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We analyze large systems of interacting proteins, using techniques from thenon-equilibrium statistical mechanics of disordered many-particle systems.Apart from protein production and removal, the most relevant microscopicprocesses in the proteome are complex formation and dissociation, and themicroscopic degrees of freedom are the evolving concentrations of unboundproteins (in multiple post-translational states) and of protein complexes. Herewe only include dimer-complexes, for mathematical simplicity, and we draw thenetwork that describes which proteins are reaction partners from an ensemble ofrandom graphs with an arbitrary degree distribution. We show how generatingfunctional analysis methods can be used successfully to derive closed equationsfor dynamical order parameters, representing an exact macroscopic descriptionof the complex formation and dissociation dynamics in the infinite systemlimit. We end this paper with a discussion of the possible routes towardssolving the nontrivial order parameter equations, either exactly (in specificlimits) or approximately.

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