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Regular Article |
a Department of Mechanical Engineering,
b College of Veterinary Medicine, and
c Department of Urologic Surgery, University of Minnesota, Minneapolis, Minnesota 55455
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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0.3°C/min in an Equitainer-I from 37°C to 4°C. By fitting a model of water transport to the experimentally obtained DSC volumetric shrinkage data, the best-fit membrane permeability parameters (Lpg and ELp) were determined. The combined best-fit parameters of water transport (at both 5°C/min and 20°C/min) in Kenney extender (absence of CPAs) are Lpg = 0.02 µm min-1 atm-1 and ELp = 32.7 kcal/mol with a goodness-of-fit parameter R2 = 0.96, and the best-fit parameters in the lactose-EDTA extender (the CPA medium) are Lpg[cpa] = 0.008 µm min-1 atm-1 and ELp[cpa] = 12.1 kcal/mol with R2 = 0.97. These parameters suggest that the optimal cooling rate for equine sperm is 
29°C/min and is 60°C/min in the Kenney extender and in the lactose-EDTA extender. These rates are predicted assuming no intracellular ice formation occurs and that the 5% of initial osmotically active water volume trapped inside the cells at -30°C will form innocuous ice on further cooling. Numerical simulations also showed that in the lactose-EDTA extender, equine sperm trap 3.4% and 7.1% of the intracellular water when cooled at 20°C/min and 100°C/min, respectively. As an independent test of this prediction, the percentage of viable equine sperm was obtained after freezing at 6 different cooling rates (2°C/min, 20°C/min, 50°C/min, 70°C/min, 130°C/min, and 200°C/min) to -80°C in the CPA medium. Sperm viability was essentially constant between 20°C/min and 130°C/min.
gamete biology, reproductive technology, sperm
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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8°C at rates greater than 0.3°C/min [2–5]. In addition, the bulk of our understanding of the cryopreservation of equine and more generally mammalian sperm is still empirical in nature, because the unique size and morphology of mammalian sperm limit the applicability of standard cellular cryomicroscopy techniques to measure the biophysical response, water transport, and intracellular ice formation in sperm during freezing. Optimization and increased acceptance of equine sperm cryopreservation procedures requires a dynamic and quantitative understanding of the biophysical response of equine sperm suspensions during freezing. Freezing of cells in suspension induces ice nucleation in the extracellular space, creating an osmotic gradient across the plasma membrane between the initially isotonic intracellular solution and the freeze-concentrated extracellular solution. Depending on whether the cooling rate is low or high, the intracellular water will either move across the cell membrane and join the extracellular ice phase or will freeze and form ice inside the cell, respectively. In most cases, cells undergoing intracellular ice formation (IIF) are rendered osmotically inactive or lysed because of the loss of cell membrane integrity [6]. Similarly, cells that experience a severe loss of intracellular water are also rendered osmotically inactive because of the extended exposure to high solute concentrations [7]. Thus, cooling rates that are either too high or too low can be lethal to cells. An optimal cooling rate exists between the high and low rates, as has been confirmed experimentally for a variety of cells. The curve of cell survival plotted as a function of the cooling rate has a characteristic inverted U-shape [8]. Whether a prescribed cooling rate is too low or too high is a function of cell membrane permeability to water and the probability that any water remaining trapped within the cell at any given subzero temperature will nucleate and turn to ice. Differences in membrane permeability to water and the probability of IIF result in different optimal cooling rates for different cells for different freezing media. Therefore, to optimize a cryopreservation protocol it is important to measure the cell membrane's permeability to water in the presence of extracellular ice and cryoprotective agents (CPAs).
We used a cell-shape-independent differential scanning calorimeter (DSC) technique [9–12] to measure the membrane permeability parameters of equine sperm during freezing in the presence of extracellular ice and in lactose-EDTA extender CPA. Experiments were performed on equine sperm suspensions collected from 3 different horses to assess the variation in the measured water transport response among stallions. The experimentally determined equine sperm membrane permeability parameters were then used to simulate the water transport response during freezing under a variety of cooling rates from 5°C/min to 200°C/min. The simulation results were analyzed to predict the amount of water left in the cell after dehydration ceases in the absence of IIF and the theoretically predicted optimal cooling rates for equine sperm cryopreservation both in the presence of extracellular ice and in the lactose-EDTA extender.
