Franck Delaplace

Kamila Barylska, Franck Delaplace, Anna Gogolińska et al.

Diabetes is a civilization chronic disease characterized by a constant elevated concentration of glucose in the blood. Many processes are involved in the glucose regulation, and their interactions are very complex. To better understand those processes we set ourselves a goal to create a Petri net model of the glucose regulation in the whole body. So far we have managed to create a model of glycolysis and synthesis of glucose in the liver, and the general overview models of the glucose regulation in a healthy and diabetic person. In this paper we introduce Petri nets models of insulin secretion in beta cell of the pancreas, and glucagon in the pancreas alpha cells. Those two hormones have mutually opposite effects: insulin preventing hyperglycemia, and glucagon preventing hypoglycemia. Understanding the mechanisms of insulin and glucagon secretion constitutes the basis for understanding diabetes. We also present a model in which both processes occur together, depending on the blood glucose level. The dynamics of each model is analysed. Additionally, we transform the overall insulin and glucagon secretion system to a Boolean network, following standard transformation rules.

Sara Sadat Aghamiri, Franck Delaplace

Recent developments in Omics-technologies revolutionized the investigation of biology by producing molecular data in multiple dimensions and scale. This breakthrough in biology raises the crucial issue of their interpretation based on modelling. In this undertaking, network provides a suitable framework for modelling the interactions between molecules. Basically a Biological network is composed of nodes referring to the components such as genes or proteins, and the edges/arcs formalizing interactions between them. The evolution of the interactions is then modelled by the definition of a dynamical system. Among the different categories of network, the Boolean network offers a reliable qualitative framework for the modelling. Automatically synthesizing a Boolean network from experimental data therefore remains a necessary but challenging issue. In this study, we present taboon, an original work-flow for synthesizing Boolean Networks from biological data. The methodology uses the data in the form of Boolean profiles for inferring all the potential local formula inference. They combine to form the model space from which the most truthful model with regards to biological knowledge and experiments must be found. In the taboon work-flow the selection of the fittest model is achieved by a Tabu-search algorithm. taboon is an automated method for Boolean Network inference from experimental data that can also assist to evaluate and optimize the dynamic behaviour of the biological networks providing a reliable platform for further modelling and predictions.

Franck Delaplace, Cinzia Di Giusto, Jean-Louis Giavitto et al.

ANDy , Activity Networks with Delays, is a discrete time framework aimed at the qualitative modelling of time-dependent activities. The modular and concise syntax makes ANDy suitable for an easy and natural modelling of time-dependent biological systems (i.e., regulatory pathways). Activities involve entities playing the role of activators, inhibitors or products of biochemical network operation. Activities may have given duration, i.e., the time required to obtain results. An entity may represent an object (e.g., an agent, a biochemical species or a family of thereof) with a local attribute, a state denoting its level (e.g., concentration, strength). Entities levels may change as a result of an activity or may decay gradually as time passes by. The semantics of ANDy is formally given via high-level Petri nets ensuring this way some modularity. As main results we show that ANDy systems have finite state representations even for potentially infinite processes and it well adapts to the modelling of toxic behaviours. As an illustration, we present a classification of toxicity properties and give some hints on how they can be verified with existing tools on ANDy systems. A small case study on blood glucose regulation is provided to exemplify the ANDy framework and the toxicity properties.