[3] Hamaneh, M. B., and Buck M. 2008, ssubmitted.

PRIMO: A Transferable Coarse-Grained Model for Proteins

Coarse-grained (CG) models for biological systems promise a considerable advantage over all atom models with respect to conformational sampling of large systems over long timescales. A major bottleneck in most existing CG modeling approaches has been a lack of transferability to a wide array of systems and physical conditions. A new, fully transferable model PRIMO (PRotein Intermediate Model) is introduced. This model is comparable to all-atom models in terms of accuracy and transferability. The PRIMO model consists of interaction sites each combining 1-3 heavy atoms. The interaction potential is similar to standard molecular dynamics (MD) forcefield terms plus additional empirical hydrogen bonding and solvation terms. PRIMO is parameterized primarily based on atomistic simulations. PRIMO has been tested by comparing energies to the CHARMM27 all-atom forcefield for (AAXAA)N peptides and protein decoy sets. We demonstrate the application of PRIMO model by comparing stability of MD simulations of proteins to results from atomistic simulations and by comparing folding studies of (AAXAA)N peptides.