Modeling Multiparticle Complexes in Fock Space

The combinatorial complexity of large macromolecular structures is central to many questions in biophysics, polymer physics, and other fields, yet hinders theoretical study of these objects using the standard methods of statistical physics. We approach this challenge by describing an operator formalism for classical multi-particle complexes. The framework, which is built from a Fock space of hard-core bosons, allows particles to be joined together into large complexes based on a small number of algebraically defined assembly rules. We further introduce diagrammatic techniques that make this algebra visually intuitive and facilitate analytical calculations through a connection with Wick’s theorem. These techniques can be used to study a wide range of systems, both in and out of thermal equilibrium. They also help to unify intuitive but seemingly distinct notions of coarse graining. We explore specific applications of these methods to the biophysical modeling of transcriptional regulation.