Qixia Yuan

ASSA-PBN: An Approximate Steady-State Analyser of Probabilistic Boolean Networks

We present ASSA-PBN, a tool for approximate steady-state analysis of large probabilistic Boolean networks (PBNs). ASSA-PBN contains a constructor, a simulator, and an analyser which can approximately compute the steady-state probabilities of PBNs. For large PBNs, such approximate analysis is the only viable way to study their long-run behaviours. Experiments show that ASSA-PBN can handle large PBNs with a few thousands of nodes.

ASSA-PBN 2.0 : A Software Tool for Probabilistic Boolean Networks

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.

Fast simulation of probabilistic Boolean networks.

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.

Parallel approximate steady-state analysis of large probabilistic Boolean networks

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.

GPU-Accelerated Steady-State Computation of Large Probabilistic Boolean Networks

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 can be successfully applied to perform the computation with the use of Markov chain state transition matrix underlying the studied networks. 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 can be an 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, and a specific way of storing predictor functions of a PBN and the state of the PBN in the GPU memory. Experimental results show that our GPU-based parallelisation gains a speedup of approximately 400 times for a real-life PBN.

Probabilistic model checking of the PDGF signaling pathway

In this paper, we apply the probabilistic symbolic model checker PRISM to the analysis of a biological system --- the Platelet-Derived Growth Factor (PDGF) signaling pathway, demonstrating in detail how this pathway can be analyzed in PRISM. Moreover, we compare the results from verification and ODE simulation on the PDGF pathway and demonstrate by examples the influence of model structure, parameter values and pathway length on the two analysis methods.

Learning probabilistic models for model checking: an evolutionary approach and an empirical study

Many automated system analysis techniques (e.g., model checking, model-based testing) rely on first obtaining a model of the system under analysis. System modeling is often done manually, which is often considered as a hindrance to adopt model-based system analysis and development techniques. To overcome this problem, researchers have proposed to automatically “learn” models based on sample system executions and shown that the learned models can be useful sometimes. There are however many questions to be answered. For instance, how much shall we generalize from the observed samples and how fast would learning converge? Or, would the analysis result based on the learned model be more accurate than the estimation we could have obtained by sampling many system executions within the same amount of time? Moreover, how well does learning scale to real-world applications? If the answer is negative, what are the potential methods to improve the efficiency of learning? In this work, we first investigate existing algorithms for learning probabilistic models for model checking and propose an evolution-based approach for better controlling the degree of generalization. Then, we present existing approaches to learn abstract models to improve the efficiency of learning for scalability reasons. Lastly, we conduct an empirical study in order to answer the above questions. Our findings include that the effectiveness of learning may sometimes be limited and it is worth investigating how abstraction should be done properly in order to learn abstract models.

Improving BDD-based attractor detection for synchronous Boolean 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.

A study of the PDGF signaling pathway with PRISM

In this paper, we apply the probabilistic model checker PRISM to the analysis of a biological system -- the Platelet-Derived Growth Factor (PDGF) signaling pathway, demonstrating in detail how this pathway can be analyzed in PRISM. We show that quantitative verification can yield a better understanding of the PDGF signaling pathway.

A New Decomposition Method for Attractor Detection in Large Synchronous Boolean Networks

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.