Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 325

were derived from different assumptions and thus they apply in somewhat
different situations. The KK and 2P formalisms are of thermodynamic nature
and do not consider microscopic details of membrane transport of water and
solute molecules. On one hand this makes them more general and more widely
applicable, on the other hand they provide only limited knowledge of the
relation between macroscopically observable flows and the underlying micro-
scopic transport mechanisms. In contrast, the ME formalism is based on a
specific model of membrane permeation—diffusion through pores. It uses con-
cepts borrowed from the KK formalism but it aims at linking the microscopic
transport properties of membranes with the macroscopic description of mass
transport. We conclude this chapter with a brief summary of the three for-
malisms, including their main equations.

1. Formalism KK (Kedem and Katchalsky 1958; Katchalsky
and Curran 1965)
Formalism KK is based on the three phenomenological coecients describ-
ing membrane transport properties: coecients of filtration, permeation, and
reflection. They are defined as L p =( J V / ∆ P ) ∆Π=0 , ω =( j S / ∆Π) J v =0 and
σ =(∆ P/ ∆Π) J v =0 . The volume flux density (i.e., the flux of water and per-
meable solute) is given as

J v = L p ∆ P − L p σ ∆Π (8.113)

and the solute flux density as

j s = ω ∆Π+(1

− σ ) c s J v (8.114)

The formalism applies to a variety of problems, independently of the nature
of membrane permeation mechanism, and has been widely used. Nevertheless,
there have been questions raised as to certain aspects of its interpretation. One
of the questions regarding the reflection coecient introduced to describe cou-
pling between water and solute fluxes, for example, when they occur through
the same pathways (Kleinhans 1998). Another question is about the interpre-
tation of the permeation coecient (Kargol 2002; Kargol and Kargol 2003,
2006). The parameter is measured with J v = 0, that is, in the presence of two
stimuli satisfying . For a membrane with σ = 1 the solute trans-

port is driven by both of these stimuli; hence, ω does not describe diffusive
solute permeation only.

| ∆ P | = | -σ ∆Π |

2. Formalism 2P (Kleinhans 1998)
The 2P formalism has been developed for situations where water and solute
fluxes are independent. In such cases the reflection coecient is redundant
and the transport equations can be simplified to the following form. Water
flux density is (assuming ∆ P= 0):

J vw = − L p RT ∆ c (8.115)