Green function of correlated genes in a minimal mechanical model of protein evolution

By S. Dutta, Jean-Pierre Eckmann, Albert Libchaber, Tsvi Tlusty. 2018

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Significance Many protein functions involve large-scale motion of their amino acids, while alignment of their sequences shows long-range correlations. This has motivated search for physical links between genetic and phenotypic collective behaviors. The major challenge is the complex nature of protein: nonrandom heteropolymers made of 20 species of amino acids that fold into a strongly coupled network. In light of this complexity, simplified models are useful. Our model describes protein in terms of the Green function, which directly links the gene to force propagation and collective dynamics in the protein. This allows for derivation of basic determinants of evolution, such as fitness landscape and epistasis, which are often hard to calculate. The function of proteins arises from cooperative interactions and rearrangements of their amino acids, which exhibit large-scale dynamical modes. Long-range correlations have also been revealed in protein sequences, and this has motivated the search for physical links between the observed genetic and dynamic cooperativity. We outline here a simplified theory of protein, which relates sequence correlations to physical interactions and to the emergence of mechanical function. Our protein is modeled as a strongly coupled amino acid network with interactions and motions that are captured by the mechanical propagator, the Green function. The propagator describes how the gene determines the connectivity of the amino acids and thereby, the transmission of forces. Mutations introduce localized perturbations to the propagator that scatter the force field. The emergence of function is manifested by a topological transition when a band of such perturbations divides the protein into subdomains. We find that epistasis—the interaction among mutations in the gene—is related to the nonlinearity of the Green function, which can be interpreted as a sum over multiple scattering paths. We apply this mechanical framework to simulations of protein evolution and observe long-range epistasis, which facilitates collective functional modes.

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  1. Kunihiko Kaneko
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