Statistical mechanics of protein sequences

A statistical mechanical treatment of biological macromolecules is presented that includes the sequence information as an internal coordinate. Using a path integral representation, the canonical partition function can be represented as a product of a polymer configurational path integral and a sequence walk path integral. In most biological instances, the sequence composition influences the potential energy of intersubunit interaction. Consequently, the two path integrals are not separable, but rather “interact” via a sequence-dependent configurational potential. In proteins and RNA, the sequence walk occurs in dimensions greater than three and, therefore, will be an ideal “polymer.” The Markovian nature of this walk can be exploited to show that all the structural information is contained in the sequence. This latter effect is a result of the dimensionality of the sequence walk and is not necessarily a result of biological optimization of the system.