Figure 10. The effects of β₁-adrenoceptor stimulation on the fast Na⁺ current.

Panel A: Markov model of the fast Na⁺ channel. State diagram consists of two similar sub-diagrams for non-phosphorylated (upper sub-diagram) and phosphorylated-trafficked states (lower sub-diagram). C_Na1, C_Na2, and C_Na3 are closed states; O_Na is the open state; IF_Na, I1_Na, and I2_Na are the fast, intermediate, and slow inactivated states, respectively; IC_Na2 and IC_Na3 are closed-inactivated states; C_Na1p, C_Na2p, and C_Na3p are closed phosphorylated states; O_Nap is the open phosphorylated state; and IF_Nap, I1_Nap, I2_Nap, IC_Na2p, and IC_Na3p are phosphorylated inactivated states. The rate constants for activation, deactivation, inactivation, phosphorylation-trafficking, and dephosphorylation are given in Appendix S1. Panel B: Time course of the activation of the fast Na⁺ current upon application 0.1 µM isoproterenol. Experimental data of Matsuda et al. [85] obtained for the normalized peak I_Na in rabbit ventricular myocytes is shown by closed circles. Data is obtained with 40-ms pulses from a holding potential of −100 mV to −30 mV at stimulation frequency 0.2 Hz. A solid line shows the time course of simulated data on relative I_Na phosphorylation upon application of 0.1 µM isoproterenol. A dashed line shows the time course of the simulated normalized peak I_Na after application of 0.1 µM isoproterenol. The simulated currents are obtained with 20-ms pulses from a holding potential of −140 mV to −30 mV at stimulation frequency 0.04 Hz. Panel C: An increase in peak I_Na availability upon application of different concentrations of isoproterenol (in %). Experimental data by Kirstein et al. [84] obtained from rat ventricular myocytes are shown by black bars with errors; corresponding simulation data are shown by gray bars. Peak current-voltage (Panel D) and steady-state inactivation (Panel E) relationships for the fast Na⁺ current in ventricular myocytes upon stimulation with 0.1 µM isoproterenol. Experimental data for rats in the absence (unfilled circles) and presence (filled circles) of 0.1 µM isoproterenol are obtained by Kirstein et al. [84] (holding potential is −100 mV, conditioning pulse duration is 2,500 ms; isoproterenol data is obtained after 10 min of application). Simulated data are shown by solid (no isoproterenol) and dashed (10 min after application of 0.1 µM isoproterenol) lines (data are obtained by two-pulse protocol, holding potential is −140 mV, first pulse duration is 500 ms for voltages from −140 to +40 mV in 10 mV steps, second pulse duration is 50 ms at voltage −20 mV). Isoproterenol increases I_Na availability, but does not affect gating properties.