Published January 1, 1968
Filtration Coefficient of the Axon
Membrane As Measured with
Hydrostatic and Osmotic Methods
F E R N A N D O F. V A R G A S
From the Laboratory of Biophysics, Faculty of Sciences, University of Chile, Clasifieador
198, Santiago, Chile
T h e filtration coefficient or h y d r a u l i c c o n d u c t i v i t y of cell m e m b r a n e s is
usually d e t e r m i n e d b y r e c o r d i n g the r a t e of swelling or shrinkage of ceils in
response to a c h a n g e of e x t e r n a l osmotic pressure. T h i s m e t h o d is based on
some assumptions a m o n g w h i c h we will m e n t i o n two: (a) the cell behaves as
a p e r f e c t o s m o m e t e r , a n d (b) the solute used does n o t e x e r t a n y effect o t h e r
t h a n the p u r e l y osmotic one u p o n the m e m b r a n e .
T h e d e v e l o p m e n t of perfusion techniques (1) has m a d e it possible to c o n t r o l
the internal composition of the a x o n a n d therefore the i n t r a c e l l u l a r osmotic
pressure. M o r e o v e r , a t e c h n i q u e w h i c h makes it possible to m o d i f y the h y d r o static pressure in perfused as well as in n o n p e r f u s e d axons has b e e n d e v e l o p e d
(2).
I3
The Journal of General Physiology
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ABSTRACT
The hydraulic conductivity of the membranes surrounding the
giant axon of the squid, Dosidicus gigas, was measured. In some axons the
axoplasm was partially removed by suction. Perfusion was then established by
insertion of a second pipette. In other axons the axoplasm was left intact and
only one pipette was inserted. In both groups hydrostatic pressure was applied
by means of a water column in a capillary manometer. Displacement of the
meniscus in time gave the rate of fluid flowing across the axon sheath. In
both groups osmotic differences across the membrane were established by the
addition of a test molecule to the external medium which was seawater. The
hydraulic conductivity determined by application of hydrostatic pressure was
10.6 4- 0.8.10 -8 cm/sec cm H 2 0 in perfused axons and 3.2 4- 0.6.10 -8 cm/sec
cm H 2 0 in intact axons. When the driving force was an osmotic pressure
gradient the conductivity was 4.5 4- 0.6 X 10-1° cm/sec em HzO and 4.8 40.9 X 10-1° cm/sec em H 2 0 in perfused and intact axons, respectively. A
comparable result was found when the internal solution was made hyperosmotic. The fluid flow was a linear function of the hydrostatic pressure up to
70 cm of water. Glycerol outflux and membrane conductance were increased
1.6 and 1.1 times by the application of hydrostatic pressure. These increments
do not give an explanation of the difference between the filtration coefficients.
Other possible explanations are suggested and discussed.
Published January 1, 1968
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THE
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• VOLUME
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• I968
I n the p r e s e n t p a p e r fluid flow across the a x o n s h e a t h h a s b e e n p r o d u c e d
b y c h a n g i n g either the h y d r o s t a t i c or the osmotic pressure. T h e h y d r a u l i c
c o n d u c t i v i t y of the m e m b r a n e has b e e n f o u n d to d e p e n d on t h e n a t u r e o f t h e
d r i v i n g force used to p r o d u c e fluid flow.
A n increase in the i n t e r n a l h y d r o s t a t i c pressure c o u l d p r o d u c e a m e c h a n i c a l
d e f o r m a t i o n of the a x o n m e m b r a n e a n d c h a n g e its properties. A s t u d y of
this was m a d e b y m e a s u r i n g glycerol outflux a n d electric c o n d u c t a n c e a t rest
a n d u n d e r pressure.
A p r e l i m i n a r y r e p o r t of this w o r k has a l r e a d y b e e n g i v e n (2, 3).
MATERIAL
AND
METHODS
Biological Material
Experimental Setup
Fig. 1 shows a diagram of the general experimental setup. The axons were placed in a
Lucite chamber 4 cm in length and 3 cm wide. The chamber was filled with seawater
which completely covered the axon. T w o Lucite stands of the same height as the
chamber were placed on each side. T h e y supported the axon and created air gaps
between the point of insertion of the pipettes and the rest of the cell. T o keep the
axon stretched, the silk threads tying its ends were fixed to the Lucite platform which
served as a base for the chamber.
Electrical Stimulation and Recording
A Grass stimulator with isolation unit was used to deliver square pulses of 0.5 msec
duration at a frequency of 1 per sec. T w o platinum wires placed on the left side of
the chamber were used as stimulating electrodes. Recording of nerve impulses was
done with a 502 A Tektronix oscilloscope connected to a pair of platinum wires placed
at the right side of the chamber.
