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Osmotic response of individual cells during freezing
CRYOBIOLOGY
20,
61-77
(1983)
Osmotic
Response
of Individual
I. Experimental
GARY J. SCHWARTZ Department
of Mechanical
Volume AND
Cells
Received February 11, 1982; accepted May 12, 1982. ’ Supported by National Science Foundation Grant ENG-7700122 and ECS-8021511.
Freezing
Measurements’
KENNETH
Engineering, Bio-Heat Transfer Laboratory, The University of Texas, Austin, Texas
The freezing of living cells presents a complex, coupled physiochemical process governed by heat and mass transport phenomena between a cell and its environment. The balance between the relative magnitudes of heat and mass transport is a function of the plasma membrane permeability characteristics and of the temperature/time history during freezing as characterized primarily by the cooling rate. At slow cooling rates freezing processes are typified by transmembrane thermal and osmotic relaxation times of a similar order of magnitude, so the compositional changes in the intracellular solution follow transients in the extracellular composition very closely. In contrast, at fast cooling rates heat transport dominates the mass transport so that as the temperature is rapidly reduced a large osmotic disequilibrium is created across the plasma membrane resulting in the supercooling of water retained within the cell. The demarcation between slow and rapid cooling is a function of the ability of the cell to quickly reduce its internal water content in comparison with the rate at which the temperature is lowered by the freezing process. The relative magnitudes of the simultaneous heat and mass fluxes across the plasma membrane dictate the volumetric response of a cell to freezing. In the pro-
During
R. DILLER Biomedical 78712
Engineering
Center.
gression of the freezing process, initially ice forms exclusively in the extracellular compartment; the initiation of freezing causes an osmotic differential between the cell and its external environment due to a concomitant concentrating of extracellular electrolytes. As depicted in Fig. 1, the plasma membrane acts as a permeability barrier between the intra- and extracellular solutions, allowing the transport of specific types of molecules on a selective basis. For a simple semipermeable membrane model only transmembrane water fluxes may occur enabling the cell to adjust to its changing osmotic environment. The interaction between thermal and osmotic parameters in governing the cellular response to freezing may be described in the context of the following paradigm. For present purposes it will be assumed that the intra- and extracellular solutions can be approximated by binary watersodium chloride mixtures, that extracellular solid and liquid phases are in thermodynamic equilibrium, and that significant property gradients occur only across the semipermeable plasma membrane. The assumed locus of states for the extracellular subsystem during a freezing process is illustrated on the phase diagram in Fig. 2, which depicts how the concentration of an aqueous sodium chloride liquid solution in equilibrium with pure ice varies as a function of temperature. The system exists initially in the liquid phase at a defined nonzero solute concentration. As the
61
001 l-2240/83/010061-17$03.00/O Copyright All rights
( 1 1983 by Academic Press, Inc. of reproductmn in any form reserved.
SCHWARTZ
INTRACELLULAR
/
COMPARTMENT
I 1
AND DILLER
EXTRACELLULAR COMPARTMENT
Ll0UlD SOLUTION
FIG. 1. Thermodynamic system to describe the freezing of a living cell with an ideal semipermeable membrane, across which concomitant heat and mass fluxes may occur.
temperature is depressed, the solute mole fraction in the liquid phase increases continuously until the eutectic point is reached. During the freezing of living cells at slow cooling rates, water is transported from within the cell at a rate consistent with that of the temperature change in order to continuously approach transmembrane thermodynamic equilibrium. As the temperature is progressively decreased, the extracellular ice mass grows, concentrating electrolytes in the remaining liquid phase. The resulting higher extracellular osmotic potential causes the cell to lose a proportional fraction of its water, producing an increase in the intracellular solute concentration. However, as the magnitude of the cooling rate is increased it becomes progressively more difficult for water to be transported out of the cell rapidly enough to maintain a transmembrane osmotic balance. There results an intracellular concentration of water greater than the equilibrium value, i.e., a supercooled state (5, 18, 21). When the degree of supercooling becomes sufficient, intracellular water will equilibrate with extracellular ice by undergoing a phase change from a liquid to solid, thereby achieving a solute concentration equal to the extracellular value (3, 28). Thus, the response of a living cell to the stress of freezing is intimately related to the balance between coupled heat and mass transport across the plasma membrane. The transient physicochemical state of the cell
SOLID -25
i,: Ot INITIAL
ICE a SOLUTION
(, I
2
MOLALITY
3
NaCl
4
,
,
4
5
hol/kq
,
t6 EUTECTIC Hz01
FIG. 2. A sample equilibrium freezing path as depicted on the binary phase diagram for a mixture of water and sodium chloride at 1 atm of pressure. Drawn from data in (2).
during freezing can be characterized by continuously monitoring the variations in volume as a function of temperature. This paper presents data for the transient volume reduction during freezing of individual yeast cells* under continuous observation on a cryomicroscope (7, 8). Numerous prior investigations have also used the technique of cryomicroscopy to assess the osmotic response of cells to freezing and thawing (12, 15, 23-25, 27, 29). Thermal protocols were defined by measured values of the cooling rate and extracellular super2 Saccharomyces cerevisiue (NRRLY-2235 Diploid), furnished by courtesy of Dr. Peter Mazur, Biology Division, Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830.
VOLUMETRIC
CHANGES
IN
cooling. Supercooling results when the nucleation event for the solid phase initiates at a temperature lower than the thermodynamically defined equilibrium freezing point. Its value was not controlled in the experimental protocol; it occured as a function of the thermal characteristics of the freezing stage. Sequential photomicrographs obtained during the freezing process were subjected to digital computer analysis to automatically identify the cell boundary and calculate the apparent volume. The measured transient volumes were compared with the values predicted by an analytical model described in an accompanying paper (26). METHODS
AND
MATERIALS
Yeast cell suspensions were prepared from stock slants in a broth medium at 134 k 1.5 mosm by incubation at 29°C for the 24 hr preceding an experiment. Approximately 2 ml of the cell/medium suspension was centrifuged at 300~ for 5 min, and one-half the supernatant was decanted to obtain a working concentration of cells. One to two microliters of cell suspension was placed on the stage of the cryomicroscope under a glass coverslip and frozen at a defined cooling rate and degree of extracellular TABLE
Trial
No.
2 3 4 6
8 9 10 II 12 13
CELLS
DURING
supercooling. The specimen temperature was monitored and recorded via a 25-pm copper-constantan thermocouple embedded in the stage surface. The combinations of cooling rate and degree of supercooling for each of 13 reported experiments are listed in Table 1. In any given experiment an average of 10 to 20 cells were identified in the field of view. However, not all visible cells were analyzed on the computer for volumetric changes due to a number of complicating factors, including (a) physical contact between adjacent cells, (b) drift of cells into or out of the field of view, and (c) vertical cellular movement across the plane of focus. The dynamics of the freezing process were recorded pictorially with an automatic exposure, motor-driven 35-mm camera3 using ASA 400 black and white negative film. Approximately 35 photomicrographs were taken for each freezing run. The pictures were taken under manual control of the cryomicroscope operator; the camera motor drive actuation signal was interfaced to the strip chart temperature recorder to provide timing marks for direct correlation s Olympus OM-2 35-mm camera, Company, Ltd. Tokyo, Japan.
Olympus
1
Number of cells measured
Cooling rate (“Wmin)
4
-9 -12 -14 -15 -19 -25 -32 -35 -37 -52 -54 -76 -82
3 2 1 1 3 2 2 2 3 3 3 2
63
FREEZING
Extracellular supercooling (“K) -1.9 -5.0 -0.8 -2.0 -3.6 -7.0 -8.9 -10.2 -17.1 - 19.3 -30.5 -28.0 -16.0
Optical
(a)
FIG.
263.5’K
W
271.2OK
3. Sequential
photomicrographs
(0
taken
260.0
269.2
(b)
during
OK
OK
the freezing
of yeast
at a cooling
on the cryomicroscope.
(h) 249.0°K
252.0°K
“K
(g) rate of 9”Wmin
(d) 265.5
VOLUMETRIC
CHANGES
IN
of pictorial and thermal data. Selected micrographs from trial 1 are shown in Fig. 3. Sequential volumetric variations of individual cells were measured by digital computer analysis of the photomicrographs. Individual film frames were converted to digital format on a Colorado Video 270A digitizeti under a direct memory-access link to a PDP 1 l/34 digital computer.5 The pictures were digitized in a 240 x 256 spatial format in the .x-r coordinates with 8 bits (256 discrete values) of gray-level resolution. Digital image analysis algorithms have been developed in our laboratory whereby individual cells can be identified and their boundaries traced automatically (14). The frozen cells present a very complex image for computer processing due to the presence of numerous extraneous optical patterns such as solid-liquid interface boundaries and large variations in background light intensity caused by nonhomogeneities in ice masses. Briefly, the processing sequence consists of an initial localized enhancement of the image following an operator interactive designation on a dynamic refresh graphics CRT display monitor” of a target cell. The computer is given a starting point interior to the cell, from which it automatically locates the cell wall according to the corresponding maximum in the gray-level intensity along a horizontal vector. Subsequently, a novel “biased trident” edge detection algorithm is used to determine the locus of the wall perimeter corresponding to a null gray-level gradient (14). Plasmolysis was not detected during freezing, and it was observed that cells could shrink at the maximum extent theoretically possible, indicating that the actual permeability barrier was being identified. Other investigators have also dem4 CVI 5 PDP Maynard, ’ VG Calif.
