Abstraction-Based Parameter Synthesis for Multiaffine Systems

International audienceMultiaffine hybrid automata (MHA) represent a powerful formalism to model complex dynamical systems. This formalism is particularly suited for the representation of biological systems which often exhibit highly non-linear behavior. In this paper, we consider the problem of parameter identification for MHA. We present an abstraction of MHA based on linear hybrid automata, which can be analyzed by the SpaceEx model checker. This abstraction enables a precise handling of time-dependent properties. We demonstrate the potential of our approach on a model of a genetic regulatory network and a myocyte model

A review of modelling and verification approaches for computational biology

This paper reviews most frequently used computational modelling approaches and formal verification techniques in computational biology. The paper also compares a number of model checking tools and software suits used in analysing biological systems and biochemical networks and verifiying a wide range of biological properties

Benchmark: Nonlinear Hybrid Automata Model of Excitable Cardiac Tissue

Implantable cardiac devices like pacemakers and defibrillators are life-saving medical devices. To verify their functionality, there is a need for heart models that can simulate interesting phenomena and are relatively computationally tractable. In this benchmark we implement a model of the electrical activity in excitable cardiac tissue as a network of nonlinear hybrid automata. The model has previously been shown to simulate fast arrhythmias. The hybrid automata are arranged in a square n-by-n grid and communicate via their voltages. Our Matlab implementation allows the user to specify any size of model $n$, thus rendering it ideal for benchmarking purposes since we can study tool efficiency as a function of size. We expect the model to be used to analyze parameter ranges and network connectivity that lead to dangerous heart conditions. It can also be connected to device models for device verification

Safety verification of nonlinear hybrid systems based on invariant clusters

In this paper, we propose an approach to automatically compute invariant clusters for nonlinear semialgebraic hybrid systems. An invariant cluster for an ordinary differential equation (ODE) is a multivariate polynomial invariant g(u→, x→) = 0, parametric in u→, which can yield an infinite number of concrete invariants by assigning different values to u→ so that every trajectory of the system can be overapproximated precisely by the intersection of a group of concrete invariants. For semialgebraic systems, which involve ODEs with multivariate polynomial right-hand sides, given a template multivariate polynomial g(u→, x→), an invariant cluster can be obtained by first computing the remainder of the Lie derivative of g(u→, x→) divided by g(u→, x→) and then solving the system of polynomial equations obtained from the coefficients of the remainder. Based on invariant clusters and sum-of-squares (SOS) programming, we present a new method for the safety verification of hybrid systems. Experiments on nonlinear benchmark systems from biology and control theory show that our approach is efficient

Computational Techniques for Analysis of Genetic Network Dynamics

In this paper we propose modeling and analysis techniques for genetic networks that provide biologists with insight into the dynamics of such systems. Central to our modeling approach is the framework of hybrid systems and our analysis tools are derived from formal analysis of such systems. Given a set of states characterizing a property of biological interest P, we present the Multi-Affine Rectangular Partition (MARP) algorithm for the construction of a set of infeasible states I that will never reach P and the Rapidly Exploring Random Forest of Trees (RRFT) algorithm for the construction of a set of feasible states F that will reach P. These techniques are scalable to high dimensions and can incorporate uncertainty (partial knowledge of kinetic parameters and state uncertainty). We apply these methods to understand the genetic interactions involved in the phenomenon of luminescence production in the marine bacterium V. fischeri