I am willing to supervise PhD projects in mathematical biology. Please email me if you are interested in the funded project(s) listed below, or in some other topic related to my research; you can find a list of past PhD projects here. Unless stated otherwise below, to apply formally for funding and a place, you must complete an online application form. Please contact me (a.g.fletcher@sheffield.ac.uk) for more information.
Unlocking the secrets of human embryo development demands a new, dynamic approach. This PhD project offers a unique opportunity to apply cutting-edge computational methods to a fundamental challenge in reproductive biology: understanding why human embryos fail. As delayed childbearing becomes more common, pinpointing the barriers to healthy development is critical. You’ll be at the forefront of this effort, transforming static biological observations into a dynamic, predictive, and virtual model of the human embryo.
Current knowledge of early human development is largely based on static snapshots. We lack a predictive framework to explain embryo-intrinsic failure. This project addresses that critical gap by hypothesizing that such failures occur at predictable developmental bottlenecks driven by intrinsic cell-to-cell variability and genetic factors.
Your core aims will be threefold:
This inherently interdisciplinary project lies at the intersection of developmental biology, computational science, and advanced data analytics. It is ideal for a student from a mathematics or physics background eager to move into biology, or for a biologist keen to gain advanced quantitative skills. You will receive comprehensive training in both computational and experimental methods.
Key techniques include: deep learning and image analysis with tools such as Cellpose-SAM for precise cell segmentation; quantitative data integration to fuse lineage-resolved 3D imaging with single-cell RNA sequencing (scRNA-seq) trajectories; agent-based and multiscale modelling using the Chaste computational platform to build the virtual embryo; and Bayesian Inference to calibrate model parameters and identify developmental control points.
You will also gain experience in the simulation-experiment loop, where computational predictions are tested in the lab - a highly sought-after skill in modern science.
The impact of this work extends beyond fundamental biology. By revealing the underlying rules of cell-fate change and identifying key developmental vulnerabilities, the virtual human embryo will serve as a powerful preclinical tool. The ultimate goal is to create a predictive framework to inform new clinical strategies - improving fertility treatments, enhancing embryo viability assessments, and shedding light on the origins of congenital conditions. You will be encouraged to practice open research and present your findings at international conferences, ensuring your discoveries rapidly benefit the global scientific community.
A competitively funded studentship is available via the MRC DiMeN Doctoral Training Partnership. Please see this link for information on how to apply. The deadline for applications will be Thursday 4th December 2025.
This is an exciting opportunity to undertake a genuinely multidisciplinary project on the health impacts of air pollution, one of the most urgent public health challenges of the next decade with direct implications for regulation and policy. This project, based at Sheffield Hallam University in partnership with The University of Sheffield, focuses specifically on carbon monoxide (CO) and brings together advanced cell biology techniques and mathematical modelling to generate mechanistic insight in the effect of this toxic gas.
CO is a widespread air pollutant and a recognised contributor to cardiovascular disease (CVD) risk. While high levels of CO are acutely toxic, chronic exposure to lower levels has been linked to long-term damage to the heart and blood vessels. However, the precise ways in which CO disrupts cellular metabolism and contributes to cardiovascular pathology remain poorly understood. This project will address this gap by investigating how CO exposure alters the function and metabolic activity of two key cardiovascular cell types: cardiomyocytes and vascular endothelial cells.
The project aims to improve quantitative and predictive understanding of human cellular metabolic responses to CO exposure. Specific objectives are: (O1) establish the impact of multiple CO levels on cell culture; (O2) determine real-time functional effects of CO on cellular respiration and glycolysis; (O3) construct and validate a mathematical model of CO-dependent metabolism.
This project will integrate state-of-the-art functional assays with high-throughput molecular analyses. Real-time metabolic function will be measured using Agilent’s Seahorse XFe Bioanalyser, enabling dynamic assessment of mitochondrial respiration and glycolysis. These functional readouts will be combined with RNA sequencing, proteomics, and metabolomics to build a comprehensive, multi-layered picture of CO-induced changes in cell toxicity, metabolism, and viability. The resulting datasets will form the basis for mathematical modelling aimed at predicting how CO exposure drives metabolic and toxic responses in cardiovascular cells. Such predictive models could improve our understanding of pollutant-driven CVD and contribute to future strategies for mitigating the health risks associated with air pollution.
This project would suit a student whose background is in cell biology, mathematical modelling, physiology or related fields. This interdisciplinary project will provide training in advanced cell culture, a custom-built air pollutant exposure system, functional metabolic assays, and multi-omics analysis, alongside opportunities to engage with data integration and modelling approaches. The successful candidate will gain a broad skill set spanning cell biology, toxicology, mathematical modelling and systems biology, preparing them for a career in both academic and applied bioscience research.
Beyond advancing fundamental science, this project has clear pathways to real-world impact through existing links with policymakers and industry. The successful candidate will join the Sheffield Hallam University CO group, a growing and vibrant research group. The supervisory team will consist of Dr Mari Herigstad (Sheffield Hallam University), Dr Daniel Kelly (Sheffield Hallam University), and myself.
A competitively funded studentship is available via the BBSRC Yorkshire Bioscience DLA Programme. Please see this link to submit your application. The deadline for applications will be Wednesday 7th January 2026.
The evolution of flight in birds is one of the most extraordinary events in natural history. A fundamental event was the formation of feathers, which first appeared in flightless ancestral theropod dinosaurs. In our previous work we showed that the transient inhibition of Sonic hedgehog (Shh) signalling in the chick embryo led to the failure of flight feather development in the wings of mature birds (Busby et al., Development, 2020). Flight feathers are found along the posterior margin of the bird wing and play a key role in enabling airborne locomotion.
This project will investigate the gene regulatory network (GRN) responsible for the development and evolutionary origin of flight feathers. Using cutting-edge techniques in embryology, comparative genomics, and mathematical modelling, we aim to understand how signalling pathways, such as Shh, Fgfs and Wnts, control the formation of these specialised feather types.
Our approach will integrate three complementary strands: (1) cross-species comparison of GRNs in chickens and ostriches to identify how flight feathers have been naturally gained or lost during evolution; (2) functional experiments using ex vivo and in vivo approaches in the chick wing to test how perturbing candidate genes alters feather identity; and (3) mathematical modelling of the GRN to predict the regulatory logic required to stabilise flight feather formation and simulate possible evolutionary scenarios.
This interdisciplinary project will provide training in developmental biology, molecular genetics, bioinformatics, and mathematical modelling, making it ideally suited to candidates with interests in evolutionary biology, embryology, or systems biology. The outcomes will not only shed light on a major evolutionary innovation-the origin of avian flight-but also provide a framework for understanding how changes in gene regulation drive evolutionary novelty more broadly.
A competitively funded studentship is available via the BBSRC Yorkshire Bioscience DLA Programme. Please see this link to submit your application. The deadline for applications will be Wednesday 7th January 2026.