Coarse-grained normal mode analysis in structural biology

The realization that experimentally observed functional motions of proteins can be predicted by coarse-grained normal mode analysis has renewed interest in applications to structural biology. Notable applications include the prediction of biologically relevant motions of proteins and supramolecular structures driven by their structure-encoded collective dynamics; the refinement of low-resolution structures, including those determined by cryo-electron microscopy; and the identification of conserved dynamic patterns and mechanically key regions within protein families. Additionally, hybrid methods that couple atomic simulations with deformations derived from coarse-grained normal mode analysis are able to sample collective motions beyond the range of conventional molecular dynamics simulations. Such applications have provided great insight into the underlying principles linking protein structures to their dynamics and their dynamics to their functions.     

Molecular dynamics simulations of peptides and proteins with amplified collective motions

We present a novel method that uses the collective modes obtained with a coarse-grained model/anisotropic network model to guide the atomic-level simulations. Based on this model, local collective modes can be calculated according to a single configuration in the conformational space of the protein. In the molecular dynamics simulations, the motions along the slowest few modes are coupled to a higher temperature by the weak coupling method to amplify the collective motions. This amplified-collective-motion (ACM) method is applied to two test systems. One is an S-peptide analog. We realized the refolding of the denatured peptide in eight simulations out of 10 using the method. The other system is bacteriophage T4 lysozyme. Much more extensive domain motions between the N-terminal and C-terminal domain of T4 lysozyme are observed in the ACM simulation compared to a conventional simulation. The ACM method allows for extensive sampling in conformational space while still restricting the sampled configurations within low energy areas. The method can be applied in both explicit and implicit solvent simulations, and may be further applied to important biological problems, such as long timescale functional motions, protein folding/unfolding, and structure prediction.     

iFold: a platform for interactive folding simulations of proteins

We built a novel web-based platform for performing discrete molecular dynamics simulations of proteins. In silico protein folding involves searching for minimal frustration in the vast conformational landscape. Conventional approaches for simulating protein folding insufficiently address the problem of simulations in relevant time and length scales necessary for a mechanistic understanding of underlying biomolecular phenomena. Discrete molecular dynamics (DMD) offers an opportunity to bridge the size and timescale gaps and uncover the structural and biological properties of experimentally undetectable protein dynamics. The iFold server supports large-scale simulations of protein folding, thermal denaturation, thermodynamic scan, simulated annealing and p(fold) analysis using DMD and coarse-grained protein model with structure-based Gō-interactions between amino acids. AVAILABILITY: http://ifold.dokhlab.org     

Principal component and normal mode analysis of proteins; a quantitative comparison using the GroEL subunit

Principal component analysis (PCA) and normal mode analysis (NMA) have emerged as two invaluable tools for studying conformational changes in proteins. To compare these approaches for studying protein dynamics, we have used a subunit of the GroEL chaperone, whose dynamics is well characterized. We first show that both PCA on trajectories from molecular dynamics (MD) simulations and NMA reveal a general dynamical behavior in agreement with what has previously been described for GroEL. We thus compare the reproducibility of PCA on independent MD runs and subsequently investigate the influence of the length of the MD simulations. We show that there is a relatively poor one-to-one correspondence between eigenvectors obtained from two independent runs and conclude that caution should be taken when analyzing principal components individually. We also observe that increasing the simulation length does not improve the agreement with the experimental structural difference. In fact, relatively short MD simulations are sufficient for this purpose. We observe a rapid convergence of the eigenvectors (after ca. 6 ns). Although there is not always a clear one-to-one correspondence, there is a qualitatively good agreement between the movements described by the first five modes obtained with the three different approaches; PCA, all-atoms NMA, and coarse-grained NMA. It is particularly interesting to relate this to the computational cost of the three methods. The results we obtain on the GroEL subunit contribute to the generalization of robust and reproducible strategies for the study of protein dynamics, using either NMA or PCA of trajectories from MD simulations.     

