Cellular reprogramming, the artificial transformation of one cell type into another, has been attracting increasing research attention due to its therapeutic potential for complex diseases. However, identifying effective reprogramming strategies through classical wet-lab experiments is hindered by long time commitments and high costs. Although computational methods have been proposed to address this challenge, exact state-of-the-art techniques suffer from limited scalability owing to the notorious state space explosion problem. To overcome this limitation, we explore deep reinforcement learning (DRL) for controlling holistic Boolean network models of complex biological systems, such as gene regulatory and signalling pathway networks. We formulate a novel control problem for Boolean network models operating under the asynchronous update mode, specifically tailored to the context of cellular reprogramming. To solve it, we devise GATTACA - a DRL-based computational framework explicitly designed for scalability, capable of handling large and complex network models where exact methods fail. To facilitate scalability of our framework, we consider our previously introduced concept of a pseudo-attractor and improve the procedure for effective identification of pseudo-attractor states. We incorporate graph neural networks with graph convolution operations into the artificial neural network approximator of the DRL agent's action-value function. The new architecture allows us to leverage the available knowledge on the structure of a biological system and to indirectly, yet effectively, encode the system's dynamics into a latent representation. Experiments on several large-scale, real-world biological networks from the literature demonstrate the scalability and effectiveness of our approach.

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.

Understanding complex dynamical systems begins with identifying their topological structures, which expose the organization of the systems. This requires robust structural inference methods that can deduce structure from observed behavior. However, existing methods are often domain-specific and lack a standardized, objective comparison framework. We address this gap by benchmarking 13 structural inference methods from various disciplines on simulations representing two types of dynamics and 11 interaction graph models, supplemented by a biological experimental dataset to mirror real-world application. We evaluated the methods for accuracy, scalability, robustness, and sensitivity to graph properties. Our findings indicate that deep learning methods excel with multi-dimensional data, while classical statistics and information theory based approaches are notably accurate and robust. Additionally, performance correlates positively with the graph's average shortest path length. This benchmark should aid researchers in selecting suitable methods for their specific needs and stimulate further methodological innovation.

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.

Abstract 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.

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.

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.

Boolean networks are an important formalism for modelling biological systems and have attracted much attention in recent years. An important direction in Boolean networks is to exhaustively find attractors, which represent steady states when a biological network evolves for a long term. 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, and two heuristics on ordering BDD variables. We demonstrate the performance of our approach on a number of examples, and compare it with one existing technique in the literature.

The expression of genes is a fundamental process in living cells, both eukaryotic and prokaryotic. The regulation of gene expression is achieved via sophisticated networks of interactions between DNA, RNA, proteins, and small chemical compounds. The qualitative and quantitative characterisation of interactions between genes is one of the major current research targets in systems biology. In this PhD research project, we view gene regulatory networks as Markov chains, resulting from popular formalisation frameworks such as Dynamic Bayesian Networks and Probabilistic Boolean Networks. This will allow us to reason about both the structure and strength of gene interactions. Our goal is to develop new algorithms and tools, which are tailored for the modelling and analysis of gene regulatory networks, by exploring model checking techniques that have been developed and widely used in computer science. More specifically, we will combine model checking techniques with sampling and optimisation methods from the literature to derive new techniques to solve the parameter estimation problem of Markov models of gene regulatory networks.

To disentangle the numerical contribution of modules to the system-level behavior of a given biomodel, one often considers knock-out mutant models, investigating the change in the model behavior when modules are systematically included and excluded f

In vitro assembly of intermediate filaments from tetrameric vimentin consists of a very rapid phase of tetramers laterally associating into unit-length filaments and a slow phase of filament elongation. We focus in this paper on a systematic quantitative investigation of two molecular models for filament assembly, recently proposed in (Kirmse et al. J. Biol. Chem. 282, 52 (2007), 18563-18572), through mathematical modeling, model fitting, and model validation. We analyze the quantitative contribution of each filament elongation strategy: with tetramers, with unit-length filaments, with longer filaments, or combinations thereof. In each case, we discuss the numerical fitting of the model with respect to one set of data, and its separate validation with respect to a second, different set of data. We introduce a high-resolution model for vimentin filament self-assembly, able to capture the detailed dynamics of filaments of arbitrary length. This provides much more predictive power for the model, in comparison to previous models where only the mean length of all filaments in the solution could be analyzed. We show how kinetic observations on low-resolution models can be extrapolated to the high-resolution model and used for lowering its complexity.

BACKGROUND: A central goal of molecular biology is to understand the regulatory mechanisms of gene transcription and protein synthesis. Because of their solid basis in statistics, allowing to deal with the stochastic aspects of gene expressions and noisy measurements in a natural way, Bayesian networks appear attractive in the field of inferring gene interactions structure from microarray experiments data. However, the basic formalism has some disadvantages, e.g. it is sometimes hard to distinguish between the origin and the target of an interaction. Two kinds of microarray experiments yield data particularly rich in information regarding the direction of interactions: time series and perturbation experiments. In order to correctly handle them, the basic formalism must be modified. For example, dynamic Bayesian networks (DBN) apply to time series microarray data. To our knowledge the DBN technique has not been applied in the context of perturbation experiments. RESULTS: We extend the framework of dynamic Bayesian networks in order to incorporate perturbations. Moreover, an exact algorithm for inferring an optimal network is proposed and a discretization method specialized for time series data from perturbation experiments is introduced. We apply our procedure to realistic simulations data. The results are compared with those obtained by standard DBN learning techniques. Moreover, the advantages of using exact learning algorithm instead of heuristic methods are analyzed. CONCLUSION: We show that the quality of inferred networks dramatically improves when using data from perturbation experiments. We also conclude that the exact algorithm should be used when it is possible, i.e. when considered set of genes is small enough.