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Regular Article |
a Fundamental and Applied Cryobiology Group, Department of Biochemistry and Cellular and Molecular Biology, The University of Tennessee, Knoxville, Tennessee 37932-2575
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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assisted reproductive technology, in vitro fertilization, male reproductive tract, sperm, sperm motility and transport
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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60% relative to that of unfrozen controls) when frozen to -70°C at cooling rates ranging from 27 to 130°C/min and then rapidly warmed at 1875°C/min. However, survival drops sharply, to less than 10%, when they are cooled to -70°C at 261 or 530°C/min (Fig. 1). In the companion paper, we suggest that the large drop in viability at these two higher rates is a consequence of the formation of lethal quantities of intracellular ice crystals. At sufficiently low cooling rates, intracellular water leaves the cells rapidly enough to keep the chemical potential of the remaining intracellular water in near-equilibrium with that of the water in the progressively freezing solution outside the cell. However, if cells are cooled too rapidly, they will undergo intracellular ice formation (IIF), because their water cannot leave fast enough to prevent extensive supercooling and eventual nucleation of that supercooled water in situ. As shown some years ago [2, 3], the kinetics of cell dehydration can be described by four coupled equations.
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The first equation relates the rate of loss of cytoplasmic water to the difference in chemical potentials of intracellular and extracellular water expressed as a vapor pressure ratio:
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The change in this vapor pressure ratio with temperature can be calculated from a second differential equation derived from the Clausius-Clapeyron relation and the Raoult law:
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Time and temperature are related by the cooling rate (B), which, if linear, is given by
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Finally, the hydraulic conductivity (Lp) decreases with falling temperature. If it is assumed to follow an Arrhenius relation, then its value at a given absolute temperature (T) is given by
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The values of R, R', Lf, and vo are constant and are given in Mazur et al. [3]. The values of A, n2, and Lpg are constant for a given cell but differ in different cells. Lp and Ea are adjustable parameters. Knowledge of Lpg, Ea, n2, and A/V (the surface:volume ratio of the cell) permit one to compute the volume of cell water (and the extent of supercooling) versus subzero temperature and cooling rate.
In the present paper, we use the above equations to compute the kinetics of water loss in mouse sperm cooled at rates ranging from 250 to 2000°C/min. From those curves and experimental estimates of the ice nucleation temperature of supercooled cells, we then discuss the probability of IIF as a function of cooling rate, and we compare those estimates with cooling rates that have been experimentally inferred to induce IIF.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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A central aim of the experiment was to estimate the nucleation temperature in supercooled sperm by determining their viability after rapid cooling to -20, -30, -40, or -70°C. One could not achieve rapid cooling of 200°C/min to a temperature such as -30°C by placing the straws in an ethanol bath at -30°C, because the rate would slow markedly when the straw temperature fell to within 5°C of the bath temperature. To obviate that problem and to obtain high cooling rates to -20, -30, and -40°C, the straws were first immersed to near their tops in ethanol baths precooled to -35, -35, and -45°C, respectively. They were removed from those ethanol baths when the thermocouple reading indicated that their temperatures had reached -20, -30, and -40°C, respectively, and were then immediately transferred to ethanol baths at the latter three temperatures. Approximately 5 min later, they were immersed in a water bath at room temperature to warm and thaw rapidly. To achieve rapid cooling to -70°C, the naked straw was immersed in a -42°C bath until its temperature fell to -30°C and was then transferred to an ethanol bath at -70°C. To achieve a somewhat lower cooling rate to -20°C (163°C/min), the straw was immersed in a -25°C ethanol bath until its temperature fell to -20°C, at which time it was transferred to a bath held at -20°C. Representative cooling curves for the above five procedures are given in Figure 2. To achieve the optimal cooling rate of 25°C/min to -70°C, the straw was inserted coaxially in an outer Pyrex tube and the assembly placed in an ethanol bath at -42°C. When the sample temperature had fallen to -30°C, the assembly was transferred to a -70°C ethanol bath. This is the procedure that yielded the optimum cooling rate in our companion study [1].
