1. Prologue 58

2. The Hodgkin–Huxley formalism for computing the action potential 59

2.1 The axon action potential model 59

2.2 Cardiac action potential models 62

3. Ion-channel based formulation of the action potential 65

3.1 Ion-channel structure 65

3.2 Markov models of ion-channel kinetics 66

3.3 Role of selected ion channels in rate dependence of the cardiac action potential 71

3.4 Physiological implications of IKs subunit interaction 77

3.5 Mechanism of cardiac action potential rate-adaptation is species dependent 78

4. Simulating ion-channel mutations and their electrophysiological consequences 81

4.1 Mutations in SCN5A, the gene that encodes the cardiac sodium channel 82

4.1.1 The ΔKPQ mutation and LQT3 82

4.1.2 SCN5A mutation that underlies a dual phenotype 87

4.2 Mutations in HERG, the gene that encodes IKr: re-examination of the ‘gain of function/loss of function’ concept 94

4.3 Role of IKs as ‘repolarization reserve’ 100

5. Modeling cell signaling in electrophysiology 102

5.1 CaMKII regulation of the Ca2+ transient 102

5.2 The β-adrenergic signaling cascade 105

6. Epilogue 107

7. Acknowledgments 108

8. References 109

The cardiac cell is a complex biological system where various processes interact to generate electrical excitation (the action potential, AP) and contraction. During AP generation, membrane ion channels interact nonlinearly with dynamically changing ionic concentrations and varying transmembrane voltage, and are subject to regulatory processes. In recent years, a large body of knowledge has accumulated on the molecular structure of cardiac ion channels, their function, and their modification by genetic mutations that are associated with cardiac arrhythmias and sudden death. However, ion channels are typically studied in isolation (in expression systems or isolated membrane patches), away from the physiological environment of the cell where they interact to generate the AP. A major challenge remains the integration of ion-channel properties into the functioning, complex and highly interactive cell system, with the objective to relate molecular-level processes and their modification by disease to whole-cell function and clinical phenotype. In this article we describe how computational biology can be used to achieve such integration. We explain how mathematical (Markov) models of ion-channel kinetics are incorporated into integrated models of cardiac cells to compute the AP. We provide examples of mathematical (computer) simulations of physiological and pathological phenomena, including AP adaptation to changes in heart rate, genetic mutations in SCN5A and HERG genes that are associated with fatal cardiac arrhythmias, and effects of the CaMKII regulatory pathway and β-adrenergic cascade on the cell electrophysiological function.