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

Figures

• 

  Fig 1. Dynamic behaviours of pacemaking action potentials in IK1/If 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 (INa), Na+/K+ pumping current (INaK) and L-type calcium channel current (ICaL) with the current densities of (IK1, If) 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 (INa), Na+/K+ pumping current (INaK) and L-type calcium channel current (ICaL) with the current densities of (IK1, If) 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 If 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 (IK1, If) 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 (Itotal), inward rectifier potassium channel current (IK1) and L-type calcium channel current (ICaL) during the simulating time course of 760–763 s. (Inset) Expanded plot during V from -75 to -45 mV and Itotal from -0.1 to 0 pA/pF marked by the asterisk in (B).

• 

  Fig 5. Measured cycle length in IK1/If parameter space. The density of IK1 is from 0 to 0.396 pA/pF and the density of If 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 If density on the pacemaking cycle length under different IK1 density. (A) Change of cycle length with the increase of If from 0 to -6.3 pA/pF when IK1 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 (INaCa), maximum funny current (If) and maximum fast sodium current (INa) during a pacemaking period with the increase of If from 0 to -6.3 pA/pF. (G-H) Change of the normalized total integral of main inward currents (Integral Iin) and normalized total integral of main outward currents (Integral Iout) during DI phase with the increase of If when IK1 density is 0.05 (solid line) and 0.198 pA/pF (dotted line). The inward currents include INa, INaCa and If; the outward currents include inward rectifier potassium channel current (IK1), Na+/K+ pumping current (INaK), rapid delayed rectifier potassium channel current (IKr) and slow delayed rectifier potassium channel current (IKs).