Systematic Measures of Biological Networks, Part II: Degeneracy, Complexity and Robustness

TL;DR

This paper develops systematic measures for biological networks, focusing on degeneracy, complexity, and robustness, using stochastic differential equations and entropy concepts to analyze their interrelations.

Contribution

It introduces new definitions and methods for quantifying degeneracy, complexity, and robustness in biological networks within a stochastic differential equations framework.

Findings

Degeneracy and complexity are characterized via stationary measures and entropy.

Robustness is linked to the strength of attraction to the global attractor.

Connections between degeneracy, complexity, and robustness are established.

Abstract

This paper is Part II of a two-part series devoting to the study of systematic measures in a complex bio-network modeled by a system of ordinary differential equations. In this part, we quantify several systematic measures of a biological network including degeneracy, complexity and robustness. We will apply the theory of stochastic differential equations to define degeneracy and complexity for a bio-network. Robustness of the network will be defined according to the strength of attractions to the global attractor. Based on the study of stationary probability measures and entropy made in Part I of the series, we will investigate some fundamental properties of these systematic measures, in particular the connections between degeneracy, complexity and robustness.