A force field for virtual atom molecular mechanics of proteins

Structural fluctuations of a protein are essential for a protein to function and fold. By using molecular dynamics (MD) simulations of the model α/β protein VA3 in its native state, the coupling between the main-chain (MC) motions [represented by coarsegrained dihedral angles (CGDAs) γ n based on four successive C α atoms (n − 1, n, n þ 1, n þ 2) along the amino acid sequence] and its side-chain (SC) motions [represented by CGDAs δ n formed by the virtual bond joining two consecutive C α atoms (n, n þ 1) and the bonds joining these C α atoms to their respective C β atoms] was analyzed. The motions of SCs (δ n ) and MC (γ n ) over time occur on similar free-energy profiles and were found to be subdiffusive. The fluctuations of the SCs (δ n ) and those of the MC (γ n ) are generally poorly correlated on a ps time-scale with a correlation increasing with time to reach a maximum value at about 10 ns. This maximum value is close to the correlation between the δ n ðtÞ and γ n ðtÞ time-series extracted from the entire duration of the MD runs (400 ns) and varies significantly along the amino acid sequence. High correlations between the SC and MC motions [δðtÞ and γðtÞ time-series] were found only in flexible regions of the protein for a few residues which contribute the most to the slowest collective modes of the molecule. These results are a possible indication of the role of the flexible regions of proteins for the biological function and folding.dihedral principal component analysis | free-energy landscape | power law | subdiffusion T he motions of the side chains and of the backbone of a protein are coupled to each other in protein folding. The removal of the nonpolar side chains from the solvent in protein folding orients the backbone locally (1), and the formation of the backbone hydrogen bonds between residues in the secondary structures induces displacements of their side chains. Therefore, in order to understand protein folding, it is necessary to understand how the motions of the side chains are propagated to the backbone and vice versa. As a prerequisite, it is necessary to understand how the motions of the side chains are coupled to those of the main chain in the native state of a protein. To address this question, five 80 ns all-atom molecular dynamics (MD) simulations of a 46-residue α/β model protein VA3 (PDB: 1ED0) (2) in its native state were analyzed. Protein VA3 was chosen here because it is highly homologous to the well-studied protein crambin, but unlike crambin (3), it is soluble in water (2).To express the correlation between the main-chain and the side-chain motions quantitatively, two coarse-grained dihedral angles (CGDAs) were defined for each residue n (Fig. S1A). The angles characterizing the fluctuations of the main chain are the CGDAs γ n (4-6) formed by the virtual bonds joining four consecutive C α atoms (n − 1, n, n þ 1 and n þ 2) along the amino acid sequence with 2 ≤ n ≤ N − 2 and N being the number of residues (Fig. S1A). The angles γ n are coordinates used to describe large changes o...

mentioning

confidence: 99%

Anomalous diffusion and dynamical correlation between the side chains and the main chain of proteins in their native state

Cote

Senet

Delarue

et al. 2012

“…First, u n ðtÞ represents the orientation of the main chain measured by a coarse-grained dihedral angle γ n (16,17) formed by the virtual bonds joining four consecutive C α atoms (n − 1, n, n þ 1, and n þ 2) along the amino acid sequence; i.e., u n ðtÞ ¼ fcos½γ n ðtÞ; sin½γ n ðtÞg with 2 < n < N − 2 and N being the number of residues. The dihedral angles γ n (16) are coordinates used to describe (large) conformational changes of proteins (18) and are part of coarse-grained models of proteins (19,20). The successive orientations of u n ðtÞ are represented by rotational diffusion on a circle (Fig.…”

mentioning

confidence: 99%

Nonexponential decay of internal rotational correlation functions of native proteins and self-similar structural fluctuations

Cote

Senet

Delarue

et al. 2010

Structural fluctuations of a protein are essential for the function of native proteins and for protein folding. To understand how the main chain in the native state of a protein fluctuates on different time scales, we examined the rotational correlation functions (RCFs), CðtÞ, of the backbone N-H bonds and of the dihedral angles γ built on four consecutive C α atoms. Using molecular dynamics simulations of a model α∕β protein (VA3) in its native state, we demonstrate that these RCFs decay as stretched exponentials, ln ½CðtÞ≈D α t α with a constant D α and an exponent α (0<α<0.35) varying with the free-energy profiles (FEPs) along the amino acid sequence. The probability distributions of the fluctuations of the main chain computed at short time scale (1 ps) were identical to those computed at large time scale (1 ns) if the time is rescaled by a factor depending on α<1. This self-similar property and the nonexponential decays (α≠1) of the RCFs are described by a rotational diffusion equation with a time-dependent diffusion coefficient DðtÞ¼αD α t α−1 . The present findings agree with observations of subdiffusion (α<1) of fluorescent probes within a protein molecule. The subdiffusion of 15 N-H bonds did not affect the value of the order parameter S 2 extracted from the NMR relaxation data by assuming normal diffusion (α¼1) of 15 N-H bonds on a nanosecond time scale. However, we found that the RCF does not converge to S 2 on the nanosecond time scale for residues with multiple-minima FEPs.anomalous diffusion | model-free approach | power law | free-energy landscape

“…where each of the terms is defined in a companion paper (19). In brief, Vbonded is the same bond-restraint term as for V Bond-restrained in Eq.…”

Section: Methodsmentioning

confidence: 99%

“…Motivated largely by transition pathway applications, we recently defined a knowledge-based potential function for large systems undergoing large conformational changes (19). We call this coarsegrained approach virtual atom molecular mechanics (VAMM).…”

mentioning

confidence: 99%

Computation of conformational transitions in proteins by virtual atom molecular mechanics as validated in application to adenylate kinase

Korkut

Hendrickson

2009

Self Cite

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...