The molecular heterogeneity of repolarizing currents produces significant spatial heterogeneity and/or dispersion of repolarization in many mammalian cardiac tissues. Transgenic mice are prominent experimental models for the study of the molecular basis of repolarization and arrhythmias. However, it is debated whether the small mouse heart can sustain physiologically relevant heterogeneity of repolarization. We used a comprehensive model of the mouse action potential (AP) to predict how small a region of the cardiac tissue can maintain spatial gradients of repolarization due to differential expression of channels. Our simulations of a 1D multicellular ring or cable predict that substantial gradients in repolarization and intracellular [Ca²⁺]_i transients can be maintained through heterogeneity of expression of potassium channels in distances of about ten cells that are sufficient to block propagation. The abruptness of expression gradients and the site of stimulation can cause calcium transient oscillations and affect the stability of calcium dynamics and AP propagation. Two different mechanisms of instability of AP propagation in 1D cable occur at fast pacing rates. Transitions from periodic activity to alternans or to irregular behavior were observed. Abrupt gradients of channel expression can cause alternans at slower pacing rates than gradual changes. Our simulations demonstrate the importance of incorporating realistic calcium dynamics and current densities into models of propagated action potential. They also emphasize that microscopic aspects of tissue organization are important for predicting large scale propagation phenomena. Finally, our results predict that the mouse heart should be able to sustain substantial molecularly based heterogeneity of repolarization.