In this work, we study the source-target control problem of Boolean networks, which has important applications for cellular reprogramming. More specifically, we want to perturb the input Boolean network such that it leaves a predetermined source attractor to eventually find itself in the target attractor. We use edge perturbations, which modify the update functions of a Boolean network without necessarily setting them to constants. This work improves an existing method in which edge perturbations are used to eliminate all but the target attractor. Both approaches are based on Thomas’ first rule: the existence of at least one positive cycle in the interaction graph of a dynamical system is a necessary condition for the existence of multiple steady states. Thus, if all positive cycles are removed, the resulting dynamical system has a single steady state. This requires removing a subset of edges so that at least one edge of every cycle in the graph is perturbed: the feedback edge set. Information on the source and target attractors allows reducing the number of relevant feedback edge sets and, subsequently, candidate perturbations. We propose a carefully designed strategy that combines exhaustive search and a heuristic inspired by Simulated Annealing to effectively reduce the number of required perturbations with respect to the feedback edge set. We evaluate our method on a wide array of Boolean networks from the literature to demonstrate its efficacy and efficiency.

Cellular reprogramming can be used for both the prevention and cure of complex diseases. However, the efficiency of discovering reprogramming strategies with classical wet-lab experiments is hindered by lengthy time commitments and high costs. In this study, we leverage deep reinforcement learning to develop a novel computational framework that facilitates the identification of reprogramming strategies. To this end, we formulate a control problem in the context of cellular reprogramming for the Boolean and probabilistic Boolean network models of gene regulatory networks under the asynchronous update mode. Furthermore, to facilitate scalability, we introduce the notion of a pseudo-attractor and a procedure for the identification of pseudo-attractor states. Finally, we devise a computational framework for solving the control problem, which we test on a number of biological networks.

In the quest to unravel the complexities of dynamical systems, the initial imperative is to unveil their inherent topological structure, a key determinant of system organization. Achieving this necessitates the deployment of robust structural inference techniques capable of deriving this structure from observed system behaviors. However, these methods are often tailor-made for specific domains and datasets, lacking a unified and objective framework for comparative assessment. In response to this pressing challenge, we present a comprehensive benchmarking study encompassing 12 structural inference methodologies sourced from diverse disciplines. Our evaluation protocol spans dynamical systems generated via two distinct simulation paradigms and encompasses 11 distinct interaction graph typologies. We gauge the methods' performance in terms of accuracy, scalability, robustness, and sensitivity to graph properties. Key findings emerge: 1) Deep learning techniques excel in the context of multi-dimensional data, 2) classical statistics and information-theory-based methods exhibit exceptional accuracy and resilience, and 3) method performance correlates positively with the average shortest path length of the graph. Our benchmark not only aids researchers in method selection for specific problem domains but also serves as a catalyst for inspiring novel methodological advancements in the field.

Cellular reprogramming can be used for both the prevention and cure of different diseases. However, the efficiency of discovering reprogramming strategies with classical wet-lab experiments is hindered by lengthy time commitments and high costs. In this study, we develop a~novel computational framework based on deep reinforcement learning that facilitates the identification of reprogramming strategies. For this aim, we formulate a~control problem in the context of cellular reprogramming for the frameworks of BNs and PBNs under the asynchronous update mode. Furthermore, we introduce the notion of a~pseudo-attractor and a~procedure for identification of pseudo-attractor state during training. Finally, we devise a~computational framework for solving the control problem, which we test on a~number of different models.

We explore the feasibility of onboard anomaly detection using artificial neural networks for CubeSat systems and related spacecraft where computing resources are limited. We gather data for training and evaluation using a CubeSat in a laboratory for a scenario where a malfunctioning component affects temperature fluctuations across the control system. This data, published in an open repository, guide the selection of suitable features, neural network architecture, and metrics comprising our anomaly detection algorithm. The precision and recall of the algorithm demonstrate improvements as compared to out-of-limit methods, whereas our open-source implementation for a typical microcontroller exhibits small memory overhead, and hence may coexist with existing control software without introducing new hardware. These features make our solution feasible to deploy on board a CubeSat, and thus on other, more advanced types of satellites.

