A Rate Distortion approach to protein symmetry

Rodrick Wallace

doi:10.1038/npre.2010.4280.2

Abstract

AbstractA 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. In the 'energy' picture, the average distortion between codon message and 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. Mechanistic models of protein folding fail to account for the observed spectrum of folding and aggregation disorders, suggesting that a biologically based cognitive paradigm describing the folding process will be needed for understanding the etiology, prevention, and treatment of these diseases. The developmental formalism introduced here may contribute significantly to such a paradigm.

Highlights

The symmetries of folded proteins remain something of a scientific mystery, in spite of decades of concerted attention
But less overtly ‘symmetric’, conformations, involve finite tilings of helices, sheets, and attachment loops that would seem better described using groupoid methods, following the arguments of Weinstein (1996): As Wolynes (1996) put the matter, “It is the inexact symmetries of biological molecules that are most striking”
The argument, an extension of Tlusty’s (2007) insights regarding the role of rate distortion constraints in evolutionary process, seems fairly direct, based on standard material from statistical physics and information theory

Summary

Introduction

The symmetries of folded proteins remain something of a scientific mystery, in spite of decades of concerted attention. We will attempt to finesse this perspective by invoking, first, a rate distortion argument applied to the transmitted signal represented by the translation of the genome into the final condensation of the molten globule of the resulting amino acid string. The second stage is to examine the likely effect of limited availability of metabolic free energy, or processing time, on the fidelity of this transmission. The observation of a possible ‘metabolic singularity’ limiting that fidelity suggests, in turn, that possible protein symmetries were, in some measure, limited by energy availability in prebiotic circumstances, leading to early evolutionary lock-in by path dependence. The argument, an extension of Tlusty’s (2007) insights regarding the role of rate distortion constraints in evolutionary process, seems fairly direct, based on standard material from statistical physics and information theory

Spontaneous symmetry breaking

A little information theory

Mixing metaphors

Metabolic singularity

Discussion and conclusions