Model of Water Transport During Freezing
Kedem and Katchalsky [13] proposed a model for water and solute transport in response to chemical potential gradients based on irreversible thermodynamics. The Kedem and Katchalsky model consists of 2 differential equations that describe the water and CPA flux across the membrane. If the flux of CPA is negligible in comparison to the water flux during freezing [14, 15], then the Kedem-Katchalsky model reduces to a model that assumes only water transport, as proposed by Mazur [6] and later modified by Levin et al. [16]. The various assumptions made in the development of Mazur's model of water transport are discussed in detail elsewhere [17, 18]. The water transport model of Mazur was further modified to incorporate the effect of CPAs on the volumetric shrinkage response of cells during freezing [19] as
with Lp, the sperm membrane permeability to water defined by Levin et al. [16] and later modified by Karlsson et al. [19], as
where Lpg[cpa] is the reference membrane permeability at a reference temperature TR = 273.15 K; ELp[cpa] is the apparent activation energy (kJ/mol) or the temperature dependence of the cell membrane permeability; V is the sperm volume at temperature T (K); Ac is the effective membrane surface area for water transport, assumed to be constant during the freezing process; and Vo and Vb are the isotonic and osmotically inactive sperm volumes, respectively. In this study, the equine sperm is modeled as a long cylinder with length L = 36.5 µm and a radius ro = 0.66 µm, which translates to Vo 50 µm3 and Ac 150 µm2 [20, 21]. The osmotically inactive cell volume (Vb) was assumed to be 0.6Vo, a value within the range reported for a variety of mammalian sperm [15, 21, 22]; R is the universal gas constant (8.314 J/mol K); B is the constant cooling rate (K/min); ncpa is the number of moles of CPA; vcpa is the molar volume of CPA (µm3/mol); vw is the molar volume of water (18 x 1012 µm3/mol); 
s is the disassociation constant for salt (2); ns is the number of moles of salt, Ci·(Vo - Vb), where Ci is the initial cell osmolality (0.285 M); 
Hf is the latent heat of fusion of water (335 mJ/mg); and 
is the density of water (1000 kg/m3). When ncpa is zero (i.e., no CPA is present), equations 1 and 2 reduce to the water transport model as described by Mazur [6] and Levin et al. [16] and Lp is an Arrhenius function of Lpg and ELp. The 2 unknown membrane permeability parameters of the model, either Lpg and ELp or Lpg[cpa] and ELp[cpa], were determined by curve-fitting the water transport model to experimentally obtained volumetric shrinkage data during freezing.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Semen samples used throughout this study were obtained from 3 stallions housed at the University of Minnesota Veterinary Teaching Facility (St. Paul, MN). One stallion was a 20-yr-old Saddlebred and the other 2 were Arabians ages 6 and 29 yr. On any particular day and no more than twice per week, a gel-free ejaculate from one of the stallions was collected with a Missouri artificial vagina (AV) and used for that day's experiments. Approximately 10–20 ejaculates were collected from each stallion over a period of 6–8 mo. The lubricant used in the AV was the water-insoluble petroleum jelly Vaseline (Cheesebrough Ponds, Greenwich, CT). The osmolality of raw semen from each stallion was routinely determined using a freeze-point depression osmometer (Precision Systems, Natick, MA). At 37°C, 15–20 ml of raw semen was diluted 1:3 in Kenney skim milk extender (Har-Vet, Spring Valley, WI), transferred to a disposable plastic bag, placed in an Equitainer-I (Hamilton-Thorn, So. Hamilton, MA) and slowly cooled (0.3°C/min) to a working temperature of 4°C. Cooling rates of >0.3°C/min between 20°C and 8°C have been shown to induce partially irreversible damage (cold shock) in equine sperm characterized by abnormal patterns of swimming (circular or backwards), rapid loss of motility, acrosomal damage, plasma membrane damage, reduced metabolism, and loss of intracellular components [23–25]. The temperature of each sample was constantly monitored using a digital thermometer with a K-type thermocouple (Fluke, Everett, WA). Approximately 5 ml of extended semen was kept at 37°C for determination of initial progressive motility using a computer-assisted semen analyzer (HTM-2030; Hamilton-Thorn). The concentration of sperm was determined using a hemacytometer and light microscopy. In general, the concentration of sperm used in the DSC experiments ranged from 200 x 106 to 700 x 106 viable cells/ml. The initial progressive motility in the Kenney extender was 87.6% ± 7.2%.
