Modelling in pharmacokinetics and mathematical pharmacology


An opportunity to apply for a full-time PhD in the Faculty of the Environment and Technology, UWE Bristol. The studentship will be funded by the Engineering and Physical Sciences Research Council (EPSRC).

Ref 2022-OCT-FET04

The expected start date of this studentship is 1 October 2022

The closing date for applications is 17 August 2022

Studentship details

In the pursuit of drug discovery and therapeutics, pharmacological analysis is required to probe mechanisms of action of drug molecules (ligands) at cell surface receptors and to understand downstream signalling dynamics. Mathematical modelling is now providing new insights and tools for quantifying receptor behaviour and predicting signalling outcomes.

Pharmacokinetics (PK) is the study of drug distribution in the body and is a topic which draws on the results of ordinary differential equation (ODE) based models. Classical PK analysis often involves modelling a drug’s route through the body as a system of compartments, with transport between the compartments following linear laws, and key parameters controlling drug absorption and elimination assumed constant.

This project has the potential for development in two directions, depending on the student’s interests in conjunction with the Director of Studies:

Firstly, the student might build on recent mathematical results for ODE models of PK with delayed absorption effects. This will contribute to the PK literature by developing and analysing new associated mathematical models through a structured work programme including consultation with industrial partners (GSK). Important mathematical and computational open challenges will be addressed, towards practical tools for the PK end-user.

Alternatively, the student might develop new minimal, differential equation-based models for cellular responses triggered by ligand-receptor interactions (which will be validated using real data), using model reduction methodology, asymptotic and numerical analysis to bridge the gap between detailed “systems biology” models and simplified operational models of agonism. New kinetic operational models of agonism, which predict time-dependent cellular responses to ligands, are largely based on low-dimensional ordinary differential equation systems. From this starting point, a comprehensive suite of kinetic operational models will be developed and analysed, encompassing important ligand-receptor binding scenarios, activation scenarios and signal regulation mechanisms. These models will be analysed with respect to the validity of their assumptions on parameter regimes, their ability to quantify efficacy, and the viability of implementation in end-user software packages. The models will be informed and validated using experimental data provided by external collaborators (Pharmechanics and University of Cambridge), towards potential impact in both academia and the pharmaceutical industry.

The student will contribute new results to the growing field of mathematical pharmacology, and will gain skills in scientific computing, mathematics and bio-modelling which will be applicable in a broad range of disciplines.

For an informal discussion about the studentship, please email Dr Andrew Smith or Dr Lloyd Bridge.


The studentship is available from 1 October 2022 for a period of four years, subject to satisfactory progress and includes a tax exempt stipend, which is currently £16,062 per annum.

In addition, full-time tuition fees will be covered for up to four years.


Applicants must have a good first degree in Mathematics, equivalent to first or upper second class honours. Ideally, applicants will have a Masters-level qualification (either postgraduate or undergraduate). The studentship is only available to UK applicants.

A background in applied mathematics, including differential equations, modelling and computation is required. Familiarity with asymptotic analysis would be helpful, and programming in MATLAB or similar will be a central component of the project. Strong interpersonal skills and an ability to work independently are also required. A background in biology or pharmacology is not required but an interest in these fields would be helpful

A recognised English language qualification is required.

How to apply

Please submit your application online. When prompted use the reference number 2022-OCT-FET04.

Submit your application

Supporting documentation

You will need to upload your research proposal, all degree certificates and transcripts and proof of English language proficiency as attachments to your application, so please have these available when you complete the application form.


You will need to provide details of two referees as part of your application.

Closing date

The closing date for applications is 17 August 2022.

Further information

It is expected that interviews will take place on weeks commencing September. If you have not heard from us by October, we thank you for your application but on this occasion you have not been successful.

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