Control of Intracellular Molecular Networks Using Algebraic Methods

Modular control of Boolean network models

The concept of control is crucial for effectively understanding and applying biological network models. Key structural features relate to control functions through gene regulation, signaling, or metabolic mechanisms, and computational models need to encode these. Applications often focus on model-based control, such as in biomedicine or metabolic engineering. In a recent paper, the authors developed a theoretical framework of modularity in Boolean networks, which lead to a canonical semidirect product decomposition of these systems. In this paper, we present an approach to model-based control that exploits this modular structure, as well as the canalizing features of the regulatory mechanisms. We show how to identify control strategies from the individual modules, and we present a criterion based on canalizing features of the regulatory rules to identify modules that do not contribute to network control and can be excluded. For even moderately sized networks, finding global control inputs is computationally challenging. Our modular approach leads to an efficient approach to solving this problem. We apply it to a published Boolean network model of blood cancer large granular lymphocyte (T-LGL) leukemia to identify a minimal control set that achieves a desired control objective.

Pancreatic cancer mutationscape: revealing the link between modular restructuring and intervention efficacy amidst common mutations

There is increasing evidence that biological systems are modular in both structure and function. Complex biological signaling networks such as gene regulatory networks (GRNs) are proving to be composed of subcategories that are interconnected and hierarchically ranked. These networks contain highly dynamic processes that ultimately dictate cellular function over time, as well as influence phenotypic fate transitions. In this work, we use a stochastic multicellular signaling network of pancreatic cancer (PC) to show that the variance in topological rankings of the most phenotypically influential modules implies a strong relationship between structure and function. We further show that induction of mutations alters the modular structure, which analogously influences the aggression and controllability of the disease in silico. We finally present evidence that the impact and location of mutations with respect to PC modular structure directly corresponds to the efficacy of single agent treatments in silico, because topologically deep mutations require deep targets for control.

A Near-Optimal Control Method for Stochastic Boolean Networks

One of the ultimate goals in systems biology is to develop control strategies to find efficient medical treatments. One step towards this goal is to develop methods for changing the state of a cell into a desirable state. We propose an efficient method that determines combinations of network perturbations to direct the system towards a predefined state. The method requires a set of control actions such as the silencing of a gene or the disruption of the interaction between two genes. An optimal control policy defined as the best intervention at each state of the system can be obtained using existing methods. However, these algorithms are computationally prohibitive for models with tens of nodes. Our method generates control actions that approximates the optimal control policy with high probability with a computational efficiency that does not depend on the size of the state space. Our C++ code is available at https://github.com/boaguilar/SDDScontrol.