Indistinguishability analysis for model discrimination in Systems Biology: A Feasibility Study applied to Bacterial Peptidoglycan Biosynthesis
Lead Research Organisation:
University of Warwick
Department Name: Sch of Engineering
Abstract
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.
Organisations
Publications
Pérez-Velázquez J
(2009)
Indistinguishability and identifiability of kinetic models for the Mur C reaction in peptidoglycan biosynthesis
in IFAC Proceedings Volumes
Chapman J
(2009)
The structural identifiability of susceptible-infective-recovered type epidemic models with incomplete immunity and birth targeted vaccination
in Biomedical Signal Processing and Control
Yates J
(2009)
Structural identifiability analysis via symmetries of differential equations
in Automatica
Hattersley JG
(2011)
Indistinguishability and identifiability of kinetic models for the MurC reaction in peptidoglycan biosynthesis.
in Computer methods and programs in biomedicine
Chapman JD
(2011)
The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies.
in Computer methods and programs in biomedicine
Chin SV
(2011)
Structural identifiability and indistinguishability analyses of the minimal model and a euglycemic hyperinsulinemic clamp model for glucose-insulin dynamics.
in Computer methods and programs in biomedicine
Bearup DJ
(2013)
The input-output relationship approach to structural identifiability analysis.
in Computer methods and programs in biomedicine
| Description | In Systems Biology mathematical models for the interactions between components of biological systems are frequently proposed that include large numbers of variables with numerous parameters, many of which are unknown, or cannot be directly measured. Often with such highly complex systems few of the underlying components can be directly observed or measured, and there is limited access for external inputs into the system, or perturbations of the system. These limitations cause immense problems when investigating the existence of hidden mechanisms, or interactions, or when attempting to estimate the unknown parameters from measurement data. These problems severely hinder validation of proposed models, which lowers confidence in predictions made using such models. It is therefore highly desirable to have a formal approach to determine what additional external 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 project considered the effectiveness of using formal structural indistinguishability techniques in model discrimination within Systems Biology networks by considering competing mechanisms for the MurA, MurB and MurC reaction steps in a key pathway for antibacterial agents (bacterial peptidoglycan biosynthesis). Understanding of the underlying biological process for this pathway is essential for developing new strategies for dealing with antibiotic resistance. The structural indistinguishability analysis could be readily performed in a computer algebra package using a standard technique and showed the schemes to be distinguishable from different proposed measurements. The analysis could also be performed when standard assumptions concerning rates of reaction were applied. The methods and techniques employed could also be used to discriminate between candidate models for infectious diseases of humans. Such competing schemes may correspond to fundamental differences in the assumptions made regarding progression of infection - such as recovery with permanent or tempory immunity to re-infection. Discriminating between possible schemes becomes even more important when also including, and analysing the effects of, vaccination strategies. Structural identifiability can be considered as a special case of the structural indistinguishability problem and considers the uniqueness of the unknown model parameters (and hence of model predictions concerning unmeasured components of the biological system) from experiments proposed for the collection of data. If parameter estimates, or model predictions, are to be used to inform intervention or inhibition strategies, or other critical decisions, then it is essential that the parameters be uniquely identifiable. Structural identifiability analyses were performed for models of the MurA, MurB and MurC reactions arising from the indistinguishability analysis. As a result of the identifiability analysis sets of reactants were generated that must be available for measurement to guarantee uniqueness of the model parameters and predictions. However, it was found that traditional symbolic computation had to be allied with numerical sensitivity analysis in order to fully explore the uniqueness of the parameters with respect to the proposed measurements. Such an analysis formally explores the sensitivity of the measurements to changes in the parameters. When applied to infectious disease models that incorporate protection derived from the mother (maternal antibodies) this leads to a better understanding of the use of particular types of data set with different model structures. In considering the case study a model of the full cytoplasmic pathway has been developed, which, when combined with robust experimental data capture should lead to a validated model that can be used to explore antibacterial resistance. |
| Exploitation Route | Any non-academic use of systems modelling, such as pharmacokinetics and pharmacodynamics, toxicity and tumour modelling, etc in pre-clinical and clinical drug development. In addition, the modelling work on the bacterial peptidoglycan biosynthesis is useful to companies developing new inhibitors to the cytoplasmic phase of this pathway. Being able to model and predict perturbation effects due to the action of inhibitors at various stages of this pathway will be invaluable. Techniques are applicable across all systems modelling in which there are competing ideas concerning proposed mechanisms of action, or in which there are unknown parameters that cannot be directly measured (and so must be inferred, or estimated, from observed behaviour). The computer implementation of the techiques developed have been provided in journal articles for reuse by other researchers. The work performed on the project provides techniques to suggest the measurement of system variables that have previously been neglected or unavailable for direct observation. In order to overcome such issues it may be necessary to develop new measurement procedures or technologies. Thus the relevant industries will benefit through the development of new technologies and products. |
| Sectors | Healthcare,Pharmaceuticals and Medical Biotechnology |
| Description | EPSRC-funded Workshop on Indistinguishability and Model Discrimination in Systems Biology |
| Form Of Engagement Activity | Participation in an activity, workshop or similar |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Other academic audiences (collaborators, peers etc.) |
| Results and Impact | Workshop organised and run at the University of Warwick to present findings from the project and to promote wider discussion on the importance of mechanism discrimination in Systems Biology. Workshop was attended by approximately 30 researchers from across the UK, including participation from AstraZeneca. After the event I was invited to spend some time with one of the industrial teams (from AstraZeneca) represented at the event to promote greater understanding in an industrial setting. |
| Year(s) Of Engagement Activity | 2009 |
| URL | http://www2.warwick.ac.uk/fac/sci/fstm/seminars/model_discrimination |