Pennisi Marzio, Cavalieri Salvatore, Motta Santo, Pappalardo Francesco
Department of Mathematics and Computer Science, University of Catania, Catania, Italy.
Department of Electrical Electronic and Computer Engineering (DIEEI), University of Catania, Catania, Italy.
BMC Bioinformatics. 2016 Dec 22;17(Suppl 19):498. doi: 10.1186/s12859-016-1361-6.
Mathematical 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.
We 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.
The 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.
数学和计算模型已被证明是理解免疫系统对病原体反应的非常重要的支持工具。模型和模拟有助于研究免疫系统行为，检验关于疾病和感染动态的生物学假设，并改进和优化新型及现有药物与疫苗。连续模型主要基于微分方程，通常能对系统进行定性研究，但描述不够细致；相反，离散模型，如基于主体的模型和细胞自动机，虽能详细描述实体属性，却失去了大多数定性分析的可能性。Petri网（PN）是一种用于对分布式系统中的并发和同步进行建模的图形化建模工具。由于多年来引入了许多特性和扩展，从而催生了“高级”PN，其应用也日益显著。
我们提出了一种基于高级PN，特别是有色Petri网（CPN）的新颖方法，可用于在细胞尺度上对免疫系统反应进行建模。为证明该方法的潜力，我们提供了一个体液免疫系统反应的简单模型，该模型能够重现适应性反应中一些最复杂的著名特征，如记忆和特异性特征。
我们提出的方法兼具基于连续和离散模型的两种经典方法的优点，因为它既能在描述细胞行为时获得良好的粒度水平，又不会失去进行定性分析的可能性。此外，基于CPN提出的方法允许生命科学家采用他们在对信号通路进行建模时熟知的相同图形化建模技术。最后，这种方法可能为实现多尺度模型打开大门，这些模型整合了基于相同技术和软件构建的信号通路（细胞内）模型和细胞（群体）模型。
