Global stabilizing control of large-scale biomolecular regulatory networks.

MOTIVATION: Cellular behavior is determined by complex non-linear 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 non-linear dynamics are not scalable. RESULTS: Here, we investigate the underlying relationship between structurally identified control targets and optimal global stabilizing control targets based on non-linear 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 AND IMPLEMENTATION: 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.

A gray box framework that optimizes a white box logical model using a black box optimizer for simulating cellular responses to perturbations.

Predicting cellular responses to perturbations requires interpretable insights into molecular regulatory dynamics to perform reliable cell fate control, despite the confounding non-linearity of the underlying interactions. There is a growing interest in developing machine learning-based perturbation response prediction models to handle the non-linearity of perturbation data, but their interpretation in terms of molecular regulatory dynamics remains a challenge. Alternatively, for meaningful biological interpretation, logical network models such as Boolean networks are widely used in systems biology to represent intracellular molecular regulation. However, determining the appropriate regulatory logic of large-scale networks remains an obstacle due to the high-dimensional and discontinuous search space. To tackle these challenges, we present a scalable derivative-free optimizer trained by meta-reinforcement learning for Boolean network models. The logical network model optimized by the trained optimizer successfully predicts anti-cancer drug responses of cancer cell lines, while simultaneously providing insight into their underlying molecular regulatory mechanisms.

Robust Stabilizing Control of Perturbed Biological Networks via Coordinate Transformation and Algebraic Analysis.

This article investigates robust stabilizing control of biological systems modeled by Boolean networks (BNs). A population of BNs is considered where a majority of BNs have the same BN dynamics, but some BNs are inflicted by mutations damaging particular nodes, leading to perturbed dynamics that prohibit global stabilization to the desired attractor. The proposed control strategy consists of two steps. First, the nominal BN is transformed and curtailed into a sub-BN via a simple coordinate transformation and network reduction associated with the desired attractor. The feedback vertex set (FVS) control is then applied to the reduced BN to determine the control inputs for the nominal BN. Next, the control inputs derived in the first step and mutated nodes are applied to the nominal BN so as to identify residual dynamics of perturbed BNs, and additional control inputs are selected according to the canalization effect of each node. The overall control inputs are applied to the BN population, so that the nominal BN converges to the desired attractor and perturbed BNs to their own attractors that are the closest possible to the desired attractor. The performance of the proposed robust control scheme is validated through numerical experiments on random BNs and a complex biological network.

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

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.