Modelling store operated calcium entry: creating a three dimensional spatio-temporal model to predict local calcium signals

Calcium is a signalling messenger that is crucial to cellular function, controlling a diverse range of processes such as apoptosis, cell proliferation and muscle contraction. Store operated calcium entry (SOCE) is a specific pathway coupling depletion of the calcium stores within the endoplasmic reticulum (ER) to calcium influx through Orai channels on the plasma membrane. SOCE occurs in small sub-cellular regions called 'ER-PM junctions' which are typically less than $300$nm in diameter. The small size of these domains prevent direct measurement of the calcium signals as current calcium imaging techniques cannot resolve the local signals within ER-PM junctions. The calcium signals associated with SOCE control many downstream cellular processes, such as gene expression and immune responses. There is substantial evidence demonstrating that the placement of the calcium signalling machinery, including Orai channels and SERCA pumps, is vital to the generation of spatially distinct calcium signals which then enhance the selectivity of the calcium signal. However, experimental techniques cannot investigate the local calcium dynamics occurring on a spatial scale of micrometres so mathematical modelling techniques can be used to close this gap in understanding how the local calcium dynamics affect the experimentally observed global calcium dynamics. In this thesis, we construct a three dimensional spatio-temporal model of calcium dynamics and investigate the relationship between the placement of core components of the calcium signalling machinery, e.g. Orai channels and SERCA pumps, and the spatial calcium profiles generated as well as the rates of ER refilling observed. The model includes a spatially extended ER-PM junction to examine the spatial signature of the calcium profiles generated and a spatially extended sub-PM ER to examine the impact of Orai channel and SERCA pump placement on ER refilling dynamics. The model is the first to include spatially extended versions of both the ER-PM junction and sub-PM ER. In this thesis, we first focus on the construction of the spatio-temporal model and the solution techniques used to solve the model. We implement a semi-analytical solution using Green's functions to calculate the analytical solution of the spatial component of the diffusion equation and use numerical time stepping methods in MATLAB to evolve the spatial calcium profile over time. We compare the predictions of the model to expected biological outcomes and then use the model to investigate how the placement of Orai channels, and in particular how clustering of Orai channels, creates spatially distinct calcium profiles. We then examine whether the spatial calcium profile affects ER refilling and what factors control ER refilling. We find that Orai channel clustering creates spatially distinct calcium profiles within the ER-PM junction but does not enhance ER refilling. ER refilling is more strongly controlled by the proximity of SERCA pumps to Orai channels. In fact, the placement of SERCA2b pumps weakly affects ER refilling but the major regulator of ER refilling is the placement of SERCA2a pumps within the ER-PM junction. However, ER refilling continues, albeit at reduced rates, regardless of Orai channel and SERCA pump placement which suggests that other factors, such as the geometry of the ER-PM junction, could be important regulators of ER refilling. This work is relevant to experimental biologists and mathematicians within the calcium signalling community as the calcium signals generated within the ER-PM junction are crucial for advancing the understanding of how calcium signals regulate cellular function. The local calcium dynamics are important regulators of whole cell calcium dynamics and so mathematical methods allowing rigorous investigation of the mechanisms controlling local calcium signalling will be invaluable to furthering our understanding of how SOCE regulates cell function