Jana Fabriková

BioDiVinE: A Framework for Parallel Analysis of Biological Models

In this paper a novel tool BioDiVinE for parallel analysis of biological models is presented. The tool allows analysis of biological models specified in terms of a set of chemical reactions. Chemical reactions are transformed into a system of multi-affine differential equations. BioDiVinE employs techniques for finite discrete abstraction of the continuous state space. At that level, parallel analysis algorithms based on model checking are provided. In the paper, the key tool features are described and their application is demonstrated by means of a case study.

On algorithmic analysis of transcriptional regulation by LTL model checking

Studies of cells in silico can greatly reduce the need for expensive and prolonged laboratory experimentation. The use of model checking for the analysis of biological networks has attracted much attention recently. The practical limitations are still the size of the model, and the time needed to generate the state space. This paper is focused on the model checking approach for analysis of piecewise-linear deterministic models of genetic regulatory networks. Firstly, the qualitative simulation algorithm of de Jong et al. that builds the heart of Genetic Network Analyzer (GNA) is revisited and its time complexity is studied in detail. Secondly, a novel algorithm that reduces the state space generation time is introduced. The new algorithm is developed as an abstraction of the original GNA algorithm. Finally, a fragment of linear time temporal logic for which the provided abstraction is conservative is identified. Efficiency of the new algorithm when implemented in the parallel model checking environment is demonstrated on a set of experiments performed on randomly modified biological models. In general, the achieved results bring a new insight into the field of qualitative simulation emerging in the context of systems biology.

Robustness Analysis for Value-Freezing Signal Temporal Logic

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 is implemented in the tool Parasim. Application of STL* robustness analysis is demonstrated on case studies.

Abstraction of Biochemical Reaction Systems on Polytopes

Analysis of the dynamic behavior of large-scale biochemical reaction systems can be facilitated by abstraction followed by model checking. A biochemical reaction system can be approximated by a multi-affine system or an affine system on a rectangle. Either of these systems can be abstracted to an automaton. Model checking can then be employed to determine whether the dynamic behavior of the automaton satisfies specific properties. A relation between the system and its abstraction is proved; it is an over-approximation: any discrete state trajectory of the abstraction of the continuous state trajectory is contained in the automaton but the automaton may contain more behavior.

ϵ-Semantics computations on biological systems☆

Abstract The assumption of being able to perform infinite precision measurements does not only lead to undecidability, but it also introduces artifacts in the mathematical models that do not correspond to observable behaviours of systems under study. When bounded spatial regions are involved, such issues can be avoided if arbitrarily small sets of points are not definable in the mathematical setting. ϵ -semantics were introduced in this spirit. In this paper we investigate the use of ϵ -semantics deeper, in the context of reachability analysis of hybrid automata. In particular, we focus on two ϵ -semantics and reason about their computability. We then try our approach on biological model analysis to give evidence about the effectiveness of the methodology.

Reachability in Biochemical Dynamical Systems by Quantitative Discrete Approximation (extended abstract)

In this paper a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect the imposed level of approximation provided that with increasing parameter value the approximation converges to the original continuous system. By employing this approximation technique, we present algorithms solving the reachability problem for biochemical dynamical systems. The presented method and algorithms are evaluated on several exemplary biological models and on a real case study. This is a full version of the paper published in the proceedings of CompMod 2011.

On approximative reachability analysis of biochemical dynamical systems

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 granularity the approximation of behaviour between a discrete state and its successor converges to the behaviour of the original continuous system in the respective part of the phase space. This paper provides a detailed description of the method and algorithms solving the reachability problem in biochemical dynamical systems. The method is supplemented with heuristics for reducing the cardinality of the reachable state space. The algorithms are evaluated on six models (with numbers of variables ranging from 2 to 12).