Boolean Networks Research Articles

Pystablemotifs: Python library for attractor identification and control in Boolean networks.

pystablemotifs is a Python 3 library for analyzing Boolean networks. Its non-heuristic and exhaustive attractor identification algorithm was previously presented in Rozum et al. (2021). Here, we illustrate its performance improvements over similar methods and discuss how it uses outputs of the attractor identification process to drive a system to one of its attractors from any initial state. We implement six attractor control algorithms, five of which are new in this work. By design, these algorithms can return different control strategies, allowing for synergistic use. We also give a brief overview of the other tools implemented in pystablemotifs. The source code is on GitHub at https://github.com/jcrozum/pystablemotifs/. Supplementary data are available at Bioinformatics online.

Stabilisation and set stabilisation of periodic switched Boolean control networks

This paper investigates the stabilisation and set stabilisation problems for a class of switched Boolean control networks (SBCNs) with periodic switching signal via a semi-tensor product method. First, algebraic forms are constructed for SBCNs with periodic switching signal. Second, based on the algebraic formulations, the stabilisation and set stabilisation of SBCNs with periodic switching signal are discussed, and some new results are presented. Furthermore, constructive procedure of open loop controllers is given, and the design algorithms of switching signal-dependent state feedback controllers via antecedence solution technique are derived. The study of illustrative examples shows the good performance of the methods presented in this paper.

Entropy analysis of Boolean network reduction according to the determinative power of nodes

Boolean networks are utilized to model systems in a variety of disciplines. The complexity of the systems under exploration often necessitates the construction of model networks with large numbers of nodes and unwieldy state spaces. A recently developed, entropy-based method for measuring the determinative power of each node offers a new method for identifying the most relevant nodes to include in subnetworks that may facilitate analysis of the parent network. We develop a determinative-power-based reduction algorithm and deploy it on 36 network types constructed through various combinations of settings with regards to the connectivity, topology, and functionality of networks. We construct subnetworks by eliminating nodes one-by-one beginning with the least determinative node. We compare entropy ratios between these subnetworks and the parent network and find that, for all network types, the change in network entropies (sums of conditional node entropies) follows a concave down decreasing curve, and the slightest reductions in network entropy occur with the initial reductions which eliminate the nodes with the least determinative power. Comparing across the three network characteristics, we find trends in the rates of decrease in the entropy ratios. In general, the decline occurs more slowly in networks with degree values assigned from a power-law distribution and canalyzing functions of higher canalization depth. We compare results of the determinative-power-based reduction with those of a randomized reduction and find that, in forming subnetworks with maximal network entropy, the determinative-power-based method performs as well as or better than the random method in all cases. Lastly, we compare findings based on this conditional-entropy-based calculation of network entropy with those of an alternative calculation using simple sums of (independent) node entropies to demonstrate the vast differences resulting from the two approaches.

Optimal control of probabilistic Boolean control networks: A scalable infinite horizon approach

AbstractOne of the major issues in systems biology is developing control theory for gene regulatory networks (GRNs). Particularly, an important objective is to develop therapeutic intervention strategies to alter regulatory dynamics of GRNs to avoid undesired or diseased states. Several optimal control strategies have been developed to find therapeutic intervention strategies for small (or medium) sized GRNs modeled as probabilistic Boolean control networks (PBCNs). However, due to the humongous nature of GRNs, we require an optimal control strategy that scales to large systems without posing any constraints on the network dynamics. In this article, we formulate the infinite horizon discounted cost optimal control problem by leveraging the Markov decision process (MDP) based PBCN structure to model GRNs. Further, we design a stationary optimal control strategy, thereby avoiding the states associated with a disease. An augmented state space is defined to facilitate the control design method. By exploiting Kullback–Leibler (KL) divergence and the log transformation of the cost function referred to as the desirability function, the optimal control is devised using the path integral (PI) approach. We propose a sampling‐based technique for the approximation of the PI and hence the optimal control of PBCNs. The sampling‐based strategy is amicable to parallel implementation, thereby addressing the optimal control problem of large‐scale PBCNs. Finally, the viability of the results in the article is shown by some illustrative examples.