Effects of surface water on protein dynamics studied by a novel coarse-grained normal mode approach

Normal mode analysis (NMA) has received much attention as a direct approach to extract the collective motions of macromolecules. However, the stringent requirement of computational resources by classical all-atom NMA limits the size of the macromolecules to which the method is normally applied. We implemented a novel coarse-grained normal mode approach based on partitioning the all-atom Hessian matrix into relevant and nonrelevant parts. It is interesting to note that, using classical all-atom NMA results as a reference, we found that this method generates more accurate results than do other coarse-grained approaches, including elastic network model and block normal mode approaches. Moreover, this new method is effective in incorporating the energetic contributions from the nonrelevant atoms, including surface water molecules, into the coarse-grained protein motions. The importance of such improvements is demonstrated by the effect of surface water to shift vibrational modes to higher frequencies and by an increase in overlap of the coarse-grained eigenvector space (the motion directions) with that obtained from molecular dynamics simulations of solvated protein in a water box. These results not only confirm the quality of our method but also point out the importance of incorporating surface structural water in studying protein dynamics.     

Evolutionary Conserved Positions Define Protein Conformational Diversity

Conformational diversity of the native state plays a central role in modulating protein function. The selection paradigm sustains that different ligands shift the conformational equilibrium through their binding to highest-affinity conformers. Intramolecular vibrational dynamics associated to each conformation should guarantee conformational transitions, which due to its importance, could possibly be associated with evolutionary conserved traits. Normal mode analysis, based on a coarse-grained model of the protein, can provide the required information to explore these features. Herein, we present a novel procedure to identify key positions sustaining the conformational diversity associated to ligand binding. The method is applied to an adequate refined dataset of 188 paired protein structures in their bound and unbound forms. Firstly, normal modes most involved in the conformational change are selected according to their corresponding overlap with structural distortions introduced by ligand binding. The subspace defined by these modes is used to analyze the effect of simulated point mutations on preserving the conformational diversity of the protein. We find a negative correlation between the effects of mutations on these normal mode subspaces associated to ligand-binding and position-specific evolutionary conservations obtained from multiple sequence-structure alignments. Positions whose mutations are found to alter the most these subspaces are defined as key positions, that is, dynamically important residues that mediate the ligand-binding conformational change. These positions are shown to be evolutionary conserved, mostly buried aliphatic residues localized in regular structural regions of the protein like β-sheets and α-helix.     

Coarse-grained simulations of protein-protein association: an energy landscape perspective

Understanding protein-protein association is crucial in revealing the molecular basis of many biological processes. Here, we describe a theoretical simulation pipeline to study protein-protein association from an energy landscape perspective. First, a coarse-grained model is implemented and its applications are demonstrated via molecular dynamics simulations for several protein complexes. Second, an enhanced search method is used to efficiently sample a broad range of protein conformations. Third, multiple conformations are identified and clustered from simulation data and further projected on a three-dimensional globe specifying protein orientations and interacting energies. Results from several complexes indicate that the crystal-like conformation is favorable on the energy landscape even if the landscape is relatively rugged with metastable conformations. A closer examination on molecular forces shows that the formation of associated protein complexes can be primarily electrostatics-driven, hydrophobics-driven, or a combination of both in stabilizing specific binding interfaces. Taken together, these results suggest that the coarse-grained simulations and analyses provide an alternative toolset to study protein-protein association occurring in functional biomolecular complexes.     

Can morphing methods predict intermediate structures?

Movement is crucial to the biological function of many proteins, yet crystallographic structures of proteins can give us only a static snapshot. The protein dynamics that are important to biological function often happen on a timescale that is unattainable through detailed simulation methods such as molecular dynamics as they often involve crossing high-energy barriers. To address this coarse-grained motion, several methods have been implemented as web servers in which a set of coordinates is usually linearly interpolated from an initial crystallographic structure to a final crystallographic structure. We present a new morphing method that does not extrapolate linearly and can therefore go around high-energy barriers and which can produce different trajectories between the same two starting points. In this work, we evaluate our method and other established coarse-grained methods according to an objective measure: how close a coarse-grained dynamics method comes to a crystallographically determined intermediate structure when calculating a trajectory between the initial and final crystal protein structure. We test this with a set of five proteins with at least three crystallographically determined on-pathway high-resolution intermediate structures from the Protein Data Bank. For simple hinging motions involving a small conformational change, segmentation of the protein into two rigid sections outperforms other more computationally involved methods. However, large-scale conformational change is best addressed using a nonlinear approach and we suggest that there is merit in further developing such methods.     