We propose a Generative Adversarial Network (GAN) based architecture for removing clouds from satellite imagery. Data used for training comprises of visible light RGB and near-infrared (NIR) band images. The novelty lies in the structure of the discriminator in the GAN architecture, which compares generated and target cloud-free RGB images concatenated with their edge-filtered versions. Experimental results show that our approach to removing clouds outperforms both visually and according to metrics, a benchmark solution that does not take edge filtering into account, and that improvements are robust when varying both training dataset size and NIR cloud penetrability.

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.

We present a major new release of ASSA-PBN, a software tool for modelling, simulation, and analysis of probabilistic Boolean networks (PBNs). The new version enables the support for context-sensitive PBNs (CPBNs), which can well balance the uncertainty and stability of the modelled biological systems. It contributes mainly in three aspects. Firstly, it designs a high-level language for specifying CPBNs. Secondly, it implements various simulation-based methods for simulating CPBNs and analysing their long-run dynamics. Last but not least, it provides an efficient method to identify all the attractors of a CPBN. Thanks to its divide and conquer strategy, the implemented detection algorithm can deal with large and realistic biological networks under both synchronous and asynchronous updating schemes.

Boolean networks is a well-established formalism for modelling biological systems. A vital challenge for analyzing a Boolean network is to identify all the attractors. This becomes more challenging for large asynchronous Boolean networks, due to the asynchronous scheme. Existing methods are prohibited due to the well-known state-space explosion problem in large Boolean networks. In this paper, we tackle this challenge by proposing a SCC-based decomposition method. We prove the correctness of our proposed method and demonstrate its efficiency with two real-life biological networks.

Boolean networks are an important formalism for modelling biological systems and have attracted much attention in recent years. An important challenge in Boolean networks is to exhaustively find attractors, which represent steady states of a biological network. In this paper, we propose a new approach to improve the efficiency of BDD-based attractor detection. Our approach includes a monolithic algorithm for small networks, an enumerative strategy to deal with large networks, a method to accelerate attractor detection based on an analysis of the network structure, and two heuristics on ordering BDD variables. We demonstrate the performance of our approach on a number of examples and on a realistic model of apoptosis in hepatocytes. We compare it with one existing technique in the literature.

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.

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.

Probabilistic Boolean networks (PBNs) is a well-established computational framework for modelling biological systems. The steady-state dynamics of PBNs is of crucial importance in the study of such systems. However, for large PBNs, which often arise in systems biology, obtaining the steady-state distribution poses a significant challenge. In this paper, we revive the two-state Markov chain approach to solve this problem. This paper contributes in three aspects. First, we identify a problem of generating biased results with the approach and we propose a few heuristics to avoid such a pitfall. Second, we conduct an extensive experimental comparison of the extended two-state Markov chain approach and another approach based on the Skart method. We analyze the results with machine learning techniques and we show that statistically the two-state Markov chain approach has a better performance. Finally, we demonstrate the potential of the extended two-state Markov chain approach on a case study of a large PBN model of apoptosis in hepatocytes.

Quantitative models may exhibit sophisticated behaviour that includes having multiple steady states, bistability, limit cycles, and period-doubling bifurcation. Such behaviour is typically driven by the numerical dynamics of the model, where the values of various numerical parameters play the crucial role. We introduce in this paper natural correspondents of these concepts to reaction systems modelling, a framework based on elementary set theoretical, forbidding/enforcing-based mechanisms. We construct several reaction systems models exhibiting these properties.

Boolean networks is a well-established formalism for modelling biological systems. An important challenge for analysing a Boolean network is to identify all its attractors. This becomes challenging for large Boolean networks due to the well-known state-space explosion problem. In this paper, we propose a new SCC-based decomposition method for attractor detection in large synchronous Boolean networks. Experimental results show that our proposed method is significantly better in terms of performance when compared to existing methods in the literature.