270A,
Colorado
11134, Mass. 3405,
Digital
Vector
Video,
Inc.,
Equipment General,
Inc.,
Boulder,
Colo.
Corporation. Woodland
Hills,
CELLS
DURING
FREEZING
65
onstrated by electron microscopy that yeast may experience extensive dehydration during freezing with no evidence of plasmolysis (1, 2). The projected cell area is calculated based on the number of picture elements enclosed within the outlined membrane. The biased trident algorithm was developed specifically to have a low level of sensitivity to variations in the background gray level of the picture and to nonoptimal focusing. A number of calibration studies were performed to test the accuracy of the technique. 20 pm-diameter microspheres were frozen and measured with a variability of 1.5% (14). In addition, yeast cells were suspended at room temperature in a series of saline solutions of several concentrations to verify the theoretical equilibrium freezing curve (15). The measured and theoretical volumes were in agreement to within a few percent. Further, numerous populations of cells were deliberately defocused on the microscope to varying degrees, and comparative volume measurements were made by several alternative methods including the biased trident finder, other less specialized computer algorithms, and direct manual determination from printed enlargements (14). The biased trident algorithm was significantly less sensitive to defocusing and the associated blurred boundaries than the other methods, and it was three times more accurate than manual measurement. This capability is particularly important in the analysis of frozen cells since, as shown in Fig. 3, the surrounding ice masses tend to reduce the resolution of the cell boundary. Under these conditions the cells take on a typical appearance of having a surrounding diffuse halo. The biased trident is particularly effective in identifying and following the actual boundary in the midst of a broad path with low gray scale resolution. A detailed discussion of this algorithm may be found in the technical literature (9, 14). Digitally enhanced and outlined cells are
66
SCHWARTZ
AND
DILLER
FIG 4. I >ig itized rendition of the photomicrograph in Fig. 3b produced on an electro static printer- plotte rL tsing an algorithm that provides 16 gray levels. (A) Unenhanced. (B) Local1 y enh anced FiVl e cells ha .ve been processed using a localized image enhancement routine to emphasize the IcKUS of
the cell w all tion scher ne
The cell boundaries T = 269.2”K
are shown
as outlined
automatically
by a biased
trident
edge detec-
VOLUMETRIC
CHANGES
IN CELLS
illustrated in Fig. 4. The apparent cell volume is approximated from the measured area by a simple geometric relationship, based on the assumption of a spherical configuration. Although it is recognized that yeast are actually prolate ellipsoids, this information was not incorporated into the volume determinations. Automatic identification of the major and minor axes in the randomly oriented cells would have required a much more sophisticated pattern recognition algorithm and, in particular, a considerable increment in computer processing time. Therefore, in the interests of expediting data analysis, spherical geometry was assumed. The limit of potential inaccuracy introduced by this assumption may be evaluated. Mazur (18) has presented data for the aspect ratio of the major and minor axes (a/h) of yeast in various unfrozen and frozen states, indicating that the ratio may vary between 0.94 and 0.86. It is easily demonstrated that the ratio of the volumes of a prolate spheroid and a sphere having identical projected cross-sectional areas varies directly with the reciprocal of the square root of the aspect ratio. Thus, the actual cell volume will be within the range of 3 to 7% smaller than the value calculated for spherical geometry for the spectrum of aspect ratios defined by Mazur. In addition, since the cells maintain a constant orientation throughout the freezing process and only normalized values of volume are considered, the compromise in accuracy introduced by this assumption is minimal. Thus, the average processing time on a per cell basis is limited to the order of 1 to 2 min, depending on how many cells can be analyzed on a single photomicrograph frame. For the experimental data to be correlated with an analytical model (26) it is necessary to relate the total cell volume to intracellular water content by accounting for impermeable solutes and solids. An appropriate conversion factor has been determined for Sacchuromyces cerevisiue by
DURING
FREEZING
67
Mazur (18). The intracellular water volume can be related to the total cell volume by the expression v\+r = v.r - v, - vcw, [II where V, = intracellular free water volume, V., = total cell volume, V, = apparent intracellular volume of solids, solutes, and bound water, and V, \, = cell wall volume. Since the cell wall is located outside the permeability barrier assumed by the thermodynamic model (i.e., the plasma membrane), it is appropriate to exclude 100% of the wall in determining the cell water volime. The intracellular volume not occupied oy water may be expressed as Vs = 0.154 (V’r,i - V,‘\v),
PI
where VT,i is the initial total volume prior to freezing. By eliminating Vs between Eqs. [I] and [2] the transient intracellular water volume can be determined by V\y = V’r - 0.154 (VT,i - V,‘\v) - V,‘, = V.F - 0.154 V,,i - 0.846 Vc\r.
[31
In applying this expression, it is assumed for all cells that the initial thickness of the cell wall is approximately 0.1 pm, (19) and that the volume and water content of the wall remains constant even though the total cell volume may change (17, 19, 30). As an example of the dimensional significance of the cell wall, for a relatively small cell (50 pm3), the wall occupies 13% of the initial volume, whereas for a relatively large cell (130 pm3) the wall represents 9% of the initial volume. Obviously, when a relatively small cell experiences a large volume decrease (as associated with a slow cooling rate process), theoretically the cell wall may constitute as much as 40% of the total volume at maximum dehydration. RESULTS
Cells were frozen in 13 different experimental protocols, as presented in Table 1, at cooling rates ranging between 9 and 82”Kimin and with a degree of extracellular supercooling between 1 and 36°K. The
68
SCHWARTZ
AND
transient volumes of individual cells were measured from serial cryomicroscope photographs from which intracellular water volumes were calculated using Eq. [3]. All volumes were normalized to the initial prefreezing value. An example sequence of selected photomicrographs from the freezing protocol at YWmin (trial 1) is shown in Fig. 3. Each of the photomicrographs was digitized and stored on the computer for analysis. The primary processing steps in the digital analysis procedure are illustrated in Figs. 4 and 5, which were produced with a 16 gray-level dot matrix printer. An unenhanced, digitized representation of the image in Fig. 3b is presented in Fig. 4. Cells were identified for volume measurements by operator intervention on an interactive video terminal. The results of a localized enhancement routine can be seen as effected for a rectangular area surrounding each cell. The biased trident edge tracking algorithm was applied to determine automatically the locus of the wall for each cell. The outlines for these individual cells were tracked through the sequential micrographs
269 2 OK
DILLER
of the freezing process, as illustrated in Fig. 5. Although the automated machine procedure for outlining cells is desirably objective, without possibility for biasing due to operator intervention and interpretation, it can be seen in Fig. 5 that the procedure may fail upon encountering image anomalies, such as apparent optical gaps in the wall which may occur at the interface between a cell and the ice-solution front. Our computer software provides the capability for operator patching across discontinuities in the wall using the interactive graphics terminal. In the present study this function was not employed, necessitating the rejection of some data for which the edge tracking routine obviously became “lost.” The volumes of each cell measured in trial 1 are plotted as a function of temperature in Fig. 6. The measured initial volumes of the individual cells are indicated. It is readily apparent that the dehydration curve is not affected by individual cell size. The volume dehydration data are presented as a composite plot in Fig. 7. The theoretical equilibrium freezing curve is also shown depicting an infinitely slow cooling rate for
269.3OK
2665 “K
8 Q
0 0
Q
0
0
Q
0 0
@ Q
r 2635%
252.0”K
FIG. 5. Computer printout of outlined cell boundaries for selected shown in Fig. 3. Note that in certain cases the biased trident algorithm properly, for which the data are eliminated from the analysis.
