Controlling complex dynamical systems based on the structure of the networks.

Abstract

Progress of molecular biology resulted in the accumulation of information on biomolecular interactions, which are complex enough to be termed as networks. Dynamical behavior generated by complex network systems is considered to be the origin of the biological functions. One of the largest missions in modern life science is to obtain logical understanding for the dynamics of complex systems based on experimentally identified networks. However, a network does not provide sufficient information to specify dynamics explicitly, i.e. it lacks information of mathematical formulae of functions or parameter values. One has to develop mathematical models under assumptions of functions and parameter values to know the detail of dynamics of network systems. In this review, on the other hand, we introduce our own mathematical theory to understand the behavior of biological systems from the information of regulatory networks alone. Using the theory, important aspects of dynamical properties can be extracted from networks. Namely, key factors for observing/controlling the whole dynamical system are determined from network structure alone. We also show an application of the theory to a real biological system, a gene regulatory network for cell-fate specification in ascidian. We demonstrate that the system was completely controllable by experimental manipulations of the key factors identified by the theory from the information of network alone. This review article is an extended version of the Japanese article, Controlling Cell-Fate Specification System Based on a Mathematical Theory of Network Dynamics, published in SEIBUTSU BUTSURI Vol. 60, p. 349-351 (2020).