optPBN: an optimisation toolbox for probabilistic Boolean networks

Bayesian Optimization for State and Parameter Estimation of Dynamic Networks with Binary Space

This paper focuses on joint state and parameter estimation in partially observed Boolean dynamical systems (POBDS), a hidden Markov model tailored for modeling complex networks with binary state variables. The majority of current techniques for parameter estimation rely on computationally expensive gradient-based methods, which become intractable in most practical applications with large size of networks. We propose a gradient-free approach that uses Gaussian processes to model the expensive log-likelihood function and utilizes Bayesian optimization for efficient likelihood search over parameter space. Joint state estimation is also achieved alongside parameter estimation using the Boolean Kalman filter. The performance of the proposed method is demonstrated using gene regulatory networks observed through synthetic gene-expression data. The numerical results demonstrate the scalability and effectiveness of the proposed method in the joint estimation of the model parameters and genes' states.

A gray box framework that optimizes a white box logical model using a black box optimizer for simulating cellular responses to perturbations

Predicting cellular responses to perturbations requires interpretable insights into molecular regulatory dynamics to perform reliable cell fate control, despite the confounding non-linearity of the underlying interactions. There is a growing interest in developing machine learning-based perturbation response prediction models to handle the non-linearity of perturbation data, but their interpretation in terms of molecular regulatory dynamics remains a challenge. Alternatively, for meaningful biological interpretation, logical network models such as Boolean networks are widely used in systems biology to represent intracellular molecular regulation. However, determining the appropriate regulatory logic of large-scale networks remains an obstacle due to the high-dimensional and discontinuous search space. To tackle these challenges, we present a scalable derivative-free optimizer trained by meta-reinforcement learning for Boolean network models. The logical network model optimized by the trained optimizer successfully predicts anti-cancer drug responses of cancer cell lines, while simultaneously providing insight into their underlying molecular regulatory mechanisms.

Identification of the Structure of a Probabilistic Boolean Network From Samples Including Frequencies of Outcomes

We study the problem of identifying the structure of a probabilistic Boolean network (PBN), a probabilistic model of biological networks, from a given set of samples. This problem can be regarded as an identification of a set of Boolean functions from samples. Existing studies on the identification of the structure of a PBN only use information on the occurrences of samples. In this paper, we also make use of the frequencies of occurrences of subtuples, information that is obtainable from the samples. We show that under this model, it is possible to identify a PBN from among a class of PBNs, for much broader classes of PBNs. In particular, we prove that, under a reasonable assumption, the structure of a PBN can be identified from among the class of PBNs that have at most three functions assigned to each node, but that identification may be impossible if four or more functions are assigned to each node. We also analyze the sample complexity for exactly identifying the structure of a PBN, and present an efficient algorithm for the identification of a PBN consisting of threshold functions from samples.

Systemic network analysis identifies XIAP and IκBα as potential drug targets in TRAIL resistant BRAF mutated melanoma

Metastatic melanoma remains a life-threatening disease because most tumors develop resistance to targeted kinase inhibitors thereby regaining tumorigenic capacity. We show the 2nd generation hexavalent TRAIL receptor-targeted agonist IZI1551 to induce pronounced apoptotic cell death in mutBRAF melanoma cells. Aiming to identify molecular changes that may confer IZI1551 resistance we combined Dynamic Bayesian Network modelling with a sophisticated regularization strategy resulting in sparse and context-sensitive networks and show the performance of this strategy in the detection of cell line-specific deregulations of a signalling network. Comparing IZI1551-sensitive to IZI1551-resistant melanoma cells the model accurately and correctly predicted activation of NFκB in concert with upregulation of the anti-apoptotic protein XIAP as the key mediator of IZI1551 resistance. Thus, the incorporation of multiple regularization functions in logical network optimization may provide a promising avenue to assess the effects of drug combinations and to identify responders to selected combination therapies.

Reviving the Two-State Markov Chain Approach

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.

FALCON: a toolbox for the fast contextualization of logical networks

Motivation

Mathematical modelling of regulatory networks allows for the discovery of knowledge at the system level. However, existing modelling tools are often computation-heavy and do not offer intuitive ways to explore the model, to test hypotheses or to interpret the results biologically.

Results

We have developed a computational approach to contextualize logical models of regulatory networks with biological measurements based on a probabilistic description of rule-based interactions between the different molecules. Here, we propose a Matlab toolbox, FALCON, to automatically and efficiently build and contextualize networks, which includes a pipeline for conducting parameter analysis, knockouts and easy and fast model investigation. The contextualized models could then provide qualitative and quantitative information about the network and suggest hypotheses about biological processes.

Availability and implementation

FALCON is freely available for non-commercial users on GitHub under the GPLv3 licence. The toolbox, installation instructions, full documentation and test datasets are available at https://github.com/sysbiolux/FALCON. FALCON runs under Matlab (MathWorks) and requires the Optimization Toolbox.

Supplementary information

Supplementary data are available at Bioinformatics online.

ASSA-PBN: A Toolbox for Probabilistic Boolean 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.