249.0”K
photomicrographs from the trial was unable to track the cell wall
VOLUMETRIC
CHANGES
IN CELLS
DURING
CELL 3!$ 0+3-
69
FREEZING
#
VT, (pm3)
145
0
I
P
0
2
65
E I-
n
3
72
0
4
51
E o-4-
D
5
64
; ;: 5
,-,
6
64
06-
s q
j
oz-
TEMPERATURE
FIG. 6. Transient normalized water volume 9”Wmin. The numbered cells are identified
(“K)
plots for individual in Fig. 5.
which osmotic equilibrium is maintained across the cell membrane continuously. Composite plots of the measured variation in cell volume as a function of temperature are presented in Figs. 8 through 13 for the experimental data obtained in trials 2 through 13, respectivley. In each case the cooling rate and number of cells measured are indicated and the equilibrium freezing curve is shown as a reference depicting the
cells during
trial
1 at a cooling
rate of
limiting conditions of osmotic equilibrium. The degree of extracellular supercooling prior to the nucleation of ice is equal to the horizontal displacement along the temperature coordinate of the experimental curve from the equilibrium curve at a normalized volume of 1.0. Ushiyama and Cravalho have previously performed cryomicroscopic measurements of the volumetric changes in individual
C.R. n=
= 9 OK/min 4
0 275
270
260
250
240 TEMPERATURE
FIG. 7. Freezing data base.
curve
for cell volumes
measured
during
230
220
210
(“K I
trial 1. n is the number
of cells included
in the
70
SCHWARTZ
275
270 0
260
AND
0
C. R. = 12 OK/min
n=3
0
C. I?. = 14°K/mln
n=3
250
-10
DILLER
240
-20
230
-30
-40
TEMPERATURE
FIG.
8. Freezing
curve
for cell volumes
yeast cells during freezing (29). Their data are presented in Fig. 14 for comparison with our present experimental results. These data exhibit considerably less sensitivity to variations in cooling rate than was measured in our experiments. No values of extracellular supercooling were identified by Ushiyama and Cravalho.
275
270 I 0
260 f
-10
-20
9. Freezing
curve
210 -60
(“K/“(Z)
during
trials
2 and 3.
Finally, in order to provide a perspective view of the interaction among the experimental parameters, all of the present data is combined in Fig. 15 into a single threedimensional plot in which the effects of temperature, cooling rate, and extracellular supercooling on cell volume are illustrated simultaneously.
a
C. R. = 15 “K/mm
ll=l
0
C R. = 19 “Khin
ll=l
240
230
-30
for cell volumes
220
I
I
TEMPERATURE
FIG.
-50
measured
250
I
220
-40
-50
during
trials
I -60
(‘K/‘C)
measured
210
I
4 and 5.
VOLUMETRIC
275
270 0
CHANGES
260
IN CELLS
250
-10
-20
10. Freezing
curve
0
C. R. =32”K/mln
n=3
220
-40
-50
210 -60
measured
during
trials
6 and 7.
teractive coupling effects remain difficult to predict quantitatively. The experimental data presented herein can be analyzed so as to describe the influence of multiple thermal factors. The two defined thermal parameters of the freezing process for the present study were the cooling rate and the extracellular supercooling.
DISCUSSION
P N i 2 5
n=3
(“K/“C)
for cell volumes
As noted in the introduction, in previous investigations it has been demonstrated repeatedly that numerous thermal and physiological parameters act in concert to dictate the volumetric response of individual cells to freezing stress. Although these parameters have been identified singularly, in-
Y E
C. R = 25 OK/min
230
-30
71
FREEZING
0
240
TEMPERATURE
FIG.
DURING
.4 -
.2-
276
270 I 0
260
0
C. I?. = 35 OK/min
IT=2
0
C.R. = 37 ‘K/min
n=2
250
I -10
I -20
240
11. Freezing
curve
for cell volumes
220 ,
-50
-60
(“K/“C)
measured
210
I
-40
-30 TEMPERATURE
FIG.
230 1
I
during
trials
8 and 9.
72
SCHWARTZ
1.0
AND
DILLER
r
1;. I 275
I 260
270
0
-20
12. Freezing
curve
n=3
0
C. R. = 54 ‘K/min
n=3
240
230
220
-40
-30 TEMPERATURE
FIG.
C. R. = 52 ‘Khin
1
250
-0
0
for cell volumes
2 10
-50
-60
(OK/%)
measured
during
trials
10 and 11.
As expected, a behavior uniformly ob- the freezing of an aqueous solution (refer served in all the data is that the cell water again to the H,O-NaCl phase diagram in volume decreases as the temperature is re- Fig. 2). The calculated equilibrium freezing curve depicted in Figures 7- 13 indicates duced during freezing. The phenomenon can be ascribed to the exposure of cells to a the loss of intracellular water that would be progressively increasing concentration of expected for a cooling rate sufficiently slow could be mainextracellular electrolytes associated with that osmotic equilibrium
I 275
270
260
I
I
0
- 10
V
C. R. = 76 OK/mm
n=3
0
C. R. = 82 OK/min
n=2
250 I -20
240
-30
TEMPERATURE
FIG.
13. Freezing
curve
230
for cell volumes
I
-40
I -60
-50
(“K/“C)
measured
210
220
I
I
during
trials
12 and 13.
VOLUMETRIC
CHANGES
IN CELLS DURING
1
-10 TEMPERATURE
-20 CC)
-30
FIG. 14. Measured intracellular water volume of yeast (S. cerevisiae) frozen at constant cooling rates by Ushiyama and Cravalho (29).
tained continuously between the intracellular and extracellular solutions by the transmembrane movement of water. Inspection of the data in Figs. 7 through 13 reveals that for each of the trials conducted, the loss of intracellular water occurred at a rate slower than required to achieve osmotic equilibrium. Thus, at all temperatures lower than the equilibrium phase change point of protoplasm, the intracellular water existed in a supercooled state. Sequential inspection of Figs. 7-13 shows that the magnitudes of both the cooling rate and extracellular supercooling exhibit a strong influence on the extent of cell water loss during freezing. A clear general trend which emerges is that at more rapid cooling, the rate of water loss is depressed so that the cumulative cellular dehydration over the entire freezing process is reduced. This observation can be explained in terms of the imbalance between simultaneous heat and mass transfer processes which occur during freezing. The rate of heat transfer within the cell system is set externally by the thermal boundary conditions, which can be regulated actively by manipulation of the freezer environmental
FREEZING
73
temperature to produce a desired thermal history. In contrast, the mass transfer is governed by internal gradients, which are established only in passive response to the chemical disequilibrium created by the freezing process. Thus, depending on the values of certain thermodynamic properties, such as thermal conductivity and membrane permeability which govern the transport of heat and mass within the cell suspension system, the corresponding rates of relaxation for heat and mass transfer during the freezing process may be quite different. For rapid cooling the rate of heat transfer will dominate that of mass transfer. Consequently, at subfreezing temperatures the intracellular water volume will be larger than that obtained for an equilibrium freezing process at a low cooling rate. In general, the larger the difference between the actual and threshold cooling rates, the greater will be the chemical disequilibrium created, with a concomitant decrease in net water efflux. The departure from a state of transmembrane chemical equilibrium during freezing is self-perpetuating on the time scale of the freezing process because the water permeability of the cells decreases exponentially as the temperature is lowered (13). Therefore, incrementing the cooling rate has the effect of further hindering cellular dehydration by more rapidly effecting a state of depressed membrane permeability before extensive net water loss can occur. The overall influence of increased cooling rate on cell water loss can be identified most readily from the composite plot of experimental data shown in Fig. 15. Both the dehydration rate and total cumulative water loss are seen to diminish with increasing cooling rate. The effects of extracellular supercooling can be observed by comparison of the transient volume curves for experimental trials with similar cooling rates and dissimilar supercooling. According to Table 1, four such pairs of trials can be identified for the
(OKI
FIG.
15. Composite freezing curve of cell water volume as a function of both cooling rate and extracellular supercooling for trials 1-13 inclusivecorresponding to the equilibrium phase change temperature for a physiologily. , Hidden isotherms. - - -, Hidden freezing curves. -, Isotherm cally equivalent concentration of sodium chloride in water. All freezing curves are extrapolated at constant volume from the minimum measured temperature to 2WK, as denoted by ----.
TEMPERATURE
VOLUMETRIC
CHANGES
IN
CELLS
TABLE
Trial
No. 3 4 8 9 10 II 12 13
Cooling rate (“Kimin) 14 15 35 31 52 54 76 82
75
FREEZING
2
Supercooling (“K) -0.75 -2.0 -10.2 -17.1 -19.3 -30.5 -28.0 -16.0
data presented in Figs. 8 and 9, 11, 12, and 13. Data for these trials are summarized in Table 2. In each case greater extracellular supercooling is seen to exert a common influence on the cell dehydration curve; i.e., net water loss is diminished. As with the cooling rate, this effect is related to the thermal depression of the membrane hydraulic permeability. Cell water efflux occurs as a result of the concentration of extracellular electrolytes associated with the freezing process. Supercooling effectively delays establishment of the conditions requisite for the water flux (i.e., the presence of extracellular ice) to a lower temperature; as a result when the transmembrane osmotic concentration potential is established by extracellular ice nucleation at a temperature lower than the equilibrium phase change value, the resistance to mass transport is greater. Consequently, the resistance to cell dehydration is higher because the water efflux process is shifted to a lower temperature. This explanation is supported by the data in Table 2 in which are tabulated the rate of water loss over the first 10°K temperature drop following extracellular nucleation and the smallest cell volume reached. For each of the four pairs of trials evaluated, increased supercooling resulted in a reduced rate of water loss and less total cell shrinkage. Thus, the experimental data demonstrate clearly that the cooling rate and the extracellular supercooling may act in concert to control the magnitude of cell water loss during freezing.
