# Colloquium of the Department and the PhD Program

## title

*(begins at 16:00 h) Hybrid modelling of biological systems for the accurate analysis of their timing features*

## speaker

Prof. Dr. Olivier Roux, Institut de Recherche en Communications et en Cybernétique de Nantes

Nantes Cedex, France

Nantes Cedex, France

## date & place

Wednesday, 08.07.2009, 16:00 h

Room C 252

Room C 252

## abstract

We want to study complex dynamical biological systems but the knowledge we can have of these systems is weak, and it mainly relies upon observations of their behaviours. For this purpose, models are built according to various approaches, and they are accompanied with many parameters that have to be introduced in order to stand for a priori unknown values. We are mostly involved in the logical modelling approach (a la Ren''e Thomas) where we want to bring in the*temporal dimension*. This leads to a

*hybrid*representation which is much intricate. As a matter of fact, we have to face the problem of dealing with models with a lot of parameters and frequently a rather huge or even sometimes unmanageable number of states. For this reason, we introduce a new approach that avoids the computation of the whole states space.

It applies naturally on Gene Regulatory Networks (GRN) which is one of these biological systems we want to study and we shortly introduce their dynamics, at first. Then, we present a new stochastic PI-calculus framework, namely the

*Process Hitting*. From this framework, we start a sequence of consistent analyses which deal with both

*stochastic*and

*temporal*aspects and reveal important features of the studied biological system.

The first result is that it makes it possible to check

*structural properties*such as the set of stable states, discrete parameters identification, specification of cooperative actions of associated genes for their coordinated interaction, and so on... As a matter of fact, it appears that very large GRNs can now be studied since such a method avoids building the actual states graph. We show that we are able to take into account a regulatory network of at least twenty genes, which means a graph of 266 states! The second stage of our approach consists in benefiting from the ability of using the

*stochastic PI-calculus*in order to execute

*simulations*with stochastic rates. We recall that these rates stand for the time delays for an interaction to take place. This allows us to tune

*stochastic and temporal parameters*so that we can implement temporal properties. We are able to perform these simulations using SPIM, which is an implementation of the stochastic PI-calculus. Furthermore, since the translation of the aforementioned Process Hitting in the language of the probabilistic model-checker PRISM is also very easy, we are able to achieve formal verification of the temporal properties that have emerged from the previous phase of the temporal parameters tuning.

Along the talk, we sketch some elements of our method through a tiny toy example.