Molecular network control through boolean canalization

Abstract

Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of network modeling where each layer of canalization adds a degree of stability in the dynamics of the network. Recently, dynamic network control approaches have been used for the design of new therapeutic interventions and for other applications such as stem cell reprogramming. This work studies the role of canalization in the control of Boolean molecular networks. It provides a method for identifying the potential edges to control in the wiring diagram of a network for avoiding undesirable state transitions. The method is based on identifying appropriate input-output combinations on undesirable transitions that can be modified using the edges in the wiring diagram of the network. Moreover, a method for estimating the number of changed transitions in the state space of the system as a result of an edge deletion in the wiring diagram is presented. The control methods of this paper were applied to a mutated cell-cycle model and to a p53-mdm2 model to identify potential control targets.

Structure-based control of complex networks with nonlinear dynamics

“…In case of systems with nonlinear dynamics it provides sufficient conditions to control the system in the neighborhood of a trajectory or a steady state ( [1,18], SI Appendix), and its definition of control (full control; from * Corresponding author: jgtz@phys.psu.edu any initial to any final state) does not always match the meaning of control in biological, technological, and social systems, in which control tends to involve only naturally occurring system states [19]. In addition to the approaches provided by nonlinear control theory [9][10][11]18], new methods of network control have been proposed to incorporate the inherent nonlinear dynamics of real systems and relax the definition of full control [4,6,11,18,20]. Only one of these methods, namely feedback vertex set control (FC), can be reliably applied to large complex networks in which only the structure is well known and the functional form of the governing equations is not specified.…”

Identification of control targets in Boolean molecular network models via computational algebra

“…For instance, the control strategies do not give any information about the basin size of a fixed point generated by the methods of this paper. However, we remark that some algebraic methods allow to estimate the change in the basin size after an edge deletion, see [59]. Nonetheless, the control targets identified by the algebraic techniques described here could be used for further analysis of the system, such as for studying reachability [60], or for designing optimal control policies in a stochastic setting [29][30][31][32].…”

Control of Intracellular Molecular Networks Using Algebraic Methods

“…Some methods of control using the dynamics of networks include methods such as stable motifs for guiding the network towards desired attractors or away from undesired attractors [54,55], using the concepts of Boolean canalization, [5,31], and using the concept of the logical domain of influence [52]. To the best of our knowledge, none of these methods have been implemented for general multistate systems.…”

“…It also extends our method for Boolean networks [32,31] to multistate networks, and thus broadening the scope of use of the PDS representation of discrete models.…”