DURING
dt’,,/dT
(“K-l) 1118 1130 1140 1148 11130 11480 11220 11125
V final 0.20 0.40 0.65 0.80 0.83 0.97 0.94 0.76
It can be observed in Fig. 6 that the fraction of free cell water expressed during the freezing process is not dependent on the absolute size of the cell. In this trial (No. l), the volumes of six cells were tracked continuously during freezing; initial intracellular water volumes varied by a factor of approximately three. There were no significant differences among the normalized volume curves for any of the cells, and no discernable size-related trends were detected. As discussed previously, cells undergo a progressive dehydration as the temperature decreases during freezing. Factors which may act to inhibit this process include (1) thermal reduction of the membrane permeability, (2) attainment of an osmotic equilibrium volume, and (3) formation of intracellular ice. Such behavior is revealed in Figs. 10 through 13 by the presence of a volumetric plateau at a value much larger than occurs for the equilibrium freezing curve. In contrast, for Figs. 7 through 9 no volumetric plateau can be identified for the experimental data. Analysis of Figs. lo- 13 shows that in general, lower cooling rates and smaller supercooling result in more extensive cellular shrinkage before a volume plateau is reached. The data also indicate that the temperature is not so low that the cell membrane hydraulic permeability has been depressed to an infinitesimally small value. Comparison of trials 6 and 7 in Fig. 10 confirm this point. In trial 7 the volumetric plateau is reached at a temperature of approximately 255°K ( - 18”C), whereas in
76
SCHWARTZ
trial 6 substantial water loss is measured between 255 (-18) and 245°K ( 28”), requiring a finite permeability coefficient. The temperature at which the volume plateau is initiated is also not consistent among all the experimental trials, implying the involvement of an additional parameter which can be unique to individual trials, such as intracellular ice formation. Unfortunately, for the yeast cells used in this study it was not possible to observe an intracellular nucleation event or the presence of an ice structure within the individual cells, probably due to the optical properties of the cell wall. Direct visual detection of intracellular ice has been a notable benefit of the technique of cryomicroscopy for other cell types such as erythrocytes (6, 8), HeLa Cells (10, 22), ova (16), and plant cells (11). Based on the evidence presented above, it is conjectured that the presence of the nonequilibrium volume plateau is due to intracellular ice formation. Further evaluation of this data by an analytical model for cell freezing, as described in a companion paper (26), lends credence to this conclusion. SUMMARY
The osmotic response of yeast to freezing was measured as a funciton of cooling rate and degree of extracellular supercooling. Thirteen experimental trials were conducted on a cryomicroscope in which incremental size changes of individual cells were recorded photographically, and the corresponding volume variations were measured using a digital computer image analysis algorithm. Plots were obtained of normalized cell volume as a function of temperature. Cellular dehydration during freezing was progressively inhibited with increasing values of cooling rate and extracellular supercooling. Normalized cell volume changes were not a function of the relative initial cell size. A constant volume plateau occurred
AND
DILLER
for conditions under which intracellular formation was expected.
ice
REFERENCES 1. Bank, H. Visualization of freezing damage. 11. Structural alterations during warming. Cvyobialogy 10, 157- 170 (1973). 2. Bank, H., and Mazur, P. Visualization of freezing damage. J. Cell. Biol. 57, 729-742 (1973). 3. Cosman, M. D., and Cravalho, E. G. Intracellular thermodynamic states critical for the formation of ice. Submitted for publication. 4. “CRC Handbook of Chemistry and Physics” (R. C. Weast, Ed.), pp. D224-D225. CRC Press, Cleveland (1979). 5. Diller, K. R. Intracellular freezing: Effect of extracellular supercooling. Cryobiology 12, 480-485 (1975). 6. Diller, K. R. Intracellular freezing of glycerolized red cells. Cryobiology 16, 125- 131 (1979). 7. Diller, K. R., and Cravalho, E. G. A cryomicroscope for the study of freezing and thawing processes in biological cells. Cryobiology 7, 191-199 (1970). 8. Diller, K. R., Cravalho, E. G., and Huggins, C. E. An experimental study of freezing in erythrocytes. Med. Biol. Eng. 14, 321-326 (1976). 9. Diller, K. R., and Knox, J. M. Identification and tracking of blurred boundaries in cluttered pictures. IEEE Proc., Pattern Recog. Image Process. l37- 139 (1981). 10. Diller, K. R., Matheson, D., and Cravalho, E. G. A high speed motion picture study of morphological changes during freezing and thawing processes in HeLa cells. Cryobiology 6, 576 (1970). 11. Dowgert, M. F., Steponkus, P. L., Levin, R. L., and Ferguson, J. R. Cryobiology of isolated plant protoplasts. II. Intracellular ice formation. Cryobiology 16, 593 (1979). 12. Griffiths, J. B., Cox, C. S., Beadle, D. J. and Reid, D. S. Changes in cell size during the cooling, warming and post-thawing periods of the freeze-thaw cycle. Cryobiology 16, 141- 151 (1979). 13. Jacobs, M. H., Glassman, H. N., and Parpart, A. K. Osmotic properties of the erythrocyte. VII. The temperature coefficients of certain hemolytic processes. J. Cell. Comp. Physiol. 7, 197-225 (1935). 14. Knox. J. M. and Diller, K. R. A biased-trident algorithm for identifying cell boundaries in a matrix of freezing ice. Submitted for publication. IS. Knox. , J. M.. , Schwartz. G. J.. and Diller. K. R. ~-
VOLUMETRIC
16.
17.
18.
19.
20. 21.
22.
CHANGES
IN CELLS DURING
Volumetric changes in cells during freezing and thawing. J. Biomech. Eng., Trans. ASME 102, 91-97 (1980). Leibo, S. P., McGrath, J. J., and Cravalho, E. G. Microscopic observation of intracellular ice formation in unfertilized mouse ova as a function of cooling rate. Crphiology 15, 257-271 (1978). Levin, R. L. Water permeability of yeast cells at subzero temperatures. J. Me&r. Biol. 46, 91-124 (1979). Mazur, P. Manifectations of injury in yeast cells exposed to subzero temperatures. I. Morphological changes in freeze-substituted and in “frozen-thawed” cells. J. Brtctcriol. 82, 662-684 (1961). Mazur, P. Studies on rapidly frozen suspensions of yeast cells by differential thermal analysis and conductometry. Biophys. J. 3, 323-353 (1963). Mazur, P. The role of intracellular freezing in the death of cells cooled at supraoptimal rates. Cryobiology 14, 251-272 (1977). Mazur, P., and Schmidt, J. J. Interactions of cooling velocity, temperature, and warming velocity on the survival of frozen and thawed yeast. Cryobiology 5, l- 17 (1968). McGrath, J. J., Cravalho, E. G., and Huggins, C. E. An experimental comparison of intracellular ice formation and freeze-thaw survival of HeLa S-3 cells. Cryobiology 12, 540-550 (1975).
FREEZING
77
23. Scheiwe, M. W., and Korber, C. Thermally defined cryomicroscopy and some applications on human leucocytes. J. Microsc. 126, 29-44 (1982). 24. Schwartz, G. J., and Diller, K. R. Volumetric changes during the thawing of frozen cells. Cryoletters 1, 129-134 (1980). 25. Schwartz, G. J., and Diller, K. R. Parameters affecting the osmmotic behavior of cells during freezing and thawing: Human granulocytes. Cryoletters 2, 359-372 (1981). 26. Schwartz, G. J., and Diller, K. R. Osmotic response of individual ceils during freezing. II. Membrane permeability analysis. Cr~obiolog~, in press 27. Steponkus, P. L., Dowgert, M. F., Levin, R. L., and Ferguson, J. F. Cryobiology of isolated plant protoplasts. IV. Cellular injury. Crwhiol0g.v 16, 593-594 (1979). 28. Toscano, W. M., Cravalho, E. G., Silvares, 0. M., and Huggins, C. E. The thermodynamics of intracellular ice nucleation in the freezing of erythrocytes. J. Heat Transfer, Trans. ASME
97, 326-332
(1975).
29. Ushiyama, M., and Cravalho, E. G. Volumetric changes in yeast cells during freezing at constant rates. J. Memhr. Bid. 46, 112- 114 (1979). Appendix to R. L. Levin, (1979). 30. Wood, T. H., and Rosenberg, A. M. Freezing in yeast cells. Biochim. Biophys. Acra 25, 78-87 (1957).
