Changes in the extracellular osmotic pressure will create a situation in
which a cell will attempt to attain equilibrium by either gaining or
losing water until there is no osmotic gradient across the plasma
membrane. The Boyle-Van't Hoff equation describes the volume change that
must occur to achieve equilibrium, but ignors the kinetics. If the cell
volume is measured as a function of time, then it can be seen that
equilibrium is only achieved after an amount of time has elapsed.
Chinese Hamster Fibroblasts exposed to a concentrated saline
The kinetics of water movement out of the cell are determined by the
physical structure of the membrane. The detailed structure of biological
membranes is extremely complicated, however, to first order we can
understand permeability from a fairly simple model of membrane
The first component of the membrane is a lipid bilayer. Most membrane
lipids are esters of glycerol in which two of the alcohol groups are
replaced by long chain fatty acids and the third is replaced by a
phosphate head group.
The structure of phosphatidylcholine (lecithin) is shown here.
The fatty acid chains are non polar and thus hydrophobic whereas the
phosphate head group is hydrophilic, making the molecule amphipathic.
When these lipids are placed in water, they spontaneously form a bilayer
arrangement in which the hydrophilic head groups are in contact with the
water and the hydrophobic tails are separated from the aqueous
A lipid bilayer in an aqueous environment.
temperatures, the lipid bilayer remains fluid but is stabilized due to
the high energy required to mix the hydrophobic region with water. The
most stable configuration for these bilayers is a water-filled sphere,
which is indeed the structure that they form spontaneously. These
liposomes also act osmotically, with the permeability properties being
due to the composition of lipids that are used in their construction.
Although the solubility of water in the hydrophobic region is low, it is
still high enough for water to cross the bilayer in a
solubility-diffusion limited manner. Using lipids found in living cells,
it is possible to construct liposomes with permeability properties that
encompass the entire spectrum seen between various living cell
The second major component of cell membranes is protein. Proteins are
embedded in the plasma membrane for structural reasons, as sensors to
gather information about the extracellular environment, as pathways for
the transport of material between the intra and extracellular spaces,
and for many other purposes (including some that we have not yet
imagined). The regions within the primary structure of proteins that
span the lipid bilayer are generally composed of hydrophobic amino
acids. They, too, are fluid, being able to diffuse freely within the
plane of the bilayer as well as rotationally. This is the fluid-mosaic
model of membrane structure.
The fluid-mosaic model of membrane structure
The protein component is also able to form aqueous pores through the
bilayer by forming a cylinder with a hydrophobic outer surface and a
hydrophilic inner surface. Water is able to move through these pores
although most such pores are for other molecules and are in low enough
concentrations to not dominate the permeability characteristics of the
membrane. There are some cell types, however, that have specific water
pore proteins that exist solely to increase the cell's water
permeability; the chip28 protein is one such water pore.
Both diffusion through the lipid bilayer and movement through aqueous
pores will be subject to a temperature dependence (the former due to the
mobility of lipids and the latter due to the stabilization of the
tertiary structure of the protein) that acts in addition to the
temperature effects of diffusion itself. Although this information can
partly be used to discern the dominant routes for water movement across
a membrane, the structures are too complex and too poorly understood at
present to be completely described. Most models assume an Arrhenius
temperature dependence for water permeability (a relation that assumes
that some activation energy must be overcome for the (energetically
favorable) process to occur).
The most problematic obstacle for modeling membrane permeability comes
from considerations of the size of the membrane. All biological cells
have vast reserves of membrane stored as intracellular vesicles. These
vesicles can fuse with the plasma membrane to increase its area, and
regions of the membrane can be pinched off from the plasma membrane to
decrease its area. In addition, almost all plasma membranes contain
thousands of microvilli--thin extensions that protrude outward from the
cell surface like hair. The two common assumptions are to either treat
the membrane as the surface of a sphere (so that the membrane changes
area as the 2/3 power of volume) or to assume a constant surface area
(usually the area of a sphere with the isotonic cell volume). Neither is
entirely accurate, but if permeability parameters are measured using one
assumption, then the model will give accurate results if the same
assumption is used. Using a different assumption in the model, however,
can lead to enormous errors, since the area has such a significant role
in the permeability equations.
Now we wish to consider the time-dependent movement of water across cell membranes.
To begin with, weíll just consider a lipid bilayer in which water is poorly
soluble in the hydrocarbon tails. Water molecules will still be able to enter
the bilayer interior, due to their thermal motion. We saw before that
hydrophobic interactions were not actually repulsive forces, but simply less
attractive. Thus a water molecule which enters a bilayer will interact with
the hydrocarbons and may either cross the bilayer or leave the way it came (the
process is simply a random walk).
So we can apply Fickís laws to this situation to see what the flux of water is
across the bilayer. Using the equation