Mathematical models of the epidermal growth factor receptor to quantify

Lead Research Organisation: University of Leeds
Department Name: Applied Mathematics


The project, in the fields of Mathematical Biology and Biological Chemistry, is based on the hypothesis that the development of novel stochastic mathematical models of receptor tyrosine kinase signalling pathways will allow us to provide answers to some biological challenges: how does the copy number of a given protein in the signalling pathway affect the type and timescale of cellular response and how does protein competition for binding sites on receptors drive different cellular fates by turning on/off different intra-cellular circuits, such as endocytosis, degradation, recycling or protein synthesis.
The objectives of the project are:
- to develop new mathematical models to understand the mechanisms that control the dynamics of the
receptor EGFR (or epidermal growth factor receptor), such as the relative importance of dimerisation,
phosphorylation, internalisation, degradation, recycling and synthesis of EGFR in relation to signalling,
- to develop new mathematical model to understand the differences across cell lines in order to be able to
predict signalling responses as a function of ligand concentration, and for different ligands,
- to develop a mathematical model that includes EGFR mutations in order to evaluate how mutations change the dynamics of the EGFR-EGF system, and thus understand how mutations confer resistance to some of the EGFR drug inhibitors currently available in the market, and
- to explore the behaviour of different mathematical models to identify ideal molecular targets for resistance breaking or even resistance-proof EGFR drugs.
Novelty of the research project
The mathematical novelty and challenge of the project is to bring together the molecular, cellular and population scales. The student will make use of birth and death Markov processes, the theory of stochastic descriptors [?] and agent-based modelling, so that together with the experimental data from AZ, she can predict patient selection for different inhibitors of the EGFR signalling pathway. The student will make use of novel matrix analytic methods to study and analyse a number of stochastic descriptors. The student will also make use of novel Bayesian statistical methods to bring together experimental data generated at AZ with the mathematical models of receptor signalling developed in the project in order to carry out parameter inference. She will also develop novel agent-based models to characterise cellular responses mediated by receptor signalling.
Potential applications of the project
From an industrial perspective the novelty of the project resides in bringing together experimental data generated at AZ and novel stochastic mathematical and computational methods to study the EGFR signalling pathway in health and disease. The mathematical models will consider that epithelial cells may have different mutant isoforms of RTKs, as well as the interactions between different number of binding complexes (or ligands) and receptors. This joint (experimental and mathematical) approach will allow us to study cell fate and thus, to understand cellular heterogeneity and the resistance mechanism discussed above.
In particular, a potential application of the project is to develop novel mathematical models of receptor signalling and the role of small molecule inhibitors in Oncology, to provide a more integrated understanding of the mechanisms of resistance emergence in order to develop both resistance-busting and even new resistance-proof drugs. AZ has been developing EGFR inhibitors for the past twenty years and remains very active in this area. In fact, their latest non-small cell lung cancer treatment, Tagrisso has raised over $143 million in the first half of 2016.

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509243/1 30/09/2015 31/12/2021
1969354 Studentship EP/N509243/1 30/09/2017 29/09/2021 Polly-Anne Jeffrey
EP/P510555/1 30/09/2016 29/09/2021
1969354 Studentship EP/P510555/1 30/09/2017 29/09/2021 Polly-Anne Jeffrey
EP/R51200X/1 30/09/2017 31/12/2022
1969354 Studentship EP/R51200X/1 30/09/2017 29/09/2021 Polly-Anne Jeffrey
Description Throughout the last year of the PhD, I have published a first author paper entitled "On Exact and Approximate Approaches for Stochastic Receptor-Ligand Competition Dynamics-An Ecological Perspective". The paper introduces a mathematical model of competition, whereby, two cellular receptors are competing for a common ligand molecule, a protein which diffuses in the extracellular medium and can bind with a receptor molecule to initiate a downstream signalling pathway. The model is analysed in order to evaluate two summary statistics, the steady state distribution, i.e. how many of each type of ligand bound receptor complex do we expect to see in the long run, and the time to reach a number, N, of receptor ligand complexes of one type. The summary statistics are evaluated for different rate constants and numbers of molecules. Each statistic is evaluated using methods already known in the literature, and our novel approximate methods, which are simpler and computationally must faster than the previous exact methods. We use a numerical analysis to infer for which parameter values in the model, our approximations work well as compared to the exact result using the method for the literature.
Exploitation Route The results in this paper could be used by anyone studying steady state distributions or timescales of formation of a complexes for a competition process. By competition process we mean a stochastic mathematical model in which two or more species of different types are competing for a common recourse. The approximations we have developed work well for regions of the parameter space which are discussed in the paper and hence using these methods could save a lot of computational time and memory in the evaluation of such summary statistics.
Sectors Healthcare,Pharmaceuticals and Medical Biotechnology