\(\text {Ca}^{\text {2}+}\) 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.
