A rate distortion approach to protein symmetry

Abstract

A spontaneous symmetry breaking argument is applied to the problem of protein folding, via a rate distortion analysis of the relation between genome coding and the final condensation of the protein molten globule that is, in spirit, analogous to Tlusty’s (2007) exploration of the evolution of the genetic code. In the ‘energy’ picture, the average distortion between codon message and final protein structure, under constraints driven by evolutionary selection, serves as a temperature analog, so that low values limit the possible distribution of protein forms, producing the canonical folding funnel. A dual ‘developmental’ perspective sees the rate distortion function itself as the temperature analog, and permits incorporation of chaperons or toxic exposures as catalysts, driving the system to different possible outcomes or affecting the rate of convergence. The rate distortion function appears constrained by the availability of metabolic free energy, with implications for prebiotic evolution, and a nonequilibrium empirical Onsager treatment provides an adaptable statistical model that can be fitted to data, in the same manner as a regression equation. In sum, mechanistic models of protein folding fail to account for the observed spectrum of protein folding and aggregation disorders, suggesting that a biologically based cognitive paradigm describing folding will be needed for understanding the etiology, prevention, and treatment of these diseases. The developmental formalism introduced here may contribute substantially to such a paradigm.