Bending elasticity of anti-parallel beta-sheets

Using a coarse-grained elastic model, we examine the bending properties of anti-parallel beta-sheets comprised of uniform amino-acid residues in vacuum as well as in explicit solvent. By comparing the conformational probability of the beta-sheet from molecular dynamics simulations with the same quantities obtained from the coarse-grained model, we compute the elastic bending constant, kappa. Equilibrium fluctuations of the beta-sheet and its response to external forces are well reproduced by a model with a uniform isotropic bending constant. An anisotropic bending model is also investigated, although the computed anisotropy is relatively weak and most of the observed properties are well described by an isotropic model. The presence of explicit solvent also lowers the bending constant. The sequence dependence of our result and its implications in protein conformational dynamics are discussed.     

Computational techniques for efficient conformational sampling of proteins

In this review, we summarize the computational methods for sampling the conformational space of biomacromolecules. We discuss the methods applicable to find only lowest energy conformations (global minimization of the potential-energy function) and to generate canonical ensembles (canonical Monte Carlo method and canonical molecular dynamics method and their extensions). Special attention is devoted to the use of coarse-grained models that enable simulations to be enhanced by several orders of magnitude.     

Simulation of nitroxide electron paramagnetic resonance spectra from brownian trajectories and molecular dynamics simulations

A simulated continuous wave electron paramagnetic resonance spectrum of a nitroxide spin label can be obtained from the Fourier transform of a free induction decay. It has been previously shown that the free induction decay can be calculated by solving the time-dependent stochastic Liouville equation for a set of Brownian trajectories defining the rotational dynamics of the label. In this work, a quaternion-based Monte Carlo algorithm has been developed to generate Brownian trajectories describing the global rotational diffusion of a spin-labeled protein. Also, molecular dynamics simulations of two spin-labeled mutants of T4 lysozyme, T4L F153R1, and T4L K65R1 have been used to generate trajectories describing the internal dynamics of the protein and the local dynamics of the spin-label side chain. Trajectories from the molecular dynamics simulations combined with trajectories describing the global rotational diffusion of the protein are used to account for all of the dynamics of a spin-labeled protein. Spectra calculated from these combined trajectories correspond well to the experimental spectra for the buried site T4L F153R1 and the helix surface site T4L K65R1. This work provides a framework to further explore the modeling of the dynamics of the spin-label side chain in the wide variety of labeling environments encountered in site-directed spin labeling studies.     

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.     

Defining Coarse-Grained Representations of Large Biomolecules and Biomolecular Complexes from Elastic Network Models

Coarse-grained (CG) models of large biomolecular complexes enable simulations of these systems over long timescales that are not accessible for atomistic molecular dynamics (MD) simulations. A systematic methodology, called essential dynamics coarse-graining (ED-CG), has been developed for defining coarse-grained sites in a large biomolecule. The method variationally determines the CG sites so that key dynamic domains in the protein are preserved in the CG representation. The original ED-CG method relies on a principal component analysis (PCA) of a MD trajectory. However, for many large proteins and multi-protein complexes such an analysis may not converge or even be possible. This work develops a new ED-CG scheme using an elastic network model (ENM) of the protein structure. In this procedure, the low-frequency normal modes obtained by ENM are used to define dynamic domains and to define the CG representation accordingly. The method is then applied to several proteins, such as the HIV-1 CA protein dimer, ATP-bound G-actin, and the Arp2/3 complex. Numerical results show that ED-CG with ENM (ENM-ED-CG) is much faster than ED-CG with PCA because no MD is necessary. The ENM-ED-CG models also capture functional essential dynamics of the proteins almost as well as those using full MD with PCA. Therefore, the ENM-ED-CG method may be better suited to coarse-grain a very large biomolecule or biomolecular complex that is too computationally expensive to be simulated by conventional MD, or when a high resolution atomic structure is not even available.     