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The thawed suspensions were diluted 15-fold with SD-PBS (containing Oxyrase) within 5 min after thawing and washed by centrifugation to reduce the raffinose concentration. The percentages of motile sperm were then determined. Details are in Koshimoto and Mazur [1].
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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The values of the parameters specific to mouse sperm that are required to solve the equations were taken from the literature. The values used in the computations were Lpg at 22°C = 1.03 µm/min atm, Ea = 12.6 kcal/mole, A = 355 µm2, and the volume of water in the isotonic cell (Viso) = 43 µm3. The value for Lpg is the mean of values ranging from 0.7 to 1.5 as reported by Noiles et al. [7] and Phelps et al. [8] for osmotic water flux in the absence of a permeating cryoprotectant at room temperature. The value of Ea is the mean of values reported by Noiles et al. [7] based on measurements of Lp between 0 and 37°C. The value for the surface area (A) is the mean of values published by Du et al. [9] and Noiles et al. [10]. The value of Viso is the average of two values reported by Du et al. [9]. Also required is a value for the number of osmoles of solute in the cell, which is calculated as the volume of cell water in the isotonic cell in liters multiplied by the isotonic osmolality (0.29 Osm). The other values required for solving the equations are independent of the cell type and have been listed elsewhere [2, 3].
Using these parameters, curves of relative cell water volume versus temperature were calculated for cooling rates of 250, 500, 1000, and 2000°C/min and are plotted in Figure 3. The values plotted are relative to the volume of water in a cell at isotonic volume (V/Viso). (Note that the initial relative cell water content at the freezing point is 0.72, because the osmolality of the raffinose + 0.25x SD-PBS in the medium is 400 mOsm, not the isotonic value of 290 mOsm.) The vertical dashed line at -20°C labeled "Nucleation Temperature" will be discussed shortly. The curve labeled "EQ" is the extent of shrinkage that would occur as a function of temperature in cells cooled infinitely slowly; this is equivalent to the water content of cells that remain in chemical potential equilibrium with the outside medium. It is calculated from analytical solutions to the following equation [2]:
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The higher the cooling rate, the more the curves shift to the right of the equilibrium curve. The number of degrees the curve is shifted is the number of degrees the cell water is supercooled at given temperatures. At these four rates, the cells are computed to lose 90% of their initial water by -7.4, -9.6, -14, and -25°C, respectively. The water content falls to 110% of the equilibrium value by -8, -11, -17, and -40°C, respectively.
Estimation of the Nucleation Temperature
At some sufficiently low temperature, supercooled water in a cell must freeze, whether by seeding from external ice or by the action of internal heterogeneous nucleators [11]. The temperature at which this occurs is referred to as the nucleation temperature. To relate the dehydration curves in Figure 3 and the degree of supercooling to the likelihood of intracellular freezing, one must have an estimate of that nucleation temperature. In cells such as mouse embryos, this can be ascertained directly with a cryomicroscope. However, that direct approach is not feasible in the sperm because of their small size and their low water content. Approximately 45% of the mouse spermatozoon is nonaqueous [9]. Thus, we chose an inferential approach in which the sperm were rapidly cooled to a series of temperatures between -20 and -70°C at rates exceeding 200°C/min. Representative cooling curves are shown in Figure 2. These rates, as shown in Figure 1, result in survival rates of less than 10% when the cells are cooled to -70°C, presumably from IIF. The argument is that if cooling at high rates produces low survivals when it is terminated at -30°C, for example, but produces high survivals when it is terminated at -20°C, then the nucleation temperature lies between -20 and -30°C.
