Analysis of the all or nothing behaviour of Ca-dependent K channels in one-step inside-out vesicles from human red cell membranes

Flux theory for Poisson distributed pores with Gaussian permeability

The mean of the solute flux through membrane pores depends on the random distribution and permeability of the pores. Mathematical models including such randomness factors make it possible to obtain statistical parameters for pore characterization. Here, assuming that pores follow a Poisson distribution in the lipid phase and that their permeabilities follow a Gaussian distribution, a mathematical model for solute dynamics is obtained by applying a general result from a previous work regarding any number of different kinds of randomly distributed pores. The new proposed theory is studied using experimental parameters obtained elsewhere, and a method for finding the mean single pore flux rate from liposome flux assays is suggested. This method is useful for pores without requiring studies by patch-clamp in single cells or single-channel recordings. However, it does not apply in the case of ion-selective channels, in which a more complex flux law combining the concentration and electrical gradient is required.

Fluxes theory in experiments with random distributed channels on vesicles

When channels are randomly distributed in a population of vesicles, disregarding the number of channels per vesicle, these channels follow a Poisson distribution. This has been verified in many cases, determining the average of channels per vesicle. However, to determine kinetic parameters in population studies, a mathematical expression for the mean flux of solute through channels per vesicle is necessary. Hence, here, this mean flux is calculated, assuming Poisson distributed channels in a population of vesicle. Moreover, this result has been generalized to any number of different kinds of channels (i.e., channels with different permeabilities). These results, useful for in vitro experiments with mixed both channels and vesicles, can be supplemented with those from other techniques, in order to understanding how the nature of the lipid membrane affects kinetic parameters of channel.

All or none cell responses of Ca2+-dependent K channels elicited by calcium or lead in human red cells can be explained by heterogeneity of agonist distribution

We have studied the all or none cell response of Ca2+-dependent K+ channels to added Ca in human red cells depleted of ATP by incubation with iodoacetate and inosine. A procedure was used which allows separation and differential analysis of responding and nonresponding cells. Responding (H for heavy) cells incubated in medium containing 5 mM K lose KCl and water and increase their density to the point of sinking on diethylphthalate (specific gravity = 1.12) on centrifugation. Nonresponding (L for light) cells do not lose KCl at all. There is no intermediate behavior. Increasing the Ca concentration in the medium increases the fraction of cells which become H. No differences in the sensitivity to Ca2+ of the individual K+ channels were detected in inside-out vesicles prepared either from H or from L cells. The Ca content of H cells was higher than that of L cells. Cells depleted of ATP by incubation with iodoacetate and inosine sustain pump-leak Ca fluxes of about 15 mumol/liter cells per hour. ATP seems to be resynthesized in these cells at the expense of cell 2,3-diphosphoglycerate stores at a rate of about 150 mumol/liter cells per hour. Inhibition of 2,3-diphosphoglycerate phosphatase by tetrathionate increased 6-8 times the measured rate of uptake of external 45Ca. This was accompanied by an increase in the fraction of H cells. All or none cell responses of Ca2+-dependent K channels have also been evidenced in intact human red cells on addition of Pb. They have the same characteristics as those in responding and nonresponding cells. The detailed study of the kinetics of Pb-induced shrinkage of red cells suspended in medium containing 5 mM K showed that changes of Pb concentration changed not only the fraction of H cells but also the rate of shrinkage of responding cells. H cells generated by Pb treatment contained significantly more lead than L cells. The above results suggest that the two all or none cell responses studied here can be explained by heterogeneity of agonist distribution among cells. Since pump-leak fluxes exist in both cases, differences of agonist distribution could be generated by heterogeneity of pumping among cells. This interpretation turns interest from K channels to Ca pumps to explain the heterogeneous behavior of red cells in response to a uniform stimulus.

An estimate of the number of Ca2+-dependent K+ channels in the human red cell

An original approach has been designed to count Ca2+-dependent K+ channels in the human red cell using a preparation of inside-out vesicles. The relative frequency of vesicles having no K+ channels is estimated from the fraction of 42K+ (or 86Rb+) which is not released from loaded vesicles on maximal stimulation with Ca2+. The mean number of channels per vesicle is then calculated from this figure assuming a Poisson distribution for the K+ channels. From this value and the mean vesicular radius, computed from the volume/surface ratio, the mean number of channels per cell can be estimated. A value of 142 +/- 27 (mean +/- S.E.) was obtained, which is well above that estimated by comparison of unitary conductance and tracer equilibration rate measurements (about 10 channels/cell, Grygorczyk, R. Schwarz, W. and Passow, H. (1984) Biophys. J. 45, 693-698), but compares favourably with the channel density inferred from comparison with the number of Na+ pumps in a similar preparation of inside-out vesicles (100-200/cell, Lew, V.L., Muallem, S. and Seymour, C.A. (1982) Nature 296, 742-744). The procedure described here can be considered for general application as an alternative to other known procedures.