Perfusion Technique
The perfusion technique was essentially the same as that developed by Tasaki et al.
(1) and slightly modified for our particular purposes.
A pipette, 500 ~ in diameter, was mounted on a micromanipulator designed by
M. Luxoro. This micromanipulator has a longitudinal excursion of 12 cm. The pipette
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The Chilean squid, Dosidicusgigas, was caught with hooks, 5 to 10 miles offshore. A
piece of the mantle containing the nerves was immediately separated and placed
in seawater cooled nearly to 0°C. 1-2 hr later, the nerves were dissected.
Four to six giant axons were obtained from each squid. The diameters ranged
from 800 to 1200 # and each was 20 cm or more in length. Usually about 10 cm of
axon was cut out near the stellate ganglion. The isolated axon was then tied at both
ends with silk thread and extensively cleaned under a microscope. Once the axons
were cleaned, they were placed in a beaker containing artificial seawater and kept
at 4°C until they were used.
Published January 1, 1968
FER_~.~x)o F. VAROAS FiltrationCoefficientof Axon Membrane
I5
was inserted through the right end of the axon and as it was pushed ahead the axoplasm was sucked out through polyethylene tubing. The insertion was continued
until a distance of 0.5 cm from the left border of the chamber was reached with the
end of the pipette. A second pipette, 200 ~ in diameter, connected to a fluid reservoir,
was then introduced through the left end of the axon. It was forced to advance until
its tip penetrated inside the large pipette. At this point, fluid was run in the same
S
R
CROSS-SECTION
VIEW FROM ABOVE
H
FIOUR~ 1. Diagram (not to scale) of the experimental setup. Cross-section at the
upper left shows the perfusion channel P.C. At the upper right the axon A is shown
sitting in the external solution ES. S and R are the stimulation and recording electrodes.
The general view (center) shows the perfusion reservoir P.R., the stopcock S.C., the
stimulator (Sfim), and the isolation unit I.U. The oscilloscope O is connected to the
external recording electrodes. The pressure device consists of a manometer M, a syringe
S, and,Yaclamp C.
direction through both pipettes to wash out any axoplasm remaining inside. Once
this procedure was completed the large pipette was moved back until its tip reached
a point 0.5 cm from the right border of the chamber. Thereafter, both ends of the
axon were firmly tied around the pipettes with silk thread.
Perfusion was considered successful when fluid was running freely out of the back
end of the large pipette and the recorded action potential was normal.
Fluid Movement in Intact Axons
When fluid movement was measured in more intact axons only one pipette was
inserted. This was 200-220 # in diameter, and had a longitudinal slit, 100/z in width,
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•
Published January 1, 1968
16
THE JOURNAL
OF GENERAL
PHYSIOLOGY
• V O L U M E 51
• 1968
which ran 3 cm down from the tip. 1 The pipette lumen was filled with an enamelled
platinum wire 100 t~ thick. I n this way, penetration of axoplasm inside the pipette
was avoided.
The pipette was inserted through the right side of the axon and moved ahead until
its tip almost reached the left border of the chamber. In some experiments the pipette
was pushed further and it emerged through a cut on the left side of the axon. I n the
former case, the wire was withdrawn through the rear end of the pipette while this
was filled with flu~id. I n the latter, the wire was withdrawn through the tip while
pressure-driven fluid filled the pipette lumen. Thereafter the pipette was moved 1 cm
back, and the distal end of the axon was tied proximal to the cut. Chlorophenol red
was added to the internal solution in order to check whether fluid was filling the
pipette lumen.
Volume Flow Measurement
Volume Recording
The diameter of the axon was measured with a Bausch and Lomb microscope with an
ocular micrometer giving a resolution of 4 ~.
Experimental Procedure
The temperature in the room was maintained constant at 16 ° 4- 1°C. The temperature of all the fluids used in the experiments was essentially the same as that of the
room.
T o start an experiment, the column of fluid in the manometer was raised to the
desired pressure by means of the syringe which was then locked. The polyethylene
1 T h e a u t h o r is d e e p l y i n d e b t e d to M r s . T a s a k i
for m a k i n g m o s t of these v e r y s p e c i a l p i p e t t e s .
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A capillary glass manometer was connected to the rear of the pipette which had been
inserted in the axon through polyethylene tubing 1.5 m m in outside diameter. A
calibration with mercury indicated a volume of 0.26 ~1 per m m for the capillary
lumen of the manometer. The flow of fluid across the axon membrane was followed
by the displacement of the meniscus on a scale attached to the manometer.
