Collective aspects of protein folding illustrated by a toy model

A simple toy model for polypeptides serves as a testbed to illuminate some nonlocal, or collective, aspects of protein folding phenomena. The model is two dimensional and has only two amino acids, but involves a continuous range of backbone bend angles. Global potential energy minima and their folding structures have been determined for leading members of two special and contrasting polypeptide sequences, center doped and Fibonacci, named descriptively for their primary structures. The results display the presence of spontaneous symmetry breaking, elastic strain, and substantial conformational variation for specific embedded amino acid strings. We conclude that collective variables generated by the primary amino acid structure may be required for fully effective protein folding predictors, including those based on neural networks