20,
61-77
(1983)
Osmotic
Response
of Individual
I. Experimental
GARY J. SCHWARTZ Department
of Mechanical
Volume AND
Cells
Received February 11, 1982; accepted May 12, 1982. ’ Supported by National Science Foundation Grant ENG-7700122 and ECS-8021511.
Freezing
Measurements’
KENNETH
Engineering, Bio-Heat Transfer Laboratory, The University of Texas, Austin, Texas
The freezing of living cells presents a complex, coupled physiochemical process governed by heat and mass transport phenomena between a cell and its environment. The balance between the relative magnitudes of heat and mass transport is a function of the plasma membrane permeability characteristics and of the temperature/time history during freezing as characterized primarily by the cooling rate. At slow cooling rates freezing processes are typified by transmembrane thermal and osmotic relaxation times of a similar order of magnitude, so the compositional changes in the intracellular solution follow transients in the extracellular composition very closely. In contrast, at fast cooling rates heat transport dominates the mass transport so that as the temperature is rapidly reduced a large osmotic disequilibrium is created across the plasma membrane resulting in the supercooling of water retained within the cell. The demarcation between slow and rapid cooling is a function of the ability of the cell to quickly reduce its internal water content in comparison with the rate at which the temperature is lowered by the freezing process. The relative magnitudes of the simultaneous heat and mass fluxes across the plasma membrane dictate the volumetric response of a cell to freezing. In the pro-
During
R. DILLER Biomedical 78712
Engineering
Center.
gression of the freezing process, initially ice forms exclusively in the extracellular compartment; the initiation of freezing causes an osmotic differential between the cell and its external environment due to a concomitant concentrating of extracellular electrolytes. As depicted in Fig. 1, the plasma membrane acts as a permeability barrier between the intra- and extracellular solutions, allowing the transport of specific types of molecules on a selective basis. For a simple semipermeable membrane model only transmembrane water fluxes may occur enabling the cell to adjust to its changing osmotic environment. The interaction between thermal and osmotic parameters in governing the cellular response to freezing may be described in the context of the following paradigm. For present purposes it will be assumed that the intra- and extracellular solutions can be approximated by binary watersodium chloride mixtures, that extracellular solid and liquid phases are in thermodynamic equilibrium, and that significant property gradients occur only across the semipermeable plasma membrane. The assumed locus of states for the extracellular subsystem during a freezing process is illustrated on the phase diagram in Fig. 2, which depicts how the concentration of an aqueous sodium chloride liquid solution in equilibrium with pure ice varies as a function of temperature. The system exists initially in the liquid phase at a defined nonzero solute concentration. As the
61
001 l-2240/83/010061-17$03.00/O Copyright All rights
( 1 1983 by Academic Press, Inc. of reproductmn in any form reserved.
SCHWARTZ
INTRACELLULAR
/
COMPARTMENT
I 1
AND DILLER
EXTRACELLULAR COMPARTMENT
Ll0UlD SOLUTION
FIG. 1. Thermodynamic system to describe the freezing of a living cell with an ideal semipermeable membrane, across which concomitant heat and mass fluxes may occur.
temperature is depressed, the solute mole fraction in the liquid phase increases continuously until the eutectic point is reached. During the freezing of living cells at slow cooling rates, water is transported from within the cell at a rate consistent with that of the temperature change in order to continuously approach transmembrane thermodynamic equilibrium. As the temperature is progressively decreased, the extracellular ice mass grows, concentrating electrolytes in the remaining liquid phase. The resulting higher extracellular osmotic potential causes the cell to lose a proportional fraction of its water, producing an increase in the intracellular solute concentration. However, as the magnitude of the cooling rate is increased it becomes progressively more difficult for water to be transported out of the cell rapidly enough to maintain a transmembrane osmotic balance. There results an intracellular concentration of water greater than the equilibrium value, i.e., a supercooled state (5, 18, 21). When the degree of supercooling becomes sufficient, intracellular water will equilibrate with extracellular ice by undergoing a phase change from a liquid to solid, thereby achieving a solute concentration equal to the extracellular value (3, 28). Thus, the response of a living cell to the stress of freezing is intimately related to the balance between coupled heat and mass transport across the plasma membrane. The transient physicochemical state of the cell
SOLID -25
i,: Ot INITIAL
ICE a SOLUTION
(, I
2
MOLALITY
3
NaCl
4
,
,
4
5
hol/kq
,
t6 EUTECTIC Hz01
FIG. 2. A sample equilibrium freezing path as depicted on the binary phase diagram for a mixture of water and sodium chloride at 1 atm of pressure. Drawn from data in (2).
during freezing can be characterized by continuously monitoring the variations in volume as a function of temperature. This paper presents data for the transient volume reduction during freezing of individual yeast cells* under continuous observation on a cryomicroscope (7, 8). Numerous prior investigations have also used the technique of cryomicroscopy to assess the osmotic response of cells to freezing and thawing (12, 15, 23-25, 27, 29). Thermal protocols were defined by measured values of the cooling rate and extracellular super2 Saccharomyces cerevisiue (NRRLY-2235 Diploid), furnished by courtesy of Dr. Peter Mazur, Biology Division, Oak Ridge National Laboratory, Oak Ridge, Tenn. 37830.
VOLUMETRIC
CHANGES
IN
cooling. Supercooling results when the nucleation event for the solid phase initiates at a temperature lower than the thermodynamically defined equilibrium freezing point. Its value was not controlled in the experimental protocol; it occured as a function of the thermal characteristics of the freezing stage. Sequential photomicrographs obtained during the freezing process were subjected to digital computer analysis to automatically identify the cell boundary and calculate the apparent volume. The measured transient volumes were compared with the values predicted by an analytical model described in an accompanying paper (26). METHODS
AND
MATERIALS
Yeast cell suspensions were prepared from stock slants in a broth medium at 134 k 1.5 mosm by incubation at 29°C for the 24 hr preceding an experiment. Approximately 2 ml of the cell/medium suspension was centrifuged at 300~ for 5 min, and one-half the supernatant was decanted to obtain a working concentration of cells. One to two microliters of cell suspension was placed on the stage of the cryomicroscope under a glass coverslip and frozen at a defined cooling rate and degree of extracellular TABLE
Trial
No.
2 3 4 6
8 9 10 II 12 13
CELLS
DURING
supercooling. The specimen temperature was monitored and recorded via a 25-pm copper-constantan thermocouple embedded in the stage surface. The combinations of cooling rate and degree of supercooling for each of 13 reported experiments are listed in Table 1. In any given experiment an average of 10 to 20 cells were identified in the field of view. However, not all visible cells were analyzed on the computer for volumetric changes due to a number of complicating factors, including (a) physical contact between adjacent cells, (b) drift of cells into or out of the field of view, and (c) vertical cellular movement across the plane of focus. The dynamics of the freezing process were recorded pictorially with an automatic exposure, motor-driven 35-mm camera3 using ASA 400 black and white negative film. Approximately 35 photomicrographs were taken for each freezing run. The pictures were taken under manual control of the cryomicroscope operator; the camera motor drive actuation signal was interfaced to the strip chart temperature recorder to provide timing marks for direct correlation s Olympus OM-2 35-mm camera, Company, Ltd. Tokyo, Japan.
Olympus
1
Number of cells measured
Cooling rate (“Wmin)
4
-9 -12 -14 -15 -19 -25 -32 -35 -37 -52 -54 -76 -82
3 2 1 1 3 2 2 2 3 3 3 2
63
FREEZING
Extracellular supercooling (“K) -1.9 -5.0 -0.8 -2.0 -3.6 -7.0 -8.9 -10.2 -17.1 - 19.3 -30.5 -28.0 -16.0
Optical
(a)
FIG.
263.5’K
W
271.2OK
3. Sequential
photomicrographs
(0
taken
260.0
269.2
(b)
during
OK
OK
the freezing
of yeast
at a cooling
on the cryomicroscope.
(h) 249.0°K
252.0°K
“K
(g) rate of 9”Wmin
(d) 265.5
VOLUMETRIC
CHANGES
IN
of pictorial and thermal data. Selected micrographs from trial 1 are shown in Fig. 3. Sequential volumetric variations of individual cells were measured by digital computer analysis of the photomicrographs. Individual film frames were converted to digital format on a Colorado Video 270A digitizeti under a direct memory-access link to a PDP 1 l/34 digital computer.5 The pictures were digitized in a 240 x 256 spatial format in the .x-r coordinates with 8 bits (256 discrete values) of gray-level resolution. Digital image analysis algorithms have been developed in our laboratory whereby individual cells can be identified and their boundaries traced automatically (14). The frozen cells present a very complex image for computer processing due to the presence of numerous extraneous optical patterns such as solid-liquid interface boundaries and large variations in background light intensity caused by nonhomogeneities in ice masses. Briefly, the processing sequence consists of an initial localized enhancement of the image following an operator interactive designation on a dynamic refresh graphics CRT display monitor” of a target cell. The computer is given a starting point interior to the cell, from which it automatically locates the cell wall according to the corresponding maximum in the gray-level intensity along a horizontal vector. Subsequently, a novel “biased trident” edge detection algorithm is used to determine the locus of the wall perimeter corresponding to a null gray-level gradient (14). Plasmolysis was not detected during freezing, and it was observed that cells could shrink at the maximum extent theoretically possible, indicating that the actual permeability barrier was being identified. Other investigators have also dem4 CVI 5 PDP Maynard, ’ VG Calif.