A careful check of all possible leaks in the system was made. T o this end, the
height of the water column was increased to 80 cm or more and the polyethylene
tube connecting the manometer to the pipette was closed. A syringe connected
through a T tube to the manometer was used to raise the pressure. The level of the
column was checked 12 hr later and a variation of less than 5 m m was found in this
period. When this was expressed as a volume change per rain, it amounted to less
than 1% of the actual flow recorded in the same period. This checking was repeated
several times during the course of the work. Some experiments were done in which
chlorophenol red was added t o t h e solution for perfusion or for filling the single pipette. After 3 hr no traces of the dye were observed in the seawater outside or in the
region where the axon was tied. Moreover, a brief check for leaks was made for each
experiment. Evaporation was not a problem since the air in the laboratory was
permanently near saturation with water vapor.
Published January 1, 1968
FE~NANDO F. VAROAS FiltrationCoefficientof Axon Membrane
17
tubing connecting the fluid reservoir to the small pipette on the left side was clamped.
After a check for possible leaks records of the axon diameter and meniscus level in
the manometer were obtained.
When perfused axons were used, the fluid was allowed to run every 30 rain or so
in order to keep the inside concentration as constant as possible.
T o switch from standard to hyperosmotic seawater a valve on the bottom of the
chamber was opened. At the same time the hyperosmotic solution was added. After
washing for nearly 30 sec the valve was closed.
T o change the internal osmolarity sucrose was added to the perfusion fluid. T h e
normal solution in the reservoir was then replaced by this hyperosmotic solution. The
polyethylene tubing connecting the reservoir to the inlet pipette was disconnected
and fluid allowed to run in order to wash the dead space in the tubing. Once this
procedure was ended the reservoir was again connected to the inlet pipette and perfusion reinitiated until the normal fluid in the axon was completely replaced by
hyperosmotic solution.
The nerves were either perfused or injected with solutions containing l~l-labeled
glycerol. T h e radioactivity used was 2 X 106 cpm/rnl for perfusion and 15.6 X 105
c p m / m l for injection. 2-3 ~1 of the radioactive solutions were injected through a
pipette 150-200 # in diameter.
The outflux of the radioactive material was followed by collecting the external
seawater (0.5 ml) and washing with another 0.5 ml of the same solution. This procedure was repeated every 10 rain. The collected seawater was dried in planchets.
T h e radiation of each sample was measured with a Nuclear Chicago counter (Nuclear Chicago Corp., Des Plaines, Ill.) in conjunction with a gas flow detector. As
each sample contained the same volume of seawater self-absorption was constant
from sample to sample,
I n axons perfused with radioactive solutions the outflux measurements were made
with the system closed so as to make the increase of the inside pressure feasible.
Measurements of Membrane Conductance
T o measure conductance two electrodes were introduced inside the perfused
axons. One was a pipette 120 # in diameter filled with 0.6 M KC1. The other electrode
consisted of a silver chloride-silver wire 100 t~ in diameter. Both electrodes were
introduced through the outflux pipette which was then sealed with a drop of sticky
wax. The KCI electrode was used to record m e m b r a n e potentials through a Bak
electrometer. T h e silver chloride wire was used to apply De pulses obtained from a
Grass stimulator.
A grounded calomel electrode was placed in the external medium to serve both as
a reference for potential measurements and to close the circuit for passing current.
Pulses of 10-15 msec duration were delivered. The current was measured in the
oscilloscope by adding a 100 kohms resistor in series with the circuit. Both ends of
the resistor were connected to the oscilloscope. T h e deflection of the b e a m was photo-
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Glycerol Outflux
Published January 1, 1968
i8
THE
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PHYSIOLOGY
• VOLUME
5I
•
I968
graphed when a pulse was delivered and the current calculated from the voltage
change produced and the known resistance.
Solutions
The perfusion medium was made up of 0.385 m (moles per liter of solution) potassium
glutamate, 0.385 m glycerol, 0.0204 g K~HPO4, and 0.0025 ~ KH~PO4 with a pH
of 7.2-7.3 and an osmolarity, as measured on a Fiske osmometer, of 1160 milliosmols
per liter. The external medium was either natural seawater or a substitute; i.e.,
0.48 ~ NaCI, 0.01 M KC1, 0.01 M CaCI~, 0.052 M MgCI2, and 0.005 g Tris, with a
pH of 8 and an osmolarity of 1000. In the measurements of Lpo the osmolarity of a
medium was increased by addition of the required quantity of sucrose, glycerol, or
NaC1.
