Reciprocal interaction between IK1 and If in biological pacemakers: A simulation study

Abstract

Pacemaking dysfunction (PD) may result in heart rhythm disorders, syncope or even death. Current treatment of PD using implanted electronic pacemakers has some limitations, such as finite battery life and the risk of repeated surgery. As such, the biological pacemaker has been proposed as a potential alternative to the electronic pacemaker for PD treatment. Experimentally and computationally, it has been shown that bio-engineered pacemaker cells can be generated from non-rhythmic ventricular myocytes (VMs) by knocking out genes related to the inward rectifier potassium channel current (IK1) or by overexpressing hyperpolarization-activated cyclic nucleotide gated channel genes responsible for the "funny" current (If). However, it is unclear if a bio-engineered pacemaker based on the modification of IK1- and If-related channels simultaneously would enhance the ability and stability of bio-engineered pacemaking action potentials. In this study, the possible mechanism(s) responsible for VMs to generate spontaneous pacemaking activity by regulating IK1 and If density were investigated by a computational approach. Our results showed that there was a reciprocal interaction between IK1 and If in ventricular pacemaker model. The effect of IK1 depression on generating ventricular pacemaker was mono-phasic while that of If augmentation was bi-phasic. A moderate increase of If promoted pacemaking activity but excessive increase of If resulted in a slowdown in the pacemaking rate and even an unstable pacemaking state. The dedicated interplay between IK1 and If in generating stable pacemaking and dysrhythmias was evaluated. Finally, a theoretical analysis in the IK1/If parameter space for generating pacemaking action potentials in different states was provided. In conclusion, to the best of our knowledge, this study provides a wide theoretical insight into understandings for generating stable and robust pacemaker cells from non-pacemaking VMs by the interplay of IK1 and If, which may be helpful in designing engineered biological pacemakers for application purposes.

Fig 1. Dynamic behaviours of pacemaking action potentials in I_K1/I_f parameter space.

Blue: stable pacemaking activity (State-5); Yellow: persistent pacemaking activity with periodic incomplete depolarization (State-4). Orange: bursting pacemaking behaviour (State-3). Green: transient spontaneous pacemaking behaviour (State-2). Gray: no spontaneous pacemaking behaviour (State-1). In each category, the typical pacemaking action potentials are illustrated at the bottom panel.

Fig 2. Transient spontaneous pacemaking behaviour.

(A-F) Membrane potential (V), intracellular Na⁺ concentration ([Na⁺]_i), intracellular Ca²⁺ concentration ([Ca²⁺]_i), fast sodium current (I_Na), Na⁺/K⁺ pumping current (I_NaK) and L-type calcium channel current (I_CaL) with the current densities of (I_K1, I_f) at (0.297 pA/pF, -1.89 pA/pF) (‘CASE 1’) during the entire simulating period of 800 s. (G) Expanded plots of (A-F) for the time course of pacemaking self-termination (160–164 s). H: Maximum diastolic potential of spontaneous pacemaking behaviour of (A).

Fig 3. Bursting pacemaking behaviour.

(A-F) Membrane potential (V), intracellular Na⁺ concentration ([Na⁺]_i), intracellular Ca²⁺ concentration ([Ca²⁺]_i), fast sodium channel current (I_Na), Na⁺/K⁺ pumping current (I_NaK) and L-type calcium channel current (I_CaL) with the current densities of (I_K1, I_f) at (0.297 pA/pF, -2.52 pA/pF) (‘CASE 2’) during the entire simulating period of 800 s. (G) Expanded plots of (A-F) for the time course of pacemaking resumption (383–385 s). H: Maximum diastolic potential of automatic pacemaking activity when I_f is -2.52 and -1.89 pA/pF (‘CASE 2’ vs. ‘CASE 1’, solid and dotted line respectively).

Fig 4. Persistent pacemaking activity.

The current densities of (I_K1, I_f) of stable pacemaking activity and periodically incomplete pacemaking activity are at (0.248 pA/pF, -3.15 pA/pF) (‘CASE 4’, black lines) and (0.297 pA/pF, -3.15 pA/pF) (‘CASE 3’, grey lines) respectively. (A-D) The membrane potential (V), phase portraits of membrane potential against the total membrane channel current (I_total), inward rectifier potassium channel current (I_K1) and L-type calcium channel current (I_CaL) during the simulating time course of 760–763 s. (Inset) Expanded plot during V from -75 to -45 mV and I_total from -0.1 to 0 pA/pF marked by the asterisk in (B).

Fig 5. Measured cycle length in I_K1/I_f parameter space.

The density of I_K1 is from 0 to 0.396 pA/pF and the density of I_f is from 0 to -6.3 pA/pF at -80 mV. The measured cycle length (CL) is coloured from 650 ms in dark red to 1000 ms in yellow. White means that there is no definitely measured pacemaking CL (i.e., the pacemaking action potential is not persistent or stable) or the pacemaking activity is ‘invalid’ (CL > 1000 ms).

Fig 6. Effect of I_f density on the pacemaking cycle length under different I_K1 density.

(A) Change of cycle length with the increase of I_f from 0 to -6.3 pA/pF when I_K1 density is 0.05 (solid line) and 0.198 pA/pF (dotted line). (B-F) Change of maximum diastolic potential (MDP), maximum intracellular Na⁺ concentration ([Na⁺]_i), maximum Na⁺/Ca²⁺ exchange current (I_NaCa), maximum funny current (I_f) and maximum fast sodium current (I_Na) during a pacemaking period with the increase of I_f from 0 to -6.3 pA/pF. (G-H) Change of the normalized total integral of main inward currents (Integral I_in) and normalized total integral of main outward currents (Integral I_out) during DI phase with the increase of I_f when I_K1 density is 0.05 (solid line) and 0.198 pA/pF (dotted line). The inward currents include I_Na, I_NaCa and I_f; the outward currents include inward rectifier potassium channel current (I_K1), Na⁺/K⁺ pumping current (I_NaK), rapid delayed rectifier potassium channel current (I_Kr) and slow delayed rectifier potassium channel current (I_Ks).