Abstract
A backbone-side-chain elastic network model (bsENM) is devised in this contribution to decipher the network of molecular interactions during protein dynamics. The chemical details in 5 μs all-atom molecular dynamics (MD) simulation are mapped onto the bsENM spring constants by self-consistent iterations. The elastic parameters obtained by this structure-mechanics statistical learning are then used to construct inter-residue rigidity graphs for the chemical components in protein amino acids. A key discovery is that the mechanical coupling strengths of both backbone and side chains exhibit heavy-tailed distributions and scale-free network properties. In both rat trypsin and PDZ3 proteins, the statistically prominent modes of rigidity graphs uncover the sequence-specific coupling patterns and mechanical hotspots. Based on the contributions to graphical modes, our residue rigidity scores in backbone and side chains are found to be very useful metrics for the biological significance. Most functional sites have high residue rigidity scores in side chains while the biologically important glycines are generally next to mechanical hotspots. Furthermore, prominent modes in the rigidity graphs involving side chains oftentimes coincide with the co-evolution patterns due to evolutionary restraints. The bsENM specifically devised to resolve the protein chemical character thus provides useful means for extracting functional information from all-atom MD.
Highlights
Proteins exhibit remarkable properties such as thermal stability, specific molecular binding, and catalytic activities
With the all-atom molecular dynamics (MD) simulation, structure-mechanics statistical learning, and rigidity graph analysis for both the rat trypsin (RT) and the PDZ3 proteins, the main text primarily uses RT for introducing the rich and quantitative information made available by our new approach
With increasing l0ij, it can be seen that the fraction of positive-definite springs drops further, and the protein mechanical coupling network is progressively sparser than the structural contact network
Summary
Proteins exhibit remarkable properties such as thermal stability, specific molecular binding, and catalytic activities These functionally important features are sensitive to mutation and can trace their origin to both the polypeptide backbone that frames the structure and the side chains that define the chemical specificity [1,2,3]. If the distance between a residue pair is within a cutoff, their edge in the adjacency matrix A is typically set to one, and the diagonal degree matrix D records the residue contact numbers. This topology-based approach corresponds to using a universal spring constant in ENM. The Laplacian matrix (L 1⁄4 D À A) [24,25] was found to offer good approximation for low-frequency motions [13,14], and the structural network is often used to study the collective vibrations that are not very sensitive to the sequence specificity due to side chains. [26,27,28,29]
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