Viability Assay
An assay of sperm plasma membrane integrity was also performed at the end of each day's DSC experiments, usually between 8 and 12 h after collection. A 50-µl aliquot of the sperm preparation was diluted directly into 450 µl of 37°C Hepes-buffered saline containing 1% bovine serum and 1 µM each of the fluorescent dyes calcein AM and propidium iodide (Molecular Probes, Eugene, OR). Calcein AM is hydrolyzed to a green fluorescent product (calcein) by esterases in live sperm. Propidium iodide is a red fluorescent nucleic acid stain that is membrane impermeable to live sperm. After 15–30 min at 37°C, 100–300 sperm were scored as live or dead by fluorescence microscopy (BX-50; Olympus, Tokyo, Japan) at 400x magnification.
Sample Preparation in the Absence of CPAs
Once removed from the Equitainer, the extended semen samples were maintained at 4°C for the duration of experiments, typically 3–4 h. Approximately, 200 µl of the extended semen was concentrated by centrifugation (400 x g) for 5 min at 4°C and the sperm pellet resuspended in 25 µl of residual supernatant, immediately prior to each DSC run. Approximately 10 µl of the concentrated sperm suspension was loaded in a DSC sample pan. The exact DSC cooling protocol is described later.
Sample Preparation in the CPA Media
For DSC experiments in the presence of cryoprotectant, the extended semen was also slow-cooled to 4°C in an Equitainer and the sperm concentrated by centrifugation (400 x g) for 10 min at 4°C. An equal volume of the 2x CPA medium was added to the centrifugated sample in 4 steps, each consecutive step consisting of 10%, 20%, 30%, and 40% of the original volume, at 2-min intervals at 4°C. Stepwise addition of CPAs was performed to ensure that during the addition of CPAs the volumetric excursions and the associated osmotic injury to the equine sperm were minimized [21]. This CPA medium was referred to as lactose-EDTA extender by Graham [2] and was described in detail elsewhere [26]. The final concentration of glycerol in the resulting cell suspension was 2.5% (0.34 M), with an osmolality of 750 mOsm/kg. Approximately 200 µl of the sperm suspension in the cryoprotective medium was concentrated by centrifugation (400 x g) for 5 min at 4°C, and the sperm pellet was resuspended in 25 µl of residual supernatant immediately prior to each DSC run. Approximately 10 µl of the concentrated CPA-loaded sperm suspension was placed in a DSC sample pan. The viability assays showed that in cryoprotective medium 61.4% ± 13.4% of sperm stained with calcein AM (were alive), at a concentration of 1.26 ± 0.42 x 109 cells/ml.
DSC Experiments
To ensure the accuracy and repeatability of the experimental data, a set of calibration and control experiments were performed as detailed previously for a DSC-7 machine (Perkin Elmer Corp., Norwalk, CT) [9–12]. These experiments included 1) calibration and minimization of the thermal lag, 2) baseline determination of the thermogram (a sigmoidal baseline was used), 3) experiments with osmotically inactive (lysed) sperm and with no sperm in suspension (qdsc = 0), and 4) predicted vs. measured magnitude of the total heat release difference, qdsc. Assuming the cell concentration in the DSC experiments is 500 x 106 viable cells/ml, the expected value of qdsc per milligram of DSC sample = mass of cell water per milligram of total sample · latent heat of fusion of water = 0.01 · 335 = 3.4 mJ/mg of total sample. The measured values of qdsc range from 2 to 7 mJ/mg (Fig. 1). The measured values of qdsc also are proportional to the initial concentration of viable cells in the DSC sample. The measured values of qdsc also agree quite closely with the predicted value of qdsc, with a correlation coefficient of 0.95. The uncertainty in the DSC reading is 0.24 mJ/mg [9] or <4% of qdsc in a typical sample.
