Refined Evaluation of the Exponential Curve Parameters and Initial Exchange Rate Constant for 22 Na + Washout in Cultured Human Skin Fibroblasts

Abstract

A technique is proposed to evaluate the exponential curve parameters and the initial exchange rate constant (k ⁱ _e) for ²²Na⁺ washout from cultured human skin fibroblasts. After loading with the isotope, the cells were subjected to cold washing and warming steps. A desaturation curve for ²²Na⁺ washout was developed including the activity in the warming medium that corresponded to t = 0 min. Using nonlinear regression analysis, a general three exponential function adequately described the ²²Na⁺ washout in the time interval of 0-70 min. A back extrapolation was performed to estimate the initial time (t _i; a negative number) when the total activity was present in the cells. The t _i was substituted into the first derivative function of the three exponents to yield the k ⁱ _e. Calculated from the equilibrium distribution of ²²Na⁺ and the specific activity of the medium, the concentration of Na⁺ (in mM; mean ± SD) for fibroblasts of two individuals were 13.3 ± 2.3, n = 3, and 19.0 ± 5.2, n = 4. This indicates that the washout originated mainly or exclusively from the cellular milieu. Therefore, the k ⁱ _e represents the equilibrium exchange rate constant for Na⁺ washout from an inhomogeneous cell-related space. Multiple experiments demonstrated that the k ⁱ _e value for the two subjects were significantly higher than the initial slopes of the washout curves (k _A), a commonly used parameter to characterize Na⁺ washout, and significantly lower than the slopes of the fastest exponential components (k ₃): k ⁱ _e = 0.531 ± 0.017, k _A = 0.502 ± 0.019, and k ₃ = 0.557 ± 0.017 min ^-1 (n = 3) for one subject, and k ⁱ _e = 0.567 ± 0.065, k _A = 0.479 ± 0.031, and k ₃ = 0.667 ± 0.094 min^-1 (n = 6) for the other subject. The respective equilibrium exchange rates for these cells, namely the products of k ⁱ _e and cellular Na⁺ contents, were 1.10 ± 0.16 and 1.19 ± 0.24 nmole/10⁵ cells. Using the exponential curve parameters, analytical solutions of a serial model and a parallel model with three compartments were performed. According to these analyses the major portion of the cellular Na⁺ comprises a fast exchangeable cellular compartment. The relative size of this compartment (expressed as a fraction of total cellular Na⁺ content) for fibroblasts of the two subjects was 96.2 and 89.2% for the serial model and 96.1 and 89.3% according to the parallel model. The proposed technical and analytical approach can be applied to other cellular tracer washout with fast initial exchange rate and multiple exponential compartments, particularly in tissue culture preparations which have a relatively small and simple extracellular space.