THE PERMEABILITY OF NORMAL AND MALIGNANT CELLS
TO WATER
AUSTIN M. BRUES
Ar>D
CLAIRE McTIERNAN MASTERS
(From the Medical Laboratories of the Collis P. Huntington Memorial Hospital
of Harvard Ulliversity)
Direct investigation of cell permeability has been necessarily limited in its
material, since most of the cells of multicellular organisms have not been
available for even roughly quantitative study during their life. Hence it is
that most of our knowledge of the permeability of cell surfaces has been derived from experiments with plant cells, the eggs of certain invertebrates, and
erythrocytes. It will readily be realized that it would be dangerous to form
generalizations as to the permeability or osmotic properties of tissue cells on
the basis of studies of other scattered types of cells. Even the red blood cells
of various groups of vertebrates show striking divergences in their permeability
both to water and to solutes (1).
Considering the permeability of cells to simple substances as one of the
fundamental phenomena of life, and in view of its importance in determining
the accessibility of material to cells for metabolism and growth, an attempt
has been made to determine quantitatively, as accurately as conditions permit,
the permeability of tissue cells to water.
In the preceding paper (2), we have described a method by which the
surface and volume of certain fibroblasts can be estimated, and in the present
study we have followed the change in cell volume while cells are subjected
to a decreasing salt concentration in the surrounding medium. As we showed
in the previous paper, it is impracticable to obtain cells which are susceptible
of exact measurement except in a medium of clotted plasma. In this medium
a number of radially symmetrical spindle-shaped or unduloidal cells can be
found and measured.
In experiments dealing with discrete cells such as the Arbacia egg or the
erythrocyte, it is possible to make the practical assumption that the cell, as
soon as placed in the anisotonic fluid medium, is surrounded by this medium
so that its behavior is that of a cell placed suddenly in a given constant environment. Our material, on the other hand, is necessarily embedded in
plasma at a greater or less distance from the experimental anisotonic medium;
the environment of the cell is undergoing constant change and tends to reach
equilibrium with the new medium more and more slowly as time goes on, as
a function of the osmotic pressure gradient in the environs of the cell. If we
consider that the diffusion coefficient and the temperature remain constant,
then the rate of diffusion across a plane sheet is proportional to the concentration gradient between two infinitesimally separated points in the line of diffusion, according to Fick's law of diffusion. This is expressed mathematically
as the second derivative formula:
324
PElWEABILITY OF NORMAL AND MALIGNANT CELLS TO WATER
2P
_ dP = K d
dt
dx 2
325
(1)
in which K is the diffusion constant for the system in question, and P is the
concentration of dissolved substance (which may be expressed in terms of
osmotic pressure) at a depth x at time t.
The solution of this formula (1) is a difficult one (3), and involves, besides the quantities mentioned, the total depth of the diffusion-cylinder, which
in our case is the depth of the plasma clot from the free surface to the impermeable coverslip. Expressing this as d, we have
[_x.st
P
4
Po = 1 -;: e
6d' •
7I'X
sin 2d
+
1
371'x
9X,.tt
j"e 'd' . sin 2d
+
1
Se
_26K~
6d
•
•
571'x
sm 2d
+ ... ]
(2)
This expression has a number of interesting characteristics. In the first
place, it will be noted that it is in the form of an infinite series; however, under
the conditions of our experiments it converges rapidly, so that in most cases
only the first term need be taken into consideration. Furthermore, .the relationship between the total depth of the diffusion system and the depth being
studied is expressed as sin 7IX/2d. This means that if the diffusion constant,
time, and total depth are kept constant, this part of the expression is unity
when x = d, is zero when x = 0, and follows a sine curve between these points.
The formula as expressed above applies only to diffusion of a salt into a
medium free from the salt; it can be generalized to apply to diffusion into or
out of a medium with a greater or less concentration of salt already present
by changing P/po to (P-PO)/(P1-PO) where Po as before is the original
concentration and P 1 is the new external concentration applied at t = O. .
