Chern-Simons-Higgs model as a theory of protein molecules

Abstract

In this paper, we discuss a one-dimensional Abelian-Higgs model with Chern-Simons interaction as an effective theory of one-dimensional curves embedded in a three-dimensional space. We demonstrate how this effective model is compatible with the geometry of protein molecules. Using standard field theory techniques, we analyze phenomenologically interesting static configurations of the model and discuss their stability. This simple model predicts some characteristic relations for the geometry of secondary structure motifs of proteins, and we show how this is consistent with the experimental data. After using the data to universally fix basic local geometric parameters, such as the curvature and torsion of the helical motifs, we are left with a single free parameter. We explain how this parameter controls the abundance and shape of the principal motifs (alpha helices, beta strands, and loops connecting them).