Boolean network sketches: a unifying framework for logical model inference.

MOTIVATION: The problem of model inference is of fundamental importance to systems biology. Logical models (e.g. Boolean networks; BNs) represent a computationally attractive approach capable of handling large biological networks. The models are typically inferred from experimental data. However, even with a substantial amount of experimental data supported by some prior knowledge, existing inference methods often focus on a small sample of admissible candidate models only. RESULTS: We propose Boolean network sketches as a new formal instrument for the inference of Boolean networks. A sketch integrates (typically partial) knowledge about the network's topology and the update logic (obtained through, e.g. a biological knowledge base or a literature search), as well as further assumptions about the properties of the network's transitions (e.g. the form of its attractor landscape), and additional restrictions on the model dynamics given by the measured experimental data. Our new BNs inference algorithm starts with an 'initial' sketch, which is extended by adding restrictions representing experimental data to a 'data-informed' sketch and subsequently computes all BNs consistent with the data-informed sketch. Our algorithm is based on a symbolic representation and coloured model-checking. Our approach is unique in its ability to cover a broad spectrum of knowledge and efficiently produce a compact representation of all inferred BNs. We evaluate the method on a non-trivial collection of real-world and simulated data. AVAILABILITY AND IMPLEMENTATION: All software and data are freely available as a reproducible artefact at https://doi.org/10.5281/zenodo.7688740.

Rule-based modelling of biological systems using regulated rewriting.

In systems biology, models play a crucial role in understanding studied systems. There are many modelling approaches, among which rewriting systems provide a framework for describing systems on a mechanistic level. Describing biochemical processes often requires incorporating knowledge on an abstract level to simplify the system description or substitute the missing details. For this purpose, we present regulation mechanisms, an extension of this formalism with additional controls on the rewriting process. We introduce several regulation mechanisms and apply them to a rule-based language, a notation suitable for modelling biological phenomena. Finally, we demonstrate the usage of such regulations on several case studies from the biochemical domain.

Temporary and permanent control of partially specified Boolean networks.

Boolean networks (BNs) are a well-accepted modelling formalism in computational systems biology. Nevertheless, modellers often cannot identify only a single BN that matches the biological reality. The typical reasons for this is insufficient knowledge or a lack of experimental data. Formally, this uncertainty can be expressed using partially specified Boolean networks (PSBNs), which encode the wide range of network candidates into a single structure. In this paper, we target the control of PSBNs. The goal of BN control is to find perturbations which guarantee stabilisation of the system in the desired state. Specifically, we consider variable perturbations (gene knock-out and over-expression) with three types of application time-window: one-step, temporary, and permanent. While the control of fully specified BNs is a thoroughly explored topic, control of PSBNs introduces additional challenges that we address in this paper. In particular, the unspecified components of the model cause a significant amount of additional state space explosion. To address this issue, we propose a fully symbolic methodology that can represent the numerous system variants in a compact form. In fully specified models, the efficiency of a perturbation is characterised by the count of perturbed variables (the perturbation size). However, in the case of a PSBN, a perturbation might work only for a subset of concrete BN models. To that end, we introduce and quantify perturbation robustness. This metric characterises how efficient the given perturbation is with respect to the model uncertainty. Finally, we evaluate the novel control methods using non-trivial real-world PSBN models. We inspect the method's scalability and efficiency with respect to the size of the state space and the number of unspecified components. We also compare the robustness metrics for all three perturbation types. Our experiments support the hypothesis that one-step perturbations are significantly less robust than temporary and permanent ones.

AEON.py: Python library for attractor analysis in asynchronous Boolean networks.

SUMMARY: AEON.py is a Python library for the analysis of the long-term behaviour in very large asynchronous Boolean networks. It provides significant computational improvements over the state-of-the-art methods for attractor detection. Furthermore, it admits the analysis of partially specified Boolean networks with uncertain update functions. It also includes techniques for identifying viable source-target control strategies and the assessment of their robustness with respect to parameter perturbations. AVAILABILITY AND IMPLEMENTATION: All relevant results are available in Supplementary Materials. The tool is accessible through https://github.com/sybila/biodivine-aeon-py. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Exploring attractor bifurcations in Boolean networks.