Probabilistic Boolean networks (PBNs) is a widely used computational framework for modelling biological systems. The steady-state dynamics of PBNs is of special interest in the analysis of biological machinery. However, obtaining the steady-state distributions for such systems poses a significant challenge due to the state space explosion problem which arises in the case of large PBNs. The only viable way is to use statistical methods. In the literature, the two-state Markov chain approach and the Skart method have been proposed for the analysis of large PBNs. However, the sample size required by both methods is often huge in the case of large PBNs and generating them is expensive in terms of computation time. Parallelising the sample generation is an ideal way to solve this issue. In this paper, we consider combining the Gelman & Rubin method with either the two-state Markov chain approach or the Skart method for parallelisation. The first method can be used to run multiple independent Markov chains in parallel and to control their convergence to the steady-state while the other two methods can be used to determine the sample size required for computing the steady-state probability of states of interest. Experimental results show that our proposed combinations can reduce time cost of computing stead-state probabilities of large PBNs significantly.

Computation of steady-state probabilities is an important aspect of analysing biological systems modelled as probabilistic Boolean networks (PBNs). For small PBNs, efficient numerical methods to compute steady-state probabilities of PBNs exist, based on the Markov chain state-transition matrix. However, for large PBNs, numerical methods suffer from the state-space explosion problem since the state-space size is exponential in the number of nodes in a PBN. In fact, the use of statistical methods and Monte Carlo methods remain the only feasible approach to address the problem for large PBNs. Such methods usually rely on long simulations of a PBN. Since slow simulation can impede the analysis, the efficiency of the simulation procedure becomes critical. Intuitively, parallelising the simulation process is the ideal way to accelerate the computation. Recent developments of general purpose graphics processing units (GPUs) provide possibilities to massively parallelise the simulation process. In this work, we propose a trajectory-level parallelisation framework to accelerate the computation of steady-state probabilities in large PBNs with the use of GPUs. To maximise the computation efficiency on a GPU, we develop a dynamical data arrangement mechanism for handling different size PBNs with a GPU. Specially, we propose a reorder-and-split method to handle both large and dense PBNs. Besides, we develop a specific way of storing predictor functions of a PBN and the state of the PBN in the GPU memory. Moreover, we introduce a strongly connected component (SCC)-based network reduction technique to further accelerate the computation speed. Experimental results show that our GPU-based parallelisation gains approximately a 600-fold speedup for a real-life PBN compared to the state-of-the-art sequential method.

We present a major new release of ASSA-PBN, a software tool for modelling, simulation, and analysis of probabilistic Boolean networks (PBNs). PBNs are a widely used computational framework for modelling biological systems. The steady-state dynamics of a PBN is of special interest and obtaining it poses a significant challenge due to the state space explosion problem which often arises in the case of large biological systems. In its previous version, ASSA-PBN applied efficient statistical methods to approximately compute steady-state probabilities of large PBNs. In this newly released version, ASSA-PBN not only speeds up the computation of steady-state probabilities with three different realisations of parallel computing, but also implements parameter estimation and techniques for in-depth analysis of PBNs, i.e., influence and sensitivity analysis of PBNs. In addition, a graphical user interface (GUI) is provided for the convenience of users.

As an important mathematical modelling framework, probabilistic Boolean networks (PBNs) are widely used for modelling and analysing biological systems. PBNs are suited for modelling large biological systems, which more and more often arise in systems biology. However, the large system size poses a significant challenge to the analysis of PBNs, in particular, to the crucial analysis of their steady-state behaviour. Numerical methods for performing steady-state analyses suffer from the state-space explosion problem, which makes the utilisation of statistical methods the only viable approach. However, such methods require long simulations of PBNs, rendering the simulation speed a crucial efficiency factor. For large PBNs and high estimation precision requirements, a slow simulation speed becomes an obstacle. In this paper, we propose a structure-based method for fast simulation of PBNs. This method first performs a network reduction operation and then divides nodes into groups for parallel simulation. Experimental results show that our method can lead to an approximately 10 times speedup for computing steady-state probabilities of a real-life biological network.

Boolean networks are an important formalism for modelling biological systems and have attracted much attention in recent years. An important challenge in Boolean networks is to exhaustively find attractors, which represent steady states of a biological network. In this paper, we propose a new approach to improve the efficiency of BDD-based attractor detection. Our approach includes a monolithic algorithm for small networks, an enumerative strategy to deal with large networks, a method to accelerate attractor detection based on an analysis of the network structure, and two heuristics on ordering BDD variables. We demonstrate the performance of our approach on a number of examples and on a realistic model of apoptosis in hepatocytes. We compare it with one existing technique in the literature.