The Nonlinearity of Regulation in Biological Networks

Abstract

Nonlinearity is a characteristic of complex biological regulatory networks that has implications ranging from therapy to control. To better understand its nature, we analyzed a suite of published Boolean network models, containing a variety of complex nonlinear interactions, using a probabilistic generalization of Boolean logic that George Boole himself had proposed. The continuous-nature of this formulation made the models amenable to Taylor decomposition that revealed their distinct layers of nonlinearity. A comparison of the resulting series of approximations of the models with the corresponding sets of randomized ensembles showed that the biological networks are on average relatively less nonlinear, suggesting that they may have been optimized for linearity by natural selection for the purpose of controllability. A further categorical analysis of the biological models revealed that the nonlinearity of cancer and disease networks could not only be sometimes higher than expected but are also relatively more variable, suggesting that the agents of disease may leverage the heterogeneity of regulatory nonlinearity to their advantage.