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

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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.