Transient receptor potential melastatin member 4 (TRPM4) channels are nonselective monovalent cationic channels found in human atria and conduction system. Overexpression of TRPM4 channels has been found in families suffering from inherited cardiac arrhythmias, notably heart block. In this study, we integrate a mathematical formulation of the TRPM4 channel into a Purkinje cell model (Pan-Rudy model). Instead of simply adding the channel to the model, a combination of existing currents equivalent to the TRPM4 current was constructed, based on TRPM4 current dynamics. The equivalent current was then replaced by the TRPM4 current to preserve the model action potential. Single-cell behavior showed early afterdepolarizations for increases in TRPM4 channel expression above twofold. In a homogeneous strand of tissue, propagation conducted faithfully for lower expression levels but failed completely for more than a doubling of TRPM4 channel expression. Only with a heterogeneous distribution of channel expression was intermittent heart block seen. This study suggests that in Purkinje fibers, TRPM4 channels may account for sodium background current (INab), and that a heterogeneous expression of TRPM4 channels in the His/Purkinje system is required for type II heart block, as seen clinically.Read less <