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，既可以解释行为和机制，也可以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，它试图通过模拟生物系统各组成部分之间的相互作用来理解生物系统，是生命科学中的一个关键学科。多尺度建模是解决具有多尺度，特别是多空间和（或）时间尺度特征的物理问题的领域。在本提案中，我们将重点关注空间方面，并将其应用于生物系统。Petri网是描述反应网络的一种自然而成熟的符号，因为它们可以很容易地表示反应和生化成分，具有正式的语义，对生物学家特别有吸引力。直观的可视化是图形形式的结果，由一组丰富的复杂分析技术补充，这些分析技术由可靠的工具支持。包括Petri网在内的当前建模方法的一个缺点是它们对相对较小的网络的限制。生物系统可以表示为网络，其本身通常包含规则（网络）结构和/或网络模式的重复出现。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甚至更远（组织、器官等）。尽管可以使用标准的Petri网来设计网络模型，但到目前为止还没有对这种结构的支持，随着要建模的网络规模的增加，它变得不切实际。除了纯粹的技术方面，由于处理大型平面网的不实用性，人类在设计中需要一些层次和组织，以便能够概念化建模对象。因此，模型应该明确地反映复杂生物系统中的组织。分层Petri网重用了已建立的分层分解的工程原理来管理大型系统的设计。子网络隐藏在宏节点内作为构建块，对整个网络的理解建立在对所有构建块及其接口互连的理解之上。彩色Petri网允许以简洁和有充分根据的方式描述类似的网络结构，为网络设计者提供灵活的模板机制。在彩色Petri网中，可以通过它们的颜色来区分标记。这允许对物种（分子、代谢物、蛋白质、次级物质、基因等）进行区分。此外，颜色可以用来区分一个物种在不同位置（细胞质、细胞核等）的亚种群。尽管分层Petri网和彩色Petri网已经广泛应用于建模技术系统中，但迄今为止，这两种方法的使用在系统生物学中都没有得到普及。它们的组合可能非常强大，但到目前为止还没有在任何应用领域进行系统的探索。具体来说，该项目的目标是通过使用Petri网中层次和颜色的新颖整合组合来开发支持大型复杂生物系统建模的方法，这在研究生物化学网络行为的空间方面特别有帮助，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构建健壮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.