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To perform the DSC dynamic cooling experiments, the concentrated equine sperm sample (10–12 µl) was placed in the standard aluminum sample pans (Perkin Elmer), and a natural ice nucleator Pseudomonas syringae (ATCC Rockville, MD) was added (0.1–0.5 mg) before the pans were sealed. The DSC experiments were performed using a dynamic cooling protocol.
DSC Dynamic Cooling Protocol
The DSC dynamic cooling protocol used to measure the water transport out of equine sperm is similar to the protocol developed previously for lymphocytes [9] and rat liver tissue [10]. The DSC protocol also has been used to measure the water transport response during freezing in mouse [11] and human [12] sperm suspensions. This DSC protocol has recently been independently validated in cell systems by Yuan and Diller [27] using an optical DSC, which visualizes cellular dehydration during the DSC cooling run. The DSC cooling protocol is used to measure 2 heat releases at a specified cooling rate (5°C/min or 20°C/min) from the same cell suspension during freezing: 1) osmotically active (live) cells in medium (where the intracellular water is being transported across the membrane to freeze in the extracellular space), qinitial and 2) osmotically inactive (dead) cells in medium, qfinal (Fig. 2). To obtain qfinal, the sample was fast cooled at 200°C/min to -150°C. The fast cooling run was independently verified to lyse all the sperm when qfinal was compared with the DSC-measured heat release from a separate control experiment composed of only osmotically inactive (or lysed) equine sperm and the magnitude of the heat releases were within ±1%. In addition, >99.7% of equine sperm stained with propidium iodide (dead cell stain) when the DSC pans were forced open after the fast cooling run.
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Translation of Heat Release to Cell Volume Data for Dynamic Cooling
The heat release measurements of interest are qdsc (=qinitial - qfinal) and q(T)dsc (=q(T)initial - q(T)final) obtained using the DSC—Pyris 1 software (Fig. 2). This difference in heat release is related to cell volume changes during freezing [9–12, 28–31] as
We can rearrange this equation to measure water transport data from the DSC-measured heat releases q(T)dsc and qdsc as
The DSC-measured heat release readings q(T)dsc and qdsc are obtained separately at 5°C/min (Fig. 2) and at 20°C/min (data not shown). The unknowns needed in equation 4 apart from the DSC heat release readings are Vi, the initial or the isotonic cell volume (assumed to be Vo in the absence of CPAs), and Ve, the end or the osmotically inactive cell volume (assumed to be 0.6Vo in the absence of CPAs). The initial volume of the sperm in the cryoprotective medium (Vi) is lower than the isotonic cell volume (Vo) because the nonpermeating CPAs, in this case lactose and glucose, reduce the osmotic potential of the extracellular medium, leading to an efflux of the intracellular water into the extracellular medium. Based on the composition of the CPA medium, this initial cell volume was found to be 0.86Vo. Similarly, the presence of permeating CPAs, in this case glycerol, increase the end volume, Ve, to 0.623Vo, a value that is slightly higher than that in the absence of CPAs (0.60Vo).
Numerical Methods
A nonlinear least squares curve-fitting technique was implemented in a computer program to calculate the membrane permeability parameters (Lpg and ELp) that best fit the volumetric shrinkage data obtained from the DSC and the low-temperature microscopy experiments as previously described [31–34]. The computer program used a fourth order Runge-Kutta method to calculate the volume as a function of temperature (based on selected parameters and cooling conditions) and then compared the simulated water transport volumes to experimental data. The optimal fit of equation 1 to the experimental data was obtained by selecting a set of parameters that minimized the residual variance, X2, and maximized a goodness-of-fit parameter, R2 [32–35]. The residual variance is given as
where yi are the experimental data points and y(xi) are the model predictions. The 
i values are the uncertainties in the experimental data points (yi) and were taken as equal to 1 in the code. The total variance (
2) is defined as
where 
is the normal mean of the experimental data,
The quality of the curve fit was also assured by maximizing the goodness of fit parameter,
where the value of R2 = 1 represents a perfect fit, i.e., the residual variance is zero.
