Generating functional analysis of complex formation and dissociation in large protein interaction networks

TL;DR

This paper applies generating functional analysis to large protein interaction networks, deriving exact macroscopic equations for complex formation and dissociation dynamics, with potential for exact or approximate solutions.

Contribution

It introduces a novel application of generating functional analysis to model complex formation and dissociation in large, random graph-based protein networks.

Findings

Derived closed equations for dynamical order parameters

Provided a framework for exact macroscopic descriptions

Discussed solution strategies for the order parameter equations

Abstract

We analyze large systems of interacting proteins, using techniques from the non-equilibrium statistical mechanics of disordered many-particle systems. Apart from protein production and removal, the most relevant microscopic processes in the proteome are complex formation and dissociation, and the microscopic degrees of freedom are the evolving concentrations of unbound proteins (in multiple post-translational states) and of protein complexes. Here we only include dimer-complexes, for mathematical simplicity, and we draw the network that describes which proteins are reaction partners from an ensemble of random graphs with an arbitrary degree distribution. We show how generating functional analysis methods can be used successfully to derive closed equations for dynamical order parameters, representing an exact macroscopic description of the complex formation and dissociation dynamics in the infinite system limit. We end this paper with a discussion of the possible routes towards solving the nontrivial order parameter equations, either exactly (in specific limits) or approximately.