ASSA-PBN: A Toolbox for Probabilistic Boolean Networks

Boolean model of the gene regulatory network of Pseudomonas aeruginosa CCBH4851

Introduction

Pseudomonas aeruginosa infections are one of the leading causes of death in immunocompromised patients with cystic fibrosis, diabetes, and lung diseases such as pneumonia and bronchiectasis. Furthermore, P. aeruginosa is one of the main multidrug-resistant bacteria responsible for nosocomial infections worldwide, including the multidrug-resistant CCBH4851 strain isolated in Brazil.

Methods

One way to analyze their dynamic cellular behavior is through computational modeling of the gene regulatory network, which represents interactions between regulatory genes and their targets. For this purpose, Boolean models are important predictive tools to analyze these interactions. They are one of the most commonly used methods for studying complex dynamic behavior in biological systems.

Results and discussion

Therefore, this research consists of building a Boolean model of the gene regulatory network of P. aeruginosa CCBH4851 using data from RNA-seq experiments. Next, the basins of attraction are estimated, as these regions and the transitions between them can help identify the attractors, representing long-term behavior in the Boolean model. The essential genes of the basins were associated with the phenotypes of the bacteria for two conditions: biofilm formation and polymyxin B treatment. Overall, the Boolean model and the analysis method proposed in this work can identify promising control actions and indicate potential therapeutic targets, which can help pinpoint new drugs and intervention strategies.

Target Control of Asynchronous Boolean Networks

We study the target control of asynchronous Boolean networks, to identify interventions that can drive the dynamics of a given Boolean network from any initial state to the desired target attractor. Based on the application time, the control can be realised with three types of perturbations, including instantaneous, temporary and permanent perturbations. We develop efficient methods to compute the target control for a given target attractor with these three types of perturbations. We compare our methods with the stable motif-based control method on a variety of real-life biological networks to evaluate their performance. We show that our methods scale well for large Boolean networks and they are able to identify a rich set of solutions with a small number of perturbations.

Exploring attractor bifurcations in Boolean networks

Background

Boolean networks (BNs) provide an effective modelling formalism for various complex biochemical phenomena. Their long term behaviour is represented by attractors–subsets of the state space towards which the BN eventually converges. These are then typically linked to different biological phenotypes. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a methodology for analysing bifurcations in asynchronous parametrised Boolean networks.

Results

In this paper, we propose a computational framework employing advanced symbolic graph algorithms that enable the analysis of large networks with hundreds of Boolean variables. To visualise the results of this analysis, we developed a novel interactive presentation technique based on decision trees, allowing us to quickly uncover parameters crucial to the changes in the attractor landscape. As a whole, the methodology is implemented in our tool AEON. We evaluate the method’s applicability on a complex human cell signalling network describing the activity of type-1 interferons and related molecules interacting with SARS-COV-2 virion. In particular, the analysis focuses on explaining the potential suppressive role of the recently proposed drug molecule GRL0617 on replication of the virus.

Conclusions

The proposed method creates a working analogy to the concept of bifurcation analysis widely used in kinetic modelling to reveal the impact of parameters on the system’s stability. The important feature of our tool is its unique capability to work fast with large-scale networks with a relatively large extent of unknown information. The results obtained in the case study are in agreement with the recent biological findings.

Towards Optimal Decomposition of Boolean Networks

In recent years, great efforts have been made to analyze biological systems to understand the long-run behaviors. As a well-established formalism for modelling real-life biological systems, Boolean networks (BNs) allow their representation and analysis using formal reasoning and tools. Most biological systems are robust-they can withstand the loss of links and cope with external environmental perturbations. Hence, the BNs used to model such systems are necessarily large and dense, and yet modular. However, existing analysis methods only work well on networks of moderate size. Thus, there is a great need for efficient methods that can handle large-scale BNs and for doing so it is inevitable to exploit both the structural and dynamic properties of the networks. In this paper, we propose a method towards the optimal decomposition of BNs to balance the relation between the structure and dynamics of a network. We show that our method can greatly improve the existing decomposition-based attractor detection by analyzing a number of large real-life biological networks.

An Efficient Approach Towards the Source-Target Control of Boolean Networks

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 optimized 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.

AEON: Attractor Bifurcation Analysis of Parametrised Boolean Networks

Boolean networks (BNs) provide an effective modelling tool for various phenomena from science and engineering. Any long-term behaviour of a BN eventually converges to a so-called attractor. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a tool for analysing bifurcations in asynchronous parametrised Boolean networks. To fight the state-space and parameter-space explosion problem the tool uses a parallel semi-symbolic algorithm.

Algorithms for the Sequential Reprogramming of Boolean Networks

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.

Tractable Learning and Inference for Large-Scale Probabilistic Boolean Networks

Probabilistic Boolean networks (PBNs) have previously been proposed so as to gain insights into complex dynamical systems. However, identification of large networks and their underlying discrete Markov chain which describes their temporal evolution still remains a challenge. In this paper, we introduce an equivalent representation for PBNs, the stochastic conjunctive normal form network (SCNFN), which enables a scalable learning algorithm and helps predict long-run dynamic behavior of large-scale systems. State-of-the-art methods turn out to be 400 times slower for middle-sized networks (i.e., containing 100 nodes) and incapable of terminating for large networks (i.e., containing 1000 nodes) compared to the SCNFN-based learning, when attempting to achieve comparable accuracy. In addition, in contrast to the currently used methods which introduce strict restrictions on the structure of the learned PBNs, the hypothesis space of our training paradigm is the set of all possible PBNs. Moreover, SCNFNs enable efficient sampling so as to statistically infer multistep transition probabilities which can provide information on the activity levels of individual nodes in the long run. Extensive experimental results showcase the scalability of the proposed approach both in terms of sample and runtime complexity. In addition, we provide examples to study large and complex cell signaling networks to show the potential of our model. Finally, we suggest several directions for future research on model variations, theoretical analysis, and potential applications of SCNFNs.

Controlling large Boolean networks with single-step perturbations

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.