Protein Folding: A New Geometric Analysis

摘要

A geometric analysis of protein folding, which complements many of the modelsin the literature, is presented. We examine the process from unfolded strand tothe point where the strand becomes self-interacting. A central question is howit is possible that so many initial configurations proceed to fold to a uniquefinal configuration. We put energy and dynamical considerations temporarilyaside and focus upon the geometry alone. We parameterize the structure of anidealized protein using the concept of a ribbon from differential geometry. Thedeformation of the ribbon is described by introducing a generic twistingAnsatz. The folding process in this picture entails a change in shape guided bythe local amino acid geometry. The theory is reparamaterization invariant fromthe start, so the final shape is independent of folding time. We developdifferential equations for the changing shape. For some parameter ranges, asine-Gordon torsion soliton is found. This purely geometric waveform hasproperties similar to dynamical solitons. Namely: A threshold distortion of themolecule is required to initiate the soliton, after which, small additionaldistortions do not change the waveform. In this analysis, the soliton twiststhe molecule until bonds form. The analysis reveals a quantitative relationshipbetween the geometry of the amino acids and the folded form.