(I asked a similar question on Mathematics SE, but based on the Help section it might be better suited for this site, as it is focused on research-level mathematical modeling.)

I am wondering if there is any reported attempt to model the interaction of two multiple-sites molecules? I could not find anything other than 1-to-N interactions; there is a lot of literature on how to model the binding of single molecules on multiple-sites molecules. For example, the Monod-Wyman-Changeux model of allostery can be used to model the concerted binding of N individual ligands on a single protein.

I am interested in a case in which protein A contains, say, N binding sites X, and protein B contains M binding sites Y, and any site X can potentially interact with any site Y. That would be somewhat equivalent to how polymers interact in a hydrogel, but at a smaller scale (i.e. with smaller molecules so that there is no "immobilization" of the system and molecules can still diffuse freely).

I am interested in both stochastic models and deterministic approximations.