RESULTS
T h e filtration coefficient, i.e. hydraulic conductivity, obtained using hydrostatic pressure, is referred to as L p h while the one obtained using osmotic
pressure is Lpo. Both are given in cmS/sec per cm ~ of m e m b r a n e area per cm
H 2 0 , the hydraulic equivalent of the osmolarity being c o m p u t e d with the assumption that the reflection coefficients of all solutes are unity. T h e evaluation of the m e m b r a n e area assumes a uniformly cylindrical axon.
Fig. 2 shows the time course of the axon volume and volume flow after the
internal pressure was raised in a perfused axon. It can be observed that there
was a swelling of the axon. T h e axon volume continued to increase for 10-15
rain after the pressure was raised. During this time the m o v e m e n t of the
meniscus in the m a n o m e t e r reflected the filling of the axon plus the volume
flow through the membrane. This explains why the flow starts high and decreases, reaching a constant level after some minutes.
T h e measurement of volume flux was initiated once the axon volume became constant. With pressures of about 13 cm of water the volume flow"
through the m e m b r a n e was zero.
In the perfused axons the volume flux was a linear function of the hydrostatic pressure as seen in Fig. 3. T h e slope of this line rendered a filtration coefficient of 10.6 -4- 0.8.10 -8 (mean i SE).
T h e intercept of the line on the abscissa did not occur at zero pressure but
at 13.5 cm of water. This should be corrected by the capillary rise which
amounts to 5 cm of water. T h e effective value is then 8.5 cm of water. Capillary rise does not influence the magnitude of L p h which was obtained as a
slope or of L p o which was obtained as a ratio between an increase in flow and
the osmolarity which produced it. T h e fact that the intercept is 8.5 cm H 2 0
instead of zero is in a g r e e m e n t with the difference in osmolarity of the internal
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The Hydraulic Conductivity Measured Using Hydrostatic Pressures As the
Driving Force
Published January 1, 1968
FERNANDO F. VAROAS Filtration Coeffident of Axon Membrane
1.40
39
1.2(3 '~
-~
x9
38
~,
i.(3(3
/"'
37
b
O.S(3
36
~-'.~ 0.60
35 >~
0.40
34
0.20
' 33
i
0
5
10
15
TIME (rain)
20
FIoum~ 2. Volume flow across
the axon membrane (open circles),
and volume of the axon (filled
circles), as a function of time in a
perfused axon. The internal pressure was raised to 60 cm of water
at time zero.
25
a n d external solutions. W e c o u l d calculate the pressure w h i c h should b a l a n c e
a c o n c e n t r a t i o n difference of 160 milliosmols b y using the e q u a t i o n
w h e r e A~r is the osmotic pressure a n d A P is the h y d r o s t a t i c pressure difference.
I n t r o d u c i n g the value of A~r, w h i c h for the c o n c e n t r a t i o n difference a n d
t e m p e r a t u r e used, a m o u n t s to 3.8 • 108 c m H 2 0 a n d taking the values of 2.2
10 -l° for L p o a n d 10 -7 for L p h w h i c h a p p e a r in T a b l e I I I , a pressure of 8.36
c m H 2 0 obtains. This is a l m o s t identical to 8.5 c m w h i c h was the c o r r e c t e d
value of the i n t e r c e p t of the flow vs. pressure line.
A plot of v o l u m e flux vs. pressure for i n t a c t axons was n o t possible because
the pressure r a n g e was too narrow. F o r this reason L p h in these axons was
o b t a i n e d as a n a r i t h m e t i c m e a n w h i c h was 3.2 ± 0.6 • 10 -s ( m e a n =E SE).
T h e flows o b t a i n e d in these e x p e r i m e n t s are s h o w n in T a b l e I. T h e internal pressure at w h i c h there was n o v o l u m e flux was d e t e r m i n e d in two exp e r i m e n t s a n d f o u n d to be 15 c m H 2 0 .
%
7-
x
E
u
,.-:,
FlouRs 3. Volume flux as a function of the hydrostatic pressure.
The line was calculated by the
least squares method, r = 0.91.
10
20
30
40
50
60
HYDROSTATIC PRESSURE (cm H20)
70
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Lpo
L p h A~r = Ap
Published January 1, 1968
THE JOURNAL OF GENERAL PHYSIOLOGY • VOLUME 5I
20
• I968
The Hydraulic Conductivity of Giant Axons Measured Using Osmotic Pressure
As the Driving Force
Fig. 4 shows the time course of volume flow when the seawater was made
hyperosmotic. The time to reach the m a x i m u m flow after switching to a
hyperosmotic solution was 2-5 min in perfused axons and 15-20 min in intact
ones. This different behavior can be ascribed to the different techniques used
in both cases.
