Boolean networks (BNs) have been widely used as a useful model for molecular regulatory networks in systems biology. In the state space of BNs, attractors represent particular cell phenotypes. For targeted therapy of cancer, there is a pressing need to control the heterogeneity of cellular responses to the targeted drug by reducing the number of attractors associated with the ill phenotypes of cancer cells. Here, we present a novel control scheme for global stabilization of BNs to a unique fixed point. Using a sufficient condition of global stabilization with respect to the adjacency matrix, we can determine a set of constant controls so that the controlled BN is steered toward an unspecified fixed point which can then be further transformed to a desired attractor by subsequent control. Our method is efficient in that it has polynomial complexity with respect to the number of state variables, while having exponential complexity with respect to in-degree of BNs. To demonstrate the applicability of the proposed control scheme, we conduct simulation studies using a regulation influence network describing the metastatic process of cells and the Mitogen-activated protein kinase (MAPK) signaling network that is crucial in cancer cell fate determination.
Motivation
Cellular behavior is determined by complex nonlinear interactions between numerous intracellular molecules that are often represented by Boolean network models. To achieve a desired cellular behavior with minimal intervention, we need to identify optimal control targets that can drive heterogeneous cellular states to the desired phenotypic cellular state with minimal node intervention. Previous attempts to realize such global stabilization were based solely on either network structure information or simple linear dynamics. Other attempts based on nonlinear dynamics are not scalable.
Results
Here, we investigate the underlying relationship between structurally identified control targets and optimal global stabilizing control targets based on nonlinear dynamics. We discovered that optimal global stabilizing control targets can be identified by analyzing the dynamics between structurally identified control targets. Utilizing these findings, we developed a scalable global stabilizing control framework using both structural and dynamic information. Our framework narrows down the search space based on strongly connected components and feedback vertex sets then identifies global stabilizing control targets based on the canalization of Boolean network dynamics. We find that the proposed global stabilizing control is superior with respect to the number of control target nodes, scalability, and computational complexity.
Availability
We provide a GitHub repository that contains the DCGS framework written in Python as well as biological random Boolean network datasets (https://github.com/sugyun/DCGS).
Supplementary information
Supplementary data are available at Bioinformatics online.
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