title: Mathematical modelling for topographically influenced cell migration and the modulating effect of Gap27 on connexin 43 cycling and 2-d scrape wound closure: applications to cutaneous wound healing
Creators: name: Mitchinson, A
Publisher: name: Liverpool John Moores University
Year: 2022

description: Cutaneous wounds represent a serious economic and health burden for many developed nations. In the U.K., around 2.2 million people a year receive wound care, absorbing roughly 4% of total annual NHS expenditure. Chronic cutaneous wounds in particular may possess poor prognoses. Diabetic foot ulcers, for example, carry a five-year mortality rate comparable to cancer. The prevalence of chronic wounds amongst developed nations is anticipated to rise further, with increasing incidence of conditions strongly associated with chronic wound aetiology, such as obesity and diabetes. A common feature among chronic wounds is the dysfunctional regulation of connexin proteins in cutaneous tissue, which ordinarily modulates in a carefully orchestrated manner post-injury to enable effective healing. Experimental studies targeted to the restoration of the typical spatio-temporal expression pattern of connexins post-injury have shown accelerated and improved healing outcomes across a range of in vitro, in vivo animal and ex vivo human models, and now clinical trials - with various connexin-targeted agents established as promising therapeutic candidates. Physical properties of the extracellular environment have long been known to regulate cellular behaviours. Cutaneous tissue presents a huge range of topographic configurations that cells must navigate in order to carry out reparative function during wound repair. Surface ‘topography’ has since been established in the experimental literature as a major regulator of cell migration behaviour. The capacity for topography to influence migration has been shown to have significant applications in biomaterial and bioimplant design and development, including advanced wound healing treatments like ‘skin substitutes’. In this thesis, we propose three new mathematical models pertaining to these applications. We derive a stochastic model for topographically influenced cell migration, based on a biased Ornstein-Uhlenbeck cell model. We use this model to probe the influence of linearly and randomly organised topographies on migration trajectory behaviour and how the gradual introduction of random perturbations to linear features changes this behaviour, with the intention to further understand how surface imperfections introduced by surface fabrication impact migration. We then derive a mathematical model for connexin 43 (Cx43) cycling dynamics and its dynamical modulation by connexin mimetic peptide Gap27, using mass action kinetics. We use this model to further understand how the introduction of Gap27 may function to affect Cx43-based species dynamics. Finally, we derive a mathematical model for Cx43-based cell-cell interaction influenced cell migration and its dynamical modulation by Gap27 within a two-dimensional computational model of a scrape wound. We use this model to investigate how Cx43 dynamics might affect cell migration behaviour and population invasion of a scrape wound and how Gap27 might modulate these cellular behaviours.