270A,
Colorado
11134, Mass. 3405,
Digital
Vector
Video,
Inc.,
Equipment General,
Inc.,
Boulder,
Colo.
Corporation. Woodland
Hills,
CELLS
DURING
FREEZING
65
onstrated by electron microscopy that yeast may experience extensive dehydration during freezing with no evidence of plasmolysis (1, 2). The projected cell area is calculated based on the number of picture elements enclosed within the outlined membrane. The biased trident algorithm was developed specifically to have a low level of sensitivity to variations in the background gray level of the picture and to nonoptimal focusing. A number of calibration studies were performed to test the accuracy of the technique. 20 pm-diameter microspheres were frozen and measured with a variability of 1.5% (14). In addition, yeast cells were suspended at room temperature in a series of saline solutions of several concentrations to verify the theoretical equilibrium freezing curve (15). The measured and theoretical volumes were in agreement to within a few percent. Further, numerous populations of cells were deliberately defocused on the microscope to varying degrees, and comparative volume measurements were made by several alternative methods including the biased trident finder, other less specialized computer algorithms, and direct manual determination from printed enlargements (14). The biased trident algorithm was significantly less sensitive to defocusing and the associated blurred boundaries than the other methods, and it was three times more accurate than manual measurement. This capability is particularly important in the analysis of frozen cells since, as shown in Fig. 3, the surrounding ice masses tend to reduce the resolution of the cell boundary. Under these conditions the cells take on a typical appearance of having a surrounding diffuse halo. The biased trident is particularly effective in identifying and following the actual boundary in the midst of a broad path with low gray scale resolution. A detailed discussion of this algorithm may be found in the technical literature (9, 14). Digitally enhanced and outlined cells are
66
SCHWARTZ
AND
DILLER
FIG 4. I >ig itized rendition of the photomicrograph in Fig. 3b produced on an electro static printer- plotte rL tsing an algorithm that provides 16 gray levels. (A) Unenhanced. (B) Local1 y enh anced FiVl e cells ha .ve been processed using a localized image enhancement routine to emphasize the IcKUS of
the cell w all tion scher ne
The cell boundaries T = 269.2”K
are shown
as outlined
automatically
by a biased
trident
edge detec-
VOLUMETRIC
CHANGES
IN CELLS
illustrated in Fig. 4. The apparent cell volume is approximated from the measured area by a simple geometric relationship, based on the assumption of a spherical configuration. Although it is recognized that yeast are actually prolate ellipsoids, this information was not incorporated into the volume determinations. Automatic identification of the major and minor axes in the randomly oriented cells would have required a much more sophisticated pattern recognition algorithm and, in particular, a considerable increment in computer processing time. Therefore, in the interests of expediting data analysis, spherical geometry was assumed. The limit of potential inaccuracy introduced by this assumption may be evaluated. Mazur (18) has presented data for the aspect ratio of the major and minor axes (a/h) of yeast in various unfrozen and frozen states, indicating that the ratio may vary between 0.94 and 0.86. It is easily demonstrated that the ratio of the volumes of a prolate spheroid and a sphere having identical projected cross-sectional areas varies directly with the reciprocal of the square root of the aspect ratio. Thus, the actual cell volume will be within the range of 3 to 7% smaller than the value calculated for spherical geometry for the spectrum of aspect ratios defined by Mazur. In addition, since the cells maintain a constant orientation throughout the freezing process and only normalized values of volume are considered, the compromise in accuracy introduced by this assumption is minimal. Thus, the average processing time on a per cell basis is limited to the order of 1 to 2 min, depending on how many cells can be analyzed on a single photomicrograph frame. For the experimental data to be correlated with an analytical model (26) it is necessary to relate the total cell volume to intracellular water content by accounting for impermeable solutes and solids. An appropriate conversion factor has been determined for Sacchuromyces cerevisiue by
DURING
FREEZING
67
Mazur (18). The intracellular water volume can be related to the total cell volume by the expression v\+r = v.r - v, - vcw, [II where V, = intracellular free water volume, V., = total cell volume, V, = apparent intracellular volume of solids, solutes, and bound water, and V, \, = cell wall volume. Since the cell wall is located outside the permeability barrier assumed by the thermodynamic model (i.e., the plasma membrane), it is appropriate to exclude 100% of the wall in determining the cell water volime. The intracellular volume not occupied oy water may be expressed as Vs = 0.154 (V’r,i - V,‘\v),
PI
where VT,i is the initial total volume prior to freezing. By eliminating Vs between Eqs. [I] and [2] the transient intracellular water volume can be determined by V\y = V’r - 0.154 (VT,i - V,‘\v) - V,‘, = V.F - 0.154 V,,i - 0.846 Vc\r.
[31
In applying this expression, it is assumed for all cells that the initial thickness of the cell wall is approximately 0.1 pm, (19) and that the volume and water content of the wall remains constant even though the total cell volume may change (17, 19, 30). As an example of the dimensional significance of the cell wall, for a relatively small cell (50 pm3), the wall occupies 13% of the initial volume, whereas for a relatively large cell (130 pm3) the wall represents 9% of the initial volume. Obviously, when a relatively small cell experiences a large volume decrease (as associated with a slow cooling rate process), theoretically the cell wall may constitute as much as 40% of the total volume at maximum dehydration. RESULTS
Cells were frozen in 13 different experimental protocols, as presented in Table 1, at cooling rates ranging between 9 and 82”Kimin and with a degree of extracellular supercooling between 1 and 36°K. The
68
SCHWARTZ
AND
transient volumes of individual cells were measured from serial cryomicroscope photographs from which intracellular water volumes were calculated using Eq. [3]. All volumes were normalized to the initial prefreezing value. An example sequence of selected photomicrographs from the freezing protocol at YWmin (trial 1) is shown in Fig. 3. Each of the photomicrographs was digitized and stored on the computer for analysis. The primary processing steps in the digital analysis procedure are illustrated in Figs. 4 and 5, which were produced with a 16 gray-level dot matrix printer. An unenhanced, digitized representation of the image in Fig. 3b is presented in Fig. 4. Cells were identified for volume measurements by operator intervention on an interactive video terminal. The results of a localized enhancement routine can be seen as effected for a rectangular area surrounding each cell. The biased trident edge tracking algorithm was applied to determine automatically the locus of the wall for each cell. The outlines for these individual cells were tracked through the sequential micrographs
269 2 OK
DILLER
of the freezing process, as illustrated in Fig. 5. Although the automated machine procedure for outlining cells is desirably objective, without possibility for biasing due to operator intervention and interpretation, it can be seen in Fig. 5 that the procedure may fail upon encountering image anomalies, such as apparent optical gaps in the wall which may occur at the interface between a cell and the ice-solution front. Our computer software provides the capability for operator patching across discontinuities in the wall using the interactive graphics terminal. In the present study this function was not employed, necessitating the rejection of some data for which the edge tracking routine obviously became “lost.” The volumes of each cell measured in trial 1 are plotted as a function of temperature in Fig. 6. The measured initial volumes of the individual cells are indicated. It is readily apparent that the dehydration curve is not affected by individual cell size. The volume dehydration data are presented as a composite plot in Fig. 7. The theoretical equilibrium freezing curve is also shown depicting an infinitely slow cooling rate for
269.3OK
2665 “K
8 Q
0 0
Q
0
0
Q
0 0
@ Q
r 2635%
252.0”K
FIG. 5. Computer printout of outlined cell boundaries for selected shown in Fig. 3. Note that in certain cases the biased trident algorithm properly, for which the data are eliminated from the analysis.
