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

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.