Indistinguishability analysis for model discrimination in Systems Biology: A Feasibility Study applied to Bacterial Peptidoglycan Biosynthesis

在系统生物学中，所产生的数学/网络模型总是包含大量具有众多参数的变量，其中许多是未知的，或者不能直接测量。对于这种高度复杂的系统，可以进行的直接测量往往很少，而且输入或扰动的访问也很有限。当研究隐藏机制的存在或试图估计未知参数时，这些限制造成了巨大的问题，并且这些问题严重阻碍了模型的验证。因此，非常需要一种正式的方法来确定哪些额外的输入和/或测量是必要的，以减少或消除这些限制，并允许更可靠地推导出可用于实际目的的模型。本项目的目的是确定在系统生物学网络中使用结构不可分辨技术进行模型识别的可能有效性。这是一个重要的问题，即如何设计一个或多个实验，以便在两个(或更多)相互竞争的生物机制之间进行区分。系统模型的结构不可区分性涉及确定模型(或机制)结构的可能候选者之间的唯一性。本项目中执行的分析的形式性质应允许生成最小的一组或多组反应物，这些反应物必须可用于测量，以便区分相互竞争的反应方案。结构可辨识性可以看作是结构不可区分性问题的一个特例，它考虑了来自输入-输出结构的未知模型参数的唯一性，所述输入-输出结构对应于所提出的用于数据收集的实验。如果要使用参数估计为干预或抑制策略或其他关键决策提供信息，则参数必须是唯一可识别的。一旦选择了合适的方案，将进行结构可辨识性分析，这将产生一组类似的反应物，这些反应物必须可用于测量，以保证模型参数相对于测量的响应的唯一性。这项分析将对整个系统的部分进行，这些部分本身可以被视为(亚)系统，然后结果将以一种新的方式组合起来，以测试整个系统的可识别性。这些理论技术将被用于为项目中考虑的案例研究(细菌肽聚糖的生物合成)提供创新的测量形式。了解病例研究的潜在生物学过程对于制定处理抗生素耐药性的新策略至关重要。此外，在案例研究中对未知成分的建模将受到理论分析的结果和从适当的生物学实验中收集的数据的驱动。此外，开发一种新的停流分光光度计将能够在一次反应中从酶底物复合体形成时的荧光变化和产物形成时的吸光度变化中收集同步测量结果。这些新的数据将进一步提供信息和测试模型。这个项目的总体目标将是开发创新的、形式化的和通用的方法来对系统生物学中的模型进行这种分析。该方法将通过应用于样本系统(细菌肽聚糖生物合成)来开发这些通用工具，然后将所获得的结果扩展到更一般的系统模型。

In Systems Biology the mathematical/network models that are generated invariably include large numbers of variables with numerous parameters, many of which are unknown, or cannot be directly measured. With such highly complex systems there are often few direct measurements that can be made and limited access for inputs or perturbations. These limitations cause immense problems when investigating the existence of hidden mechanisms or attempting to estimate unknown parameters and these problems severely hinder validation of the model. It is therefore highly desirable to have a formal approach to determine what additional inputs and/or measurements are necessary in order to reduce, or remove, these limitations and permit the derivation of models that can be used for practical purposes with greater confidence.The purpose of this project is to ascertain the possible effectiveness of using structural indistinguishability techniques in model discrimination within Systems Biology networks. This is the important question of how to design an experiment, or experiments, to allow discrimination between two (or more) competing biological mechanisms. Structural indistinguishability for systems models is concerned with determining the uniqueness between possible candidates for the model (or mechanism) structure. The formal nature of the analysis performed in this project should permit the generation of a minimal set, or sets, of reactants that must be available for measurement in order to distinguish between competing reaction schemes. Structural identifiability can be considered as a special case of the structural indistinguishability problem and considers the uniqueness of the unknown model parameters from the input-output structure corresponding to proposed experiments for data collection. If parameter estimates are to be used to inform intervention or inhibition strategies, or other critical decisions, then it is essential that the parameters be uniquely identifiable. Once an appropriate scheme has been selected, a structural identifiability analysis will be performed, which should generate a similar set of reactants that must be available for measurement in order to guarantee uniqueness of the model parameters with respect to the responses measured. This analysis will be performed on parts of the overall system, that can themselves be considered as (sub)systems, and then the results will be combined in a novel way to test for the identifiability of the complete system.These theoretical techniques will be used to suggest innovative forms of measurement for a case study (Bacterial Peptidoglycan Biosynthesis) considered within the project. Understanding of the underlying biological process for the case study is essential for developing new strategies for dealing with antibiotic resistance. In addition, modelling of the unknown components within the case study will be driven by the results obtained from the theoretical analysis and data collected from appropriate biological experiments. In addition, the development of a new stopped flow spectrophotometer will have the capacity to collect simultaneous measurements, within a single reaction, from fluoresence changes upon formation of the enzyme substrate complex and absorbance changes upon product formation. These novel data will further inform and test the model.The overall aim of this project will be to develop, innovative, formal and generic methods for performing this analysis for models in Systems Biology. The approach will be to develop these generic tools via application to the exemplar system (Bacterial Peptidoglycan Biosynthesis), then to extend the results obtained to more general systems models.