249.0”K
photomicrographs from the trial was unable to track the cell wall
VOLUMETRIC
CHANGES
IN CELLS
DURING
CELL 3!$ 0+3-
69
FREEZING
#
VT, (pm3)
145
0
I
P
0
2
65
E I-
n
3
72
0
4
51
E o-4-
D
5
64
; ;: 5
,-,
6
64
06-
s q
j
oz-
TEMPERATURE
FIG. 6. Transient normalized water volume 9”Wmin. The numbered cells are identified
(“K)
plots for individual in Fig. 5.
which osmotic equilibrium is maintained across the cell membrane continuously. Composite plots of the measured variation in cell volume as a function of temperature are presented in Figs. 8 through 13 for the experimental data obtained in trials 2 through 13, respectivley. In each case the cooling rate and number of cells measured are indicated and the equilibrium freezing curve is shown as a reference depicting the
cells during
trial
1 at a cooling
rate of
limiting conditions of osmotic equilibrium. The degree of extracellular supercooling prior to the nucleation of ice is equal to the horizontal displacement along the temperature coordinate of the experimental curve from the equilibrium curve at a normalized volume of 1.0. Ushiyama and Cravalho have previously performed cryomicroscopic measurements of the volumetric changes in individual
C.R. n=
= 9 OK/min 4
0 275
270
260
250
240 TEMPERATURE
FIG. 7. Freezing data base.
curve
for cell volumes
measured
during
230
220
210
(“K I
trial 1. n is the number
of cells included
in the
70
SCHWARTZ
275
270 0
260
AND
0
C. R. = 12 OK/min
n=3
0
C. I?. = 14°K/mln
n=3
250
-10
DILLER
240
-20
230
-30
-40
TEMPERATURE
FIG.
8. Freezing
curve
for cell volumes
yeast cells during freezing (29). Their data are presented in Fig. 14 for comparison with our present experimental results. These data exhibit considerably less sensitivity to variations in cooling rate than was measured in our experiments. No values of extracellular supercooling were identified by Ushiyama and Cravalho.
275
270 I 0
260 f
-10
-20
9. Freezing
curve
210 -60
(“K/“(Z)
during
trials
2 and 3.
Finally, in order to provide a perspective view of the interaction among the experimental parameters, all of the present data is combined in Fig. 15 into a single threedimensional plot in which the effects of temperature, cooling rate, and extracellular supercooling on cell volume are illustrated simultaneously.
a
C. R. = 15 “K/mm
ll=l
0
C R. = 19 “Khin
ll=l
240
230
-30
for cell volumes
220
I
I
TEMPERATURE
FIG.
-50
measured
250
I
220
-40
-50
during
trials
I -60
(‘K/‘C)
measured
210
I
4 and 5.
VOLUMETRIC
275
270 0
CHANGES
260
IN CELLS
250
-10
-20
10. Freezing
curve
0
C. R. =32”K/mln
n=3
220
-40
-50
210 -60
measured
during
trials
6 and 7.
teractive coupling effects remain difficult to predict quantitatively. The experimental data presented herein can be analyzed so as to describe the influence of multiple thermal factors. The two defined thermal parameters of the freezing process for the present study were the cooling rate and the extracellular supercooling.
DISCUSSION
P N i 2 5
n=3
(“K/“C)
for cell volumes
As noted in the introduction, in previous investigations it has been demonstrated repeatedly that numerous thermal and physiological parameters act in concert to dictate the volumetric response of individual cells to freezing stress. Although these parameters have been identified singularly, in-
Y E
C. R = 25 OK/min
230
-30
71
FREEZING
0
240
TEMPERATURE
FIG.
DURING
.4 -
.2-
276
270 I 0
260
0
C. I?. = 35 OK/min
IT=2
0
C.R. = 37 ‘K/min
n=2
250
I -10
I -20
240
11. Freezing
curve
for cell volumes
220 ,
-50
-60
(“K/“C)
measured
210
I
-40
-30 TEMPERATURE
FIG.
230 1
I
during
trials
8 and 9.
72
SCHWARTZ
1.0
AND
DILLER
r
1;. I 275
I 260
270
0
-20
12. Freezing
curve
n=3
0
C. R. = 54 ‘K/min
n=3
240
230
220
-40
-30 TEMPERATURE
FIG.
C. R. = 52 ‘Khin
1
250
-0
0
for cell volumes
2 10
-50
-60
(OK/%)
measured
during
trials
10 and 11.
As expected, a behavior uniformly ob- the freezing of an aqueous solution (refer served in all the data is that the cell water again to the H,O-NaCl phase diagram in volume decreases as the temperature is re- Fig. 2). The calculated equilibrium freezing curve depicted in Figures 7- 13 indicates duced during freezing. The phenomenon can be ascribed to the exposure of cells to a the loss of intracellular water that would be progressively increasing concentration of expected for a cooling rate sufficiently slow could be mainextracellular electrolytes associated with that osmotic equilibrium
I 275
270
260
I
I
0
- 10
V
C. R. = 76 OK/mm
n=3
0
C. R. = 82 OK/min
n=2
250 I -20
240
-30
TEMPERATURE
FIG.
13. Freezing
curve
230
for cell volumes
I
-40
I -60
-50
(“K/“C)
measured
210
220
I
I
during
trials
12 and 13.
VOLUMETRIC
CHANGES
IN CELLS DURING
1
-10 TEMPERATURE
-20 CC)
-30
FIG. 14. Measured intracellular water volume of yeast (S. cerevisiae) frozen at constant cooling rates by Ushiyama and Cravalho (29).
tained continuously between the intracellular and extracellular solutions by the transmembrane movement of water. Inspection of the data in Figs. 7 through 13 reveals that for each of the trials conducted, the loss of intracellular water occurred at a rate slower than required to achieve osmotic equilibrium. Thus, at all temperatures lower than the equilibrium phase change point of protoplasm, the intracellular water existed in a supercooled state. Sequential inspection of Figs. 7-13 shows that the magnitudes of both the cooling rate and extracellular supercooling exhibit a strong influence on the extent of cell water loss during freezing. A clear general trend which emerges is that at more rapid cooling, the rate of water loss is depressed so that the cumulative cellular dehydration over the entire freezing process is reduced. This observation can be explained in terms of the imbalance between simultaneous heat and mass transfer processes which occur during freezing. The rate of heat transfer within the cell system is set externally by the thermal boundary conditions, which can be regulated actively by manipulation of the freezer environmental
FREEZING
73
temperature to produce a desired thermal history. In contrast, the mass transfer is governed by internal gradients, which are established only in passive response to the chemical disequilibrium created by the freezing process. Thus, depending on the values of certain thermodynamic properties, such as thermal conductivity and membrane permeability which govern the transport of heat and mass within the cell suspension system, the corresponding rates of relaxation for heat and mass transfer during the freezing process may be quite different. For rapid cooling the rate of heat transfer will dominate that of mass transfer. Consequently, at subfreezing temperatures the intracellular water volume will be larger than that obtained for an equilibrium freezing process at a low cooling rate. In general, the larger the difference between the actual and threshold cooling rates, the greater will be the chemical disequilibrium created, with a concomitant decrease in net water efflux. The departure from a state of transmembrane chemical equilibrium during freezing is self-perpetuating on the time scale of the freezing process because the water permeability of the cells decreases exponentially as the temperature is lowered (13). Therefore, incrementing the cooling rate has the effect of further hindering cellular dehydration by more rapidly effecting a state of depressed membrane permeability before extensive net water loss can occur. The overall influence of increased cooling rate on cell water loss can be identified most readily from the composite plot of experimental data shown in Fig. 15. Both the dehydration rate and total cumulative water loss are seen to diminish with increasing cooling rate. The effects of extracellular supercooling can be observed by comparison of the transient volume curves for experimental trials with similar cooling rates and dissimilar supercooling. According to Table 1, four such pairs of trials can be identified for the
(OKI
FIG.
15. Composite freezing curve of cell water volume as a function of both cooling rate and extracellular supercooling for trials 1-13 inclusivecorresponding to the equilibrium phase change temperature for a physiologily. , Hidden isotherms. - - -, Hidden freezing curves. -, Isotherm cally equivalent concentration of sodium chloride in water. All freezing curves are extrapolated at constant volume from the minimum measured temperature to 2WK, as denoted by ----.
TEMPERATURE
VOLUMETRIC
CHANGES
IN
CELLS
TABLE
Trial
No. 3 4 8 9 10 II 12 13
Cooling rate (“Kimin) 14 15 35 31 52 54 76 82
75
FREEZING
2
Supercooling (“K) -0.75 -2.0 -10.2 -17.1 -19.3 -30.5 -28.0 -16.0
data presented in Figs. 8 and 9, 11, 12, and 13. Data for these trials are summarized in Table 2. In each case greater extracellular supercooling is seen to exert a common influence on the cell dehydration curve; i.e., net water loss is diminished. As with the cooling rate, this effect is related to the thermal depression of the membrane hydraulic permeability. Cell water efflux occurs as a result of the concentration of extracellular electrolytes associated with the freezing process. Supercooling effectively delays establishment of the conditions requisite for the water flux (i.e., the presence of extracellular ice) to a lower temperature; as a result when the transmembrane osmotic concentration potential is established by extracellular ice nucleation at a temperature lower than the equilibrium phase change value, the resistance to mass transport is greater. Consequently, the resistance to cell dehydration is higher because the water efflux process is shifted to a lower temperature. This explanation is supported by the data in Table 2 in which are tabulated the rate of water loss over the first 10°K temperature drop following extracellular nucleation and the smallest cell volume reached. For each of the four pairs of trials evaluated, increased supercooling resulted in a reduced rate of water loss and less total cell shrinkage. Thus, the experimental data demonstrate clearly that the cooling rate and the extracellular supercooling may act in concert to control the magnitude of cell water loss during freezing.
