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

Abstract

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...

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