BACKGROUND: Boolean networks (BNs) provide an effective modelling formalism for various complex biochemical phenomena. Their long term behaviour is represented by attractors-subsets of the state space towards which the BN eventually converges. These are then typically linked to different biological phenotypes. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a methodology for analysing bifurcations in asynchronous parametrised Boolean networks. RESULTS: In this paper, we propose a computational framework employing advanced symbolic graph algorithms that enable the analysis of large networks with hundreds of Boolean variables. To visualise the results of this analysis, we developed a novel interactive presentation technique based on decision trees, allowing us to quickly uncover parameters crucial to the changes in the attractor landscape. As a whole, the methodology is implemented in our tool AEON. We evaluate the method's applicability on a complex human cell signalling network describing the activity of type-1 interferons and related molecules interacting with SARS-COV-2 virion. In particular, the analysis focuses on explaining the potential suppressive role of the recently proposed drug molecule GRL0617 on replication of the virus. CONCLUSIONS: The proposed method creates a working analogy to the concept of bifurcation analysis widely used in kinetic modelling to reveal the impact of parameters on the system's stability. The important feature of our tool is its unique capability to work fast with large-scale networks with a relatively large extent of unknown information. The results obtained in the case study are in agreement with the recent biological findings.

Executable biochemical space for specification and analysis of biochemical systems.

Computational systems biology provides multiple formalisms for modelling of biochemical processes among which the rule-based approach is one of the most suitable. Its main advantage is a compact and precise mechanistic description of complex processes. However, state-of-the-art rule-based languages still suffer several shortcomings that limit their use in practice. In particular, the elementary (low-level) syntax and semantics of rule-based languages complicate model construction and maintenance for users outside computer science. On the other hand, mathematical models based on differential equations (ODEs) still make the most typical used modelling framework. In consequence, robust re-interpretation and integration of models are difficult, thus making the systems biology paradigm technically challenging. Though several high-level languages have been developed at the top of rule-based principles, none of them provides a satisfactory and complete solution for semi-automated description and annotation of heterogeneous biophysical processes integrated at the cellular level. We present the second generation of a rule-based language called Biochemical Space Language (BCSL) that combines the advantages of different approaches and thus makes an effort to overcome several problems of existing solutions. BCSL relies on the formal basis of the rule-based methodology while preserving user-friendly syntax of plain chemical equations. BCSL combines the following aspects: the level of abstraction that hides structural and quantitative details but yet gives a precise mechanistic view of systems dynamics; executable semantics allowing formal analysis and consistency checking at the level of the language; universality allowing the integration of different biochemical mechanisms; scalability and compactness of the specification; hierarchical specification and composability of chemical entities; and support for genome-scale annotation.

Robustness analysis of stochastic biochemical systems.

We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.

On parameter synthesis by parallel model checking.

An important problem in current computational systems biology is to analyze models of biological systems dynamics under parameter uncertainty. This paper presents a novel algorithm for parameter synthesis based on parallel model checking. The algorithm is conceptually universal with respect to the modeling approach employed. We introduce the algorithm, show its scalability, and examine its applicability on several biological models.

E-photosynthesis: web-based platform for modeling of complex photosynthetic processes.

E-photosynthesis framework is a web-based platform for modeling and analysis of photosynthetic processes. Compared to its earlier version, the present platform employs advanced software methods and technologies to support an effective implementation of vastly diverse kinetic models of photosynthesis. We report on the first phase implementation of the tool new version and demonstrate the functionalities of model visualization, presentation of model components, rate constants, initial conditions and of model annotation. The demonstration also includes export of a model to the Systems Biology Markup Language format and remote numerical simulation of the model.

High-performance analysis of biological systems dynamics with the DiVinE model checker.

The current interest in systems biology is to gain a better understanding of how the complex dynamic behaviour of the cell emerges from mutual interactions of molecular species. When solving such a nontrivial goal, biological data have to be necessarily integrated with mathematical modelling and computer analysis. Since the key aspect of biological modelling is based on unifying several kinds of data captured in terms of large-scale biological networks, scalable and automatized methods are necessary to obtain novel predictions and understanding. In this review, we provide a brief description of the tool DiVinE adapted for automatized analysis of biological systems dynamics. The tool employs high-performance computing techniques to enable analysis of large models.