Now, if the value of K for the system in question can be derived experimentally, it will be possible to calculate the pressure external to a cell in any
given position at any time t, under conditions where (for example) a culture
at a concentration of 0.9 per cent NaCI is brought into equilibrium with a
large quantity of solution at a concentration of 0.3 per cent NaCI.
CALCULATION OF THE DIFFUSION CONSTANT
Inasmuch as it is impracticable to determine the concentration of salts in
clotted plasma at various depths over short intervals of time by any more
direct method, the hemolysis time of erythrocytes at various depths was observed in a series of experiments. The erythrocyte seems to be the most
suitable natural osmometer for the purpose, since its permeability is high, and,
on account of its small size, its surface: volume ratio is large and it tends to
reach equilibrium with an external solution rapidly. Red blood cells of the
rat were embedded in heparinized plasma of the same rat and clotted with a
small amount of tissue juice so as to make hanging plasma-drops containing
erythrocytes under similar conditions to the tissue-culture cells, which will be
discussed later. The point at which hemolysis of about 70 to 80 per cent of
326
AUSTIN M. BRUES AND CLAIRE MCTIERNAN MASTERS
these erythrocytes takes place was determined to be in about 0.50 per cent
NaCI. A series of these hanging drops were brought into equilibrium with
0.9 per cent NaCI and then placed in contact with distilled water, and the
time was noted which elapsed before seventy to eighty per cent of these cells
hemolyzed. The depth of the clot was noted in each case, and the observed
cells were very close to the coverslip to which the hanging drop was attached,
so that x and d of equation (2) could be considered equal.
300
•
2.70
240
210
.
e 180
t-
.~
~
150
.E
s: 120
~
Q.
GJ
90
1:1
60
30
O........-,--.....----r---"T---,--,----r---r---r---1
o 2.0 40 60 80 100 12.0 140 160 180
Time in ,second"
FIG.
1.
HEMOLYSIS TIME OF RED CELLS (RAT) IN DISTILLED WATER AT VARIOUS DEPTHS OF
PLASMA CLOT (~ HEMOLYSIS OBSERVED)
- _.. - - .... -. = Theoretical curve. Diffusion constant = 1 X 10-4.
- - - - = Curve corrected for estimated permeability of rat corpuscles.
Following these experiments, a tentative value of K in equation (2) was
assigned for NaCI in water at 25° C. K was taken to equal 1· 10-4 where t
was expressed in minutes, and d and x in centimeters.
A curve was then constructed on the basis of this tentative coefficient and
the diffusion formula given above, showing on the ordinates thickness of the
plasma clot, and on the abscissae the time at which the deepest point in this
clot would reach a concentration of 0.50 per cent NaCI if distilled water
began passing over the free surface of the plasma at t = O. This curve is
shown by the broken line in Fig. 1. Inasmuch as the internal salt concentration of the erythrocyte lags behind the external concentration because of the
time necessary for water to pass across the cell surface, a second curve was
PERMEABILITY OF NORMAL AND MALIGNANT CELLS TO WATER
327
constructed showing the expected hemolysis time, assuming that the cells have
a permeability of 3.0. The meaning of this figure and the method of curve
building will be apparent later in this paper. The second curve shows a very
good agreement with times actually observed (Fig. 1). This agreement is
consistently good where the thickness of clot is less than 300 !J-, and none of
our experiments deal with cells in clots exceeding that thickness.
We now come to consider the process of osmosis across a cell membrane.
If we take the membrane to be freely permeable to water and, for purposes of
an acute experiment, impermeable to electrolytes, we may consider the rate of
passage of water across the membrane to be proportional to the osmotic pressure difference between the two sides of the membrane, to a constant (c) of
permeability, and to the cell surface. This could be expressed mathematically
thus:
dW
crt
= c.s, (PI -
Pe)
(3)
where dW /dt is the amount of water passing across the boundary in unit
time, s is the cell surface, PI is the osmotic pressure inside, and P, is that external to the cell. Bearing in mind that the amount of water entering the cell
increases cell volume by an equal amount, and that P e is the same as P as
defined above, we may express it thus:
dV
crt
(4)
= c.s, (PI - P)
where dV/dt represents the increase in cell volume in unit time.
