Modeling Immune Networks with Petri Nets Bogdan Tanasa 1 and Stefan-Ciprian Tanasa 2 1 Faculty of Medicine, “Gr. T. Popa” University, Iasi, Romania 2 Faculty of Computer Science, “Al. I. Cuza” University, Iasi, Romania Abstract  Multiple immune cell types and soluble mediators interact with each other and form a complex network of interactions.  The interactions give rise to different types of responses with various amplitudes, durations and clinical outcomes.  We consider the immune network that is driven against M. tuberculosis.  We introduce a model of the immune interactions network that is based on coloured Petri nets.  We developed a software system - IMMUNET, that allows computer simulations of the immune responses during disease progression. The Petri nets  A colored Petri net (CPN) is a graphical-oriented language for the design, specification, simulation and verification of systems. It is particularly well-suited for systems in which communication, synchronization and resource sharing are important.  A CPN consists of places, transitions, and arcs that connect them.  Places can contain tokens which represents numbers; the current state of the system is given by the numbers from each place.  Transitions model activities which can occur (the transition fires), thus changing the state of the system. Transitions are only allowed to fire if they are enabled (all the preconditions for the activity must be fulfilled). When the transition fires, it removes tokens from its input places and adds some at all of its output places. The Petri nets model of the immune networks  Petri nets locations: cells (various functional states), molecules (cytokines) and pathogens (bacteria).  Petri nets transitions: proliferation, differentiation, production of antibodies or phagocytosis, secretion of cytokines or induced cell death.  The parameters of the mathematical functions that characterize transitions are obtained from various cytokine assays (cytokine secretion levels, synergy and antagonism parameters), intra- cellular staining and flow cytometry (differentiation parameters), cytotoxicity (parameters for T cell mediated lysis), chemotaxis assays (parameters for cell recruitment) etc. The immune networks In the basal conditions or during the immunological responses, the immune cells communicate with each other either directly (surface molecules) or indirectly (cytokines). Tuberculosis: the second world death leading cause among the infectious diseases (World Health Report 2000). The main players responsible for immunity in TB:  the immune cells (NK, macrophages, CD8, Th1 and Th2)  the cytokines (IFN , IL-4, IL-12, IL-10, TNF  )  the bacteria reside in macrophages (chronically infected macrophages) or within the extra-cellular environment. MR MA MCI Th 1 CD8 Th 0 NK IFN  IL-12 IL-10 EB The software system: IMMUNET Two software systems were used for simulations: Renew (a Petri net simulator: IMMUNET Preliminary results Question: Is IFN-  sufficient to control TB? Discussions and further work The model allows the identification of the key elements that contribute to different disease outcome (latency, active disease, reactivation) and the properties of the cytokine networks (redundancy, pleiotropism). Software tools to check the network properties will be added. The influence of various drugs on disease progression could be tested with IMMUNET. The approach could be extended to other diseases (infectious or autoimmune). Immune and/or non-immune networks may be considered. Model simulation results for M. tuberculosis (extra-cellular bacteria ). Model simulation results for MCI when IFN-  that is secreted byTh1 decreases. The model diagram of the immune interactions The Petri nets model for the (initial) immune interactions