TABLE
I
H Y D R A U L I C C O N D U C T I V I T I E S (Lph) O F I N T A C T A X O N S
AS M E A S U R E D U S I N G H Y D R O S T A T I C P R E S S U R E
Experiment No. Axondiameter
Ap*
o n 1-12o
No. 12
1000
700
800
800
800
1000
900
1000
1000
970
1000
930
M e a n = 900
43.13
50.48
43.10
24.20
63.15
44.70
46.90
44.61
43.97
37.93
42. O0
43. O0
Lph 108
em /sec
0.87
1.50
1.60
0.58
2.12
1.20
0.38
0.85
0.85
3.22
1.25
2.32
2.02
3.01
3.72
2.39
3.36
2.65
0.81
1.91
1.93
8.72
2.99
5.40
M e a n 4- sE = 3.2 4- 0 . 6
* P is the h e i g h t of the w a t e r c o l u m n in each e x p e r i m e n t m i n u s 15
c m H 2 0 , t h e b a l a n c i n g p r e s s u r e at w h i c h v o l u m e flux was zero.
As can be seen in Fig. 4 the increase in external osmolarity produced a
volume flux superimposed upon the flux produced by the hydrostatic pressure. T h e volume flux in the steady state reached before the osmotic change
was subtracted from the total flux found after switching to the hyperosmotic
solution. The difference was divided by the osmotic pressure in centimeters of
H~O and an osmotic Lp obtained.
As can be seen in Table II the filtration coefficient of perfused axons, 4.8
-4- 0.92 × 10 -1° crn/sec cm H20, was almost identical with the Lp for intact
ones which was 4.5 + 0.5 X 10-1°. It is noteworthy that Lpo was significantly
smaller than L p h (P < 0.001), their difference being of two orders of magnitude as seen in Table III.
In five experiments in which sodium chloride and glycerol were the test
molecules used to make the external solution hyperosmotic the responses were
very similar to that obtained with sucrose. T h e filtration coefficients obtained
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1
2
3
3
3
4
5
6
7
8
9
10
Volume flux 10a
Published January 1, 1968
FERNANDO
Filtration Goefficient of Axon Membrane
F. V A R G A S
oI
%
9"
"; 7t
SEAWATER
J
/
:,,.
~ z
o
".-,"
1"¢
~)
_j
r
" 11/ . . . .
~
~
1
/;
0.1 0.2 0.3 0.4
CONCENTRATIOND'FFERENCE(M/L)
/
/
j
i
h
[
/
=
0
~
0.4 M SUCROSE
'
~'s
'
2's
'
gs
'
TIME (MIN)
is
'
~
~'s
'
b
6's
~
FxouR~ 4. T i m e course of the volume flux across the axon m e m b r a n e in two experiments in which 0.4 M sucrose was a d d e d to the seawater. Filled circles, perfused axon;
o p e n circles, intact axon. Small g r a p h inserted shows volume flux as a function of the
external concentration of sucrose in a perfused axon.
TABLE
II
H Y D R A U L I C C O N D U C T I V I T I E S (Lpo) AS
MEASURED USING OSMOTIC PRESSURE
Experiment No. Axon diameter
It
Osmotic pressure Volume fluffi 10G
arm
1010 Lpo
cm]sec
Perfased axon
7
8
26
26
26
19
1060
855
850
850
850
850
700
No. 7
M e a n = 860
8
9.50
9.50
14.22
4.75
9.50
11.85
9.50
6.10
4.5
4.1
2.43
4.43
5.17
4.92
6.40
2.65
2.90
5.10
4.56
4.36
5.20
M e a n 4 - s E = 4.5 4- 0.5
Inta6t axon
1
2
3
7
No. 4
1000
700
800
1000
M e a n = 870
28.8
9.6
9.6
2.38
7.00
4.00
6.30
2.30
2.43
4.17
6.50
6.00
M e a n 4-sF. = 4.8 4- 0.9
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g
Published January 1, 1968
THE J O U R N A L OF GENERAL P H Y S I O L O G Y
22
• VOLUME 51
• I968
were 2.8 × 10-1° for glycerol (three experiments) and 4.1 × 10-1° for NaC1
(two experiments). Even though the Lp for glycerol was slightly smaller,
both Lp's agree well with the one obtained with sucrose.
