Effective connectivity determines the critical dynamics of biochemical networks

TL;DR

This paper introduces a canalization-based theory of criticality that improves the prediction of dynamical regimes in biochemical networks by accounting for redundancy and effective connectivity, revealing that biological systems reduce their apparent connectivity.

Contribution

The authors develop a new 'canalization theory' of criticality that incorporates effective connectivity, enhancing the prediction accuracy for biochemical network dynamics over traditional structural models.

Findings

Effective connectivity better predicts critical behavior in network ensembles.

Biological networks exhibit lower effective connectivity than their structural connectivity.

Canalization reduces and homogenizes network connectivity in biochemical systems.

Abstract

Living systems operate in a critical dynamical regime -- between order and chaos -- where they are both resilient to perturbation, and flexible enough to evolve. To characterize such critical dynamics, the established 'structural theory' of criticality uses automata network connectivity and node bias (to be on or off) as tuning parameters. This parsimony in the number of parameters needed sometimes leads to uncertain predictions about the dynamical regime of both random and systems biology models of biochemical regulation. We derive a more accurate theory of criticality by accounting for canalization, the existence of redundancy that buffers automata response to inputs -- a known mechanism that buffers the expression of traits, keeping them close to optimal states despite genetic and environmental perturbations. The new 'canalization theory' of criticality is based on a measure of effective connectivity. It contributes to resolving the problem of finding precise ways to design or control network models of biochemical regulation for desired dynamical behavior. Our analyses reveal that effective connectivity significantly improves the prediction of critical behavior in random automata network ensembles. We also show that the average effective connectivity of a large battery of systems biology models is much lower than the connectivity of their original interaction structure. This suggests that canalization has been selected to dynamically reduce and homogenize the seemingly heterogeneous connectivity of biochemical networks.