The results of these experiments are summarized in Figure 4. The four white bars show the motilities of samples cooled at 200–300°C/min to -20, -30, -40, and -70°C, respectively. These rates are calculated from -10°C to the final temperature. Survival after rapid thawing was reduced to 16% or less in each case. In contrast, the motilities of sperm cooled to -30° and -70°C at an approximately 10-fold lower rate (28°C/min; solid bars) were 81% and 64%, respectively. The motility of sperm cooled to -20°C at 163°C/min (leftmost bar) is 35%, which is more than double that of sperm cooled to the same temperature at a higher rate. Recall from Figure 1 that the break in the survival curve in cells cooled to -70°C occurs somewhere between a cooling rate of 130 and 261°C/min.
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Because slow warming tends to exacerbate the detrimental effects of IIF [11], one might ask why we used rapid warming in estimating the nucleation temperature. The answer is twofold. First, from Figure 1, we see that the rate of warming was nearly without effect in cells cooled at the high rate that we had hypothesized as inducing intracellular ice; that is, nearly all cells cooled at 261°C/min or greater are killed after either slow or rapid subsequent warming. Second, slow warming is highly detrimental to cells cooled at 27–130°C/min, rates that we think do not induce IIF during cooling. Rather, we believe that within this cooling rate range, the damage from slow warming is a consequence of recrystallization or devitrification of the external medium.
Our inference from these data in Figure 4 is that most of the sperm are undergoing intracellular ice nucleation by -20°C. The region above -20°C is difficult to study by our procedure. If, for example, one attempts to cool a straw to -15°C at rates >250°C/min by placing it in a bath at -35°C until its temperature has fallen to -15°C, then the cooling rate in the region of -5 to -15°C will be capriciously affected by how much the sample supercools before extracellular nucleation occurs and by the shape and duration of the temperature plateau associated with the release of the latent heat of fusion.
Using a somewhat different approach, but one similar in concept to that used here, Watson et al. [12] concluded that the ice nucleation temperature of bull sperm lies between -20 and -40°C, a value that is lower than that which we infer for mouse sperm. Also, Woelders et al. [13] found that a cooling rate of 250°C/min was lethal to bull sperm, as is the case here in mouse sperm.
Probability of Intracellular Freezing as a Function of Cooling Rate
The vertical dashed line at -20°C in Figure 3 represents our estimate of the intracellular ice nucleation temperature of rapidly cooled mouse sperm. Mazur [14] has suggested that intracellular freezing will not occur if cells enter the nucleation zone with less than 10% of their isotonic water or if the water is supercooled to less than 2°C. Toner et al. [15, 16] have defined much more mechanistic criteria based on heterogeneous nucleation theory, but the inferences with respect of IIF using that mechanistic theory agree quite closely with those drawn from the more qualitative criteria of Mazur [14]. Based on the qualitative criteria, we conclude from Figure 3 that most sperm cooled at 250, 500, or 1000°C/min should not undergo intracellular freezing, but that sperm cooled at 2000°C/min should do so. The reason for this conclusion is that, at the three lower rates, the curve of the volume of intracellular water merges with the equilibrium curve well before the temperature has fallen to the nucleation zone. If the chemical potential of the cell water is equal to that of the water in the external medium, it is, by definition, not supercooled, and if it is not supercooled, then it cannot freeze. (The boundary of the nucleation zone has been drawn vertical in Fig. 3, implying that the nucleation temperature is independent of the cooling rate and the extent of dehydration of the cell. In some cells, this is so, but in others, the nucleation temperature is cooling-rate dependent, commonly rising with increasing rate [11]. If the nucleation temperature were to depart greatly from the vertical line drawn, then it could affect conclusions regarding the cooling rate dependence of IIF. However, the procedures used here do not permit us to draw conclusions with respect to this point.)
