Modelling the role of STIM1 and STIM2 in Ca 2 + oscillations in T-lymphocytes

${\text{Ca}}^{\text{2}+}$ is a ubiquitous signalling mechanism across different cell types. In T-cells, ${\text{Ca}}^{\text{2}+}$ signalling relies on extracellular ${\text{Ca}}^{\text{2}+}$ influx, which itself relies on the Stromal Interaction Molecule 1 & 2 (STIM1 & STIM2) proteins to function. ${\text{Ca}}^{\text{2}+}$ oscillations in Jurkat T-cells usually have a sinusoidal form on a raised baseline. However, T-cells modified to express only one of the two STIM proteins show mixed oscillations containing ${\text{Ca}}^{\text{2}+}$ spikes along with bursting and sinusoidal periods. We construct a mathematical model consisting of six ordinary differential equations that reproduces the behaviour of both the wildtype cells and the cells missing either STIM protein. We also present a new model of cooperative interaction between STIM1 and STIM2 that supports ${\text{Ca}}^{\text{2}+}$ oscillations in T-cells. Our model predicts that the mixed oscillations seen in the edited cells are a result of both ${\text{Ca}}^{\text{2}+}$ influx from the extracellular medium and ${\text{Ca}}^{\text{2}+}$ release from the internal ${\text{Ca}}^{\text{2}+}$ stores.