Effects of the Enantiomers of BayK 8644 on the Charge Movement of L-type Ca Channels in Guinea-pig Ventricular Myocytes

Appendix

The four-states model proposed by Brum et al. (1988) for the voltage sensor of excitation contraction coupling of the skeletal muscle of the frog has been also used to reproduce some of the properties of the cardiac L-type Ca channel by Shirokov et al. (1992). This basic model (Scheme 1) consists of four states: closed (C), open (O) (admittedly an oversimplification as there is evidence for more than one closed state and the maximum P _o of Ca channels is ~0.1 when all the activating charge has moved, a property not reproduced by this simple model), and two inactivated states (I _o and I _c) connected in a ring. The transitions between closed and open states and between inactivated states (horizontal transitions) are intrinsically voltage-dependent and generate charge 1 and charge 2, respectively. The transitions between available and inactivated states (vertical transitions) are assumed voltage-independent. An extension of this model assuming binding of DHP to all four states yields the eight-states model depicted in Scheme 2. Drug bound states are indicated by adding a D to the notation. The equilibrium constants between states are defined as follows:

The equilibrium between drug-free and drug-bound states is characterized by dissociation constants defined as K _dO = O [D]/OD, K _dC = C[D]/CD, K _d1O = I _O [D]/I _O D, K _d1C = I _C [D]/I _C D, where [D] is the DHP concentration.

Following Brum et al. (1988) K ₁ = exp{(V−V ₁)/k}, K ₂ = exp{(V−V ₂)/k}, K′₁ = exp{(V−V′₁)/k}, K′₂ = exp{(V−V′₂)/k}, where V ₁ and V ₂ are the half-distribution voltages for charge 1 and charge 2, respectively, in the drug-free form, and V′₁ and V′₂ in the drug-bound form. k is the e-fold voltage sensitivity, assumed to be the same for all the voltage-dependent steps. All these parameters of the model can be experimentally determined by the corresponding measurements in drug-free conditions and in the presence of saturating drug concentration.

As demonstrated by Brum et al. (1988), the four-state model steady-state availability curve is a Boltzmann function plus a constant. Its half distribution voltage, V _1/2, is given by

where k, the slope factor, has the same value as for Q1 and Q2 distributions. This equation is a reliable way to determine K ₁, which can also be obtained as the ratio between the fraction of the total charge that inactivates and the fraction of the total charge that resists inactivation, provided that both measurements originate in the same set of channels.

The fourth equilibrium constant is not independent and is fixed by microscopic reversibility.

Similarly, the parameters for the drug-bound states were estimated in the presence of saturating drug concentration.

As microscopic reversibility applies to every possible cycle in the model, the twelve equilibrium constants are determined by five independent equations and only seven independent constants. As mentioned above, six of them were experimentally determined from the charge distributions and steady-state availability curves while the seventh is constrained by the dose-response curve. For instance,

Some general conclusions can be drawn, from (v) K _dO/K _dC = K _I/K′₁ = exp{(K′₁−V ₁)/k}<1 since V′₁ < V ₁ therefore, the dissociation constant of the open state is smaller than that of the closed state. From (iv) since K′₂/K ₂ = 1, based on the lack of change of the half distribution voltage of Q2 upon drug application, the drug should bind to both inactivated states with equal affinity. Finally from (iii) it is concluded that K _dO/K _d1O>1, since K′₁/K ₁>1, given the more negative mid-voltage of the availability curve of the drug-bound form. Thus, the inactivated states have higher affinity for the drug, consistent with the promotion of inactivation by agonist drugs.

To simulate the experimental data with the agonist Bay K we chose the following values for the constants: V ₁ = 3 mV, V′₁ = −5 mV, V ₂ = V′₂ = −90 mV, K ₁ = 1.5, K′₁ = 4, K _dO = 20 nM. The chosen value for K _dO is equal to the K _0.5 value obtained by Lacerda and Brown (1989) for S(−)Bay K in their study of tail currents in ventricular myocytes. With the values used, above calculations based on microscopic reversibility yield K _dI = 8 nM and K _dC = 34 nM. The outcome of such simulations, as shown in Fig. 7. A, B, C, were calculated at 250 nM Bay K, a condition in which all the channels are in the drug-bound form, at the V _h indicated in the figure. In D, the dose-response curve was calculated at V _h = −40 mV and the parameters plotted, ΔQ _1max and ΔV ₁, were obtained by fitting a Boltzmann function to the simulated data. This rather simple model successfully reproduces the stationary data, suggesting the plausibility of modulated receptor binding of DHP to the L-type channel.

From (A1), (A2), (iii), (iv) and (v) it follows that the shift in the mid point of the steady-state availability curve, ΔV _1/2 = V′_1/2 − V _1/2, is given by:

Equation A3 expresses the contribution of drug binding to the different states to the overall effect on the availability curve. On this basis the statement that promotion of the open state will only shift V _1/2 by the same amount as V ₁ can be put in quantitatively. If this is the case, as in Sanguinetti et al. (1986), K _I is the same for both drug-free and drug-bound forms and K _dI = K _dO. Thus ΔV _1/2 = k ln (K _dO /K _dC), which is the shift in V ₁.

This model is also able to reproduce the effects of the antagonist (simulations not shown), by setting −2 mV as the shift in the activation curve and most important, K _d0 = 10 K _dI, a requirement to account for the ~30% reduction in Q1 _max from V _h = −40 mV and a shift of −25 mV in the availability curve.