A network model predicts the intensity of residue-protein thermal coupling.

Abstract

The flow of vibrational energy in proteins has been shown not to obey expectations for isotropic media. The existence of preferential pathways for energy transport, with probable connections to allostery mechanisms, has been repeatedly demonstrated. Here, we investigate whether, by representing a set of protein structures as networks of interacting amino acid residues, we are able to model heat diffusion and predict residue-protein vibrational couplings, as measured by the Anisotropic Thermal Diffusion (ATD) computational protocol of modified molecular dynamics simulations. We revisit the structural rationales for the precise definition of a contact between amino acid residues. Using this definition to describe a set of proteins as contact networks where each node corresponds to a residue, we show that node centrality, particularly closeness centrality and eigenvector centrality , correlates to the strength of the vibrational coupling of each residue to the rest of the structure. We then construct an analytically solvable model of heat diffusion on a network, whose solution incorporates an explicit dependence on the connectivity of the heated node, as described by a perturbed graph Laplacian Matrix. An implementation of the described model is available at http://leandro.iqm.unicamp.br/atd-scripts . leandro@iqm.unicamp.br.