Multiscale modeling of lipids and lipid bilayers

A multiscale modeling approach is applied for simulations of lipids and lipid assemblies on mesoscale. First, molecular dynamics simulation of initially disordered system of lipid molecules in water within all-atomic model was carried out. On the next stage, structural data obtained from the molecular dynamics (MD) simulation were used to build a coarse-grained (ten sites) lipid model, with effective interaction potentials computed by the inverse Monte Carlo method. Finally, several simulations of the coarse-grained model on longer length- and time-scale were performed, both within Monte Carlo and molecular dynamics simulations: a periodical sample of lipid molecules ordered in bilayer, a free sheet of such bilayer without periodic boundary conditions, formation of vesicle from a plain membrane, process of self-assembly of lipids randomly dispersed in volume. It was shown that the coarse-grained model, developed exclusively from all-atomic simulation data, reproduces well all the basic features of lipids in water solution.     

Coarse-grained simulations of conformational dynamics of proteins: Application to apomyoglobin

A coarse-grained dynamic Monte Carlo method is proposed for investigating the conformational dynamics of proteins. Each residue is represented by two interaction sites, one at the α-carbon, and the other on the amino acid sidechain. Geometry and energy parameters extracted from databank structures are used. The method is applied to the crystal structure of apomyoglobin (apo-Mb). Equilibrium and dynamic properties of apo-Mb are characterized within computation times one order of magnitude shorter than conventional molecular dynamics (MD) simulations. The calculated rms fluctuations in α-carbons are in good agreement with crystallographic temperature factors. Regions exhibiting enhanced conformational mobilities are identified. Among the loops connecting the eight helices A to H, the loop CD undergoes the fastest motions, leading to partial unwinding of helix D. Helix G is the most stable helix on the basis of the kinetic stability of dihedral angles, followed by the respective helices A, E, H, and B. These results, in agreement with H/D exchange and two-dimensional NMR experiments, as well as with MD simulations, lend support to the use of the proposed approach as an efficient, yet physically plausible, means of characterizing protein conformational dynamics. Proteins 31:271–281, 1998. © 1998 Wiley-Liss, Inc.     

Efficient modelling protocols for oligosaccharides: from vacuum to solvent

The determination of conformational preferences of oligosaccharides is best approached by describing their preferred conformations on potential energy surfaces as a function of the glycosidic linkage φ, ψ torsional angles. For proper molecular mechanics modelling the flexibility of the rotatable pendant groups must also be considered. The so called adiabatic maps partially mimic the flexibility within the 10 dimensional conformational space of the pendant groups of the given disaccharide. These molecular mechanics maps are considered to be the state-of-the art of the φ, ψ potential energy surface of disaccharides recently calculated. The RAMM (RAndom Molecular Mechanics) method was shown to be able to calculate such profiles automatically. Additionally, based on the continuum solvent approach, RAMM allows the calculation of the effects of solvent on conformational energy profiles. Molecular dynamics simulations are also useful tools to study the influence of solvent on conformational behaviour of oligosaccharides. The capability of the RAMM calculational protocol to locate low-energy conformers on the multidimensional potential energy hypersurfaces of disaccharides is illustrated and compared with molecular dynamics simulations with and without inclusion of the solvent. This revised version was published online in August 2006 with corrections to the Cover Date.     

Investigation of ribosomes using molecular dynamics simulation methods

The ribosome as a complex molecular machine undergoes significant conformational changes while synthesizing a protein molecule. Molecular dynamics simulations have been used as complementary approaches to X-ray crystallography and cryoelectron microscopy, as well as biochemical methods, to answer many questions that modern structural methods leave unsolved. In this review, we demonstrate that all-atom modeling of ribosome molecular dynamics is particularly useful in describing the process of tRNA translocation, atomic details of behavior of nascent peptides, antibiotics, and other small molecules in the ribosomal tunnel, and the putative mechanism of allosteric signal transmission to functional sites of the ribosome.