Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 316

c si > c so

Extracellular
medium

r w

J va =J vwa

Cell

(a)

r s

J vb =J vwb +J vsb

J vsb
J vwb

J vsb =J vsd +J vsk

J vs

J vwb =J ∆ P +J ∆π

vwb vwb

(b)

r N

P i > P o
M

FIGURE 8.5
Model of an aquatic plant cell ( M is the cell membrane; c si ,c so is the concen-
trations; P i ,P o is the pressures; J va ,J vb ,J vwb ,J vsb ,J v s is the volume fluxes).
(Reprinted from publication, Kargol, A., Przestalski, M., and Kargol, M.,
Cryobiol. , 50, 2005. c

2005, with permission from Elsevier.)

pores is represented as membrane M and that the pores are ordered according
to sizes from top to bottom. All pores with radii r<r s , that is, pores imper-
meable to the solute are in part (a) of the membrane and all pores larger
than the size of solute molecule, that is, permeable pores are in part (b) of the
membrane. Membrane M has a filtration coecient L p , reflection coecient σ,
and the diffusive permeation coecient ω d . Parts (a) and (b) of the membrane
have filtration coecients L pa and L pb and reflection coecients σ a = 1 and
σ b = 0, respectively. We also assume there is an active solute volume flux, J vs .
Again, in a stationary state there is a constant osmotic pressure, hydraulic
pressure, and concentration gradient across the membrane.
The net volume flux across membrane M is

J v = J vM + J vs = 0

(8.93)

where J vM = J va + J vb is the passive volume flux, and J va , J vb are the vol-
ume fluxes across parts (a) and (b) of the membrane, respectively. From the
mechanistic volume flux equation (8.43) we can find the following expression
for the turgor pressure:

J vs
L p

∆ P = σ ∆Π − (8.94)

where ∆Π = RT ( c si − c s 0 ). In the stationary state, the solute volume flux

is zero as well, that is, J vs = J vsM + J vs =0 . From the mechanistic solute