Movement of Molecules Across Cell Membranes
99
speed of molecular movement and the greater the net fl
ux;
(2) mass of the molecule—large molecules such as proteins
have a greater mass and lower speed than smaller molecules
such as glucose, and thus have a smaller net fl ux; (3) surface
area—the greater the surface area between two regions, the
greater the space available for diffusion and thus the greater
the net fl ux; and (4) the medium through which the mole-
cules are moving—molecules diffuse more rapidly in air than
in water because collisions are less frequent in a gas phase,
and, as we will see, when a membrane is involved, its chemical
composition infl uences diffusion rates.
Diffusion Rate Versus Distance
The distance over which molecules diffuse is an important
factor in determining the rate at which they can reach a cell
from the blood or move throughout the interior of a cell after
crossing the plasma membrane. Although individual mol-
ecules travel at high speeds, the number of collisions they
undergo prevents them from traveling very far in a straight
line. Diffusion times increase in proportion to the
square
of
the distance over which the molecules diffuse. For example,
it takes glucose only a few seconds to reach diffusion equilib-
rium at a point 10 μm away from a source of glucose, but it
would take over 11 years to reach the same concentration at a
point 10 cm away from the source.
Thus, although diffusion equilibrium can be reached
rapidly over distances of cellular dimensions, it takes a very
long time when distances of a few centimeters or more are
involved. For an organism as large as a human being, the dif-
fusion of oxygen and nutrients from the body surface to tis-
sues located only a few centimeters below the surface would
be far too slow to provide adequate nourishment. Accordingly,
the circulatory system provides the mechanism for rapidly
moving materials over large distances using a pressure source
(the heart). This process, known as bulk fl ow, is described in
Chapter 12. Diffusion, on the other hand, provides movement
over the short distance between the blood and tissue cells.
The rate at which diffusion can move molecules
within
a cell is one of the reasons cells must be small. A cell would
not have to be very large before diffusion failed to provide suf-
fi cient nutrients to its central regions. For example, the center
of a 20-μm diameter cell reaches diffusion equilibrium with
extracellular oxygen in about 15 ms, but it would take 265
days to reach equilibrium at the center of a cell the size of a
basketball.
Diffusion Through Membranes
The rate at which a substance diffuses across a plasma mem-
brane can be measured by monitoring the rate at which its
intracellular concentration approaches diffusion equilibrium
with its concentration in the extracellular fl uid. For simplici-
ty’s sake, let us assume that because the volume of extracellu-
lar fl uid is large, its solute concentration will remain essentially
constant as the substance diffuses into the small intracellular
volume (
Figure 4–4
). As with all diffusion processes, the net
ux,
J,
of material across the membrane is from the region of
higher concentration (the extracellular solution in this case)
to the region of lower concentration (the intracellular fl
uid).
The magnitude of the net fl
ux is directly proportional to the
difference in concentration across the membrane (
C
o
C
i
), the
surface area of the membrane
A
, and the membrane
perme-
ability coeffi
cient
P
:
J
=
PA
(
C
o
C
i
)
The numerical value of the permeability coeffi cient
P
is
an experimentally determined number for a particular type of
molecule at a given temperature, and it refl ects the ease with
which the molecule is able to move through a given mem-
brane. In other words, the greater the permeability coeffi cient,
the larger the net fl ux across the membrane for any given con-
centration difference and membrane surface area.
The rates at which molecules diffuse across membranes,
as measured by their permeability coeffi cients, are a thou-
sand to a million times slower than the diffusion rates of the
same molecules through a water layer of equal thickness.
Membranes, therefore, act as barriers that considerably slow
the diffusion of molecules across their surfaces. The major fac-
tor limiting diffusion across a membrane is the hydrophobic
interior of its lipid bilayer.
Diffusion Through the Lipid Bilayer
When the permeability coeffi cients of different organic mol-
ecules are examined in relation to their molecular structures,
a correlation emerges. Whereas most polar molecules diffuse
into cells very slowly or not at all, nonpolar molecules diffuse
much more rapidly across plasma membranes—that is, they
have large permeability constants. The reason is that non-
polar molecules can dissolve in the nonpolar regions of the
membrane occupied by the fatty acid chains of the membrane
phospholipids. In contrast, polar molecules have a much lower
solubility in the membrane lipids. Increasing the lipid solubil-
ity of a substance by decreasing the number of polar or ion-
ized groups it contains, will increase the number of molecules
dissolved in the membrane lipids. This will increase the fl
ux
i
Time
Concentration
C
i
=
C
o
C
= intracellular concentration
C
o
= constant extracellular concentration
Figure 4–4
The increase in intracellular concentration as a solute diffuses from
a constant extracellular concentration until diffusion equilibrium
(
C
i
=
C
o
) is reached across the plasma membrane of a cell.
previous page 127 Vander's Human Physiology The Mechanisms of Body Function read online next page 129 Vander's Human Physiology The Mechanisms of Body Function read online Home Toggle text on/off