Biomedical Engineering Reference
In-Depth Information
TABLE 14.3
Relative Diffusion Rates as a Function of Size of Species Compared to the Size of a Pore
Diameter (
˚
)
Substance
Ratio to Pore D
Relative Diffusion Rate
Water
3
0.38
50,000,000
Urea
3.6
0.45
40,000,000
Chloride ion
3.86
0.48
36,000,000
Potassium ion
3.96
0.49
200
Sodium ion
5.12
0.64
100
Glycerol
6.2
0.77
1
Galactose
8.4
1.03
0
Glucose
8.6
1.04
0
Lactose
10.8
1.35
0
From Cooney (1976).
other elements. The lipids include phospholipids (65 percent), cholesterol (25 percent), and
other lipids (10 percent). As was previously mentioned, substances that are not lipid soluble
must travel through pores within the cell membrane wall. Such transport of these sub-
stances depends on their relative size with respect to the pore size. Table 14.3 lists various
substances that can only travel through pores and their relative diffusion rates, which are
related to their permeability. An 8
˚
pore diameter is chosen for the purposes of compari-
son of diffusion rates.
Note that potassium and sodium have smaller diffusion rates despite their size, due to a
positively charged electrical potential. The pores also have a positive charge that affects the
transport of positively charged ions. The transport of substances is primarily due to the sub-
stance's individual concentration gradients across the cell membrane. However, substances
such as ions, which are suspended in water, are affected not only by their concentrations
and charge but also by their diffusivities. The
can be used to compute the rel-
ative electrical potential across a cell as a function of the concentrations of the ions as well as
their diffusivities. The Nernst equation for the three primary ions (Na, K, Cl) is as follows:
Nernst equation
RT
F
ln
D
Cl
Cl
1
þ
D
K
K
2
þ
D
Na
Na
2
E
¼
D
Na
Na
1
where R is the gas constant, T is the absolute temperature, and F is Faraday's constant.
Using the resting concentrations of the ions inside and outside a cell membrane, it is pos-
sible to compute the resting electrical potential across a cell. Note that the inside and out-
side concentrations of the positive ions (Na, K) are opposite to those of the negatively
charged ion (Cl). With RT/F
D
Cl
Cl
2
þ
D
K
K
1
þ
¼
26.5 mv (at body temperature), the resting transmembrane
potential is
5ln
(1
=
60
Þ
(103
Þþ
(1
Þ
(141
Þþ
(1
=
75
Þ
(10
Þ
E
¼
26
:
¼
74 mv
(1
=
60
Þ
(4
Þþ
(1
Þ
(5
Þþ
(1
=
75
Þ
(142
Þ
