Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 296

8.1 Introduction
Water is the most abundant and also one of the smallest molecules in liv-
ing organisms. It plays a fundamental role in many biological and physi-
ological processes. A living cell, whether it exists as a separate organism
or as a part of a multicellular organ or organism, in the course of all its
physiological functions continuously exchanges with the extracellular medium
water, nutrients, and metabolic waste products. This exchange takes place
across cellular membranes and is controlled by the transport properties of the
membranes.
Physical foundations of mechanisms of water and solute transport across
cell membranes have been subjects of numerous research and review papers
(Disalvo et al. 1989; Zeuthen and MacAulay 2002; Walsh et al. 2004; Kargol
2007, Elmoazzen et al. 2008). Initially, the processes of transport of non-
electrolytic substances across cell membranes have been described using the
Fick's law of diffusion. In 1932, Jacobs and Stewart (Elmoazzen et al. 2008)
gave quantitative estimates of membrane permeability and developed a dif-
ferential equation describing the rate of water and solute permeation as a
function of concentration, cell size, and the membrane permeation coe -
cient. They have made certain simplifying assumptions, such as the constancy
of membrane thickness and the extracellular concentration. Also, assuming
that the osmotic pressure for a given substance is proportional to its con-
centration, they de facto introduced an assumption that solutions are dilute.
This is also an assumption made in a vast majority of papers on membrane
transport.
Another assumption was that the transport is passive, that is, it is driven
by thermodynamic forces, such as concentration or pressure difference. This
is in contrast to active transport, which requires energy input from some
source, typically from the adenosine triphosphate (ATP) hydrolysis. Kedem
and Katchalsky (1958) (Katchalsky and Curran 1965) developed a formal-
ism describing transport properties of membranes using three parameters: the
coecients of filtration L p , permeation ω , and reflection σ . Starting from
the laws of linear thermodynamics of irreversible processes, they derived
equations for the volume flux and the solute flux induced by the osmotic
pressure and hydraulic pressure gradients. These equations, known as the
Kedem-Katchalsky (KK) equations, have been widely used in studies of pas-
sive membrane transport processes. Coecients of filtration, permeation,
and reflection have been found experimentally for numerous membranes and
solutes.
Despite its successes, the KK formalism has also certain limitations. In par-
ticular, often questioned is the reflection coe cient introduced to account for
interaction of water and solute fluxes permeating via the same channels. Many
authors believe that this coecient is frequently incorrectly interpreted and