To predict the membrane permeability parameters that produced a combined best fit to the experimental water transport data at both the cooling rates, the nonlinear curve-fitting code was slightly modified [30, 34]. A new residual variance (X2) was calculated as the sum of the residual variances at both the cooling rates, where the model predictions y(xi) were obtained using 1 set of membrane permeability parameters for both the cooling rates. The goodness-of-fit parameter (R2) was calculated using the new residual and total variances. Thus, a set of combined best-fit membrane permeability parameters that maximized R2 for both the cooling rates was found, as previously reported [30, 34]. All the curve-fitting results presented have an R2 value 
0.96, indicating that there was reasonably good agreement between the experimental data points and the fit calculated using the estimated membrane permeability parameters.
Computer Simulations
To simulate the biophysical response of equine sperm under a variety of cooling rates, the best-fit parameters were substituted in equation 2, and the water transport equation (equations 1 and 2) was numerically solved using a fourth order Runge-Kutta method with a temperature step of 0.1°C using a FORTRAN code on an SGI workstation. The sensitivity of the model solution was tested by decreasing the temperature step to 0.01°C, and the simulation was repeated. This test had no effect on the results, thus confirming the convergence of our solution.
Freeze/Thaw Experiments
As an independent verification of the range of cooling rates appropriate for cryopreservation, equine sperm were frozen and thawed using the DSC to -80°C at various cooling rates (2°C/min, 20°C/min, 50°C/min, 70°C/min, 130°C/min, and 200°C/min). The DSC samples for the freeze/thaw experiments were prepared exactly as described for the DSC CPA experiments. After nucleation of extracellular ice, the sperm suspensions were equilibrated at the phase-change temperature before the desired cooling rate was imposed. After freezing to -80°C, the sperm suspensions were immediately thawed and the DSC pans were forced open. All samples were diluted 1:20 (v:v ratio) with 1% BSA/Hepes-buffered saline (BSA/HBS; Life Technologies, Grand Island, NY), pH 7.4, at room temperature. Viability of the sperm samples was then assessed using the calcein AM and propidium iodide assay and normalized to the viability of a CPA-loaded unfrozen sample.
Statistical Analyses
Unless indicated otherwise, all measurements were performed using sperm from 3 different horses, with 6 different ejaculates from each horse for every cooling and collection condition studied. Statements reporting no difference or change imply no significant difference based on a Student t-test with P < 0.05, unless otherwise noted.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Given the variation that can occur in sperm quality between stallions, the water transport properties from each stallion in this study were determined independently. Figure 3 shows a comparison of the water transport data at 20°C/min in the absence of CPAs for 3 different stallions (Chief, Legionnaire, and Rooster). Table 1 shows the best-fit membrane permeability parameters for the 3 individual stallions along with the best-fit parameters obtained for the average water transport response. The model-simulated equilibrium cooling response (Fig. 3) is generated by setting the left side of equation 1 equal to 0 and balancing the intracellular and extracellular unfrozen chemical activity of water on the right side at a particular subzero temperature, i.e., equilibrium is achieved at each temperature when the internal and external osmotic pressures are equal (i.e., 
i = o). The water transport data between horses was equivalent at the 99% confidence level based on a Student t-test. Therefore, the DSC data from the remaining experiments in this study are the average volumetric shrinkage data for all horses. However, to generate representative water transport data, at least 2 different samples were obtained from each horse on 2 different days. An average of 6 DSC experiments were performed using each sample.
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Figure 4A shows a comparison of the water transport data at cooling rates of 5°C/min and 20°C/min for equine sperm in the Kenney extender or in the absence of CPAs. The dynamic portion of the cooling curve is between -0.53°C and -15°C at these cooling rates. Water transport cessation is observed in the DSC heat-release data as an overlap of the initial and final thermograms (Fig. 2). The best fit of equations 1 and 2 to the 5°C/min water transport data was obtained for membrane permeability parameter values of Lpg = 0.022 µm min-1 atm-1 and ELp = 67.9 kcal/mole with an R2 value of 0.99, and the corresponding values for the 20°C/min data were Lpg = 0.033 µm min-1 atm-1 and ELp = 47.2 kcal/mole with an R2 value of 0.99 (Table 2).
