A computational model of Purkinje fibre single cell electrophysiology: implications for the long QT syndrome

Abstract

Computer modelling has emerged as a particularly useful tool in understanding the physiology and pathophysiology of cardiac tissues. Models of ventricular, atrial and nodal tissue have evolved and include detailed ion channel kinetics and intercellular Ca(2+) handling. Purkinje fibre cells play a central role in the electrophysiology of the heart and in the genesis of cardiac arrhythmias. In this study, a new computational model has been constructed that incorporates the major membrane currents that have been isolated in recent experiments using Purkinje fibre cells. The model, which integrates mathematical models of human ion channels based on detailed biophysical studies of their kinetic and voltage-dependent properties, recapitulates distinct electrophysiological characteristics unique to Purkinje fibre cells compared to neighbouring ventricular myocytes. These characteristics include automaticity, hyperpolarized voltage range of the action potential plateau potential, and prolonged action potential duration. Simulations of selective ion channel blockade reproduce responses to pharmacological challenges characteristic of isolated Purkinje fibres in vitro, and importantly, the model predicts that Purkinje fibre cells are prone to severe arrhythmogenic activity in patients harbouring long QT syndrome 3 but much less so for other common forms of long QT. This new Purkinje cellular model can be a useful tool to study tissue-specific drug interactions and the effects of disease-related ion channel dysfunction on the cardiac conduction system.

Figure 1. Schematic representation of the model of cardiac Purkinje fibre cellular electrophysiology presented in this study

The local Ca²⁺ handling subspace is illustrated as is the network sarcoplasmic reticulum (NSR) and the junctional sarcoplasmic reticulum (JSR).

Figure 2. Late current contributions from the cardiac sodium channel (Na_v1.5, A) and non-cardiac sodium channel (Na_vTTX, B) in response to a 300 ms step to −10 mV

Insets show peak Na⁺ currents, illustrating both the hyperpolarized shift in activation and larger magnitude of the Na_v1.5 channel leading to its role as the prime determinant of action potential amplitude and V_max.

Figure 3. The action potential generated in the absence (A) and presence of external pacing (B)

The intrinsic PF AP fires every 2.25 s and has an action potential duration of 425 ms whereas the 1 Hz paced action potential has a shorter APD (366 ms). C, illustration of the mechanism of intrinsic pacing; the HCN channel opens at hyperpolarized potential and eventually overtakes the inward rectifying potassium channel (I_K1) leading to phase 4 depolarization. In D, the contribution of I_K1 in the final repolarization of the action potential is highlighted.

Figure 4. Potassium channel contributions to the steady-state 1 Hz PF action potential

B, the time course of I_Kr and I_Ks during the steady-state AP, both peaking during repolarization. C, in comparison, I_to1 and I_sus play their largest roles in governing phase 1 repolarization and the plateau potential, respectively.

Figure 5. Examination of the inward currents during the 1 Hz steady-state PF action potential

A, typical action potential. In B, the large contribution of late sodium channel activity through the TTX-sensitive channel is observed throughout the plateau into repolarization. Conversely, the L-type and T-type calcium channels are largest early in the action potential (C).

Figure 6. Simulated block of individual ion channels reveals their role in governing AP morphology and duration

Simulation versus experiment for complete block of individual ion currents I_Na,TTX (A and B), I_Kr (C and D), I_Ks (E and F) and I_CaL (G and H).

Figure 7. Long QT syndrome variant 3 mutation ΔKPQ has a severe cellular phenotype in the PF model

A shows the steady-state action potential for the heterozygous (blue) and homozygous (red) APs versus WT (black). B illustrates the effect of slowing the pacing frequency to 0.5 Hz. Lastly, in C, a series of progressively longer pulses were applied to the end of the 1 Hz steady-state protocol to examine the APD prolongation, shown normalized to the steady-state APD, induced by the delay.