Abstract
BackgroundMathematical and computational models showed to be a very important support tool for the comprehension of the immune system response against pathogens. Models and simulations allowed to study the immune system behavior, to test biological hypotheses about diseases and infection dynamics, and to improve and optimize novel and existing drugs and vaccines.Continuous models, mainly based on differential equations, usually allow to qualitatively study the system but lack in description; conversely discrete models, such as agent based models and cellular automata, permit to describe in detail entities properties at the cost of losing most qualitative analyses. Petri Nets (PN) are a graphical modeling tool developed to model concurrency and synchronization in distributed systems. Their use has become increasingly marked also thanks to the introduction in the years of many features and extensions which lead to the born of “high level” PN.ResultsWe propose a novel methodological approach that is based on high level PN, and in particular on Colored Petri Nets (CPN), that can be used to model the immune system response at the cellular scale. To demonstrate the potentiality of the approach we provide a simple model of the humoral immune system response that is able of reproducing some of the most complex well-known features of the adaptive response like memory and specificity features.ConclusionsThe methodology we present has advantages of both the two classical approaches based on continuous and discrete models, since it allows to gain good level of granularity in the description of cells behavior without losing the possibility of having a qualitative analysis. Furthermore, the presented methodology based on CPN allows the adoption of the same graphical modeling technique well known to life scientists that use PN for the modeling of signaling pathways. Finally, such an approach may open the floodgates to the realization of multi scale models that integrate both signaling pathways (intra cellular) models and cellular (population) models built upon the same technique and software.
Highlights
Memory B cells will live longer and Results and discussion Immune responses are specific for distinct antigens that are recognized by individual lymphocytes
Even if Petri Nets (PN) have been initially used by computer science and engineering theoreticians only, thanks to the introduction of many extensions of the PN framework, PN have been successfully applied in many other fields, e.g., for the modeling of biochemical pathways
Their initial application to the modeling of the immune system response has been taken into account
Summary
For some scenarios it is requested to model the introduction of new entities at a given time, for example to reproduce the injection of a given treatment or compound. If such situation holds, it is possible to substitute the simple (stochastic) transition with a scheduled transition that allows the definition of an initial time, period, and final time of activation of the transition. Petri Nets (PN) are a graphical modeling tool developed to model concurrency and synchronization in distributed systems Their use has become increasingly marked thanks to the introduction in the years of many features and extensions which lead to the born of “high level” PN. There are as many stimulated lymphocytes as determinants forming the antigen
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