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

在系统生物学中，生成的数学/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，通常很少有可以进行的直接测量，并且对输入或扰动的访问有限。这些限制在研究隐藏机制的存在性或试图估计未知参数时造成了巨大的问题，这些问题严重阻碍了模型的验证。因此，非常需要有一种正式的方法来确定需要哪些额外的输入和/或测量，以减少或消除这些限制，并允许推导出可以更有信心地用于实际目的的模型。该项目的目的是确定在系统生物学网络中使用结构不可区分技术进行模型判别的可能有效性。这是一个重要的问题，即如何设计一个或多个实验，以允许区分两种（或更多）相互竞争的生物机制。系统模型的结构不可区分性与确定模型（或机制）结构的可能候选之间的唯一性有关。在这个项目中进行的分析的正式性质应该允许生成最小的一组或几组反应物，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。结构可识别性可以看作是结构不可区分问题的一种特殊情况，考虑了所提出的实验对应的输入输出结构中未知模型参数的唯一性，用于数据采集。如果参数估计要用于干预或抑制策略，或其他关键决策，那么参数必须是唯一可识别的。一旦选择了合适的方案，将执行结构可识别性分析，该分析应生成一组类似的反应物，这些反应物必须可用于测量，以保证模型参数相对于所测量的响应的唯一性。该分析将在整个系统的部分上执行，这些部分本身可以被视为（子）系统，然后将结果以一种新颖的方式组合起来，以测试整个系统的可识别性。这些理论技术将用于为项目中考虑的案例研究（细菌肽聚糖生物合成）提出创新的测量形式。了解案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，案例研究中未知成分的建模将由理论分析结果和从适当的生物实验中收集的数据驱动。此外，新型止流分光光度计的开发将有能力在单个反应中同时收集酶底物复合物形成时的荧光变化和产物形成时的吸光度变化。这些新数据将进一步为该模型提供信息和检验。该项目的总体目标是开发创新的、正式的和通用的方法来对系统生物学中的模型进行分析。该方法将通过应用于范例系统（细菌肽聚糖生物合成）来开发这些通用工具，然后将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.