Membrane permeability modeling: Kedem-Katchalsky vs a two-parameter formalism

Abstract

The analysis of experiments for the purpose of determining cell membrane permeability parameters is often done using the Kedem-Katchalsky (KK) formalism (1958). In this formalism, three parameters, the hydraulic conductivity (Lp), the solute permeability (Ps), and a reflection coefficient (final sigma), are used to characterize the membrane. Sigma was introduced to characterize flux interactions when water and solute (cryoprotectant) cross the membrane through a common channel. However, the recent discovery and characterization of water channels (aquaporins) in biological membranes reveals that aquaporins are highly selective for water and do not typically cotransport cryoprotectants. In this circumstance, sigma is a superfluous parameter, as pointed out by Kedem and Katchalsky. When sigma is unneeded, a two-parameter model (2P) utilizing only Lp and Ps is sufficient, simpler to implement, and less prone to spurious results. In this paper we demonstrate that the 2P and KK formalism yield essentially the same result (Lp and Ps) when cotransporting channels are absent. This demonstration is accomplished using simulation techniques to compare the transport response of a model cell using a KK or 2P formalism. Sigma is often misunderstood, even when its use is appropriate. It is discussed extensively here and several simulations are used to illustrate and clarify its meaning. We also discuss the phenomenological nature of transport parameters in many experiments, especially when both bilayer and channel transport are present.