Mathematical models for cell-substrate interaction

McNicol, Gordon Robert (2024) Mathematical models for cell-substrate interaction. PhD thesis, University of Glasgow.

Abstract

To function and survive cells need to be able to sense and respond to their local environment through mechanotransduction. Crucially, mechanical and biochemical perturbations initiate cell signaling cascades, which can induce responses such as growth, apoptosis, proliferation and differentiation. At the heart of this process are actomyosin stress fibres (SFs), which form part of the cell cytoskeleton, and focal adhesions (FAs), which bind this cytoskeleton to the extra-cellular matrix (ECM). In addition to their structural role, FAs additionally serve as signaling hubs for changes in cell function. It follows that understanding the formation of these structures is a prerequisite for any attempt to elucidate how mechanical and biochemical cues influence cell behaviour.

The focus of this thesis is on the development of mathematical models to describe the coupled formation and maturation of cell-substrate adhesions and cell cytoskeleton in non-motile cells. In particular, we formulate a zero-dimensional bio-chemical model and one- and two-dimensional bio-chemo-mechanical models to describe the development of SFs and FAs and activation of ROCK signaling. We use a large family of PDEs (or ODEs) to describe three sets of biochemical events: the polymerisation of actin and subsequent bundling into contractile SFs; the formation and maturation of cell-substrate adhesions; and the activation of signaling proteins in response to FA and SF formation. In our one- and two-dimensional models, the evolution of these key proteins is coupled to a Kelvin-Voigt viscoelastic description of the cell cytoplasm and the ECM. We employ these various models to understand how cells respond to external and intracellular cues in vitro and are able to reproduce, and elucidate the mechanism of, a range of experimentally observed phenomena. This includes non-uniform cell striation and cells forming weaker SFs and FAs on softer substrates. It follows that the developed models provide a platform for systematic investigation into how the cell biochemistry and mechanics influence cell development and facilitates prediction of internal cell measurements that are difficult to ascertain experimentally.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Supported by funding from a Lord Kelvin Adam Smith Scholarship.
• Subjects: Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Funder's Name: Lord Kelvin Adam Smith Scholarship
• Supervisor's Name: Stewart, Professor Peter and Dalby, Professor Matthew
• Date of Award: 2024
• Depositing User: Theses Team
• Unique ID: glathesis:2024-84581
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 19 Sep 2024 12:57
• Last Modified: 19 Sep 2024 13:00
• Thesis DOI: 10.5525/gla.thesis.84581
• URI: https://theses.gla.ac.uk/id/eprint/84581