Short-circuit current overshoot in epithelial sodium channels following apical sodium jump.

Following a jump in the sodium concentration of the solution bathing the apical surface of frog skin, the inward sodium current rises rapidly to a peak and then falls to a steady-state plateau. Lindemann suggested that this fall is due to rapid closing (in 2 to 3 s) of Na channels. However, the lack of a corresponding corner frequency in the sodium-noise spectrum indicates a much slower closing. We propose a compartmental mechanism for the overshoot: the inward Na current causes Na to accumulate in the intracellular region adjacent to the sodium channel--a virtual compartment--thereby decreasing the outside/inside [Na] ratio. As that ratio falls with rising [Na] in the virtual compartment, the force driving the current falls. The predictions of such a model have been curve-fitted to the time-course of the current overshoot. The differential equation describing the rate of change of [Na] in the virtual compartment has several time constants: a filling time for the compartment, a leakage time for escape of Na into the larger intracellular space, a mixing time in the apical bathing solution, and, of course, the channel-closing time. This curve fitting shows that channel closing becomes important only in the tail of the overshoot (> 15 s) with mean open times in a range from 7 s to 3 min. Similarly, the time-course of the current after washout of apical [Na] was fitted using the same differential equation, with the channel-closing time replaced with a channel-opening time. Other phenomena explainable by this compartmental model but not by fast channel closing include the open-circuit-potential overshoot, current overshoot through nystatin channels, and the less-than-59-mV-per-decade slopes of semilog plots of open-circuit potential vs. [Na].

Effects of basolateral ouabain, amphotericin B, cyanide and potassium on amiloride noise during voltage clamp of Rana pipiens skin support sodium-amiloride competition.

In a previous study, the amiloride-induced corner frequency (fc) was found to decrease as apical sodium was increased. This effect was small or absent when the basolateral surface was exposed to high potassium. It has been suggested that the apical sodium effect may be indirect, due either to increased intracellular [Na+] which repelled amiloride or to an increased potential at the apical surface which reduced amiloride affinity. High basolateral K+ might then suppress the sodium effect either by preventing intracellular [Na+] from increasing or by allowing a better clamp of the apical membrane potential by reducing basolateral membrane resistance and potential. We checked the effects of basolateral [K+], of cyanide and of ouabain at concentrations known to increase intracellular [Na+]. We found only negligible effects on fc. In addition, amphotericin B added to the basolateral bathing solution either in 115 mM Na+ or in 120 mM K+ had no significant effect on fc. We found that relatively wide variation in clamp potential under all conditions, even with active transport severely inhibited, left fc virtually constant. Since the amiloride kinetics were independent of clamp potential, we were able to measure paracellular and transcellular conductances separately by examining the voltage dependence of clamp current (linear) and amiloride noise power (quadratic). This made possible estimation of channel density and single-channel current.

Competitive blocking of apical sodium channels in epithelia.

Apical sodium-selective channels in frog skin, when blocked by amiloride or triamterene, exhibit fluctuations in current, the spectra of which are Lorentzian. These effects have been modeled previously with two-state and three-state models by Lindemann and Van Driessche. A recent observation by Hoshiko and Van Driessche that corner frequencies are lowered by increasing the apical sodium concentration cannot be accounted for by these models. We explore the possibility that sodium (S) and amiloride (A) compete for a site at the mouth of the channel. A new three-state channel model (sodium-occupied, open/unoccupied, open/amiloride-blocked) is analyzed. Its corner frequency is of the form fc = fco [1 + (A/KA)/(1 + S/KS)], consistent with the observed sodium dependence of the corner frequency. The minimum frequency, fco, and the inhibition constants, KA and KS, are expressed in terms of the rate constants of the model. To account for sodium self-inhibition, we postulate that two sodium ions in the channel may result in clogging--a fourth state. The two corner frequencies are calculated; so are the plateau values of the noise power. The noise power shows a maximum as a function of blocker concentration, as observed previously using triamterene. The four-state model predicts the observed suppression by small amounts of blocker of the low-frequency sodium (clogging) noise.

Oscillatory chemical reactions: the Tomita-Kitahara model.

Biological clocks share with excitable membrane (nerve, muscle) the requirement that the chemical systems that underlie them have unstable steady states, and hence are capable of limit-cycle oscillations. A particularly simple model of a chemical oscillator is discussed, especially with reference to the reverse reaction, which tends to damp the oscillations. For thermodynamic reasons (entropy production) reversibility can not, however, be neglected. The steady state, even when stable, does not minimize the dissipation function. Computer studies show the response to sinusoidal variation of the rate constant governing the autocatalytic step.