Abstract
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.
Highlights
As a biology-based interdisciplinary field, systems biology is receiving a great interest in recent years as it can investigate complex interactions within biological systems using holistic approaches to biological research (Park et al, 2006; Kim et al, 2007; Murray et al, 2010)
Though any subsequent control is unnecessary in this case, we note that the proposed algorithm of global stabilization is not able to specify the features of the obtained fixed points in general since it does not use any parameter associated with the desirable phenotypes
The problem of global stabilization of Boolean networks (BNs) has been addressed in this paper to control the heterogeneous cellular behavior for homogeneous responses
Summary
As a biology-based interdisciplinary field, systems biology is receiving a great interest in recent years as it can investigate complex interactions within biological systems using holistic approaches to biological research (Park et al, 2006; Kim et al, 2007; Murray et al, 2010). We address the aforementioned problem, termed global stabilization of BNs. The main objective is to determine a set of constant controls that drive the BN toward a unique fixed point. In Zañudo et al (2017), a scheme of feedback vertex set control is proposed that drives biological systems described by general non-linear dynamics (including BNs) toward a desired attractor. We adopt the result of Robert (1986) and Cheng et al (2011b) to determine constant controls that ensure global stability of BNs. In particular, we utilize the sufficient condition that if the influence graph of a BN is acyclic, there is only one fixed point and from each state there should be a trajectory to it. A comparative study with feedback vertex set control, the control kernel method, and the stable motif control is provided to highlight the efficiency of the proposed scheme
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