On the sufficiency of pairwise interactions in maximum entropy models of biological networks

TL;DR

This paper investigates why maximum entropy models with only pairwise interactions often suffice to describe biological networks, suggesting this may be a natural property of densely interacting systems rather than a biological peculiarity.

Contribution

It demonstrates through simulations that the sufficiency of pairwise models can arise from the inherent properties of densely connected networks, not just biological systems.

Findings

Pairwise maximum entropy models often approximate biological data well.

Dense interactions in networks can naturally lead to effective pairwise descriptions.

This phenomenon is linked to properties of random constraint satisfaction problems.

Abstract

Biological information processing networks consist of many components, which are coupled by an even larger number of complex multivariate interactions. However, analyses of data sets from fields as diverse as neuroscience, molecular biology, and behavior have reported that observed statistics of states of some biological networks can be approximated well by maximum entropy models with only pairwise interactions among the components. Based on simulations of random Ising spin networks with $p$-spin ($p>2$) interactions, here we argue that this reduction in complexity can be thought of as a natural property of densely interacting networks in certain regimes, and not necessarily as a special property of living systems. By connecting our analysis to the theory of random constraint satisfaction problems, we suggest a reason for why some biological systems may operate in this regime.