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Modelling the control mechanisms underpinning hormone dynamics in humans

   School of Mathematics

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  Dr Eder Zavala  No more applications being accepted  Funded PhD Project (UK Students Only)

About the Project

Hormonal concentrations are regulated by endocrine axes and are the perfect example of complex regulatory systems involving multiple levels of organisation: from gene regulatory networks, to cells, to entire secretory gland systems [1, 2]. Endocrine regulation is highly dynamic, with hormone levels exhibiting complex periodic behaviour over short and long timescales (e.g., hourly, daily and monthly rhythms). These systems also exhibit nonlinear responses to perturbations [3, 4], typically mediated by feedback loops involving multiple components and crosstalk interactions with other endocrine systems [5, 6]. At the same time, endocrine systems exhibit tradeoffs between sensitivity and robustness, which allows adaptability to physiological challenges. Importantly, dysregulation of these dynamic processes (particularly when it is irreversible) can lead to disease.

The goal of this project is to develop a mathematical understanding of normal endocrine function and its dynamic responses to perturbations, particularly those that elicit a “stress response” (e.g., physical and psychological stressors, inflammation, mistiming of meals, sleep disruptions). You will develop mathematical models that test our understanding of hormonal regulation, generate hypotheses about the underlying physiology, and use state-of-the-art datasets to predict hormonal responses to perturbations of different magnitude, duration and type, as well as how such responses differ when baseline rhythmicity is affected. The models will be calibrated to data from human studies and geared toward biomedical research needs and clinical decision-making, including diagnosis, disease management and chronotherapy.

Entry requirements

We are looking for a creative and enthusiastic graduate with:

  • a first-class degree in Mathematics or a closely related discipline with a strong mathematical component (Master’s level or equivalent),
  • a solid background in ordinary and/or delay differential equations, model parameterisation, sensitivity analysis and optimisation,
  • excellent programming skills (Python, Matlab or Julia),
  • good knowledge of dynamical systems theory and bifurcation analysis is desirable,
  • good communication skills (oral and written).

Environment and support

I want to support ambitious students to develop their full potential and reach the next level of their careers, whichever path they choose to follow. During your PhD, you will be part of a team of interdisciplinary researchers spanning mathematics, physics, computer science and biomedicine. As part of this project, you will also have access to an international collaborative network of world-leading experts in mathematical biomedicine, endocrinology and chronophysiology. We value basic and translational research equally, and are passionate about delivering transformative research that innovates and impacts positively upon lives. Training opportunities on in industry engagement, securing research funds, and Patient and Public Involvement and Engagement (PPIE) activities will be available. Applications from underrepresented groups in STEM subjects are strongly encouraged. For example this may include (but is not limited to) students with disabilities, students from ethnic minority backgrounds, female or non-binary students, first generation students, or students from the LGBTQ+ community.

Application process and enquiries

The application procedure and the deadlines for scholarship applications are advertised at 

Informal enquiries should be addressed to Dr Eder Zavala via email: [Email Address Removed] 

Funding Notes

A funded scholarship is available for an excellent UK candidate with a stipend at standard rates for 3-3.5 years.
For EU candidates funding may be available through a college or EPSRC scholarship in competition with all other PhD applications. The scholarship will cover tuition fees, training support, and a stipend at standard rates for 3-3.5 years.
Strong non-UK/non-EU self-funded applicants will be considered. Exceptionally strong candidates in this category may be awarded a tuition fee waiver (for up to 3 years) in competition with all other PhD applications.


[1] Zavala E, et al. Mathematical modelling of endocrine systems. Trends Endo & Metab 30(4):244-57 (2019)
[2] Bertram R. Mathematical modeling in neuroendocrinology. Comprehensive Physiology. 5(2):911-27 (2015)
[3] Spiga F, Zavala E, Walker JJ, et al. Dynamic responses of the adrenal steroidogenic regulatory network. PNAS 114(31):E6466-74 (2017)
[4] Galvis D, Zavala E, et al. Modelling the dynamic interaction of systemic inflammation and the hypothalamic-pituitary-adrenal (HPA) axis during and after cardiac surgery. J Roy Soc Interface 19(189):20210925 (2022)
[5] Zavala E, Voliotis M, Zerenner T, et al. Dynamic hormone control of stress and fertility. Frontiers Physiol 11:1457 (2020)
[6] Zavala E, Gil-Gómez CA, et al. Dynamic modulation of glucose utilisation by glucocorticoid rhythms in health and disease. bioRxiv 10.1101/2020.02.27.968354 (2020)

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