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Possible Causes for the Discrepancy
One contributor to the discrepancy could be that the actual upper boundary of the nucleation temperature is higher than the value of -20°C depicted in Figure 3. Indeed, the data shown in Figure 4 suggest that -20°C is the lower limit. If, for example, the nucleation temperature were -10°C, then intracellular freezing would be predicted to occur at or above a cooling rate of 1000°C/min. Unfortunately, for the reasons given, the region above -20°C cannot be explored by the approach used in the present study. However, the literature provides a number of examples in which direct microscopic observation of larger cells (mouse oocytes and embryos, V79 hamster cells, hepatocytes) has demonstrated nucleation temperatures of -12°C and higher [15, 21–24]. Most of these instances, however, have involved cells frozen in the absence of cryoprotective agents. In the presence of 1.0–1.5 molar concentrations of permeating cryoprotective agents, the nucleation temperature is suppressed to less than -30°C in mouse embryo and oocytes [21, 25]. Whether comparable reductions in nucleation temperature occur in the presence of nonpermeating cryoprotectants, such as the raffinose used in the present study, is unknown; however, the nucleation temperature of mouse oocytes is reduced in hyperosmotic (nonpermeating) NaCl [15].
Two other possible contributors to the discrepancy are the value used for Lp at 22°C in the calculations and the value for its activation energy (Ea). If, for example, the actual value of Lp at 22°C were half of that used, then the cooling rates assigned to each of the curves in Figure 3 would be half of those shown; for example, the curve labeled 1000°C/min would become 500°C/min. The value used in the calculations (1.03 µm/min atm) was based on determinations of the rate of osmotic volume changes in an isosmotic medium lacking a cryoprotectant. Phelps et al. [8] reported that, in the presence of ethylene glycol or glycerol, the value of Lp at 22°C for mouse sperm drops to 0.38 µm/min atm. This decrease is consistent with the general finding that Lp in the presence of a cryoprotectant is roughly half that in the absence of cryoprotectant in a variety of cells [20, 26, 27].
Changes in Lp shift the dehydration curves left or right, but they do not change their shapes. Changes in Ea, in contrast, shift the curves and produce major changes in shape. This is illustrated in Figure 5, in which we plot the kinetic dehydration curves for a cooling rate of 500°C/min for activation energies of 12, 16, and 20 kcal/mole. With an Ea of 20 kcal/mole, a cooling rate of 500°C/min would now be predicted to cause intracellular freezing in the mouse sperm. The published value of Ea used in the calculation was based on Arrhenius plots of measurements of Lp at several temperatures between 0 and 37°C. Our equations assume that the value of Ea continues to be applicable when freezing occurs at less than 0°C. Two published experimental reports, one involving yeast [28] and one involving mouse oocytes [15], support this assumption. In these studies, Lp in the partly frozen state was calculated from fits to microscope-derived measurements of cell shrinkage during cooling at given rates to -20 or -30°C. When these Lp values were extrapolated back to 22 or 0°C, the extrapolated values were quite similar to those directly measured at 22 or 0°C. However, that agreement may not necessarily be maintained as freezing progresses to yet lower temperature. This is because, as freezing progresses, the viscosity of the medium rises sharply as the raffinose concentrates, and the high viscosities may lower the rate of water efflux above and beyond the effect of lowered temperature per se. In addition, and more speculatively, the inherent permeability of the plasma membrane may change.
