Global Stabilization of Boolean Networks to Control the Heterogeneity of Cellular Responses

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.

Identification of dynamic driver sets controlling phenotypical landscapes

“…Here, we want to define the minimal set of compounds sufficient to determine the full dynamics, thus reaching all attractors of the examined model. Following prior approaches [34] , [35] , [36] , we used 35 logic-based Boolean network models ( Table 1 ) for our investigations. This model type belongs to one of the simplest dynamic models where molecular compounds are represented as nodes (n), and their interactions are summarized in Boolean functions ( f ).…”

A Middle-Out Modeling Strategy to Extend a Colon Cancer Logical Model Improves Drug Synergy Predictions in Epithelial-Derived Cancer Cell Lines

“…The noticeable variation of the performance with different training data even for a specific cell line underlines the importance of correctly assessing the entities' states before training a model, which would need careful, high-quality assays for all proteins represented in the logical model. In most biological systems, however, it is assumed that the state of only a specific subset of its nodes is rather sufficient to control the global state of the system (Gao et al, 2014;Dnyane et al, 2018;Yang J. M. et al, 2018). Based on this, the accurate identification of the states of a well-chosen subset of nodes in the model rather than the majority of its nodes can be an attractive alternative (Niederdorfer et al, 2020).…”

“…Attractor analysis is also important to identify trajectories (a series of states that the network traverses through while reaching a stable state) in the system's behavior (Huang et al, 2005). In the case of gene regulatory networks, attractors are usually associated with specific phenotypes (Cho et al, 2016;Yang J. M. et al, 2018). Furthermore, a disruption of the balance found in these stable states of normal cellular systems can many times be associated with specific diseases, including cancers, allowing the mechanistic understanding of cancer development and progression (Bachmann et al, 2012), which can provide an important advantage when designing cancer therapies.…”

Discrete Dynamic Model of the Mammalian Sperm Acrosome Reaction: The Influence of Acrosomal pH and Physiological Heterogeneity

“…To describe and analyze the dynamical properties of this model, we use a generalization of the Boolean gene regulatory networks proposed by Stuart Kauffman in 1969 (Kauffman, 1969 ) that have been successfully used in different gene regulation studies (Kauffman, 1969 ; Mendoza and Alvarez-Buylla, 1998 , 2000 ), as well as in biochemical regulation (Thieffry, 2007 ; Espinal et al, 2011 ; Chaouiya et al, 2012 ; Yang et al, 2018 ). In this model, the state of the whole network is described by a set of N discrete variables x 1 , x 2 , ..., x N , each one representing the state of one node.…”

“…In the present work, we implement a generalization of the Gene Regulatory Network as formalized by Stuart Kauffman in 1969 (Kauffman, 1969 ) and used in many different systems (Mendoza and Alvarez-Buylla, 1998 , 2000 ; Espinal et al, 2011 ; Yang et al, 2018 ) to construct a mathematical and computational model that represents the main physiological interactions involved in AR. We show that this model can qualitatively reproduce many of the experimental results reported in literature and we use it to characterize how the physiological heterogeneity in a sperm population affects the proportion of cells capable of displaying spontaneous and Pg-induced AR.…”