DURING
dt’,,/dT
(“K-l) 1118 1130 1140 1148 11130 11480 11220 11125
V final 0.20 0.40 0.65 0.80 0.83 0.97 0.94 0.76
It can be observed in Fig. 6 that the fraction of free cell water expressed during the freezing process is not dependent on the absolute size of the cell. In this trial (No. l), the volumes of six cells were tracked continuously during freezing; initial intracellular water volumes varied by a factor of approximately three. There were no significant differences among the normalized volume curves for any of the cells, and no discernable size-related trends were detected. As discussed previously, cells undergo a progressive dehydration as the temperature decreases during freezing. Factors which may act to inhibit this process include (1) thermal reduction of the membrane permeability, (2) attainment of an osmotic equilibrium volume, and (3) formation of intracellular ice. Such behavior is revealed in Figs. 10 through 13 by the presence of a volumetric plateau at a value much larger than occurs for the equilibrium freezing curve. In contrast, for Figs. 7 through 9 no volumetric plateau can be identified for the experimental data. Analysis of Figs. lo- 13 shows that in general, lower cooling rates and smaller supercooling result in more extensive cellular shrinkage before a volume plateau is reached. The data also indicate that the temperature is not so low that the cell membrane hydraulic permeability has been depressed to an infinitesimally small value. Comparison of trials 6 and 7 in Fig. 10 confirm this point. In trial 7 the volumetric plateau is reached at a temperature of approximately 255°K ( - 18”C), whereas in
76
SCHWARTZ
trial 6 substantial water loss is measured between 255 (-18) and 245°K ( 28”), requiring a finite permeability coefficient. The temperature at which the volume plateau is initiated is also not consistent among all the experimental trials, implying the involvement of an additional parameter which can be unique to individual trials, such as intracellular ice formation. Unfortunately, for the yeast cells used in this study it was not possible to observe an intracellular nucleation event or the presence of an ice structure within the individual cells, probably due to the optical properties of the cell wall. Direct visual detection of intracellular ice has been a notable benefit of the technique of cryomicroscopy for other cell types such as erythrocytes (6, 8), HeLa Cells (10, 22), ova (16), and plant cells (11). Based on the evidence presented above, it is conjectured that the presence of the nonequilibrium volume plateau is due to intracellular ice formation. Further evaluation of this data by an analytical model for cell freezing, as described in a companion paper (26), lends credence to this conclusion. SUMMARY
The osmotic response of yeast to freezing was measured as a funciton of cooling rate and degree of extracellular supercooling. Thirteen experimental trials were conducted on a cryomicroscope in which incremental size changes of individual cells were recorded photographically, and the corresponding volume variations were measured using a digital computer image analysis algorithm. Plots were obtained of normalized cell volume as a function of temperature. Cellular dehydration during freezing was progressively inhibited with increasing values of cooling rate and extracellular supercooling. Normalized cell volume changes were not a function of the relative initial cell size. A constant volume plateau occurred
AND
DILLER
for conditions under which intracellular formation was expected.
ice
REFERENCES 1. Bank, H. Visualization of freezing damage. 11. Structural alterations during warming. Cvyobialogy 10, 157- 170 (1973). 2. Bank, H., and Mazur, P. Visualization of freezing damage. J. Cell. Biol. 57, 729-742 (1973). 3. Cosman, M. D., and Cravalho, E. G. Intracellular thermodynamic states critical for the formation of ice. Submitted for publication. 4. “CRC Handbook of Chemistry and Physics” (R. C. Weast, Ed.), pp. D224-D225. CRC Press, Cleveland (1979). 5. Diller, K. R. Intracellular freezing: Effect of extracellular supercooling. Cryobiology 12, 480-485 (1975). 6. Diller, K. R. Intracellular freezing of glycerolized red cells. Cryobiology 16, 125- 131 (1979). 7. Diller, K. R., and Cravalho, E. G. A cryomicroscope for the study of freezing and thawing processes in biological cells. Cryobiology 7, 191-199 (1970). 8. Diller, K. R., Cravalho, E. G., and Huggins, C. E. An experimental study of freezing in erythrocytes. Med. Biol. Eng. 14, 321-326 (1976). 9. Diller, K. R., and Knox, J. M. Identification and tracking of blurred boundaries in cluttered pictures. IEEE Proc., Pattern Recog. Image Process. l37- 139 (1981). 10. Diller, K. R., Matheson, D., and Cravalho, E. G. A high speed motion picture study of morphological changes during freezing and thawing processes in HeLa cells. Cryobiology 6, 576 (1970). 11. Dowgert, M. F., Steponkus, P. L., Levin, R. L., and Ferguson, J. R. Cryobiology of isolated plant protoplasts. II. Intracellular ice formation. Cryobiology 16, 593 (1979). 12. Griffiths, J. B., Cox, C. S., Beadle, D. J. and Reid, D. S. Changes in cell size during the cooling, warming and post-thawing periods of the freeze-thaw cycle. Cryobiology 16, 141- 151 (1979). 13. Jacobs, M. H., Glassman, H. N., and Parpart, A. K. Osmotic properties of the erythrocyte. VII. The temperature coefficients of certain hemolytic processes. J. Cell. Comp. Physiol. 7, 197-225 (1935). 14. Knox. J. M. and Diller, K. R. A biased-trident algorithm for identifying cell boundaries in a matrix of freezing ice. Submitted for publication. IS. Knox. , J. M.. , Schwartz. G. J.. and Diller. K. R. ~-
VOLUMETRIC
16.
17.
18.
19.
20. 21.
22.
CHANGES
IN CELLS DURING
Volumetric changes in cells during freezing and thawing. J. Biomech. Eng., Trans. ASME 102, 91-97 (1980). Leibo, S. P., McGrath, J. J., and Cravalho, E. G. Microscopic observation of intracellular ice formation in unfertilized mouse ova as a function of cooling rate. Crphiology 15, 257-271 (1978). Levin, R. L. Water permeability of yeast cells at subzero temperatures. J. Me&r. Biol. 46, 91-124 (1979). Mazur, P. Manifectations of injury in yeast cells exposed to subzero temperatures. I. Morphological changes in freeze-substituted and in “frozen-thawed” cells. J. Brtctcriol. 82, 662-684 (1961). Mazur, P. Studies on rapidly frozen suspensions of yeast cells by differential thermal analysis and conductometry. Biophys. J. 3, 323-353 (1963). Mazur, P. The role of intracellular freezing in the death of cells cooled at supraoptimal rates. Cryobiology 14, 251-272 (1977). Mazur, P., and Schmidt, J. J. Interactions of cooling velocity, temperature, and warming velocity on the survival of frozen and thawed yeast. Cryobiology 5, l- 17 (1968). McGrath, J. J., Cravalho, E. G., and Huggins, C. E. An experimental comparison of intracellular ice formation and freeze-thaw survival of HeLa S-3 cells. Cryobiology 12, 540-550 (1975).
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23. Scheiwe, M. W., and Korber, C. Thermally defined cryomicroscopy and some applications on human leucocytes. J. Microsc. 126, 29-44 (1982). 24. Schwartz, G. J., and Diller, K. R. Volumetric changes during the thawing of frozen cells. Cryoletters 1, 129-134 (1980). 25. Schwartz, G. J., and Diller, K. R. Parameters affecting the osmmotic behavior of cells during freezing and thawing: Human granulocytes. Cryoletters 2, 359-372 (1981). 26. Schwartz, G. J., and Diller, K. R. Osmotic response of individual ceils during freezing. II. Membrane permeability analysis. Cr~obiolog~, in press 27. Steponkus, P. L., Dowgert, M. F., Levin, R. L., and Ferguson, J. F. Cryobiology of isolated plant protoplasts. IV. Cellular injury. Crwhiol0g.v 16, 593-594 (1979). 28. Toscano, W. M., Cravalho, E. G., Silvares, 0. M., and Huggins, C. E. The thermodynamics of intracellular ice nucleation in the freezing of erythrocytes. J. Heat Transfer, Trans. ASME
97, 326-332
(1975).
29. Ushiyama, M., and Cravalho, E. G. Volumetric changes in yeast cells during freezing at constant rates. J. Memhr. Bid. 46, 112- 114 (1979). Appendix to R. L. Levin, (1979). 30. Wood, T. H., and Rosenberg, A. M. Freezing in yeast cells. Biochim. Biophys. Acra 25, 78-87 (1957).