Modularity of biological systems: a link between structure and function

Abstract

This paper addresses two topics in systems biology, the hypothesis that biological systems are modular and the problem of relating structure and function of biological systems. The focus here is on gene regulatory networks, represented by Boolean network models, a commonly used tool. Most of the research on gene regulatory network modularity has focused on network structure, typically represented through either directed or undirected graphs. But since gene regulation is a highly dynamic process as it determines the function of cells over time, it is natural to consider functional modularity as well. One of the main results is that the structural decomposition of a network into modules induces an analogous decomposition of the dynamic structure, exhibiting a strong relationship between network structure and function. An extensive simulation study provides evidence for the hypothesis that modularity might have evolved to increase phenotypic complexity while maintaining maximal dynamic robustness to external perturbations.

Modularity of biological systems: a link between structure and function

“…A set of controls μ stabilizes a Boolean network at an attractor C when the resulting network after applying μ possesses C as its only attractor. As described in detail in [33], the decomposition into modules can be used to obtain controls for each module, which can then be combined to obtain a control for an entire network. Specifically, for a decomposable network F=F1⋊PF2, if μ 1 is a set of controls that stabilizes F 1 in scriptC1 and μ 2 is a control that stabilizes F2scriptC1 in scriptC2, then μ=μ1∪μ2 is a set of control that stabilizes F in C=scriptC1⊕scriptC2, as long as scriptC1 or scriptC2 is a steady state.…”