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Figure 4B shows the water transport data and simulation using best-fit parameters in equations 1 and 2 at cooling rates of 5°C/min and 20°C/min in the CPA medium. The dynamic portion of the cooling curve is between -0.53°C and -10°C at these cooling rates. The best fit of equations 1 and 2 to the 5°C/min water transport data was obtained for membrane permeability parameter values of Lpg[cpa] = 0.007 µm min-1 atm-1 and ELp[cpa] = 27.0 kcal/mole with an R2 value of 0.99, and the corresponding values for the 20°C/min data were Lpg[cpa] = 0.008 µm min-1 atm-1 and ELp[cpa] = 10.9 kcal/mole with an R2 value of 0.99 (Table 2).
Statistical Analysis
The DSC water transport data at 5°C/min and 20°C/min were significantly different at the 95% confidence level in the dynamic part of the cooling curve in both the Kenney extender and the CPA medium. The differences in the water transport data between the Kenney extender and the CPA medium at both the cooling rates were also significant at a confidence level of 95% in the dynamic part of the cooling curve.
Combined Best-Fit Parameters
A new set of membrane permeability parameters (Lpg and ELp) were obtained that produced a combined best fit to the experimentally determined water transport data (Table 2). The combined best-fit membrane permeability parameters maximized the goodness-of-fit parameter (R2) concurrently for both the cooling rates studied. Figure 5 shows the contour plots of the goodness-of-fit parameter (R2 = 0.95) in the Lpg and ELp space that fit the water transport data at 5°C/min and 20°C/min for the data shown in Figure 4, A and B. Any combination of Lpg and ELp within the contour will fit the water transport data at that cooling rate with an R2 value of >0.95. The predicted combined best-fit parameters are denoted by an asterisk in Figure 5 and fall within the overlap of the 2 contours. The predicted individual best-fit parameters for the 5°C/min and 20°C/min water transport data (Table 2) are also shown in Figure 5. The combined best-fit parameters are quite close to the parameters obtained at the higher cooling rate of 20°C/min, presumably because the water transport data from the higher cooling rate are farther away from equilibrium than are the data from the lower cooling rate of 5°C/min. Thus, the membrane permeability parameters obtained using the higher cooling rate water transport data could predict the volumetric response of the sperm at the lower cooling rate quite accurately, but the converse is not true. Therefore, to obtain the membrane permeability parameters that best predict the behavior of a biological system, water transport data must be obtained at the highest possible cooling rate at which dehydration can be exclusively measured, as reported previously [11, 12, 29, 30, 34].
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Water Transport Simulations
In Figure 6, the numerically simulated nondimensional cellular volume (V/Vo) obtained using the combined best-fit parameters (Table 2) is shown for a variety of cooling rates (from 5°C/min to 200°C/min). The V/Vo values, which decrease because of dehydration during freezing, are plotted on the y-axis, and the subzero temperatures are plotted on the x-axis. From the simulations, the amount of trapped water, or a lower bound on the intracellular ice, was computed as a ratio of the volume of the water trapped inside the sperm at approximately -30°C to the initial sperm water volume, (V - Vb)/(Vo - Vb), where V is the equine sperm volume at approximately -30°C and Vo and Vb are the initial (isotonic) and final (osmotically inactive) equine sperm volumes, respectively. (The initial and final volumes in the presence of CPA are 0.86Vo and 0.623Vo, respectively.) This procedure also has been used for mouse and human sperm suspensions [11, 12]. In the absence of CPAs (Fig. 6A), for cooling rates of 5°C/min, 20°C/min, 50°C/min, 100°C/min, and 200°C/min the trapped water volume was 1.8%, 2%, 41.3%, 70.3%, and 85% of initial osmotically active water volume, respectively, and the corresponding end volumes were 0.607Vo, 0.608Vo, 0.765Vo, 0.881Vo, and 0.94Vo, respectively. In the presence of CPAs (Fig. 6B), for cooling rates of 5°C/min, 20°C/min, 50°C/min, 100°C/min, and 200°C/min, the trapped water volume was 1.6%, 3.4%, 4.6%, 7.1%, and 53.5% of initial osmotically active water volume, respectively, and the corresponding end volumes were 0.627Vo, 0.631Vo, 0.633Vo, 0.639Vo, and 0.75Vo, respectively. We assumed that this trapped water will ultimately form intracellular ice with sufficient supercooling.
