Petri nets for multiscale Systems Biology

生物化学网络的计算建模和分析有助于更好地理解生物系统，既能解释行为和机制，也能预测系统在不同条件下的行为。这些方法是系统生物学的核心，系统生物学试图通过模拟其组成部分的相互作用来理解生物系统，并且是生命科学中的一个关键学科。多尺度建模是解决在多个尺度，特别是多个空间和（或）时间尺度上具有重要特征的物理问题的领域。在本提案中，我们将侧重于空间方面，并将其应用于生物系统。Petri网是描述反应网络的一种自然和既定的符号，因为它们可以很容易地表示反应和生化成分，具有形式化的语义，对生物学家特别有吸引力。图形化的直观可视化是一个结果，是由一组丰富的复杂的分析技术，这是由可靠的工具支持的补充。目前的建模方法，包括Petri网的一个缺点，是他们的局限性相对较小的网络。生物系统可以表示为网络，其本身通常包含规则的（网络）结构和/或重复出现的网络模式。此外，这种组织以分层的方式发生，反映了生物体的物理和空间组织，从细胞内到细胞间水平以及更高水平（组织，器官等）。虽然可以使用标准的Petri网来设计网络模型，但到目前为止，还没有对这种结构化的支持，随着要建模的网络规模的增加，这种结构化变得不切实际。除了纯粹的技术方面，由于处理大型平面网的不切实际性，人类需要一些层次和组织在他们设计的，以便能够概念化的建模对象。因此，模型应该明确地反映复杂生物系统的组织。分层Petri网重用了分层分解的成熟工程原理来管理大规模系统的设计。子网络作为构件隐藏在宏节点中，对整个网络的理解建立在对所有构件及其接口互连的理解之上。有色Petri网允许以简洁和有根据的方式描述类似的网络结构，为网络设计者提供了灵活的模板机制。在有色Petri网中，标记可以通过它们的颜色来区分。这允许区分物种（分子、代谢物、蛋白质、次级物质、基因等）。此外，颜色可以用来区分不同位置（细胞质，细胞核等）的物种亚群。虽然层次和有色Petri网已被广泛部署在建模技术系统，使用这两种方法都没有得到普及，到目前为止，在系统生物学。它们的组合是潜在的非常强大的，但还没有系统地探索到目前为止在任何领域的应用。具体来说，这个项目的目标是开发方法，以支持大型和复杂的生物系统的建模，通过使用一个新的综合组合的层次和颜色的Petri网，这有望是特别有助于调查生化网络行为的空间方面，例如细胞内和细胞间水平的通信。我们对该领域的具体贡献将是开发一种合适的方法，以支持为这种复杂的生物系统设计强大而有用的模型的过程。

Computational modelling and analysis of biochemical networks contribute to a better understanding of biological systems in terms of both the ability to explain behaviours and mechanisms as well as being able to predict the behaviour of a system under different conditions. Such approaches are at the core of Systems Biology, which attempts to understand biological systems by modelling the interaction of their components, and is a crucial discipline in the life sciences. Multiscale modeling is the field of solving physical problems which have important features at multiple scales, particularly multiple spatial and(or) temporal scales. In this proposal, we will focus on spatial aspects, with an application to biological systems. Petri nets are a natural and established notation for describing reaction networks because they can easily represent reactions and biochemical components, have a formal semantics and are particularly attractive to biologists. The intuitive visualization that is a consequence of the graphical formalism is complemented by a rich set of sophisticated analysis techniques, which are supported by reliable tools.A drawback of current modelling approaches, including Petri nets, are their limitation to relatively small networks. Biological systems can be represented as networks which themselves typically contain regular (network) structures, and/or repeated occurrences of network patterns. Moreover, this organisation occurs in a hierarchical manner, reflecting the physical and spatial organisation of the organism, from the intracellular to the intercellular level and beyond (tissues, organs etc.).Although network models can be designed using standard Petri nets, so far there is no support for such structuring, it becomes impractical as the size of the networks to be modelled increases. Besides the purely technical aspect due to the impracticality of handling large flat nets, humans need some hierarchy and organisation in what they are designing in order to be able to conceptualise the modelled object. Thus, models should explicitly reflect the organisation in complex biological systems.Hierarchical Petri nets reuse the well-established engineering principle of hierarchical decomposition to manage the design of large-scale systems. Sub-networks are hidden as building blocks within macro nodes, and the comprehension of the whole network builds upon the understanding of all building blocks and the interconnection of their interfacesColoured Petri nets allow the description of similar network structures in a concise and well-founded way, providing a flexible template mechanism for network designers. In coloured Petri nets, tokens can be distinguished via their colours. This allows for the discrimination of species (molecules, metabolites, proteins, secondary substances, genes, etc.). In addition, colours can be used to distinguish between sub-populations of a species in different locations (cytosol, nucleus and so on). Although Hierarchical and Coloured Petri nets have been extensively deployed in modelling technical systems, the use of neither approach has gained popularity so far in Systems Biology. Their combination is potentially extremely powerful, and but has not been explored systematically so far in any area of application.Specifically, the goal of this project is to develop approaches to support the modelling of large and complex biological systems by the use of a novel integrative combination of hierarchy and colour in Petri nets, which promises to be particularly helpful in investigating spatial aspects of biochemical network behaviour, such as communication at the intra and intercellular levels. Our concrete contribution to the area will be the development of a suitable methodology to underpin the process of engineering robust and useful models for such complex biological systems.