Biomolecules, Combinatorics, and Statistical Physics

Abstract

Motivated by the combinatorial properties of the protein-design problem and the specific and non-specific interactions in biomolecular systems, we build exactly-solved models for the statistical physics of the symmetric group, permutation glasses, and the self-assembly of dimer systems. The first two models are studied for their statistical physics properties apart from the motivating system, and the third model is used to better understand the constraints of correct dimerization in biomolecular systems. These models are exactly-solved in the sense that the sum-over-states defining their partition functions can be reduced to analytically more tractable expressions, and unlike most exactly-solved models in statistical physics whose motivations lie in condensed matter scenarios, these models are found by abstractly considering the combinatorial properties of biomolecular systems. This work suggests that there is a class of interesting but unexplored models in the statistical physics of biomolecules. We conclude by suggesting extensions to our presented models and starting points for new ones.