David Šafránek

Masaryk University | MUNI · Faculty of Informatics

Background Stochastic models are commonly employed in the system and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. Many important models feature complex dynamics, involving a state-space explosion, stiffness, and multimodality, that complicate the quantitative ana...

Background: Stochastic models are commonly employed in the system and synthetic biology to study the effectsof stochastic fluctuations emanating from reactions involving species with lowcopy-numbers. Many important models feature complex dynamics, involving a state-space explosion, stiffness, and multimodality, that complicate the quantitative anal...

In this white paper, we describe the founding of a new ELIXIR Community - the Systems Biology Community - and its proposed future contributions to both ELIXIR and the broader community of systems biologists in Europe and worldwide. The Community believes that the infrastructure aspects of systems biology - databases, (modelling) tools and standards...

Stochastic population models are widely used to model phenomena in different areas such as cyber-physical systems, chemical kinetics, collective animal behaviour, and beyond. Quantitative analysis of stochastic population models easily becomes challenging due to the combinatorial number of possible states of the population. Moreover, while the mode...

Partially specified Boolean networks (PSBNs) represent a promising framework for the qualitative modelling of biological systems in which the logic of interactions is not completely known. Phenotype control aims to stabilise the network in states exhibiting specific traits.In this paper, we define the phenotype control problem in the context of asy...

Recent developments in both computational analysis and data-driven synthesis enable a new era of automated reasoning with logical models (Boolean networks in particular) in systems biology. However, these advancements also motivate an increased focus on quality control and performance comparisons between tools. At the moment, to illustrate real-wor...

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 dat...

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 subs...

In this white paper, we describe the founding of a new ELIXIR Community - the Systems Biology Community - and its proposed future contributions to both ELIXIR and the broader community of systems biologists in Europe and worldwide. The Community believes that the infrastructure aspects of systems biology - databases, (modelling) tools and standards...

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 specif...

Honeybees protect their colony against vertebrates by mass stinging and they coordinate their actions during this crucial event thanks to an alarm pheromone carried directly on the stinger, which is therefore released upon stinging. The pheromone then recruits nearby bees so that more and more bees participate in the defence. However, a quantitativ...

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 includ...

eBCSgen is a software tool for developing and analysing models written in Biochemical Space Language (BCSL). BCSL is a rule-based language designed for the description of biological systems with rewriting rules in the form of behavioural patterns. This tool paper describes a new version of the tool, implementing the support for regulations, a mecha...

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...

Edge-coloured directed graphs provide an essential structure for modelling and analysis of complex systems arising in many scientific disciplines (e.g. feature-oriented systems, gene regulatory networks, etc.). One of the fundamental problems for edge-coloured graphs is the detection of strongly connected components, or SCCs. The size of edge-colou...

Regulatory networks (RNs) are a well-accepted modelling formalism in computational systems biology. The control of RNs is currently receiving a lot of attention because it provides a computational basis for cell reprogramming -- an attractive technology developed in regenerative medicine. By solving the control problem, we learn which parts of a bi...

Polyhydroxyalkanoates (PHA) are microbial polyesters produced by numerous prokaryotes. These materials are generally considered to be renewable and biodegradable alternatives to petrochemical polymers in numerous applications. PHA are accumulated by microbial cells in form of intracellular granules primarily as storage compounds; nevertheless, nume...

This technical report relates Biochemical Space Language (BCSL) to Multiset rewriting systems (MRS). For a BCSL model, the semantics are defined in terms of transition systems, while for an MRS, they are defined in terms of a set of runs. In this report, we relate BCSL to MRS by first showing how the transition system is related to a set of runs an...

We present a tool for inferring the parameters of a Discrete-time Markov chain (DTMC) with respect to properties written in probabilistic temporal logic (PCTL) informed by data observations. The tool combines, in a modular and user-friendly way, the existing methods and tools for parameter synthesis of DTMCs. On top of this, the tool implements sev...

Multiset rewriting systems provide a formalism particularly suitable for the description of biological systems. We present an extension of this formalism with additional controls on the derivations as a tool for reducing possible non-deterministic behaviour by providing additional knowledge about the system. We introduce several regulation mechanis...

