John R. Howell

Computer simulation of sodium fluxes in frog skin epidermis

SummaryThe 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=115mm. Print-out data were obtained at 0.5-min intervals for 30 min, when steady states were obtained in 13 models studied, varying certainks 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 inks. These results are compared to published data on frog skin and good agreement between operation of skin epidermis and model was found.

Metabolic compartmentation in amphibian skin epidermis: A computer simulation study

Abstract In earlier publications a multicompartmental model of amphibian epidermis has been proposed and used to study the kinetics of flow of Na+ within and across the epidermis. The model featured two Na+ pumps, one located in the outermost, the other in the remaining inner epithelial cell layers. In the present study this model was applied to investigate effects of varying the activity of one or the other Na+ pump. By computer simulation data were obtained on: Transient and steady state flux rates under influx, backflux, and net flux initial conditions; steady state Na+ pool sizes in all compartments; flow of Na+ between compartments; pathways of flow; “outer border” electrical potential, and O2 consumption for Na+ transport. Each pump accomplishes a certain task (transepidermal Na+ transport; maintenance of bulk Na+ balance) with little overlap in the respective domains of activities. Certain exceptions are discussed. This model is consistent with data in the literature on the effects of drugs or temperature on Na+ transport and bulk Na+ balance.

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

SummaryThe operation of the multicompartmental frog skin epidermal model 10E described in the preceding paper was tested to find out by computer simulation whether it responds to changes in [Na+] in the same manner as frog skin. In the range from 5 to 115mm [Na+]0, the rate of net Na+ flux across skin is known to increase. The results can be fitted to Michaelis-Mentens law of reaction kinetics, or, alternately, to Hoshikos linear function, plotting fluxvs. log [Na+]0. Model 10E simulated the laboratory results on skin, provided that the rate coefficients at the site of entry of Na+ into the system were varied in exactly the same manner as they actually were found to vary in skin. In model studies, Na+ backflux (outflux) decreased with increasing [Na+]0, contrary to observations on skin. This discrepancy may be related to adaptive reactions in skins (decrease in permeability) when [Na+]0 is lowered, a feature that has not been modeled. It is known that the skin p.d. changes, mostly, by approximately 35 mV per decade change in [Na+]0. Model 10E gave very nearly the same result when the rate coefficients for entry of Na+ were changed as mentioned above (i.e., varied exactly as they were found to vary in skin). Skin and model 10E behaved similarly in that, at [Na+]0=[Na+]i=115mm, the extent to which labeling with Na* from the outside (12%) and from the inside (88%) is possible was the same. Model data are presented which show in which way the Na+ pools, [Na+] in the individual compartments, and intercompartmental fluxes changed with changing [Na+]0. Because of lack of experimental data on skin for comparison, these calculated results are purely hypothetical, but they are not unreasonable.

Computer simulation of Na* wash-out kinetics in frog skin epidermis

SummaryThe multicompartmental frog skin epidermis model proposed in a previous paper was applied to computer simulation studies on the kinetics of the wash-out process of Na* from frog skin. Both the kinetics of loading of the model membrane with Na* from the outside to reach steady-state conditions in all internal compartments, and of the wash-out process were followed. This was done for the case when two Na+ pumps were operative, or inoperative, simulating the inhibitory effect of ouabain on active Na+ transport in frog skin. The two pumps were characterized as transmembrane Na+ flow pumps, and internal Na+ maintenance pumps which contribute but little to net inward Na+ flux. The simulation results were in good agreement, both qualitatively and quantitatively, with data in the literature on the behavior of frog skin epidermis. This analysis gives support especially to the views held by Zerahn on location and size of the active Na+ transport pool in skin epithelium. Beyond this, however, this study clearly delineates the experimental conditions under which the estimation of the Na+ transport pool by the method of measuring the wash-out rate of Na* may be successful, and under which conditions this method will fail.

Model studies on Na∗ wash-out kinetics in frog skin epidermis☆

Abstract Employing a multicompartment frog skin epidermis model, a computer analysis of the wash-out process of Na∗ is presented. After loading the system from the outside to steady state level, wash-out is followed under the conditions that Na∗ could escape (a) to the outside (epidermal side) (b) to the inside (corium side) only, or (c) to both the outside and the inside. Controls were compared with studies simulating the effect of ouabain poisoning of the epidermis. In most cases two or three exponential terms were needed to fit the computer data on rate of appearance of Na∗ in the wash-out fluid, or on the decrease of Na∗ in the compartments. Comparing data in the literature on the behavior of stripped epidermis with the model data, it is found that the th values bear resemblance.

Computer analysis of the Na+ shunt pathways in frog skin epidermis.

Abstract By computer analysis of the flow of Na+ within and across a model membrane designed after the fine structure of frog skin epidermis, information was obtained on the role of the extracellular Na+ shunt pathway. The results obtained simulated known laboratory data on the changes that occur when the tight cell junctions in epidermis are made leaky. This is seen in: slight increase in rate of Na+ influx; slight decrease in Na+ net flux; considerable increase in Na+ backflux; increase in the amount of recirculating Na+ in the membranes; decrease in membrane potential and resistance, based on calculations, making certain assumptions. A detailed picture is given on compartmental characteristics that are very difficult to obtain experimentally, including flows of Na+ between compartments, and the kinetics of all washout process of Na∗ from the model membranes with closed and open extracellular shunt pathway.

Experimental verification of a multicompartment Na+-flow model of frog skin epidermis

Abstract A re-investigation was undertaken to consider the rates of transepidermal Na+-influx and Na+-backflux in the undamaged, isolated normal and Ouabain poisoned skins of Rana pipiens. The experimentally obtained rate values agreed with predictions derived from a computer model of skin epidermis. Both laboratory results and data computed by the use of a multicompartment epidermis model led to the conclusion that Ouabain greatly affects the flow of Na+ via the cellular, and not via the extracellular pathways. This study is presented to demonstrate the usefulness of the computer simulation technique in the analysis of the kinetics of flow of material across an epithelial membrane of considerable anatomical complexity.

Numerical simulation of Na washout rates in whole frog skin.

In this study we have applied a multicompartment whole frog skin model to a kinetic analysis of the process of washout of radioactive sodium (Na*) from both the epidermis and the underlying corium (dermis). This work is different from earlier publications from this laboratory in which only epidermis was considered. The whole skin model is designed in accordance with presently known anatomical and physiological information on frog skin. The chief aim of this analysis of well-known kinetic laboratory data was to present numerical computer data suggesting that the slow Na* washout component (t1/2≅15 min) seen in laboratory studies, results from the participation of cellular (glandular) structures in the corium, not those in the epidermis. In addition, computed data on [Na+] profiles in the model membrane are briefly presented. Although the [Na+] values appear intuitively reasonable, they await experimental confirmation, which requires an analytical technique with a resolution power far superior over that of conventional histochemical methods. The [Na+] gradients are, however, compatible with the known total Na+ content of skin and the overall input-output flows of Na+ across frog skin.

Nonlinear regression on multiple-dose data.

Two examples are given to show how Metzlers nonlinear regression program can be used to estimate parameters in a model with multiple dosing. The model of one example is a set of equations involving sums of exponentials, whereas the other model is a set of differential equations reflecting first order absorption and Michaelis-Menten excretion. In both cases no data were given in one of the dosing intervals.