Activities of many biological macromolecules involve large conformational transitions for which crystallography can specify atomic details of alternative end states, but the course of transitions is often beyond the reach of computations based on full-atomic potential functions. We have developed a coarse-grained force field for molecular mechanics calculations based on the virtual interactions of C␣ atoms in protein molecules. This force field is parameterized based on the statistical distribution of the energy terms extracted from crystallographic data, and it is formulated to capture features dependent on secondary structure and on residue-specific contact information. The resulting force field is applied to energy minimization and normal mode analysis of several proteins. We find robust convergence in minimizations to low energies and energy gradients with low degrees of structural distortion, and atomic fluctuations calculated from the normal mode analyses correlate well with the experimental B-factors obtained from high-resolution crystal structures. These findings suggest that the virtual atom force field is a suitable tool for various molecular mechanics applications on large macromolecular systems undergoing large conformational changes.energy minimization ͉ normal modes ͉ transition pathways A ccurate understanding of the dynamic properties of proteins has been a major challenge in biophysics (1, 2). With advances in macromolecular crystallography, structural information has been obtained on very large complexes such as ribosome particles (3), chaperone complexes (4), virus particles (5), and RNA polymerases (6) as well as on thousands of individual proteins. In addition, snapshots of protein structures in different states of activity demonstrate the existence of very large conformational changes (7,8). Computational analysis of the dynamics of such systems is extremely difficult, if not impossible, when using full-atomic computational approaches, due not only to computational limitations but also to the complexity of the resulting information. Thus, coarse-grained approaches have gained importance for addressing large systems and large conformational changes (9-11).Coarse graining reduces computational complexity by greatly decreasing degrees of freedom of a molecular system with appropriate assumptions to achieve simplification without compromise of essential features (12). For reducing complexity in proteins, C␣-only models have been the most popular, but other coarse-graining approaches have also been taken, such as the inclusion of side-chain centroids (SCs) (13). An important aspect of coarse-grained analysis is the use of an appropriate pseudoforce field to model the forces and constraints exerted on the molecular system.The use of simple harmonic potentials to model the C␣-to-C␣ interactions in proteins as flexible springs has been most popular (14). Such simple harmonic potentials are very effective in defining the near-native-state fluctuations of proteins calculated by elastic network models...

Many proteins function through conformational transitions between structurally disparate states, and there is a need to explore transition pathways between experimentally accessible states by computation. The sizes of systems of interest and the scale of conformational changes are often beyond the scope of full atomic models, but appropriate coarse-grained approaches can capture significant features. We have designed a comprehensive knowledge-based potential function based on a C␣ representation for proteins that we call the virtual atom molecular mechanics (VAMM) force field. Here, we describe an algorithm for using the VAMM potential to describe conformational transitions, and we validate this algorithm in application to a transition between open and closed states of adenylate kinase (ADK). The VAMM algorithm computes normal modes for each state and iteratively moves each structure toward the other through a series of intermediates. The move from each side at each step is taken along that normal mode showing greatest engagement with the other state. The process continues to convergence of terminal intermediates to within a defined limit-here, a root-mean-square deviation of 1 Å. Validations show that the VAMM algorithm is highly effective, and the transition pathways examined for ADK are compatible with other structural and biophysical information. We expect that the VAMM algorithm can address many biological systems.coarse grained ͉ potential function ͉ transition pathways L arge-scale conformational transitions mediate allosteric regulation and play other critical roles in protein function (1, 2). Crystallographic studies have provided various snapshots of some proteins in different conformational states, yet the transition mechanisms and the allosteric couplings of these proteins remain incompletely understood at best. In addition to experimental techniques, the near-native state dynamics of proteins have been studied using various full atomic (3) and coarse-grained computational approaches (4). Conformational changes may span an extensive range of amplitudes and time scales, and relevant systems can be quite large. Such transitions typically entail the crossing of large energetic and entropic barriers and involve the collective motions of very large protein complexes that are not readily accessible to experiments and not easily modeled for computations. Accurate and efficient molecular mechanics approaches are needed to analyze such large-scale motions and relate the complex dynamic behaviors of proteins to their function.Adenylate kinase (ADK) is prototypic of proteins that undergo large-scale conformational change during functional transitions (5). ADKs regulate energy homeostasis in cells by catalyzing the transfer of a phosphate group from ATP to AMP to yield two ADP molecules. ADK comprises three domains: a core domain, an ATP-binding lid domain, and an AMP-binding lid domain. It has been well characterized by structural (5-9), biophysical (9, 10), and theoretical (11-14) studies that large conformati...

HIV envelope glycoproteins undergo large-scale conformational changes as they interact with cellular receptors to cause the fusion of viral and cellular membranes that permits viral entry to infect targeted cells. Conformational dynamics in HIV gp120 are also important in masking conserved receptor epitopes from being detected for effective neutralization by the human immune system. Crystal structures of HIV gp120 and its complexes with receptors and antibody fragments provide high-resolution pictures of selected conformational states accessible to gp120. Here we describe systematic computational analyses of HIV gp120 plasticity in such complexes with CD4 binding fragments, CD4 mimetic proteins, and various antibody fragments. We used three computational approaches: an isotropic elastic network analysis of conformational plasticity, a full atomic normal mode analysis, and simulation of conformational transitions with our coarse-grained virtual atom molecular mechanics (VAMM) potential function. We observe collective sub-domain motions about hinge points that coordinate those motions, correlated local fluctuations at the interfacial cavity formed when gp120 binds to CD4, and concerted changes in structural elements that form at the CD4 interface during large-scale conformational transitions to the CD4-bound state from the deformed states of gp120 in certain antibody complexes.

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The conformations available to polypeptides are determined by the interatomic forces acting on the peptide units, whereby backbone torsion angles are restricted as described by the Ramachandran plot. Although typical proteins are composed predominantly from α-helices and β-sheets, they nevertheless adopt diverse tertiary structure, each folded as dictated by its unique amino-acid sequence. Despite such uniqueness, however, the functioning of many proteins involves changes between quite different conformations.The study of large-scale conformational changes, particularly in large systems, is facilitated by a coarse-grained representation such as provided by virtually bonded Cα atoms. We have developed a virtual atom molecular mechanics (VAMM) force field to describe conformational dynamics in proteins and a VAMM-based algorithm for computing conformational transition pathways. Here we describe the stereochemical analysis of proteins in this coarse-grained representation, comparing the relevant plots in coarse-grained conformational space to the corresponding Ramachandran plots, having contoured each at levels determined statistically from residues in a large database. The distributions shown for an all-α protein, two all-β proteins and one α+β protein serve to relate the coarse-grained distributions to the familiar Ramachandran plot.