Mathematical modelling of tissue self-assembly

Lead Research Organisation: University of Sheffield
Department Name: Mathematics and Statistics

Abstract

Brief description of research context: How tissues self-assemble, and how different cell types are established and maintained in such tissues, are fundamental questions in developmental biology with profound implications for tissue engineering and regeneration strategies. While the signalling molecules involved are increasingly well characterised, we still lack a mechanistic understanding of the contribution and timing of short- vs long-range signalling, and their effect on cell proliferation and adhesion. Alongside experimental studies, mathematical models offer an increasingly useful tool to help challenge and refine our understanding of these processes.

Aims and objectives: Building on recent work by the project supervisor Dr Alexander Fletcher, this project will develop new models of tissue growth and patterning, incorporating multiple signalling mechanisms (autocrine, juxtacrine, paracrine). Detailed analysis will identify how different modes of tissue self-assembly emerge from combinations of these mechanisms in time and space. This work will be applied to the hypothalamus, which regulates core body processes that are essential for survival. Informed by recent findings by the project co-supervisor Prof. Marysia Placzek on hypothalamus self-assembly, and in vitro organoid data that recapitulates development in vivo. Models will be developed to understand whether and how local versus longer-range signalling events underlie hypothalamic cellular homeostasis, cellular architecture and self-assembly.

Research methodology: A hierarchy of new mathematical models will be developed and analysed, which couple short-range (autocrine, juxtacrine) and long-range (paracrine) signalling mechanisms to tissue growth and self-renewal: (1) continuum models, tracking cell density and molecular concentrations; (2) if required, cell-based models that tracking the proliferation and adhesion of individual cells within a tissue. For tractability, and with epithelial tissues as a general focus, we will restrict our focus to one and two spatial dimensions. In each case, systematic analysis will reveal the possible modes of tissue growth and stability generated by different molecular 'wirings' (considering up to three interacting signalling molecules) and initial conditions (reflecting positional information / pre-patterning). These models will be applied to study the self-assembly of the hypothalamus. Placzek recently showed that the hypothalamus is built from a stem-like population expressing the signalling molecule FGF10. Through division at a growth front, this population generates a progenitor population that transiently expresses the signalling molecule Shh. Once set up, these FGF10+ and Shh+ populations are maintained at steady-state throughout embryogenesis, ultimately differentiating to hypothalamic neurons. Informed by in vivo and in vitro data on cell proliferation and expression domains in time and space, generated by the student with the support of the Placzek lab, models will be applied to study: (1) the possible feed-forward and feed-back mechanisms underlying the establishment and maintenance of these stable cell populations; (2) autocrine, juxtacrine and paracrine signalling interactions between FGF10 and Shh that underlie cellular homeostasis and self-assembly.

Alignment with EPSRC strategies and research areas: The project aligns with (1) Mathematical Biology, as it involves the development and application of novel mathematical tools to study biological processes; (2) Complexity Science, as it involves a systems approach to understand how tissue-scale behaviour emerges from feed-forward/feed-back loops between cellular components; (3) Biomaterials and Tissue Engineering, as the models will be widely applicable for studying the cellular, molecular and biomechanical mechanisms that promote self-assembly of a tissue from a stem cell, in tissue development/regeneration/engineering contexts.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/S515577/1 01/10/2018 30/09/2022
2116525 Studentship EP/S515577/1 01/10/2018 30/09/2022 Ian Groves