David Šafránek

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.

Exploring parameter space of stochastic biochemical systems using quantitative model checking

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 parameter space, returns the quantitative model checking result for the respective continuous time Markov chain. Since the parameter space is in principle dense, it is infeasible to compute the landscape function directly. Hence, we design an effective method that iteratively approximates the lower and upper bounds of the landscape function with respect to a given accuracy. To this end, we modify the standard uniformization technique and introduce an iterative parameter space decomposition. We also demonstrate our approach on two biologically motivated case studies.

Model Checking of Biological Systems

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 case studies that demonstrate the use of model checking in computational systems biology. The primary aim is to give a reference for further reading.

STL*: Extending signal temporal logic with signal-value freezing operator

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 properties important in biology. In this paper we introduce the extended logic STL* in which STL is augmented with a signal-value freezing operator allowing to express (and distinguish) various dynamic aspects of oscillations. This operator may be nested for further increase of expressiveness. The logic is supported by a monitoring algorithm prototyped in Matlab for the fragment that avoids nesting of the freezing operator. The monitoring procedure for STL* is evaluated on a sample oscillatory signal with varied parameters. Application of the extended logic is demonstrated on a case study of a biological oscillator. We also discuss expressive power of STL with respect to STL*.

Parameter Identification and Model Ranking of Thomas Networks

We propose a new methodology for identification and analysis of discrete gene networks as defined by Rene 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 improved technique of coloured LTL model checking performing efficiently on Thomas networks in distributed environment; (ii) we introduce classification of acceptable parametrizations to identify most optimal ones; (iii) we propose two ways of visualising parametrizations dynamics wrt time-series data. Finally, computational efficiency is evaluated and the methodology is validated on bacteriophage λ case study.

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.

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 Expressing and Monitoring Oscillatory Dynamics

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 expressive enough to sufficiently distinguish oscillatory properties important in biology. In this paper we define the extended logic STL* in which STL is augmented with a signal-value freezing operator allowing us to express (and distinguish) detailed properties of biological oscillations. The logic is supported by a monitoring algorithm prototyped in Matlab. The monitoring procedure of STL* is evaluated on a biologically-relevant case study.

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.

Parameter Synthesis by Parallel Coloured CTL Model Checking

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 scalability of our approach and demonstrate its applicability in the case study of a genetic switch controlling decisions in the cell cycle.