Rediscovering the power of pairwise interactions

TL;DR

This paper explores the equivalence of two approaches using pairwise interactions to model complex biological systems, highlighting their potential to capture system behavior with simplified models.

Contribution

It demonstrates the mathematical equivalence of Monte Carlo annealing and maximum entropy models in certain limits for biological systems.

Findings

Pairwise interactions can effectively model biological complexity.

Monte Carlo annealing and maximum entropy approaches are mathematically equivalent.

Open problems in modeling biological systems with pairwise interactions are discussed.

Abstract

Two recent streams of work suggest that pairwise interactions may be sufficient to capture the complexity of biological systems ranging from protein structure to networks of neurons. In one approach, possible amino acid sequences in a family of proteins are generated by Monte Carlo annealing of a "Hamiltonian" that forces pairwise correlations among amino acid substitutions to be close to the observed correlations. In the other approach, the observed correlations among pairs of neurons are used to construct a maximum entropy model for the states of the network as a whole. We show that, in certain limits, these two approaches are mathematically equivalent, and we comment on open problems suggested by this framework