Fusion of KATZ measure and space projection to fast probe potential lncRNA-disease associations in bipartite graphs.

It is well known that numerous long noncoding RNAs (lncRNAs) closely relate to the physiological and pathological processes of human diseases and can serves as potential biomarkers. Therefore, lncRNA-disease associations that are identified by computational methods as the targeted candidates reduce the cost of biological experiments focusing on deep study furtherly. However, inaccurate construction of similarity networks and inadequate numbers of observed known lncRNA–disease associations, such inherent problems make many mature computational methods that have been developed for many years still exit some limitations. It motivates us to explore a new computational method that was fused with KATZ measure and space projection to fast probing potential lncRNA-disease associations (namely KATZSP). KATZSP is comprised of following key steps: combining all the global information with which to change Boolean network of known lncRNA–disease associations into the weighted networks; changing the similarities calculation into counting the number of walks that connect lncRNA nodes and disease nodes in bipartite graphs; obtaining the space projection scores to refine the primary prediction scores. The process to fuse KATZ measure and space projection was simplified and uncomplicated with needing only one attenuation factor. The leave-one-out cross validation (LOOCV) experimental results showed that, compared with other state-of-the-art methods (NCPLDA, LDAI-ISPS and IIRWR), KATZSP had a higher predictive accuracy shown with area-under-the-curve (AUC) value on the three datasets built, while KATZSP well worked on inferring potential associations related to new lncRNAs (or isolated diseases). The results from real cases study (such as pancreas cancer, lung cancer and colorectal cancer) further confirmed that KATZSP is capable of superior predictive ability to be applied as a guide for traditional biological experiments.

WebMaBoSS: A Web Interface for Simulating Boolean Models Stochastically.

WebMaBoSS is an easy-to-use web interface for conversion, storage, simulation and analysis of Boolean models that allows to get insight from these models without any specific knowledge of modeling or coding. It relies on an existing software, MaBoSS, which simulates Boolean models using a stochastic approach: it applies continuous time Markov processes over the Boolean network. It was initially built to fill the gap between Boolean and continuous formalisms, i.e., providing semi-quantitative results using a simple representation with a minimum number of parameters to fit. The goal of WebMaBoSS is to simplify the use and the analysis of Boolean models coping with two main issues: 1) the simulation of Boolean models of intracellular processes with MaBoSS, or any modeling tool, may appear as non-intuitive for non-experts; 2) the simulation of already-published models available in current model databases (e.g., Cell Collective, BioModels) may require some extra steps to ensure compatibility with modeling tools such as MaBoSS. With WebMaBoSS, new models can be created or imported directly from existing databases. They can then be simulated, modified and stored in personal folders. Model simulations are performed easily, results visualized interactively, and figures can be exported in a preferred format. Extensive model analyses such as mutant screening or parameter sensitivity can also be performed. For all these tasks, results are stored and can be subsequently filtered to look for specific outputs. This web interface can be accessed at the address: https://maboss.curie.fr/webmaboss/ and deployed locally using docker. This application is open-source under LGPL license, and available at https://github.com/sysbio-curie/WebMaBoSS.

Relationships among generalized positive feedback loops determine possible community outcomes in plant-pollinator interaction networks.

Attractors in Boolean network models representing complex systems such as ecological communities correspond to long-term outcomes (e.g., stable communities) in such systems. As a result, identifying efficient methods to find and characterize these attractors allows for a better understanding of the diversity of possible outcomes. Here we analyze networks that model mutualistic communities of plant and pollinator species governed by Boolean threshold functions. We propose a novel attractor identification method based on generalized positive feedback loops and their functional relationships in such networks. We show that these relationships determine the mechanisms by which groups of stable positive feedback loops collectively trap the system in specific regions of the state space and lead to attractors. Put into the ecological context, we show how survival units-small groups of species in which species can maintain a specific survival state-and their relationships determine the final community outcomes in plant-pollinator networks. We find a remarkable diversity of community outcomes: up to an average of 43 attractors possible for networks with 100 species. This diversity is due to the multiplicity of survival units (up to 34) and stable subcommunities (up to 14). The timing of species influx or outflux does not affect the number of attractors, but it may influence their basins of attraction.

