Model development and simulation of biological networks is recognized as a key task in Systems Biology. Integrated with in vitro and in vivo experimental data, network simulation allows for the discovery of the dynamics that regulate biological systems. Stochastic Petri Nets (SPNs) have become a widespread and reference formalism to model metabolic networks thanks to their natural expressiveness to represent metabolites, reactions, molecule interactions, and simulation randomness due to system fluctuations and environmental noise. In the literature, starting from the network model and the complete set of system parameters, there exist frameworks that allow for dynamic system simulation. Nevertheless, they do not allow for automatic model parameterization, which is a crucial task to identify, in silico, the network configurations that lead the model to satisfy specific temporal properties. To cover such a gap, this work first presents a framework to implement SPN models into SystemC code. Then, it shows how the framework allows for automatic parameterization of the networks. The user formally defines the network properties to be observed and the framework automatically extrapolates, through Assertion-based Verification (ABV), the parameter configurations that satisfy such properties. We present the results obtained by applying the proposed framework to model the complex metabolic network of the purine metabolism. We show how the automatic extrapolation of the system parameters allowed us to simulate the model under different conditions, which led to the understanding of behavioral differences in the regulation of the entire purine network. We also show the scalability of the approach through the modeling and simulation of four biological networks, each one with different structural characteristics.

中文翻译：

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用于生物网络模拟和参数化的随机 Petri 网的 SystemC 实现

生物网络的模型开发和模拟被认为是系统生物学的一项关键任务。网络模拟与体外和体内实验数据相结合，可以发现调节生物系统的动力学。随机 Petri 网 (SPN) 已成为模拟代谢网络的一种广泛和参考的形式，这要归功于它们的自然表现力来表示代谢物、反应、分子相互作用以及由于系统波动和环境噪声引起的模拟随机性。在文献中，从网络模型和完整的系统参数集开始，存在允许动态系统仿真的框架。然而，它们不允许自动模型参数化，这是在计算机上识别的一项关键任务，导致模型满足特定时间属性的网络配置。为了弥补这样的差距，这项工作首先提出了一个将 SPN 模型实现到 SystemC 代码中的框架。然后，它展示了该框架如何允许网络的自动参数化。用户正式定义要观察的网络属性，框架通过基于断言的验证 (ABV) 自动推断满足这些属性的参数配置。我们展示了通过应用所提出的框架来模拟嘌呤代谢的复杂代谢网络所获得的结果。我们展示了系统参数的自动外推如何使我们能够在不同条件下模拟模型，从而了解整个嘌呤网络调节中的行为差异。