We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be controlled to drive its dynamics from an initial steady state (or attractor) to a target steady state. Due to the phenomenon of state-space explosion, a simple global approach that performs computations on the entire network, may not scale well for large networks. We believe that efficient algorithms for such networks must exploit the structure of the networks together with their dynamics. Taking such an approach, we derive a decomposition-based solution to the minimal control problem which can be significantly faster than the existing approaches on large networks. We apply our solution to both real-life biological networks and randomly generated networks, demonstrating promising results.

We address the sequential reprogramming of gene regulatory networks modelled as Boolean networks. We develop an attractor-based sequential reprogramming method to compute all sequential reprogramming paths from a source attractor to a target attractor, where only attractors of the network are used as intermediates. Our method is more practical than existing reprogramming methods as it incorporates several practical constraints: (1) only biologically observable states, viz. attractors, can act as intermediates; (2) certain attractors, such as apoptosis, can be avoided as intermediates; (3) certain nodes can be avoided to perturb as they may be essential for cell survival or difficult to perturb with biomolecular techniques; and (4) given a threshold k, all sequential reprogramming paths with no more than k perturbations are computed. We compare our method with the minimal one-step reprogramming and the minimal sequential reprogramming on a variety of biological networks. The results show that our method can greatly reduce the number of perturbations compared to the one-step reprogramming, while having comparable results with the minimal sequential reprogramming. Moreover, our implementation is scalable for networks of more than 60 nodes.

A salient objective of studying gene regulatory networks (GRNs) is to identify potential target genes whose perturbations would lead to effective treatment of diseases. In this paper, we develop two control methods for GRNs in the context of asynchronous Boolean networks. Our methods compute a minimal subset of nodes of a given Boolean network, such that temporary or permanent perturbations of these nodes drive the network from an initial state to a target steady state. The main advantages of our methods include: (1) temporary and permanent perturbations can be feasibly conducted with techniques for genetic modifications in biological experiments; and (2) the minimality of the identified control sets can reduce the cost of experiments to a great extent. We apply our methods to several real-life biological networks in silico to show their efficiency in terms of computation time and their efficacy with respect to the number of nodes to be perturbed.

We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be perturbed in a single-step to drive its dynamics from an initial state to a target steady state (or attractor), which we call the source-target control of Boolean networks. Due to the phenomenon of state-space explosion, a simple global approach that performs computations on the entire network, may not scale well for large networks. We believe that efficient algorithms for such networks must exploit the structure of the networks together with their dynamics. Taking this view, we derive a decomposition-based solution to the minimal source-target control problem which can be significantly faster than the existing approaches on large networks. We then show that the solution can be further optimised if we take into account appropriate information about the source state. We apply our solutions to both real-life biological networks and randomly generated networks, demonstrating the efficiency and efficacy of our approach.

As a well-established computational framework, probabilistic Boolean networks (PBNs) are widely used for modelling, simulation, and analysis of biological systems. To analyze the steady-state dynamics of PBNs is of crucial importance to explore the characteristics of biological systems. However, the analysis of large PBNs, which often arise in systems biology, is prone to the infamous state-space explosion problem. Therefore, the employment of statistical methods often remains the only feasible solution. We present ${\mathsf{ASSA-PBN}}$ , a software toolbox for modelling, simulation, and analysis of PBNs. ${\mathsf{ASSA-PBN}}$ provides efficient statistical methods with three parallel techniques to speed up the computation of steady-state probabilities. Moreover, particle swarm optimisation (PSO) and differential evolution (DE) are implemented for the estimation of PBN parameters. Additionally, we implement in-depth analyses of PBNs, including long-run influence analysis, long-run sensitivity analysis, computation of one-parameter profile likelihoods, and the visualization of one-parameter profile likelihoods. A PBN model of apoptosis is used as a case study to illustrate the main functionalities of ${\mathsf{ASSA-PBN}}$ and to demonstrate the capabilities of ${\mathsf{ASSA-PBN}}$ to effectively analyse biological systems modelled as PBNs.

Motivation The control of Boolean networks has traditionally focussed on strategies where the perturbations are applied to the nodes of the network for an extended period of time. In this work, we study if and how a Boolean network can be controlled by perturbing a minimal set of nodes for a single-step and letting the system evolve afterwards according to its original dynamics. More precisely, given a Boolean network (BN), we compute a minimal subset Cmin of the nodes such that BN can be driven from any initial state in an attractor to another ‘desired’ attractor by perturbing some or all of the nodes of Cmin for a single-step. Such kind of control is attractive for biological systems because they are less time consuming than the traditional strategies for control while also being financially more viable. However, due to the phenomenon of state-space explosion, computing such a minimal subset is computationally inefficient and an approach that deals with the entire network in one-go, does not scale well for large networks. Results We develop a ‘divide-and-conquer’ approach by decomposing the network into smaller partitions, computing the minimal control on the projection of the attractors to these partitions and then composing the results to obtain Cmin for the whole network. We implement our method and test it on various real-life biological networks to demonstrate its applicability and efficiency. Supplementary information Supplementary data are available at Bioinformatics online.

Cellular reprogramming, a technique that opens huge opportunities in modern and regenerative medicine, heavily relies on identifying key genes to perturb. Most of the existing computational methods for controlling which attractor (steady state) the cell will reach focus on finding mutations to apply to the initial state. However, it has been shown, and is proved in this article, that waiting between perturbations so that the update dynamics of the system prepares the ground, allows for new reprogramming strategies. To identify such sequential perturbations, we consider a qualitative model of regulatory networks, and rely on Binary Decision Diagrams to model their dynamics and the putative perturbations. Our method establishes a set identification of sequential perturbations, whether permanent (mutations) or only temporary, to achieve the existential or inevitable reachability of an arbitrary state of the system. We apply an implementation for temporary perturbations on models from the literature, illustrating that we are able to derive sequential perturbations to achieve trans-differentiation. !

Summary Direct cell reprogramming, also called transdifferentiation, has great potential for tissue engineering and regenerative medicine. Boolean networks, a popular modelling framework for gene regulatory networks, make it possible to identify intervention targets for direct cell reprogramming with computational methods. In this work, we present our software, CABEAN, for the control of asynchronous Boolean networks. CABEAN identifies efficacious nodes, whose perturbations can drive the dynamics of a network from a source attractor (the initial cell type) to a target attractor (the desired cell type). CABEAN provides several control methods integrating practical constraints. Thus, it has the ability to provide a rich set of control sets, such that biologists can select suitable ones for validation based on specific experimental settings. Availability and Implementation The executable binary and the user guide of the software are publicly available at https://satoss.uni.lu/software/CABEAN/. Supplementary information Supplementary data are available at Bioinformatics online.