Determining the Maximum States of the Ensemble Distribution of Boolean Networks

Inference of the gene regulation mechanism from gene expression patterns has become increasingly popular, in recent years, with the advent of microarray technology. Obtaining the states of genes and their regulatory relationships would greatly enable the scientists to investigate and understand the mechanisms of the diseases. However, it is still a big challenge to determine relationships from several thousands of genes. Here, we simplify the above complex gene state determination problem as an inference of the distribution of the ensemble Boolean networks (BNs). In order to investigate and calculate the distribution of the BNs’ states, we first compute the probabilities of the different BNs’ states and obtain the number of statesΩ. Then, we find the maximum possible distribution of the number of the BNs’ states and calculate the fluctuation of the distribution. Finally, two representative experiments are conducted, and the efficiency of the obtained results is verified. The proposed algorithm is conceptually concise and easily applicable to many other realistic models; furthermore, it is highly extensible for various situations.

Set Stability and Set Stabilization of Boolean Control Networks Avoiding Undesirable Set

The traditional set stability of Boolean networks (BNs) refers to whether all the states can converge to a given state subset. Different from the existing results, the set stability investigated in this paper is whether all states in a given initial set can converge to a given destination set. This paper studies the set stability and set stabilization avoiding undesirable sets of BNs and Boolean control networks (BCNs), respectively. First, by virtue of the semi-tensor product (STP) of matrices, the dynamics of BNs avoiding a given undesirable set are established. Then, the set reachability and set stability of BNs from the initial set to destination set avoiding an undesirable set are investigated, respectively. Furthermore, the set stabilization of BCNs from the initial set to destination set avoiding a given undesirable set are investigated. Finally, a design method for finding the time optimal set stabilizer is proposed, and an example is provided to illustrate the effectiveness of the results.

Overcoming the complexity barrier of the dynamic message-passing method in networks with fat-tailed degree distributions.

The dynamic cavity method provides the most efficient way to evaluate probabilities of dynamic trajectories in systems of stochastic units with unidirectional sparse interactions. It is closely related to sum-product algorithms widely used to compute marginal functions from complicated global functions of many variables, with applications in disordered systems, combinatorial optimization, and computer science. However, the complexity of the cavity approach grows exponentially with the in-degrees of the interacting units, which creates a defacto barrier for the successful analysis of systems with fat-tailed in-degree distributions. In this paper, we present a dynamic programming algorithm that overcomes this barrier by reducing the computational complexity in the in-degrees from exponential to quadratic, whenever couplings are chosen randomly from (or can be approximated in terms of) discrete, possibly unit-dependent, sets of equidistant values. As a case study, we analyze the dynamics of a random Boolean network with a fat-tailed degree distribution and fully asymmetric binary ±J couplings, and we use the power of the algorithm to unlock the noise-dependent heterogeneity of stationary node activation patterns in such a system.

An Integrated View of Virus-Triggered Cellular Plasticity Using Boolean Networks.

Virus-related mortality and morbidity are due to cell/tissue damage caused by replicative pressure and resource exhaustion, e.g., HBV or HIV; exaggerated immune responses, e.g., SARS-CoV-2; and cancer, e.g., EBV or HPV. In this context, oncogenic and other types of viruses drive genetic and epigenetic changes that expand the tumorigenic program, including modifications to the ability of cancer cells to migrate. The best-characterized group of changes is collectively known as the epithelial–mesenchymal transition, or EMT. This is a complex phenomenon classically described using biochemistry, cell biology and genetics. However, these methods require enormous, often slow, efforts to identify and validate novel therapeutic targets. Systems biology can complement and accelerate discoveries in this field. One example of such an approach is Boolean networks, which make complex biological problems tractable by modeling data (“nodes”) connected by logical operators. Here, we focus on virus-induced cellular plasticity and cell reprogramming in mammals, and how Boolean networks could provide novel insights into the ability of some viruses to trigger uncontrolled cell proliferation and EMT, two key hallmarks of cancer.

Set Stability of Probabilistic Time-Delay Boolean Networks with Impulsive Effect

Set Stability of Probabilistic Time-Delay Boolean Networks with Impulsive Effect

Data-Driven Modeling of Breast Cancer Tumors Using Boolean Networks.

