Modeling the effect of Kv1.5 block on the canine action potential

Abstract

A wide range of ion channels have been considered as potential targets for pharmacological treatment of atrial fibrillation. The Kv1.5 channel, carrying the I(Kur) current, has received special attention because it contributes to repolarization in the atria but is absent or weakly expressed in ventricular tissue. The dog serves as an important animal model for electrophysiological studies of the heart and mathematical models of the canine atrial action potential (CAAP) have been developed to study the interplay between ionic currents. To enable more-realistic studies on the effects of Kv1.5 blockers on the CAAP in silico, two continuous-time Markov models of the guarded receptor type were formulated for Kv1.5 and subsequently inserted into the Ramirez-Nattel-Courtemanche model of the CAAP. The main findings were: 1), time- and state-dependent Markov models of open-channel Kv1.5 block gave significantly different results compared to a time- and state-independent model with a downscaled conductance; 2), the outcome of Kv1.5 block on the macroscopic system variable APD(90) was dependent on the precise mechanism of block; and 3), open-channel block produced a reverse use-dependent prolongation of APD(90). This study suggests that more-complex ion-channel models are a prerequisite for quantitative modeling of drug effects.

Figure 1

Five-state Kv1.5 model (A). Transitions between the states are determined by the rates α and β. Six-state Kv1.5 model with an open-channel block (B). Transitions between the open and the blocked state are determined by the rates γ and δ and by the drug concentration. Ten-state Kv1.5 model with several blocked states (C). Transitions between the blocked states are determined by the rates ζ and ɛ.

Figure 2

Action potential waveforms (A) and corresponding I_Kurd (B) generated by the remodeled PM-cell model stimulated at a frequency of 1 Hz. Bold traces corresponds to no drug, solid traces to drug concentrations of 1, 2, 3, 5, 8, and 13 μM, respectively, and dashed traces to 21 μM. The drug-blocking action was defined by the parameter values γ = 10 μM^–1 s^–1, δ = 2 s^–1, and Z_γ = Z_δ = 0. The APD₉₀ is marked by a dashed line in the plot of the membrane potential. (Insets) Magnification of the traces during the spike.

Figure 3

APD₉₀ as function of effective on-rate and off-rate of an uncharged drug at a stimulation frequency of 1 Hz (A). APD₉₀ as function of effective on-rate and off-rate of an uncharged drug at a stimulation frequency of 4 Hz (B). Absolute difference between APD₉₀ at stimulation frequencies of 1 and 4 Hz as function of effective on-rate and off-rate of an uncharged drug (C). Absolute difference between APD₉₀ calculated from the time- and voltage-independent model and from the six-state model, as function of effective on-rate and off-rate of an uncharged drug at a stimulation frequency of 4 Hz (D).

Figure 4

AP frequency dependence of 8 μM test drug defined by γ = 10 μM^–1 s^–1, δ = 2 s^–1, and Z_γ = Z_δ = 0. Left column uses the AF setting, right column uses the normal cell setting. Row A shows APD₉₀ as function of frequency in absence of the test drug (dashed) and with the test drug (solid). Row B shows the fraction open Kv1.5, O, during the first 100 ms of the AP in absence of the test drug while rows C and D show the fraction of open, O, and blocked, B, Kv1.5, respectively, in the presence of the test drug during the first 100 ms of the AP. Bold traces correspond to a stimulation frequency of 0.5 Hz, solid traces to 1 and 2 Hz, respectively, and dashed traces to 4 Hz.

Figure 5

APD₉₀ values and difference between APD₉₀ values generated by the remodeled PM-cell model using the 10-state blocking model and four versions of compound 1 and compound 2, respectively. Versions 1–4 are encoded by black, blue, green, and red. Upper and lower row are for frequencies 1 Hz and 4 Hz, respectively. Columns A and B correspond to compound 1 and compound 2, respectively. Column C shows the difference between A and B. Drug concentration is given by the expression K_d2ⁿ , where K_d is the dissociation constant, and where n = −3, −2,…, 7.