Aeon is a recent tool which enables efficient analysis of long-term behaviour of asynchronous Boolean networks with unknown parameters. In this tool paper, we present a novel major release of Aeon (Aeon 2021) which introduces substantial new features compared to the original version. These include (i) enhanced static analysis functionality that ver...

Edge-coloured directed graphs provide an essential structure for modelling and computing complex problems arising in many scientific disciplines. The size of edge-coloured graphs appearing in practice can be enormous in the number of both vertices and colours. An important fundamental problem that needs to be solved over edge-coloured graphs is det...

Detection of bottom strongly connected components (BSCC) in state-transition graphs is an important problem with many applications, such as detecting recurrent states in Markov chains or attractors in dynamical systems. However, these graphs’ size is often entirely out of reach for algorithms using explicit state-space exploration, necessitating al...

Today, academic researchers benefit from the changes driven by digital technologies and the enormous growth of knowledge and data, on globalisation, enlargement of the scientific community, and the linkage between different scientific communities and the society. To fully benefit from this development, however, information needs to be shared openly...

Boolean network (BN) is a simple model widely used to study complex dynamic behaviour of biological systems. Nonetheless, it might be difficult to gather enough data to precisely capture the behavior of a biological system into a set of Boolean functions. These issues can be dealt with to some extent using parametrised Boolean networks (ParBNs), as...

Problems arising in many scientific disciplines are often modelled using edge-coloured directed graphs. These can be enormous in the number of both vertices and colours. Given such a graph, the original problem frequently translates to the detection of the graph’s strongly connected components, which is challenging at this scale. We propose a new,...

Today, academic researchers benefit from the changes driven by digital technologies and the enormous growth of knowledge and data, on globalisation, enlargement of the scientific community, and the linkage between different scientific communities and the society. To fully benefit from this development, however, information needs to be shared openly...

Digital bifurcation analysis is a new algorithmic method for exploring how the behavior of a parameter-dependent discrete system varies with a change in its parameters and, in particular, for the identification of bifurcation points where such variation becomes dramatic. We have developed the method in an analogy with the traditional bifurcation th...

We consider the parameter synthesis problem for multi-affine hybrid systems and properties specified using a hybrid extension of CTL (HCTL). The goal is to determine the sets of parameter valuations for which the given hybrid system satisfies the desired HCTL property. As our main contribution, we propose a shared-memory parallel algorithm which ef...

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...

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 with existing solutions. The key aspect of the language is the level of abstraction it uses, which allows scalable and compact hierarchical spec...

Boolean network (BN) is a simple model widely used to study complex dynamic behaviour of biological systems. Nonetheless, it might be difficult to gather enough data to precisely capture the behavior of a biological system into a set of Boolean functions. These issues can be dealt with to some extent using parametrised Boolean networks (ParBNs), as...

eBCSgen is a tool for development and analysis of models written in Biochemical Space Language (BCSL). BCSL is a rule-based language for biological systems designed to combine compact description with a specific level of abstraction which makes it accessible to users from life sciences. Currently, eBCSgen represents the only tool completely support...

We introduce the Quantitative Biochemical Space Language, a rule-based language for a compact modelling of probabilistic behaviour of complex parameter-dependent biological systems. Application of rules is governed by an associated parametrised rate function, expressing partially known information about the behaviour of the modelled system. The par...

Boolean networks (BNs) provide an effective modelling tool for various phenomena from science and engineering. Any long-term behaviour of a BN eventually converges to a so-called attractor. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a tool for...

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 with existing solutions. The key aspect of the language is the level of abstraction it uses, which allows scalable and compact hierarchical spec...

In our previous work, we designed and implemented a synthetic metabolic pathway for 1,2,3-trichloropropane (TCP) biodegradation in Escherichia coli. Significant effects of metabolic burden and toxicity exacerbation were observed on single cell and population levels. Deeper understanding of mechanisms underlying these effects is extremely important...

We propose a novel approach to parameter synthesis for parametrised Kripke structures and CTL specifications. In our method, we suppose the parametrisations form a semi-algebraic set and we utilise a symbolic representation using the so-called cylindrical algebraic decomposition of corresponding multivariate polynomials. Specifically, we propose a...

