Passive Mass Transport Processes in Cellular Membranes and their Biophysical Implications - Porous Media: Applications in Biological Systems and Biotechnology - page 321

6 × 10 -8
J v [m/sec]

4

J vwb

2

0

-2

J vwa

-4

-6

L p [m 3 N -1 s -1 ]
0.9

-8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 × 10 -12

FIGURE 8.7
Relations: J vwa = f ( L p ) and J vwb = f ( L p ), for human erythrocytes. (Reprinted
from publication, Kargol, A., Przestalski, M., and Kargol, M., Cryobiol. , 50,
2005. c

2005, with permission from Elsevier.)

of pore size distribution for a particular membrane and derived membrane
transport parameters from this knowledge. In practice it is the reverse, that
is, the transport parameters can be determined experimentally and we would
like to deduce some information about the pore numbers and sizes. In this
section we illustrate a proposed method for determining pore distribution
from known membrane transport properties and illustrate it on the example
of human erythrocytes (Kargol et al. 2005).
In previous paragraphs we assumed pore sizes are random. Let us also
assume that the distribution of pore cross-section areas is Gaussian (Kargol
et al. 2005):

h √ 2 π exp

s ) 2
2 h 2

N ( s −

f ( s )= − (8.103)

where s is the distribution mean, h is the standard deviation, and N is a
normalization constant. In the ME the reflection coecient for individual
pores can be either 0 or 1. However, the reflection coecient for the entire
membrane can be any number between 0 and 1, depending on the ratio of
permeable and impermeable pores for a given solute. Let us choose a particular
solute (s) with molecular radius r s . Let A at , A bt denote the total cross-section