Exploiting Stochastic Petri Net formalism to capture the Relapsing Remitting Multiple Sclerosis variability under Daclizumab administration It is well known that the response of individuals to disease varies, either because of unpredictable exogenous events, such as possibly unknown environmental effects, or just because of endogenous factors, i.e. different genetic background. In particular, when a treatment effectiveness has to be validated, the individual variability should be taken into account by exploiting stochastic models. Relapsing Remitting Multiple Sclerosis (RRMS) is an unpredictable and complex disease, whose random behaviour perfectly fits the study with stochastic models. RRMS is the most common form of Multiple Sclerosis (MS), an immunemediated inflammatory disease of the central nervous system, characterized by alternate episodes of symptom exacerbation (relapses) with periods of disease stability (remission). Several treatments were proposed to contrast the disease progression. Among these, Daclizumab initially exhibited promising results. However, due to the risk of serious side effects the treatment has been retired. We propose a stochastic and an hybrid extension, based on a generalization of the high level Petri Net formalism, of an existing model of Daclizumab effects on RRMS. The model is developed to investigate the complex mechanisms and unpredictable behaviour characterizing the RRMS disease and its relapsing, especially under the Daclizumab administration.

Stochastic Petri Net Models for the Study of Macrophage Reprogramming In recent years, Petri nets are being used for modeling complex biological systems. Examples include the modeling of biochemical reactions, protein interaction networks, gene regulation networks and the immune system. In this work, Petri nets are used to model the innate immune response to a bacterial infection. The objective of this work is to study how changes in macrophage phenotype impact the regulation and resolution of the immune response. From simulations performed, we have observed that the conversion between a M1 proinflammatory phenotype to a M2 regulatory phenotype during an inflammatory response is an important process to avoid a state of persistent inflammation.