Strictly speaking, if we were to consider this process one of diffusion, it
would follow Fick's law as above and would be proportional to the pressure
gradient. It has been customary, however, to simplify the matter as above,
since we do not know the thickness of the cell surface.
It now remains desirable to express PI in terms of cell volume, since that
is what we measure from time to time. If the cell were an ideal osmometer,
we would expect the volume and internal osmotic pressure to follow the following equation:
PoV0
=
PV, or P
=
vO
Po' V
(5)
where Po and Vo are the original pressure and volume, and P and V the simultaneous pressure and volume at any time during the experiment.
It will be noted that from this equation it should be possible to calculate
the volume at equilibrium with an external medium of any given osmotic pressure, since here the quantity P is known. It is, however, well known that a
correction must be made for the actual equilibrium volume of the cell. For
such material as has been adequately studied has shown that the equilibrium
value is a little less than that which would be expected ideally; it has been supposed that this is due to the presence within the cell of "osmotically inactive" material. Ponder (4) gives reasons to suppose that this correction
328
AUSTIN M. BRUES AND CLAIRE MCTIERNAN MASTERS
may be due to the fact that the cell is not the perfect osmometer, even in acute
experiments, which it has been thought to be. In any case, equation (5) must
be corrected to the following form:
P
_ p
-
O'
(V o - b)
V-b
(6)
This quantity (b) has been ascertained in the previous communication
(2), on the basis of changing the salt concentration from 0.9 per cent to 0.3
per cent NaCl. Determinations on chick fibroblasts gave b a value of 22.2
per cent of the cell volume in 0.9 per cent NaCI, and on sarcoma 180 fibroblasts the value was 26.0 per cent. In view of the individual variations found
in this value, we have assumed in our calculations that b was in all cases 25
per cent of cell volume at initial equilibrium.
Assuming that the above equations hold true, exactly or as a near approximation to the endosmotic sweIIing of the cells with which we are dealing,
it should be possible, after measuring the volume and surface changes in cells
in endosmosis as a function of time, to calculate the unknown permeability
constant c from the other data. Our reasons for making these assumptions
will be discussed later, and an interpretation of the meaning of c will be
offered.
In the case of the Arbacia egg and the erythrocyte it has been possible
(with the aid, at times, of simplifying assumptions) to get the corresponding
formulae in shape for integration. Since our material is necessarily placed in
plasma, however, we must take cognizance of formula (2), which places the
time factor inextricably on the wrong side of the equation. This makes integration an apparently impossible task, and so we have resorted to reconstructing a sweIIing curve at appropriately short intervals, assuming (c) at the outset as a probable value. A little experimentation with curve building showed
that for optimal results the volume increase had to be calculated at five-second
intervals while it was most rapid, and at less frequent intervals as the volume
approached equilibrium value. Any further interpolated calculation made no
essential difference in the curve. This is the most tedious part of the experiment, for curves had to be reconstructed for each cell studied.
METHOD
The material used in these experiments consisted of fibroblasts in cultures
of chick and rat embryo heart, and in cultures of mouse sarcoma 180 and
Walker rat tumor 256.1
These tissues were grown in hanging drop plasma cultures under conditions which have been described in the previous paper (2). Briefly, bits of
tissue not over 1 mm. in diameter were explanted in 25 per cent heparinized
chicken plasma to which a little dilute embryo extract was added. Such cultures were chosen for observation as contained a 'symmetrical bipolar fibro1 It may be well to point out that the Abroblasts of Walker tumor 256 are probably stroma
cells (5). The cells which we chose for study were bipolar and fusiform, but in width and density
of cytoplasm were more Uke the cells of sarcoma 180 than the embryo nbroblasts which we employed.
