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，既有能力解释行为和机制，也有能力预测系统在不同条件下的行为。这种方法是系统生物学的核心，它试图通过对生物系统的组成部分之间的相互作用进行建模来理解生物系统，是生命科学中的一门重要学科。多尺度建模是解决在多个尺度上，特别是在多个空间和(或)时间尺度上具有重要特征的物理问题的领域。在这项提案中，我们将重点放在空间方面，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成熟的符号，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。作为图形形式主义的结果的直观可视化得到了一套丰富的复杂分析技术的补充，这些技术由可靠的工具支持。当前建模方法的一个缺点是它们局限于相对较小的网络。生物系统可以被表示为网络，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，从细胞内到细胞间和细胞外(组织、器官等)。尽管网络模型可以使用标准的PETRI网来设计，但到目前为止还不支持这种结构，随着要建模的网络的规模的增加，它变得不实用。除了纯粹的技术方面，由于处理大型平面网的不切实际，人类在他们正在设计的东西中需要一些等级和组织，以便能够概念化建模的对象。因此，模型应该清楚地反映复杂生物系统中的组织结构。层次结构的Petri网重用了成熟的工程原理--层次分解来管理大规模系统的设计。子网络被隐藏为宏节点中的构建块，而对整个网络的理解建立在对所有构建块及其接口的互连的理解之上。有色Petri网允许以简洁和有理有据的方式描述相似的网络结构，为网络设计者提供了一种灵活的模板机制。在有色Petri网中，可以通过颜色来区分令牌。这允许区分物种(分子、代谢物、蛋白质、次生物质、基因等)。此外，颜色还可以用来区分不同位置(细胞质、细胞核等)的物种亚群。尽管分层和有色Petri网已被广泛应用于技术系统的建模，但到目前为止，这两种方法在系统生物学中都没有流行起来。它们的结合是非常强大的，但到目前为止还没有在任何应用领域得到系统的探索。具体地说，这个项目的目标是开发一种方法，通过使用一种新的集成的层次和颜色组合来支持大型和复杂的生物系统的建模，这有望在研究生化网络行为的空间方面特别有用，例如细胞内和细胞间的通信。我们对这一领域的具体贡献将是发展一种适当的方法，以支持为这种复杂的生物系统设计健壮和有用的模型的过程。

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.