In two experiments the inside osmolarity was increased by addition of
sucrose to the perfusion fluid. A filtration coefficient of 2.2 • 10 -1° was obtained. This value was not very different from the one found when the
osmotic difference was in the opposite direction. In one of these experiments
an osmotic pressure difference of 642 milliosmols per liter (higher inside) was
balanced by a hydrostatic pressure of 56 cm of water. Multiplication of the
osmotic pressure produced by the above-mentioned osmolarity difference,
which amounts to 15.3 atm, by the osmotic filtration coefficient gives a flow
TABLE
III
HYDRAULIC CONDUCTIVITIES
(Lp)
X 10 s O F T H E A X O N M E M B R A N E
Experimental
technique
Lp :t: sE
cm/(sec cm/-/20)
20
12
7
Hydrostatic pressure
Perfused
Intact
Osmotic pressure
Perfused
Intact
Perfused*
10.0
3.2
0.045
0.048
0.022
0.8
0.6
0.005
0.009
* Hyperosmotic inside.
of 3.4 • 10 -6 cm/sec. A hydrostatic pressure of 56 cm H 2 0 should produce a
flow of 5.6 • 10-6 cm/sec. T h e balance between both pressures in this particular experiment was maintained for more than 1 hr.
Glycerol Outflux
T h e outflux was expressed in cpm per 10 rain. A semilogarithmic plot of the
percentage of outflux at each time with respect to the initial one gave a
straight line as seen in Fig. 5. The slope of this line is the rate constant k
which was 1.3 × 10-4 see -I. F r o m the values of the radii of the axons and the
rate constant a permeability coefficient of 6 × 10-6 cm/sec was obtained.
This P for glycerol is slightly higher than the one found by R. Villegas et al.
in the giant axon of the squid Doryteuthis plei (4).
In four experiments the outflux was measured at zero pressure for the first
10 rain. In the following 10 min periods pressures of 20, 40, and 60 cm of
water were applied. As seen in Fig. 6 the outfluxes at 10 and 20 rain when
pressures of 20 and 40 cm of water were used showed only a slight increase
over the normal line. But at 30 rain when a pressure of 60 cm H 20 was used,
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No. of
experiments Driving force for volume flux
Published January 1, 1968
Fsm~A~mo F. VARCAS Filtration Coeffdent of Axon Membrane
I.o 1
23
T z,
o 0.8
0.6
E
o
0.4
c,
0.2
I
,o
I
;0
,o
,'o
6'0
TIME ( m i n i
a clear rise could be observed. At that pressure the value of the glycerol outflux was 1.6 times that of the normal.
Conductance Measurements
In the conductance measurements the axons were perfused with 0.6 ~ K F
while the external solution was 0.6 M KC1. Both solutions contained 10 n ~
Tris as a buffer and were adjusted to p H 7.3 with hydrochloric acid.
T h e results of two experiments done at zero pressure and at 60 cm of water
are shown in Fig. 6. T h e conductance in a m p - c m -~ v -1 is the slope of the
straight line obtained. In both experiments the conductance increased slightly
when pressure was applied. In one experiment it changed from 2.36 to 2.74
× 10 -4 a m p -2 v -1 and in the o t h e r one from 2.14 to 2.36 × 10 -~ a m p - c m -
26
FmUR~ 6. Current density as a
function of the potential. T h e
straight line for experiment 58 at
60 cm of water is not drawn in
the graph.
~6
¢J
2
0
20
40
60
80
100
MEMBRANE POTENTIAl. (rnv)
120
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F m t n ~ 5. Efflux curve of z'C-glycerol from the giant ~Lxon. Numerals beside each
point denote the number of independent experiments upon which each mean and its
standard error are based. Filled circles correspond to experiments in which the internal
hydrostatic pressure was increased. Points at 10 and 20 rain were obtained under pressures of 20 and 40 cm of water. Point at 30 rain was obtained under a pressure of 60 cm
of water.
Published January 1, 1968
"4
THE JOURNAL OF GENERAL PHYSIOLOGY • VOLUME 51 • I968
v -1. Both measurements gave an average ratio of 1.1 between the values obtained at 60 cm and those obtained at zero pressure.
DISCUSSION
T h e Lp measured with hydrostatic pressure is larger than the ones reported
in the literature for most of the cells as can be seen in Table IV. As for the
osmotic Lp this is in very good agreement with the one reported for the giant
axon of the squid, Doryleuthis plei, and the algal cell, Valonia ventricosa (Table
IV). The latter Lp's were also measured using osmotic pressure as the driving
force.