PERMEABILITY OF NORMAL AND MALIGNANT CELLS TO WATER
329
blast which could be seen clearly and was entirely in focus at one time. In
addition to these qualifications a cell chosen for study had to be in a region
where the total thickness of the plasma dot was not over 150 (Jo, since in
deeper clots diffusion was so slow that permeability could not be accurately
estimated. Furthermore, the selected cell could not be very close to the
coverslip nor to the free edge of the plasma. It was soon found that consistent results could be obtained only when these rules were followed.
Such a cell was examined under the oil immersion objective and drawn by
means of an Abbe camera lucida to a total magnification of 1400 diameters.
The cells were viewed usually by green monochromatic light. The depth of
the medium was measured by a micrometer on the microscope, and any errors
due to refraction in reading this apparent depth should be the same in the experiments establishing the diffusion constant and in those with fibroblasts.
After four or five drawings had been made under the conditions of culture, the well under the culture was filled with 0.9 per cent NaCI slightly
buffered with a mixture of Na2HPO, and KH 2PO, to a pH of 7.4. Five
minutes were allowed to elapse after the salt solution came in contact with the
culture medium, and then several more drawings of the cell outline were made.
The coverslip was then removed and transferred to another chamber in which
the experiment could take place.
This chamber consisted of a rubber cylinder cemented to a glass slide so
that it made a well 10 mm. deep and 12 mm. in diameter. The coverslip was
secured to the top of the cylinder by a vaseline ring. Two glass tubes entered
the cylinder from the sides; fluid entered through one of these and left
through the other. The flow of fluid, under pressure of gravity, was kept
constant at about fifty drops a minute by a constant drip chamber. This was
done in order to ensure that the fluid in the chamber was kept agitated, thus
renewing the fluid at the surface of the plasma clot, from which sodium chloride was constantly diffusing out.
.
In the experiments described in this paper, the culture which had been
brought into equilibrium with 0.9 per cent NaCI was in this way placed in
contact with 0.3 per cent NaCI, which was kept continually renewed. If the
second solution was much more hypotonic than this, the cells would slowly
disintegrate, or else after apparent equilibrium had been reached, visible
particles inside the cells would go into Brownian movement, suggesting that
substances were diffusing out through the cell surface or that in some other
way the normal viscosity of the cell contents had been lost. All the experiments here recorded deal with endosmosis of water under the influence of
hypotonic solutions, since, where shrinkage of the cell was caused by hypertonic solutions, the surface of the cell usually became irregular during the
course of exosmosis and estimation of cell volume was impracticable. We
have found that cells in 0.3 per cent NaCI for not over an hour can be returned to approximately their original volume, in 0.9 per cent NaCl.
At the moment when the weaker salt solution came in contact with the
plasma culture, a stop watch was started running, and drawings of the cell
outline were made as frequently as possible until apparent equilibrium was
reached. During the process of making each drawing, the time was noted,
usually by an assistant. All drawings were made by the same observer, after
330
AUSTIN M. BRUES AND CLAIRE MCTIERNAN MASTERS
considerable practice at using the camera lucida for this purpose. All drawings which appeared at the time of making them to be inaccurate were deleted
from the record without being measured.
Measurements of the cell surface and volume were then made on the several drawings in each experiment, according to the method previously described (2), which makes use of the symmetry of the cells chosen. According to this method, the. cell diagram was divided into segments which represented approximate cylinders in the original cell; the volume and lateral surface of these cylinders were then calculated and reduced, on a basis of the
magnification, to give measurements of the original cell. It was shown that
by using sufficiently small segments (5 mm. wide on the diagram) consistent
results could be obtained.