Parametrised models of dynamical systems arise in various areas of science. In this work, we focus on models described as parametrised Kripke structures with properties formulated in a hybrid extension of the Computation Tree Logic. Our goal is to identify all the parametrisations under which the given model satisfies the properties. To that end, w...

Boolean networks offer an elegant way to model the behaviour of complex systems with positive and negative feedback. The long-term behaviour of a Boolean network is characterised by its attractors. Depending on various logical parameters, a Boolean network can exhibit vastly different types of behaviour. Hence, the structure and quality of attracto...

Population models are widely used to model different phenomena: animal collectives such as social insects, flocking birds, schooling fish, or humans within societies, as well as molecular species inside a cell, cells forming a tissue. Animal collectives show remarkable self-organisation towards emergent behaviours without centralised control. Quant...

In our previous work, we have introduced an extension of signal temporal logic called STL* that allows expressing freezing of values referred within temporal operators. The extension is important especially to express several aspects of signals that cannot be expressed in plain STL (e.g., presence of local extremes and their mutual relationships, n...

Stochastic population models are widely used to model phenomena in different areas such as chemical kinetics or collective animal behaviour. Quantitative analysis of stochastic population models easily becomes challenging, due to the combinatorial propagation of dependencies across the population. The complexity becomes especially prominent when mo...

Formal verification techniques together with other computer science formal methods have been recently tailored for applications to biological and biomedical systems. In contrast to traditional simulation-based approaches, model checking opens an entirely novel way of viewing and analysing the dynamics of such systems. In particular, it can help in...

Formal analysis of non-linear continuous and hybrid systems is a hot topic. A common approach builds on computing a suitable finite discrete abstraction of the continuous system. In this paper, we propose a facetal abstraction which eliminates certain drawbacks of existing abstractions. The states of our abstraction are built primarily from facets...

Digital bifurcation analysis is a new algorithmic method for exploring how the behaviour of a parameter-dependent computer system varies with a change in its parameters and, in particular, for identification of bifurcation points where such variation becomes dramatic. We have developed the method in an analogy with the traditional bifurcation theor...

In systems biology, models of cellular regulatory processes such as gene regulatory networks or signalling pathways are crucial to understanding the behaviour of living cells. Available biological data are however often insufficient for full model specification. In this paper, we focus on partially specified models where the missing information is...

The modelling of discrete regulatory networks combines a graph specifying the pairwise influences between the variables of the system, and a parametrisation from which can be derived a discrete transition system. Given the influence graph only, the exploration of admissible parametrisations and the behaviours they enable is computationally demandin...

Chapters 3, 9 and 10 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Complex behaviour arising in biological systems is typically characterised by various kinds of attractors. An important problem in this area is to determine these attractors. Biological systems are usually described by highly parametrised dynamical models that can be represented as parametrised graphs typically constructed as discrete abstractions...

We present a novel tool for parameter synthesis of piecewise multi-affine dynamical systems from specifications expressed in a hybrid branching-time temporal logic. The tool is based on the algorithm of parallel semi-symbolic coloured model checking that extends standard model checking methods to cope with parametrised Kripke structures. The tool i...

Bifurcation analysis is a central task of the analysis of parameterised high-dimensional dynamical systems that undergo transitions as parameters are changed. The classical numerical and analytical methods are typically limited to a small number of system parameters. In this paper we propose a novel approach to bifurcation analysis that is based on...

Signalling pathways provide a complex cellular information processing machinery that evaluates particular input stimuli and transfers them into the genome by means of regulation of specific genes expression. In this short paper, we provide a preliminary study targeting minimal models representing the topology of main signalling mechanisms. A specia...

We propose a novel scalable parallel algorithm for synthesis of interdependent parameters from CTL specifications for non-linear dynamical systems. The method employs a symbolic representation of sets of parameter valuations in terms of the first-order theory of the reals. To demonstrate its practicability, we apply the method to a class of piecewi...

Biochemical Space (BCS) has been introduced as a semi-formal notation for reaction networks of biological processes. It provides a concise mapping of mathematical models to their biological description established at a desired level of abstraction. In this paper, we first turn BCS into a completely formal language with rigorously defined semantics...

