•  We used a novel high performance computing approach to conduct a sensitivity analysis of emergent properties of simulated ECGs from a transmural cable of cells. •  The rapid delayed rectifier and inward rectifying potassium currents are the primary determinants of the height of the T wave in this system. •  Theight is correlated with the temporal dispersion of repolarisation in the transmural cable while Tpeak– Tend is correlated with the interval from the time of maximum total rate of repolarisation to the end of repolarisation in the cable of cells. •  This study advances our understanding of the molecular basis of T wave morphology and the role of epistatis in the modification of cardiac electrical phenotypes. Abstract  Altered function of ion channels in the heart can increase the risk of sudden arrhythmic death. Hundreds of genetic variants exist in these cardiac ion channel genes. The challenge is how to interpret the effects of multiple conductance perturbations on the complex multi‐variable cardiac electrical system? In theory, sensitivity analysis can address this question. However, to date this approach has been restricted by computational overheads to analysis of isolated cells, which has limited extrapolation to physiologically relevant scales. The goal of this study was to extend existing sensitivity analyses to electrocardiogram (ECG) signals derived from multicellular systems and quantify the contribution of ionic conductances to emergent properties of the ECG. To achieve this, we have developed a highly parallelised simulation environment using unconventional high performance computing architectures to analyse the emergent electrical properties of a multicellular system. This has permitted the first systematic analysis of the molecular basis of the T wave amplitude, revealing important but distinct roles for delayed rectifier and inward rectifier K+ currents. In addition to quantifying how interactions between multiple ion channels influence ECG parameters we show that these sensitivities are dynamic functions of heart rate. This study provides a significant advance in our understanding both of how individual ion conductances define ECG signals and of epistatic modification of cardiac electrical phenotypes. The parallelised simulation environment we have developed removes the computational roadblock that has limited this approach and so provides the framework for future analysis of more complex tissue and whole organ systems.