Computer simulation of sodium fluxes in frog skin epidermis

Abstract

Summary. The operation of a seven-compartment model is described with respect to flows of Na + within and across this system, simulating published results obtained on frog skin. The seven compartments represent: one outside and one inside solution compartment; the subcorneal space; the first reacting cell layer (1.RCL); the remaining cell compartment; the non-, or slowly exchangeable Na + compartment; the extracellular space. Assuming reasonable volumes for the epidermal compartments and further chosing, by trial and error, appropriate rate constants, a set of seven simultaneous linear differential equations was solved by the application of the Continuous System Modeling Program (CSMP), using an IBM 1130 computer. Initial conditions for influx, backflux and net flux were taken which correspond to [Na+]0; [Na+]i= 115 mM. Print-out data were obtained at 0.5-min intervals for 30 min, when steady states were obtained in 13 models studied, varying certain k's thus simulating actions of chemical agents (hormones; drugs). Simulation was achieved with regard to rate of influx, backflux and net flux, steady-state time (30 min), and electrical potentials. In addition, this approach gave detailed information on Na + pool sizes and their variations with changes in k's. These results are compared to published data on frog skin and good agreement between operation of skin epidermis and model was found.During the last decade the three-compartment model proposed by Curran, Herrera and Flanigan [14] has frequently been used in kinetic studies of movement of ions across epithelial membranes. Some applications have recently been reviewed [38]. In this model, compartments 1 and 3 represent, respectively, the outside and the inside fluid compartments, and compartment 2 is an epithelial compartment located between two major barriers to Na § movement. From light-and electron-microscopic studies on frog skin epidermis [18,19,[32][33][34] it would appear that in inward and outward movement of Na + several epithelial compartments should be considered as significant parts of a flow model. For instance, Zerahn [43] has found it useful to consider three epithelial compartments in the interpreta-

Computer simulation of the response of frog skin epidermis to changes in [Na+]0

“…Compartments 1 and 7 in Fig. 1 of the preceding paper [10] correspond to "outside" (o), and "inside" (i) solution in skin experiments. Subscripts 1 (o) and 7 (i) are used interchangeably in the following text and illustrations.…”

“…The basic model used in this study is in all respects identical to model 10E described earlier [10]. Compartments 1 and 7 in Fig.…”

“…(b) Calculations by using the integrated steady-state flux Eqs. (8) and (9) given in the preceding paper [10]. Flux rates are given as gEquiv x cm-z x hr-1.…”

“…The six simultaneous linear differential flow equations describing the operation of the models, both in conventional and matrix form are given in the preceding paper [10]. Estimations for the amounts of Na § in the compartments (S-values) were obtained by the use of an IBM 360 computer with application of the Continuous System Modeling Program (CSMP).…”

“…The operation of the model, designated earlier [10] as model 10E, simulated to a remarkable degree the facts as we know them from studying Na § transport in frog skin.…”