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Devireddy et al. [20] have used a very different approach to estimate the Lp and Ea of mouse sperm (and other cells) at subzero temperatures. Their procedure yields very different values for Lp at 0°C and for Ea than those based on above-zero water permeability measurements. They used differential scanning calorimetry to estimate the rate at which the water leaves the sperm cells and freezes externally in cells cooled at 5 or 25°C/min. They did this by measuring the increase in the exotherm contributed by the freezing of the cell water that has left the intact cells and then comparing that to the exotherm contributed by the freezing of the water in the same sample in which the cells are disrupted. They then used an Arrhenius equation to back-calculate the value of Lp at 0°C. In the absence of cryoprotectant, their approach yields an Lp at 0°C of 0.01 µm/min atm, which is 30-fold lower than the measured value of 0.33 µm/min atm at 0°C reported by Noiles et al. [7]. In the presence of cryoprotectant, their value of Lp at 0°C (0.004 µm/min atm) is also approximately 30-fold lower than the value measured at 0°C by Phelps et al. (0.10 µm/min atm [8]). In the absence of cryoprotectant, their approach yields a value of Ea of 22.5 kcal/mole, which is approximately double that obtained from measurements made at above-zero temperatures. If the values of Devireddy et al. [20] for Lp and Ea are used to calculate shrinkage curves like those shown in Figures 3 and 5, then the resulting curves lead to the conclusion that mouse sperm will undergo intracellular freezing at a cooling rate of approximately 25–40°C/min, which is approximately 50-fold lower than the rate estimated in the present study and approximately fivefold lower than that inferred from our experimental data. Devireddy et al. [20] concluded that their study shows mouse sperm to have dramatically different water transport properties at superzero temperatures in the absence of extracellular ice and at subzero temperatures in the presence of extracellular ice. Perhaps a more cautious statement would be that a large discrepancy exists between the two sets of data for the mouse, and currently, no independent evidence is available for deciding which is the more applicable to subzero events.
Clearly, the range of possible values for the critical parameters is large enough to account for the approximately eightfold discrepancy between the cooling rates we calculate to induce intracellular ice and those cooling rates inferred to do so from the measurements of survival as a function of cooling rate. However, we cannot currently exclude two alternative explanations. One, pointed out by Gao et al. [19], is that injury could be a consequence of internal freezing in critical organelles such as mitochondria rather than a consequence of ice formation in the whole cytoplasm. If so, then the applicable permeability parameters would be those of the organelle's membrane rather than those of the plasma membrane, and the two sets of values could be different.
A second alternative is that the abrupt drop in survival at cooling rates greater than 130°C/min is caused by something other than IIF. One possible "something other" is cold shock—the inactivation of cells from a rapid fall in temperature per se. Whereas this is possible, we think it is unlikely. Although rapid chilling is well documented in porcine, ram, and bovine sperm [12], it occurs at cooling rates of approximately 10–15°C/min, and we have found that mouse sperm cooled from room temperature to 0°C at those rates show, at most, a marginal loss in motility [4, 5, 29]. Moreover, Watson et al. [12] have found that although bull spermatozoa are sensitive to chilling injury from room temperature to 10°C, they undergo little injury when cooled from 10 to 0 or -5°C at 220 and 300°C/min, which are rates similar to those used in the present study.
The discrepancies observed in mouse and other sperm between the rates calculated from permeability parameters to produce IIF and those that produce major drops in survival are unusual. In mouse oocytes and embryos, yeast, human red cells, human lymphocytes, hamster tissue culture cells, and plant protoplasts, a close correlation is observed between the cooling rates that produce a drop in survival, the cooling rates that are visually observed to produce IIF, and the cooling rates that are predicted to do so from modeling (see [11] for older references and [16] for a more recent study). As discussed, the discrepancy in mouse sperm is resolvable if other possible values of Lp and Ea are substituted for those used in the present study. However, at the moment, that resolution is a hypothesis, not a fact.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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1 Supported by NIH grant R24-RR13194 (J. Critser, PI) under subcontract with Indiana University. A preliminary report was presented at the 37th Annual Meeting of the Society of Cryobiology; Cambridge, MA; 30 July to 1 August 2000. 
2 Correspondence: Peter Mazur, Fundamental and Applied Cryobiology Group, Dept. of Biochemistry and Cellular and Molecular Biology, The University of Tennessee, 10515 Research Dr., Suite 300/10, Knoxville, TN 37932-2575. FAX: 865 974 8027; pmazur{at}utk.edu
3 Permanent address: Experimental Animal Center, 5200 Miyazaki Medical College, Kiyotake, Miyazaki 889-1692, Japan
Accepted: December 10, 2001.
Received: September 10, 2001.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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