Fast sodium current in cardiac muscle. A quantitative description.

The voltage and time-dependence of the tetrodotoxin sensitive, fast sodium current in cardiac muscle is described with the Hodgkin-Huxley formalism using two microelectrode, voltage-clamp data obtained by Ebihara et al. (1980, J. Gen. Physiol., 75:437) from small spherical clusters of tissue-cultured 11-d-old embryonic heart cells. The data chosen from that study for quantitative analysis was obtained at 37 degrees C and in standard tissue-culture medium; it was not smoothed, and the capacitive transient was sufficiently brief to make its removal unnecessary. The sodium current, INa, is considered to be given by the following equation: INa = gNa m3h(V - VNa), where gNa is a constant (23 mS), VNa is the sodium equilibrium potential (29 mV), and m and h are independent, first order, dimensionless variables, which can vary between 0 and 1, as defined by the following differential equations, dm/dt = alpha m(1 - m) - beta mm and dh/dt = alpha h(1 - h) - beta hh, where the rate coefficients, alpha m = [0.32 x (V + 47.13)]/[1 - exp(V + 47.13)] and beta m = 0.08 x exp (-V/11). For potentials more positive than -40 mV, alpha h = 0 and beta h = 1/0.13 (exp [(V + 10.66)/ - 11.1] + 1), and for potentials more negative than -40 mV, alpha h = 0.135 x exp [(-80 - V)/6.8] and beta h = 3.56 x exp (0.079V) + 3.1 x 10(5) exp (0.35V). These functions of potential are similar to those of the squid at 15 degrees C, except that their magnitudes are larger (faster). Using these model equations the membrane current in a membrane patch with and without a series resistance was simulated. For the value of series resistance estimated for the preparation from which the analyzed data were obtained, the effects of series resistance on the shape and magnitude of the inward transient current were found to be minimal. It was concluded that their should be no large errors in the data, even in the absence of complete series resistance compensation.