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Modelling calcium signalling and its coupling with mechanics

Chakraborty, Abhishek 2020. Modelling calcium signalling and its coupling with mechanics. MPhil Thesis, Cardiff University.
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Calcium (Ca2+) signalling is one of the most important mechanisms of information propagation in the body (M. J. Berridge et al., 2000). Recently, experiments have shown that the coupling between Ca2+ signalling and mechanical forces plays a crucial role in fertilisation, embryogenesis, wound healing, and cancer. However, this mechanochemical coupling is poorly understood and few mechanochemical models exist to date. We first study the Atri et al. (1993) model - a nonlinear, excitable system of two ODEs, neglecting Ca2+ diffusion effects. As the IP3 concentration increases, this model exhibits action potentials and limit cycles (Ca2+ oscillations). Subsequently, we study the Atri model with Ca2+ diffusion, in one spatial dimension. This system consists of a reaction-diffusion PDE for Ca2+ and generates an interesting repertoire of behaviours – solitary waves and periodic wavetrains. To study the mechanochemical coupling of Ca2+, we begin with the mechanochemical model by Kaouri et al. (2019). The Atri model is coupled with a force balance equation for embryonic tissue, which is modelled as a linear, viscoelastic material. The mechanics equation includes a Ca2+-dependent traction term. This has been modelled with a Hill function in Kaouri et al. (2019), reflecting the saturation effect that has been observed in some experiments (Christodoulou & Skourides, 2015). However, in other experiments (Ajduk et al., 2011), there is evidence that the actomyosin network in the cytosol solates at high Ca2+ levels. Hence, we model a traction term that rises and then falls with the Ca2+ level. Upon increasing the width of the traction function, we find that the frequency of contractions decreases whereas the frequency of Ca2+ oscillations remains unaltered. We then incorporate Ca2+ diffusion and study the system’s behaviour in one spatial dimension. Finally, we return to the Atri model and solve it on a disc, obtaining solitary waves and periodic wavetrains. i

Item Type: Thesis (MPhil)
Date Type: Completion
Status: Unpublished
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Date of First Compliant Deposit: 20 October 2020
Last Modified: 21 Oct 2020 10:18

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