The long QT syndrome type-3 (LQT3) is an inherited cardiac disorder caused by mutations in the sodium channel gene SCN5A. LQT3 has been associated with ventricular arrhythmias and sudden cardiac death, specially at low heart rates. Based on computer simulations and experimental investigations, analysis of the morphology of the Action Potential (AP) has shown that it undergoes early afterdepolarizations (EADs) and spontaneous discharges, which are thought to be the trigger for reentry like-activity. However, dynamic characteristics of cardiac tissue are also important factors of arrhythmia mechanisms. In this work, we propose a dynamical analysis of the LQT3 at cellular level. We use a detailed Markovian model of the DeltaKPQ mutation, which is associated with LQT3, and we study beat-to-beat AP Duration (APD) variations by using a long-term stimulation protocol. Compared to wild-type (WT) cells, DeltaKPQ mutant cells are found to develop APD alternans over a narrow range of stimulation frequencies. Moreover, the interval of frequency dependence of APD alternans is related to the degree of severity of the EADs present in the AP. In conclusion, dynamical analysis of paced cells is a useful approach to understand the mechanisms of rate dependent arrhythmias.