TABLE
I: Chick Embryo Heart Fibroblast (d = 701', x = 121')
Time
(seconds)
0.9 per cent NaCl
o
Mean values
0.3 per cent NaCI
15
30
48
70
90
Equilibrium
110
130
195
1050
Volume
Surface
(1'3)
(1'2)
1971
2183
2115
1741
1087
1123
1051
2002
1096
2794
3432
3038
3711
4193
4213
4333
4923
5038
1280
1449
1292
1497
1485
1582
1642
1715
1642
1123
In this way, the cell surface and volume were calculated at initial and final
equilibrium (using in each the mean values from four or more drawings), and
at each time interval during the swelling. Theoretical curves were then constructed for the expected rate of swelling, assuming that it took place as a
function of cell surface and of osmotic pressure difference across the cell
surface. The" osmotically inactive" correction was taken as 25 per cent of
the entire volume in 0.9 per cent saline.
For each experiment, the first curve was constructed on a basis of a
permeability constant (c) of 0.75 (Jo3 per (Jo2 of surface per minute per atmosphere difference in osmotic pressure across the cell surface. Further curves
were then made, with greater or smaller permeability constants, till one was
found which most satisfactorily paralleled the measured course of swelling.
It was thought best, at first, to apply a permeability constant to each volumeobservation made, but since a few observations were sufficiently in error to be
far from any curve which could be drawn, it was decided to select a median
swelling curve, on each side of which fell half of the observations, and consider that this curve represented the most probable permeability constant.
PERMEABILITY OF NORMAL AND MALIGNANT CELLS TO WATER
331
Table I shows the data used in estimating the permeability constant of a
single cell, and Fig. 2 shows graphically how these data were used to obtain
a figure.
Observations were made on fibroblasts derived from the various tissues
enumerated above. The chick embryos were of ten to thirteen days' incubation, and the rat embryos were at about two-thirds term. In all cases healthy
appearing cells were used, although the duration of the culture after explantation varied from two to six days without apparently affecting the permeability
constant. All experiments were done at temperatures between 24° and 28° C.
~ooo
e
s,
.~
~
U
4000
.D
:J
L>
c
II)
5
3000
~
Expel";lIIent
7
b=70
x:: 12.
2.000
~--r----.----r--r--,---"'"
o
50
100
150
200
2~0
Time in Seconds
FIG. 2.
VOLUME DETERMINATIONS AND CALCULATION OF PERMEABILITY CONSTANT,
CHICK EMBRYO FIBROBLAST
At t = 0 the culture in equilibrium with 0.9 per cent NaCI was placed in contact with 0.3 per
cent NaCl. The dots represent actual volume determinations on the cell. Lines represent theoretical swelling rate, assuming the various permeability constants (as defined) indicated at the end
of each curve. Value assigned for c = 0.7.
Under the conditions of growing these tissues the normal and sarcomatous
cells showed roughly the same degree of migration and activity.
Table II shows, for each cell of which a complete study was made, the
permeability constant (C) assigned and the volume of the cell initially in 0.9
per cent NaCl.
It will be seen that there is very little difference in the rate at which these
various types of cells take up water under the constant conditions. The
average permeability constants of the four groups, expressed in the usual
units, range from 0.5 to 0.9, and in individual cases from 0.4 to 1.0 (this
range of variation is found in a single group, that of chick embryo cells). It
332
AUSTIN M. BRUES AND CLAIRE MCTIERNAN MASTERS
appears likely to us that the degree of variation between the individual cases
is beyond the experimental errors and represents a real difference in the permeability of different cells, although the magnitude of these errors makes it
impossible to be certain of this. Parker (6) has shown that fibroblasts from
different parts of the same heart have greatly different growth rates under
constant conditions.
TABLE
II
Malignant tissues
Normal tissues
Exp, no.
c
Volume
Chick
2002
0.7
7
19
0.8
1013
20
0.8
799
21
1192
1.0
1347
35
0.4
22
0.9
863
40
1.0
420
41
0.3
444
Rat
50
0.4
573
0.4
51
878
52
0.9
531
0.74
Average chick
0.56
Average rat
Exp. no.
S 180
2
26
29
W 256
37
38
39
c
Volume
0.6
0.9
0.5
2961
926
1457
0.9
1.0
0.7
1164
690
1140
Average sarcoma 180
Average walker 256
0.67
0.87
Although the averages differ, the wide range of individual values makes it impossible to take
them as slgnificantly different.
