3. CELLULAR ASPECTS OF ACTIVE TRANSPORT
181
(I) the equivalent pore radius in the membrane may be determined
from the study of the relative rates of water movement under osmotic
pressure gradient. An equivalent membrane with uniform cylindrical
pores is thus considered. If it is assumed that the only force available
for the transfer of water is the difference of osmotic pressure across the
membrane, the diameter of the pores may be calculated using the wellknown Poiseuille equation.
In various cells measurements have led to a calculated pore radius
around 4 A. Since the calculations rest upon the macroscopic laws of
Poiseuille and of Fick, Solomon and associates (156-158) have checked
the application of these laws to water flow and diffusion through pores of
such small radii. According to Renkin (159) the laws apply to equivalent
pore radii of 15-20 A. In view of the problem raised by the small pore
radius in cells, it is of importance to find an independent method of
measuring the diameter of cell pores. Such a method is afforded from a
consideration of the osmotic pressure developed across the membrane
in the presence of solute which can cross the membrane. The osmotic
pressure under these conditions differs from the classical van't Hoff
osmotic pressure (160). The relationship of these osmotic pressures may
be expressed in terms of a reflection coefficient σ, equal to OP obs /OP t heor
where OP 0 b S
=
osmotic pressure measured; OP t heor — osmotic pressure
calculated according to van't Hoff.
σ may take on all values between 0, characteristic of a membrane
with pores so large that they cannot discriminate between solvent and
solute, and 1 the value for a membrane which can discriminate between
solvent and solute.
When σ = 0, osmotic pressure disappears; if σ = 1, van't Hoff osmotic
pressure will be developed. As shown by Solomon and his associates
(161, 162) the determination of σ for a given solute may lead to a
description of the cellular membrane in terms of its equivalent pore
radius. The quantitative relationship between σ and the equivalent pore
radius rests upon two equations. One relating σ to the apparent pore
area for solute and solvent filtration, the other relating the apparent area
for solute and solvent filtration to the equivalent pore radius and the
radius of the solute molecule.
The results obtained show that the values for the pore radius are very
close to 4.5 A. for most of the cell studied; thus they are in fair agreement
with the value derived from the analysis of water flux.
It should, however, be pointed out that there is still a possibility that
the general agreement in the results is purely fortuitous. According to
the theory, the expression for the flux ratio of an uncharged substances
is (J)
181
(I) the equivalent pore radius in the membrane may be determined
from the study of the relative rates of water movement under osmotic
pressure gradient. An equivalent membrane with uniform cylindrical
pores is thus considered. If it is assumed that the only force available
for the transfer of water is the difference of osmotic pressure across the
membrane, the diameter of the pores may be calculated using the wellknown Poiseuille equation.
In various cells measurements have led to a calculated pore radius
around 4 A. Since the calculations rest upon the macroscopic laws of
Poiseuille and of Fick, Solomon and associates (156-158) have checked
the application of these laws to water flow and diffusion through pores of
such small radii. According to Renkin (159) the laws apply to equivalent
pore radii of 15-20 A. In view of the problem raised by the small pore
radius in cells, it is of importance to find an independent method of
measuring the diameter of cell pores. Such a method is afforded from a
consideration of the osmotic pressure developed across the membrane
in the presence of solute which can cross the membrane. The osmotic
pressure under these conditions differs from the classical van't Hoff
osmotic pressure (160). The relationship of these osmotic pressures may
be expressed in terms of a reflection coefficient σ, equal to OP obs /OP t heor
where OP 0 b S
=
osmotic pressure measured; OP t heor — osmotic pressure
calculated according to van't Hoff.
σ may take on all values between 0, characteristic of a membrane
with pores so large that they cannot discriminate between solvent and
solute, and 1 the value for a membrane which can discriminate between
solvent and solute.
When σ = 0, osmotic pressure disappears; if σ = 1, van't Hoff osmotic
pressure will be developed. As shown by Solomon and his associates
(161, 162) the determination of σ for a given solute may lead to a
description of the cellular membrane in terms of its equivalent pore
radius. The quantitative relationship between σ and the equivalent pore
radius rests upon two equations. One relating σ to the apparent pore
area for solute and solvent filtration, the other relating the apparent area
for solute and solvent filtration to the equivalent pore radius and the
radius of the solute molecule.
The results obtained show that the values for the pore radius are very
close to 4.5 A. for most of the cell studied; thus they are in fair agreement
with the value derived from the analysis of water flux.
It should, however, be pointed out that there is still a possibility that
the general agreement in the results is purely fortuitous. According to
the theory, the expression for the flux ratio of an uncharged substances
is (J)