Andrzej Mizera

Applying dynamic Bayesian networks to perturbed gene expression data

BackgroundA 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.ResultsWe 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.ConclusionWe 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.

Recent development and biomedical applications of probabilistic Boolean networks

Probabilistic Boolean network (PBN) modelling is a semi-quantitative approach widely used for the study of the topology and dynamic aspects of biological systems. The combined use of rule-based representation and probability makes PBN appealing for large-scale modelling of biological networks where degrees of uncertainty need to be considered.A considerable expansion of our knowledge in the field of theoretical research on PBN can be observed over the past few years, with a focus on network inference, network intervention and control. With respect to areas of applications, PBN is mainly used for the study of gene regulatory networks though with an increasing emergence in signal transduction, metabolic, and also physiological networks. At the same time, a number of computational tools, facilitating the modelling and analysis of PBNs, are continuously developed.A concise yet comprehensive review of the state-of-the-art on PBN modelling is offered in this article, including a comparative discussion on PBN versus similar models with respect to concepts and biomedical applications. Due to their many advantages, we consider PBN to stand as a suitable modelling framework for the description and analysis of complex biological systems, ranging from molecular to physiological levels.

A simple mass-action model for the eukaryotic heat shock response and its mathematical validation

The heat shock response is a primordial defense mechanism against cell stress and protein misfolding. It proceeds with the minimum number of mechanisms that any regulatory network must include, a stress-induced activation and a feedback regulation, and can thus be regarded as the archetype for a cellular regulatory process. We propose here a simple mechanistic model for the eukaryotic heat shock response, including its mathematical validation. Based on numerical predictions of the model and on its sensitivity analysis, we minimize the model by identifying the reactions with marginal contribution to the heat shock response. As the heat shock response is a very basic and conserved regulatory network, our analysis of the network provides a useful foundation for modeling strategies of more complex cellular processes.

optPBN: An Optimisation Toolbox for Probabilistic Boolean Networks

Background There exist several computational tools which allow for the optimisation and inference of biological networks using a Boolean formalism. Nevertheless, the results from such tools yield only limited quantitative insights into the complexity of biological systems because of the inherited qualitative nature of Boolean networks. Results We introduce optPBN, a Matlab-based toolbox for the optimisation of probabilistic Boolean networks (PBN) which operates under the framework of the BN/PBN toolbox. optPBN offers an easy generation of probabilistic Boolean networks from rule-based Boolean model specification and it allows for flexible measurement data integration from multiple experiments. Subsequently, optPBN generates integrated optimisation problems which can be solved by various optimisers. In term of functionalities, optPBN allows for the construction of a probabilistic Boolean network from a given set of potential constitutive Boolean networks by optimising the selection probabilities for these networks so that the resulting PBN fits experimental data. Furthermore, the optPBN pipeline can also be operated on large-scale computational platforms to solve complex optimisation problems. Apart from exemplary case studies which we correctly inferred the original network, we also successfully applied optPBN to study a large-scale Boolean model of apoptosis where it allows identifying the inverse correlation between UVB irradiation, NFκB and Caspase 3 activations, and apoptosis in primary hepatocytes quantitatively. Also, the results from optPBN help elucidating the relevancy of crosstalk interactions in the apoptotic network. Summary The optPBN toolbox provides a simple yet comprehensive pipeline for integrated optimisation problem generation in the PBN formalism that can readily be solved by various optimisers on local or grid-based computational platforms. optPBN can be further applied to various biological studies such as the inference of gene regulatory networks or the identification of the interactions relevancy in signal transduction networks.

A New Mathematical Model for the Heat Shock Response

We present in this paper a novel molecular model for the gene regulatory network responsible for the eukaryotic heat shock response. Our model includes the temperature-induced protein misfolding, the chaperone activity of the heat shock proteins, and the backregulation of their gene transcription. We then build a mathematical model for it, based on ordinary differential equations. Finally, we discuss the parameter fit and the implications of the sensitivity analysis for our model.

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.

Quantitative Analysis of the Self-Assembly Strategies of Intermediate Filaments from Tetrameric Vimentin

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.