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

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.

References in corpus (6)

• Identification of direct residue contacts in protein-protein interaction by message passing
• Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
• Small-correlation expansions for the inverse Ising problem
• On the freezing of variables in random constraint satisfaction problems
• Mean-field theory for the inverse Ising problem at low temperatures
• Learning probabilities from random observables in high dimensions: the maximum entropy distribution and others

Cited by in corpus (17)

• The physics of higher-order interactions in complex systems
• Inverse statistical problems: from the inverse Ising problem to data science
• How pairwise coevolutionary models capture the collective residue variability in proteins
• Multivariate Dependence Beyond Shannon Information
• Topological Information Data Analysis
• Understanding interdependency through complex information sharing
• Maximum entropy models reveal the excitatory and inhibitory correlation structures in cortical neuronal activity
• Receptor crosstalk improves concentration sensing of multiple ligands
• Machine-learning-assisted Monte Carlo fails at sampling computationally hard problems
• Random versus maximum entropy models of neural population activity
• The Stochastic complexity of spin models: Are pairwise models really simple?
• On Maximum Entropy and Inference
• Evolution of biomedical innovation quantified via billions of distinct article-level MeSH keyword combinations
• Higher-Order Interactions and Their Duals Reveal Synergy and Logical Dependence beyond Shannon-Information
• Maximum Entropy Principle Analysis in Network Systems with Short-time Recordings
• Message-Passing on Hypergraphs: Detectability, Phase Transitions and Higher-Order Information
• Discovering sparse control strategies in C. elegans