These figures, it will be noted, lie between that given for the much smaller
erythrocyte, which is 3.0 (7), and for the much larger Arbacia egg, which
when unfertilized is 0.1, and after fertilization is two to four times as great
(8). There is no significant divergence between the groups of cells we have
studied, in so far as the method is sufficiently accurate to determine it by
means of volume changes. In the previous paper, we have shown (2) that
various other osmotic phenomena are similar in the case of normal and malignant cells.
We must remember, of course, that we are dealing with tissues from
rapidly growing embryos and tumors which have been placed under conditions optimal for growth, and. that this may not represent the circumstances
found in an adult organism, where growth of normal fibroblasts is nearly at a
standstill. It is possible, therefore, that the permeability of such normal resting cells might differ from those of a tumor, and this is suggested by Waterman (9) in work on the electrical resistance and polarization of excised living
tissues. That any wide alteration in surface permeability to water might be a
fundamental characteristic of malignancy, however, seems denied by these
experiments.
DISCUSSION
It will be noted that we have calculated a "permeability constant" for
each cell as if swelling took place in a simple system, susceptible in these experiments only to change in total osmotic pressure. There may, of course, be
PERMEABILITY OF NORMAL AND MALIGNANT CELLS TO WATJ::R
333
other factors involved which, because of the limitations of the method, cannot
be detected. Bearing in mind these limitations, it still appears as if, at least
in the main, the swelling does follow such simple rules; because of the critical
way in which volume change responds to environmental change in osmotic
pressure, it seems that the important factor conditioning swelling must be the
rate at which water can enter the cell. The method is incapable of determining such points as whether this constant is at all stages of swelling proportional to cell surface, although we have made such assumptions because of the
analogous behavior of other material which can be more accurately studied.
It certainly seems unlikely that the effect of colloid osmotic pressure can
be significant in these experiments, for two reasons: because all cells were first
put into equilibrium with isotonic saline solutions before the experiments, and
because we have observed further clear surface swellings (2) similar to those
described by Shear (10, 11) as dependent on decreasing the environmental
colloid concentration.
SUMMARY
1. Measurements of the volume and surface of fibroblasts growing in
plasma have been made during the course of cell swelling in hypotonic solutions. Taking into account the diffusion rate of salts from clotted plasma
into fluid of lower salt concentration, an attempt has been made to determine
the rate at which various cells take up water.
2. The apparent permeability constants of fibroblasts of rat and chick
embryo heart and of mouse sarcoma 180 and Walker rat tumor 256 range
from 0.4 to 1.0 in the customary units. This lies between the permeability of
the Arbacia egg and that of the erythrocyte. The amount of significance
which can be attached to these constants is discussed.
3. We have been unable to establish any significant differences in permeability between avian and mammalian cells, or between embryonic and sarcomatous fibroblasts.
NOTE: We wish to express thanks to Dr. J. C. Aub for suggesting this problem, and to
Professor E. B. Wilson for examining it from the mathematical standpoint.
BIBLIOGRAPHY
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
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BRUES, A. M., AND MASTERS, C. M.: Am. J. Cancer 28: 314, 1936.
HILL, A. V.: Proc. Roy. Soc., ser B 104: 39, 1928.
PONDER, E., Cold Spring Harbor Symposia on Quant. Biol. 1: 170, 1933.
EARLE, W. R.: Am. J. Cancer 24: 566, 1935.
PARKER, R. C.: J. Exper. Med. 58: 401, 1933.
JACOBS, M. H.: Ergebn. d. biol, 7: 1, 1931.
LUCKE, B., AND MCCUTCHEON, M.: Physiol. Rev. 12: 68, 1932.
WATERMAN, N.: Ztschr. f. Krebsforsch. 27: 228, 1928.
SHEAR, M. J., AND FOGG, L. C.: U. S. Public Health Rep. 49: 225, 1934.
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