The large difference between the Lp's obtained with the two methods used
in the present work deserves a careful analysis. There are very few data a b o u t
TABLE
IV
Cell
Species
Driving force
Lp
References
cm/sec cm 1t20
Skeletal muscle
Erythrocyte
Giant axon
Alga cell
Alga cell
Capillary
Capillary
G i a n t axon
Giant axon
Frog
Human
Squid
Valonia ventricosa
Valonia ventricosa
Rabbit
Rabbit
Squid
Squid
Osmotic
Osmotic
Osmotic
Osmotic
Hydrostatic
Osmotic
Hydrostatic
Osmotic
Hydrostatic
0.92
0.92
0.078
0.012
2.3
0.15
10.0
0.045-0.048
3.2-10.6
(5)
(6)
(7)
*
*
(9)
(8)
Present experiment
Present experiment
* L. Villegas. Private c o m m u n i c a t i o n .
the determination of filtration coefficients using hydrostatic and osmotic pressure in the same living membrane. It has been a surprise for us to find that
those few existing data coincide in showing a difference of approximately two
orders of magnitude between the two Lp's.
Coulter (8) determined the filtration coefficient of the blood-brain barrier
by applying hydrostatic pressure. H e found a value of 10 -7 cm/sec cm H 2 0
for Lp. Fenstermacher and Johnson (9) measured the filtration coefficient
across the same barrier by using osmotic pressure and found a value of 1.5 ×
10 -9 cm/sec cm H~O. L . Villegas ~ used both methods in the algal cell,
Valonia ventricosa, and also found a difference of two orders of magnitude between L p h and Lpo (see Table IV).
F r o m the many possible explanations for the large difference between the
hydrostatic and osmotic conductivities we have selected three which seem
2 L. Villegas. Private communication.
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H Y D R A U L I C C O N D U C T I V I T Y (Lp)
X 108 OF D I F F E R E N T CELLS
Published January 1, 1968
FERNANDOF. V~a~OAS FiltrationCoel~dentof Axon Membrane
25
r4
Jv cc A-~ ( A P -
~A~r)
(1)
where o: stands for proportional to, r is the pore radius, Ax, the m e m b r a n e
thickness, or, the reflection coefficient, and Air, the difference in osmotic pressure. Jvh, the flow produced b y hydrostatic pressure, should be
Jvh ~ (nr4 -b n'R4)AP
Ax
(2)
where n is the n u m b e r and r the radius of small pores, n', the number and R,
the radius of large pores. Jvo, the flow induced by osmotic pressure, could be
written as:
nr4
Jvo ~ A~
(3)
if a reflection coefficient or equal to 1 is assumed for the small pores and a or
of zero for the large ones.
J v h / A P _ 1 q- n' R' _ Lph
Jvo/Azr
n r
Lpo
(4)
R. Villegas (7) has estimated that there are 1.3 X 101° pores of 4.25 A radius
per cm" of axolemma. As for the ratio L p h / L p o , this can be approximated to
100.
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worthwhile to discuss. (a) There is a heterogeneity in the size of the natural
openings in the axon membrane. (b) T h e channels in the m e m b r a n e are
homogeneous with respect to size b u t are all expanded b y the stretch produced
b y the pressure. (c) T h e increase in osmotic pressure itself produces structural changes in the membranes surrounding the axons which decrease the
hydraulic conductivity.
Let us a n a l y z e them separately.
(a) O n e or more channels of large diameter in comparison to the normal
population of pores could permit a high flux when a hydrostatic pressure is
applied. O n the other hand the reflection coefficient of solutes in these large
channels should be very small. Therefore we should have a larger area for
flux associated with hydrostatic pressure and a smaller area associated with
osmotic pressure. According to this hypothesis in the situation in which the
volume flux is zero, water is flowing through large pores driven b y hydrostatic
pressure and an almost equal b u t opposite flow is occurring through small
pores driven b y the osmotic gradient.
Following this line of thought we could write the volume flux J v as :
Published January 1, 1968
26
THE
JOURNAL
OF
GENERAL
PHYSIOLOGY
• VOLUME
51
•
1968
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By introducing these figures for n, r, and L p h / L p o and assuming n t = 1,
i.e. only one big pore, equation 4 gives a value of 0.4 # for R. Taking other
values for n', different R's will be obtained. Therefore the existence of one
or several big pores could explain the difference between L p h and Lpo.
Since the ratio of L p h / L p o was independent of the hydrostatic pressure
used and since during the introduction of the pipette the membrane was
not touched (the action potential remained unaltered), one is tempted to
think that some large pores are present--if this explanation is t r u e - - e v e n
in the normal intact axon. W e lack the necessary information to accept or
reject the possibility discussed above.
