PhD studentship opportunity at the University of Bath.
Cross-disciplinary investigation of pattern formation in Zebrafish using spatially extended mathematical models with volume exclusion
Dr Christian Yates (Mathematical Sciences, University of Bath),
Professor Ruth Baker (Mathematics, University of Oxford),
Professor Robert Kelsh (Biology and Biochemistry, University of Bath).
Pigment pattern formation – the process generating functional and often beautiful distributions of pigment cells in the skin – represents a classic problem in pattern formation. Pigment pattern formation in adult zebrafish is now one of the best-studied examples. Three cell types are known to contribute to the striped pigment patterns of zebrafish; xanthophores, melanophores and iridophores. We have also recently identified Agouti Signalling Peptide (ASIP) as a further patterning component. Traditionally zebrafish pattern modelling has been conducted at the continuum level with Turing instability the proposed mechanism. However, the discrete nature of the agents (cells) involved suggests that individual-based models might be preferable, to allow inclusion of biological noise and to account for the finite volume of the cells.
Under the supervision of leading experts in stochastic mathematical modelling and developmental biology of pattern formation the student will generate a versatile framework to investigate the effects of stochasticity and finite cell size upon pattern formation models which include all cell-types and ASIP signalling. This model will be informed by the experimental data on zebrafish skin patterning. Biological predictions of the model will then be tested experimentally and the findings used to feedback into the model as part of an iterative model-development cycle.
In particular, the student will construct an on-lattice exclusion-process model in which cells interact with neighbours, and move to neighbouring lattice sites. A detailed investigation of the relationship between key length scales in the model, the system size and compartment size, and their impact on the patterns formed, will be carried out. Subsequently hypotheses on pigment cell interactions will be explicitly encoded into this framework to explore the potential of the model to replicate the patterns of both wild-type and mutant fish.
Guided by the modelling outputs, the student will generate data to test the models’ efficacy. Data will be obtained from the literature and targeted experimental studies. Experimental studies will include direct quantitative measurements of important properties of the pigment cell pattern, e.g. dynamic cell-cell distances and density; pair-correlation functions; and gene expression (e.g. using qRT-PCR) in skin samples at different stages.
The student selected for this project will develop invaluable skill sets in both mathematical modelling and experimental genetics and cell biology whilst also making a significant contribution to the
understanding of a canonical biological pattern formation system. These mixed skill sets will make the candidate a highly desirable recruitment prospect for future employers.