Cancer is a genomic disease involving various intertwined pathways with complex cross-communication links. Conceptually, this complex interconnected system forms a network, which allows one to model the dynamic behavior of the elements that characterize it to describe the entire system’s development in its various evolutionary stages of carcinogenesis. Knowing the activation or inhibition status of the genes that make up the network during its temporal evolution is necessary for the rational intervention on the critical factors for controlling the system’s dynamic evolution. In this report, we proposed a methodology for building data-driven boolean networks that model breast cancer tumors. We defined the network components and topology based on gene expression data from RNA-seq of breast cancer cell lines. We used a Boolean logic formalism to describe the network dynamics. The combination of single-cell RNA-seq and interactome data enabled us to study the dynamics of malignant subnetworks of up-regulated genes. First, we used the same Boolean function construction scheme for each network node, based on canalyzing functions. Using single-cell breast cancer datasets from The Cancer Genome Atlas, we applied a binarization algorithm. The binarized version of scRNA-seq data allowed identifying attractors specific to patients and critical genes related to each breast cancer subtype. The model proposed in this report may serve as a basis for a methodology to detect critical genes involved in malignant attractor stability, whose inhibition could have potential applications in cancer theranostics.

Bilevel integer programming on a Boolean network for discovering critical genetic alterations in cancer development and therapy

Boolean network is a modeling tool that describes a dynamic system with binary variables and their logical transition formulas. Recent studies in precision medicine use a Boolean network to discover critical genetic alterations that may lead to cancer or target genes for effective therapies to individuals. In this paper, we study a logical inference problem in a Boolean network to find all such critical genetic alterations in a minimal (parsimonious) way. We propose a bilevel integer programming model to find a single minimal genetic alteration. Using the bilevel integer programming model, we develop a branch and bound algorithm that effectively finds all of the minimal alterations. Through a computational study with eleven Boolean networks from the literature, we show that the proposed algorithm finds solutions much faster than the state-of-the-art algorithms in large data sets.

Robust set stability of probabilistic Boolean networks under general stochastic function perturbation

This paper concentrates on the impact of stochastic function perturbation (SFP) on the set stability of PBNs. The problem of robust set stability is divided into two cases, and they are respectively the perturbed column of the structure matrix does not belong to/belongs to the stabilizing set. For the first case, two necessary and sufficient conditions are obtained to guarantee that the system can keep finite-time stable unchanged and the system becomes asymptotically stable, respectively. For the second case, i.e., the perturbed column in the stabilizing set, the condition which can keep the stability of the system unchanged is obtained. Lastly, an example is provided to illustrate the obtained theoretical results.

Modeling the Pancreatic Cancer Microenvironment in Search of Control Targets.

Pancreatic ductal adenocarcinoma is among the leading causes of cancer-related deaths globally due to its extreme difficulty to detect and treat. Recently, research focus has shifted to analyzing the microenvironment of pancreatic cancer to better understand its key molecular mechanisms. This microenvironment can be represented with a multi-scale model consisting of pancreatic cancer cells (PCCs) and pancreatic stellate cells (PSCs), as well as cytokines and growth factors which are responsible for intercellular communication between the PCCs and PSCs. We have built a stochastic Boolean network (BN) model, validated by literature and clinical data, in which we probed for intervention strategies that force this gene regulatory network (GRN) from a diseased state to a healthy state. To do so, we implemented methods from phenotype control theory to determine a procedure for regulating specific genes within the microenvironment. We identified target genes and molecules, such that the application of their control drives the GRN to the desired state by suppression (or expression) and disruption of specific signaling pathways that may eventually lead to the eradication of the cancer cells. After applying well-studied control methods such as stable motifs, feedback vertex sets, and computational algebra, we discovered that each produces a different set of control targets that are not necessarily minimal nor unique. Yet, we were able to gain more insight about the performance of each process and the overlap of targets discovered. Nearly every control set contains cytokines, KRas, and HER2/neu, which suggests they are key players in the system's dynamics. To that end, this model can be used to produce further insight into the complex biological system of pancreatic cancer with hopes of finding new potential targets.