E-cyanobacterium.org is an online platform providing tools for public sharing, annotation, analysis, and visualization of dynamical models and wet-lab experiments related to cyanobacteria. The platform is unique in integrating abstract mathematical models with a precise consortium-agreed biochemical description provided in a rule-based formalism. T...

Complex behaviour arising in biological systems is described by highly parameterised dynamical models. Most of the parameters are mutually dependent and therefore it is hard and computationally demanding to find admissible parameter values with respect to hypothesised constraints and wet-lab measurements. Recently, we have developed several high-pe...

We propose a new distributed-memory parallel algorithm for parameter synthesis from CTL hypotheses. The algorithm colours the state space transitions by different parameterisations and extends CTL model checking to identify the maximal set of parameters that guarantee the satisfaction of the given CTL property. We experimentally confirm good scalab...

Analysis of equilibria, their stability and instability, is an unavoidable ingredient of model analysis in systems biology. In particular , bifurcation analysis which focuses on behaviour of phase portraits under variations of parameters is of great importance. We propose a novel method for bifurcation analysis that employs coloured model checking...

Traditional mathematical models of photosynthesis are based on mass action kinetics of light reactions. This approach requires the modeller to enumerate all the possible state combinations of the modelled chemical species. This leads to combinatorial explosion in the number of reactions although the structure of the model could be expressed more co...

To express temporal properties of dense-time real-valued signals, the Signal Temporal Logic (STL) has been defined by Maler et al. The work presented a monitoring algorithm deciding the satisfiability of STL formulae on finite discrete samples of continuous signals. The logic is not expressive enough to sufficiently distinguish oscillatory properti...

In this tool paper, we target the problem of unique annotation of organism-specific computational models presented in a public model database. In particular, we present Biochemical Space, a novel annotation methodology accompanied with a set of software tools that allow to create, manage and maintain the Biochemical Space content. The main idea beh...

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...

A Comprehensive Modeling Platform, that is, a general framework for public sharing, annotation, and visualization of domain-specific biological models, is presented. For a selected organism, the framework is instantiated as a web-based application which allows to capture several aspects of biological models represented as biochemical reaction netwo...

This report proposes a novel framework for a rigorous robustness analysis of stochastic biochemical systems. The technique is based on probabilistic model checking. 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 compa...

In our previous work we have introduced the logic STL*, an extension of Signal Temporal Logic (STL) that allows value freezing. In this paper, we define robustness measures for STL* by adapting the robustness measures previously introduced for Metric Temporal Logic (MTL). Furthermore, we present an algorithm for STL* robustness computation, which i...

We propose an automated method for exploring kinetic parameters of stochastic biochemical systems. The main question addressed is how the validity of an a priori given hypothesis expressed as a temporal logic property depends on kinetic parameters. Our aim is to compute a landscape function that, for each parameter point from the inspected paramete...

Model checking together with other formal methods and techniques is being adapted for applications to biological systems. We present a selection of approaches used for modeling biological systems and formalizing their interesting properties in temporal logics. We also give a brief account of high performance model checking techniques and add a few...

In this paper, a work-in-progress aiming at qualitative modelling of photosynthesis at the mechanistic cellular level by means of Petri nets is described. Presented preliminary results concentrate on modelling and analysis of photosystem II, a crucial component of photosynthesis. By employing qualitative model checking combined with invariant analy...

We propose a new methodology for identification and analysis of discrete gene networks as defined by René Thomas, supported by a tool chain: (i) given a Thomas network with partially known kinetic parameters, we reduce the number of acceptable parametrizations to those that fit time-series measurements and reflect other known constraints by an impr...

To express temporal properties of dense-time real-valued signals, the Signal Temporal Logic (STL) has been defined by Maler et al. The work presented a monitoring algorithm deciding the satisfiability of STL formulae on finite discrete samples of continuous signals. The logic has been used to express and analyse biological systems, but it is not ex...

This is an extended version of the workshop paper [1], in which a new computational technique called quantitative discrete approximation has been introduced. The technique provides finite discrete approximation of continuous dynamical systems which is suitable especially for a significant class of biochemical dynamical systems. With decreasing gran...