(b) An expansion of the pores caused by pressure should increase the
permeability to water and solutes. As seen in Fig. 3, the hydraulic conductivity was constant at different pressures. As for the solute permeability, the
increase of 1.6 times in the outttux of glycerol indicates a higher permeability
under pressure. However, if solvent drag is taken into account this rise in
permeability should be less. As a consequence a rise of 1.6 times the resting
value could be attributed partially to solvent drag whose magnitude we
ignore and partially to possible increase in pore size.
Conductance showed a slight increase of 1.1 times over the resting value.
Conductance is a function of mobility which is proportional to the permeability coefficient. Therefore the observed rise could have been produced b y
an increase in pore size if the effect of solvent drag upon conductance were
neglected.
However, an increase in solute permeability such as the ones here reported
could not account for the difference between L p h and Lpo. If we assume
that solute flow is a function of r 2 and volume flow one of r 4, an increase in
r 2 of 1.6 or even two times should produce only an increase in volume flow
of about four times. T o explain our results the glycerol outflux and the conductance should have increased about 10 times. In consequence we dismiss
the possibility of a substantial widening of the axolemma channels as an
explanation for our results. However, a slight increase in pore area seems
to occur due to an increased pressure.
(c) According to Robertson (10) the channels in the Schwann cell layer
of frog unmyelinated nerves are widened when the medium is made hypoosmotic and tend to close when the osmolarity is increased. However, this
phenomenon could not explain the low Lpo found when the inside of the
axon was made hyperosmotic with respect to the external medium. Furthermore in giant axons (7) the change in diameter of the channels in response
to osmotic changes seems to be opposite to that mentioned above.
A n y specific effect of sucrose on the axolemma can be excluded since similar results were obtained with other test molecules. However, an unspecific
effect of osmo]arity itself on the axolemma cannot be completely excluded.
Published January 1, 1968
FEI~ANDO F. V,~ROAS Filtration Coeffdent of Axon Membrane
27
The finding that Lph in intact axons is smaller than in perfused ones
(Table III) suggests that there is a restriction to water flow in the axoplasmic
layer. The hydraulic conductivity of the axoplasm in series with that of the
membrane seems, however, to be high enough to produce no detectable
effect upon the value of Lpo which is two orders of magnitude smaller than
Lph. This would explain the fact that Lpo is the same in intact and perfused
axons.
The author is grateful to Dr. Ichiji Tasaki for his help and encouragement in the course of this work
and to Drs. M. Canessa, J. A. Johnson, M. Luxoro, and E. Rojas for helpful discussion and technical
suggestions. He is also grateful to Miss M. E. Yafiez and Mr. R. Latorre for help in some of the
experiments.
This research was supported in part by The Rockefeller Foundation, United States Air Force (Grant
AF-AFOSR-788-66), and Fundaci6n Otero.
Receivedfor publication 23 August 1966.
I. TASAKI,I., A. WATANABE,and T. TAKENAKA.1962. Resting and action potential
of intracellularlyperfusedsquid giant axon. Proc. Natl. Acad. Sd. U.S. 48:1177.
2. VARGAS,F. F. 1965. Determinationof the permeabilityto water of the membrane
of axons from Dosidicus gigas. Biochim. Biophys. Acta. 109:309.
3. LUXORO, M., M. CANF.SSA, and F. F. VARGAS. 1965. Physiological properties of
the giant axon from Dosidicus gigas. Excerpta Med. Intern. Congr. Ser. No. 87. 507.
4. VmI~eas, R., C. CAPUTO, and L VILLF.CAS. 1962. Diffusion barriers in the squid
nerve fiber. J. Gen. Physiol. 46:245.
5. ZADUNAISKY,J. A., M. N. PARISI, and R. MONTOREANO. 1963. Effect of antidiuretic hormone on permeability of single muscle fibres. Nature. 200:365.
6. Sm~L, W. V., and A. K. SOLOMON. 1957. Entrance of water into h u m a n red
cells under an osmotic pressure gradient. J. Gen. Physiol. 41:243.
7. VmLEOAS, R., and G. M. VILLEOAS. 1960. Characterization of the membranes in
the giant nerve fiber of the squid. J. Gen. Physiol. 43(5, Pt. 2):73.
8. COULTER, N. A. 1958. Filtration coefficient of the capillaries of the brain. Am.
.7. Physiol. 195:459.
9. FENSTERMACHER, J. D., and J. A. JOHNSON. 1966. Filtration and reflection coefficients of the rabbit blood-brain barrier. Am. or. Physiol. 211:341.
10. ROa~.RTSON, J. D. 1958. Structural alterations in nerve fibers produced by hypotonic and hypertonic solutions. J. Biophys. Biochem. Cytol. 4:349.
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REFERENCES