Finite horizon tracking control of probabilistic Boolean control networks

In this paper, the finite horizon tracking control problem of probabilistic Boolean control networks (PBCNs) is studied. For a given reference output trajectory, two trackability definitions are introduced according to whether the tracking probability is 1. Under the framework of the semi-tensor product, some necessary and sufficient conditions are obtained to determine whether the reference output trajectory is trackable with probability (probability one) by a PBCN starting from a given initial state. Based on this, two algorithms are proposed to determine the maximum tracking probability and the corresponding optimal control policy sequence. By determining the tracking error of the reference output trajectory, two related optimal control problems are considered: one is to minimize the expected value of the total tracking error, and the other is to minimize the maximum tracking error. Inspired by dynamic programming, corresponding algorithms are given to solve these two problems. Finally, two examples are given to verify the validity and correctness of the results.

Analysis and improvement of Boolean chaos robustness to noise

Boolean chaos generated by autonomous Boolean networks has been successfully applied to random number generation, physical unclonable function, gene regulation and reservoir computing, because it can generate complex dynamics with very simple structure. Influences of noise on autonomous Boolean networks chaotic system in delay time parameter spaces are analyzed by simulation and experiments in this article. It is found that the influences of noise on Boolean chaotic system is two-sided. What is new is that noise may lead to chaos instability, i.e., the noise transforms the original chaotic outputs into periodic outputs, which means the Boolean chaos lacks robustness to noise. Then like other chaotic systems noise contributes to Boolean chaotic unpredictability. The physical origin of noise induced Boolean chaos instability is analyzed that noise may easily change delay time parameter no longer a chaotic parameter in discontinuous chaotic parameter spaces. In addition, simulation and experiments on FPGA show that the increase of the number of nonlinear elements of the chaotic system can improve the Boolean chaos robustness to noise. This research is significant to the design of autonomous Boolean networks.

Optimal control of multi-task Boolean control networks via temporal logic

Boolean control networks (BCNs) with temporal logic specifications have great potential to deal with multiple tasks or complex environments. We first express the tasks of BCNs with temporal logic specifications, and transform these specifications into finite time sets dwell problems. By using the semi-tensor product (STP), some results that satisfying the specifications of temporal logic through time-varying control are obtained. Our method provides a unified framework for studying the stabilizability, synchronizability, path planning and other issues of BCNs. The controller design algorithms are then proposed to generate state sequences that fulfill the given tasks as much as possible while minimizing the cost function. Finally, two examples are given to verify the effectiveness of the theoretical results.

Novel approach towards antimicrobial chemotherapy optimization in lower respiratory tract infections in children: An observational study.

The use of local antibiogram in guiding clinical decisions is an integral part of the antimicrobial stewardship program. Conventional antibiograms are not disease-specific, ignore the distribution of microorganisms, obscure the in-vitro efficacy interrelationships, and have limited use in polymicrobial infections.We aimed to develop an in-house empiric, disease-specific, antimicrobial prescription auxiliary for the treatment of hospitalized pediatric pneumonia patients and to present the methods which help to choose the first and the second line antimicrobial therapy, while accounting for cost and safety aspects.A retrospective single center observational study was conducted on bronchoscopy obtained sputum culture. Analysis of probabilities, variance minimization, Boolean network modeling, and dominance analysis were applied to analyze antibiogram data. The Kirby–Bauer disk diffusion method was used to test the susceptibility of all isolates. Final optimization analysis included local drug acquisition cost (standardized to price per DDD) and safety profile.Data of 145 pediatric patients hospitalized with pneumonia with 218 isolates over 5 years was collected. A combination of statistical methods such as probabilities of drug efficacy, variance minimization, Boolean network modeling, and dominance analysis can help to choose the optimal first-line and the second-line antimicrobial treatment and optimize patient care. This research reveals that ampicillin is the optimal choice as the first-line drug and piperacillin-tazobactam is the second-line antimicrobial drug if the first one is not effective, while accounting for cost and safety aspects.The paper proposes a new methodology to adapt empiric antimicrobial therapy recommendations based on real world data and accout for costs and risk of adverse events.