ATLANTIS - Attractor Landscape Analysis Toolbox for Cell Fate Discovery and Reprogramming

Boolean modelling of biological networks is a well-established technique for abstracting dynamical biomolecular regulation in cells. Specifically, decoding linkages between salient regulatory network states and corresponding cell fate outcomes can help uncover pathological foundations of diseases such as cancer. Attractor landscape analysis is one such methodology which converts complex network behavior into a landscape of network states wherein each state is represented by propensity of its occurrence. Towards undertaking attractor landscape analysis of Boolean networks, we propose an Attractor Landscape Analysis Toolbox (ATLANTIS) for cell fate discovery, from biomolecular networks, and reprogramming upon network perturbation. ATLANTIS can be employed to perform both deterministic and probabilistic analyses. It has been validated by successfully reconstructing attractor landscapes from several published case studies followed by reprogramming of cell fates upon therapeutic treatment of network. Additionally, the biomolecular network of HCT-116 colorectal cancer cell line has been screened for therapeutic evaluation of drug-targets. Our results show agreement between therapeutic efficacies reported by ATLANTIS and the published literature. These case studies sufficiently highlight the in silico cell fate prediction and therapeutic screening potential of the toolbox. Lastly, ATLANTIS can also help guide single or combinatorial therapy responses towards reprogramming biomolecular networks to recover cell fates.

Boolean network modeling in systems pharmacology

Quantitative systems pharmacology (QSP) is an emerging discipline that aims to discover how drugs modulate the dynamics of biological components in molecular and cellular networks and the impact of those perturbations on human pathophysiology. The integration of systems-based experimental and computational approaches is required to facilitate the advancement of this field. QSP models typically consist of a series of ordinary differential equations (ODE). However, this mathematical framework requires extensive knowledge of parameters pertaining to biological processes, which is often unavailable. An alternative framework that does not require knowledge of system-specific parameters, such as Boolean network modeling, could serve as an initial foundation prior to the development of an ODE-based model. Boolean network models have been shown to efficiently describe, in a qualitative manner, the complex behavior of signal transduction and gene/protein regulatory processes. In addition to providing a starting point prior to quantitative modeling, Boolean network models can also be utilized to discover novel therapeutic targets and combinatorial treatment strategies. Identifying drug targets using a network-based approach could supplement current drug discovery methodologies and help to fill the innovation gap across the pharmaceutical industry. In this review, we discuss the process of developing Boolean network models and the various analyses that can be performed to identify novel drug targets and combinatorial approaches. An example for each of these analyses is provided using a previously developed Boolean network of signaling pathways in multiple myeloma. Selected examples of Boolean network models of human (patho-)physiological systems are also reviewed in brief.

Mathematical and Computational Modeling in Complex Biological Systems

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology.

Exact Identification of the Structure of a Probabilistic Boolean Network from Samples

We study the number of samples required to uniquely determine the structure of a probabilistic Boolean network (PBN), where PBNs are probabilistic extensions of Boolean networks. We show via theoretical analysis and computational analysis that the structure of a PBN can be exactly identified with high probability from a relatively small number of samples for interesting classes of PBNs of bounded indegree. On the other hand, we also show that there exist classes of PBNs for which it is impossible to uniquely determine the structure of a PBN from samples.

A Probabilistic Boolean Network Approach for the Analysis of Cancer-Specific Signalling: A Case Study of Deregulated PDGF Signalling in GIST

BACKGROUND

Signal transduction networks are increasingly studied with mathematical modelling approaches while each of them is suited for a particular problem. For the contextualisation and analysis of signalling networks with steady-state protein data, we identified probabilistic Boolean network (PBN) as a promising framework which could capture quantitative changes of molecular changes at steady-state with a minimal parameterisation.

RESULTS AND CONCLUSION

In our case study, we successfully applied the PBN approach to model and analyse the deregulated Platelet-Derived Growth Factor (PDGF) signalling pathway in Gastrointestinal Stromal Tumour (GIST). We experimentally determined a rich and accurate dataset of steady-state profiles of selected downstream kinases of PDGF-receptor-alpha mutants in combination with inhibitor treatments. Applying the tool optPBN, we fitted a literature-derived candidate network model to the training dataset consisting of single perturbation conditions. Model analysis suggested several important crosstalk interactions. The validity of these predictions was further investigated experimentally pointing to relevant ongoing crosstalk from PI3K to MAPK signalling in tumour cells. The refined model was evaluated with a validation dataset comprising multiple perturbation conditions. The model thereby showed excellent performance allowing to quantitatively predict the combinatorial responses from the individual treatment results in this cancer setting. The established optPBN pipeline is also widely applicable to gain a better understanding of other signalling networks at steady-state in a context-specific fashion.

L-plastin Ser5 phosphorylation in breast cancer cells and in vitro is mediated by RSK downstream of the ERK/MAPK pathway

Deregulated cell migration and invasion are hallmarks of metastatic cancer cells. Phosphorylation on residue Ser5 of the actin-bundling protein L-plastin activates L-plastin and has been reported to be crucial for invasion and metastasis. Here, we investigate signal transduction leading to L-plastin Ser5 phosphorylation using 4 human breast cancer cell lines. Whole-genome microarray analysis comparing cell lines with different invasive capacities and corresponding variations in L-plastin Ser5 phosphorylation level revealed that genes of the ERK/MAPK pathway are differentially expressed. It is noteworthy that in vitro kinase assays showed that ERK/MAPK pathway downstream ribosomal protein S6 kinases α-1 (RSK1) and α-3 (RSK2) are able to directly phosphorylate L-plastin on Ser5. Small interfering RNA- or short hairpin RNA-mediated knockdown and activation/inhibition studies followed by immunoblot analysis and computational modeling confirmed that ribosomal S6 kinase (RSK) is an essential activator of L-plastin. Migration and invasion assays showed that RSK knockdown led to a decrease of up to 30% of migration and invasion of MDA-MB-435S cells. Although the presence of L-plastin was not necessary for migration/invasion of these cells, immunofluorescence assays illustrated RSK-dependent recruitment of Ser5-phosphorylated L-plastin to migratory structures. Altogether, we provide evidence that the ERK/MAPK pathway is involved in L-plastin Ser5 phosphorylation in breast cancer cells with RSK1 and RSK2 kinases able to directly phosphorylate L-plastin residue Ser5.