Complex network controllability and applications to biomolecular networks

Abstract

Within living cells, biomolecules rarely function as isolated elements, but rather interact with each other to perform various biological functions. Biomolecules and their interactions can be represented as biomolecular networks, in which nodes represent different biomolecules and edges represent interactions among biomolecules. The studies of biomolecular networks are critical for understanding the roles of biomolecules within cells and the mechanisms of cellular behaviors. Due to the interactions among biomolecules, the perturbation of some biomolecules may affect others which may eventually change the states of biomolecular networks and corresponding cellular behaviors. Therefore, it is essential and helpful to study biomolecular networks from the viewpoint of control theory.

This thesis investigates the controllability of biomolecular networks based on modern control theory, especially the structural controllability of complex networks. Controllability, which is an important concept in modern control theory, measures the ability of moving a network around in its state space via proper input control signals. To control a complex network, the first step is to identify steering nodes that guarantee the controllability of the network, where steering nodes are nodes directly actuated by input control signals. Although various algorithms have been proposed to identify steering nodes for general complex networks, the applications of the algorithms to biomolecular networks are limited and still have room to be further improved. This thesis focuses on identifying steering nodes, which are biomolecules, for different control scenarios in biomolecular networks.

Three different control scenarios are considered in this thesis. First, to control a network, it's meaningful to determine the least number of nodes which should be actuated by input control signals. To deal with this problem, an algorithm to identify the minimum steering node sets (MSSs) required to have complex networks completely controllable is presented and its applications to biomolecular networks are given. Second, sometimes the minimum number of steering nodes for complete controllability of a network is too large in practical applications. Actually in practice, the complete controllability of all nodes is not necessary. Therefore, an algorithm is developed to identify steering node sets for output controllability, which measures the controllability of a portion of nodes. The algorithm provides a novel method for drug target identification in biomolecular networks: the states of disease related biomolecules can be controlled by actuating the identified steering nodes, which are potential drug targets. Third, to improve feasibility of identified steering nodes in real applications to biomolecular networks, the ability of steering nodes to bind drugs should be considered. An algorithm is proposed to identify steering node sets with drug binding preference. It is expected that steering node sets identified with drug binding preference have more chances to bind to existing drugs, compared to other feasible steering node sets, which facilitates the subsequent procedures of realizing the control of biomolecular networks via drugs.

In addition, in this thesis a software system called CytoCtrlAnalyser is implemented, which contains nine recent algorithms for users to conveniently investigate controllability of biomolecular networks within the Cytoscape environment. The algorithms integrated in CytoCtrlAnalyser can be divided into two aspects based on their functions: identifying steering nodes for different control objectives and qualifying or quantifying importance of individual nodes to the controllability of networks.