Aminophylline at clinically relevant concentrations affects inward rectifier potassium current in a dual way

Abstract

Bronchodilator aminophylline may induce atrial or less often ventricular arrhythmias. The mechanism of this proarrhythmic side effect has not been fully explained. Modifications of inward rectifier potassium (Kir) currents including I_K1 are known to play an important role in arrhythmogenesis; however, no data on the aminophylline effect on these currents have been published. Hence, we tested the effect of aminophylline (3–100 µM) on I_K1 in enzymatically isolated rat ventricular myocytes using the whole-cell patch-clamp technique. A dual steady-state effect of aminophylline was observed; either inhibition or activation was apparent in individual cells during the application of aminophylline at a given concentration. The smaller the magnitude of the control I_K1, the more likely the activation of the current by aminophylline and vice versa. The effect was reversible; the relative changes at −50 and −110 mV did not differ. Using I_K1 channel population model, the dual effect was explained by the interaction of aminophylline with two different channel populations, the first one being inhibited and the second one being activated. Considering various fractions of these two channel populations in individual cells, varying effects observed in the measured cells could be simulated. We propose that the dual aminophylline effect may be related to the direct and indirect effect of the drug on various Kir2.x subunits forming the homo- and heterotetrameric I_K1 channels in a single cell. The observed I_K1 changes induced by clinically relevant concentrations of aminophylline might contribute to arrhythmogenesis related to the use of this bronchodilator in clinical medicine.

Appendix

The minimum number of populations n = 2 was sufficient to simulate available experimental data. Let f₁ and f₂ be fractions of the first and the second population of identical channels, G₁ and G₂ fractional conductivities, and I₁ and I₂ contributions of channel populations to the total I_K1 current marked here I for simplicity. U and U_K denote membrane voltage and equilibrium voltage for potassium ions, respectively. I can be expressed as

$$I= I1+ I2 =\left(f1 G1+f2 G2\right)\left(U-{U}_{K}\right), f1 +f2 =1.$$

(1)

Both populations (f₁, f₂) may include activation and inhibition binding sites. Fractional conductivities G₁ and G₂ depend on occupation of binding sites of the respective population as illustrated on the following scheme.

The symbols x_{0_1} and x_{0_2} denote probabilities of the channels belonging to population j to be found drug-free. The probabilities that channels belonging to population j = 1 are occupied by one or two drug molecules are designated x_{1_1} and x_{2_1}, respectively. Probability that the binding sites in channels of population j = 2 are occupied by a drug molecule is designated x_{1_2}.

$$\begin{array}{cc}\mathrm{Evidently}& {x}_{{0}_{1}}+{x}_{{1}_{1}}+{x}_{{2}_{1}}=1,\hspace{1em}\hspace{0.33em}{x}_{{0}_{2}}+{x}_{{1}_{2}}=1\end{array}.$$

(2)

Conductivities of the first and the second population (G₁ and G₂) under steady-state conditions may be expressed as

$${G}_{1}={x}_{{0}_{1}}{G}_{{0}_{1}}+{x}_{{1}_{1}}{G}_{{1}_{1}}+{x}_{{2}_{1}}{G}_{{2}_{1}},\hspace{1em}{G}_{2}={x}_{{0}_{2}}{G}_{{0}_{2}}+{x}_{{1}_{2}}{G}_{{1}_{2}}.$$

(3)

Obviously, if all channels of the given population were found in one of the states shown in the scheme above, the conductivity of this population would take one of the corresponding values G_{0_1}, G_{1_1}, G_{2_1}, or G_{0_2}, G_{1_2}.

Transient changes of Kir currents caused by application of some drugs appeared to be slow, lasting up to 10² s [21, 45, 46]. The same applies to the effect of aminophylline on I_K1. Assuming (in line with ref. [20]) that the drug binding velocity is much higher than the subsequent (allosteric) conformational changes governing channel conductivities, the probabilities x_{k_j} (k refers to occupation of binding sites, j to populations of identical channels) may be assumed to keep their steady-state values depending only on the drug concentration c and the dissociation constants K₁, K₂, and K₃. In this case, x_{k_j} can be expressed as solutions of linear algebraic equations related to the above schemes describing drug-binding in the channel population 1 and 2.

$${x}_{{0}_{1}}=\frac{1}{1+\frac{c}{{K}_{1}}+\frac{{c}^{2}}{{K}_{1}{K}_{2}}}, {x}_{1\_1}={x}_{0\_1}\frac{c}{{K}_{1}}, {x}_{2\_1}={x}_{0\_1}\frac{{c}^{2}}{{K}_{1}{K}_{2}}, {x}_{{0}_{2}}=\frac{1}{1+\frac{c}{{K}_{3}}}, {x}_{1\_2}={x}_{0\_2}\frac{c}{{K}_{3}}$$

(4)

The conductivities G₁ and G₂ are generally voltage dependent. If, however, the drug does not interfere with the structures responsible for inward rectification, the drug effect alone is voltage independent. All conductivities may then be regarded as equally dependent on the membrane voltage and the ratio

$$F=\frac{{f}_{1} {G}_{1}+{f}_{2} {G}_{2}}{{f}_{1} {G}_{{0}_{1}}+{f}_{2} {G}_{02}}=\frac{I}{{I}_{0}}$$

(5)

may be interpreted as a voltage-independent indicator of the drug effect. It applies to the aminophylline action as documented by negligible differences between mean values of the drug effect at −110 and −50 mV (Figs. 2(A) and 3(A)). We can therefore express all the above-defined conductivities G_{k_j} as products of voltage-independent dimensionless parameters h_{k_j} and a common voltage-dependent conductivity g(U) describing inward rectification:

$${G}_{{\text{k}}{\_j}}={h}_{\text{k\_j}}g\left(U\right).$$

(6)

To simulate the results related to absolute values (in nA) of the measured currents, the conductivity g(U) was approximated by the function

$$g\left(U\right)=0.08\left(\hspace{0.33em}\frac{0.9}{1+{e}^{\frac{U+85}{11}}}\hspace{0.33em}+\hspace{0.33em}\frac{4}{1+{e}^{\frac{U+150}{20}}}\hspace{0.33em}\right).$$

(7)

The parameters h_{k_j} and the dissociation constants used without any change in all simulations are summarised in Table 1.

Table 1 Parameters of the model used in all performed simulations

Importantly, the only variable parameter used in simulations of all experimental results was the fraction f₁ of the channels belonging to the first population (taking into account that f₂ = 1 − f₁). This supports the hypothesis that all observed manifestations of the dual effect could be explained by the random assembly of channels from subunits.

As mentioned above, the conductivities under the effect of the drug were regarded as equilibrated. The experimental data related to ethanol effect on I_K1 [21, 46] revealed dual effect also in transient changes of the current in response to the onset of ethanol. Corresponding transients in conductivities were described in ref. [20] by the first-order differential equations with different time constants. As the transient responses to aminophylline did not exhibit well distinguishable dual effect, transients of I_K1 following aminophylline application and washout were simulated by single exponentials with a time constant of 15 s which roughly corresponded to experimental results.