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Effect of Varying the Osmotically Inactive Cell Volume
The value of the osmotically inactive cell volume of equine sperm has not been reported in the literature. However, after a review of published data we determined that the osmotically inactive cell volume of mammalian sperm is 0.6Vo ± 0.2Vo [15, 21–23]. To study the effect of varying the osmotically inactive cell volume on the predicted membrane permeability parameters (Lpg and ELp), the value of Vb was changed to 0.4Vo and 0.8Vo. The DSC water transport data in the absence of CPA was correspondingly modified using equation 4, and the modified data were curve fitted to the water transport model (equations 1 and 2) using the nonlinear least squares curve-fitting technique previously described. The predicted values of the membrane permeability parameters (Lpg and ELp) using the new osmotically inactive cell volumes are shown in Table 3. An increase or decrease of 33% in the value of Vb from 0.6Vo results in model-predicted membrane permeability parameter values within 10% of each other (Table 3). The predicted optimal cooling rates are within 5% of the value obtained using Vb = 0.6Vo (Table 3). A similar analysis was also performed to assess the effect of changing the osmotically inactive cell volume from 0.6 Vo to 0.4Vo and 0.8Vo in the CPA medium (data not shown). The simulations showed that predicted optimal cooling rates in the CPA medium with Vb = 0.4Vo and Vb = 0.8Vo were within 3% of the values obtained using Vb = 0.6Vo, a behavior similar to that observed in the absence of CPAs. This lack of sensitivity in the membrane permeability parameters to the value of the osmotically inactive cell volume has been reported for a variety of cell and tissue systems [11, 12, 30, 34]. Thus, errors in the estimated value of Vb can modestly alter the model-predicted membrane permeability parameters (Lpg and ELp), but the trends remain the same.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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The cooling rate that optimizes the freeze/thaw response of any cellular system can be defined as the fastest cooling rate in a given medium that precludes the formation of damaging intracellular ice [8]. Mazur [35] defined IIF as damaging and lethal if >10%–15% of the initial intracellular water were involved. For the purpose of this study, we defined the optimal cooling rate as the cooling rate at which 5% of the initial osmotically active water volume is trapped inside the cells at a temperature of approximately -30°C. The simulations show that the optimal cooling rate is 29°C/min in the absence of CPAs and 60°C/min in the presence of CPAs (Table 2 and Fig. 6). However, if IIF occurs by a heterogeneous or surface-catalyzed nucleation mechanism [18] (generally between -5°C and -20°C for a variety of single cells), which our model does not predict, then potentially even more water will be trapped in the sperm than predicted by water transport alone, i.e., the optimal cooling rates for cryopreservation of equine sperm suspensions are probably lower than those shown in Table 2. Thus, the optimal cooling rates based on the lower bound of intracellular ice are probably overestimated. The volume of water trapped in the presence of CPAs ranges from 3.4% to 7.1% when the cooling rate increases from 20°C/min to 100°C/min, i.e., a 5-fold increase in the cooling rate only leads to a doubling of the intracellular water trapped. However, in Kenney extender the amount of intracellular trapped water increased from 3% to 7% when the cooling rate increased from only 27°C/min to 31°C/min, suggesting a much narrower range of optimal cooling rates in Kenney extender (27–31°C/min) than in CPA medium (20–100°C/min). This behavior of the equine sperm was corroborated by the preliminary post freeze/thaw viability measurements shown in Figure 7, where the normalized viability results obtained at 20°C/min, 50°C/min, 70°C/min, and 130°C/min in CPA were not significantly different from one another (>99% confidence level, Student t-test). An analysis of the water transport simulations (data not shown) suggests that the trapped water volume at the cooling rate of 130°C/min is 14.7%. Figure 7 also shows a measurable drop in the postthaw viability of equine sperm cooled at 2°C/min and 200°C/min, probably because of the slow cooling and IIF injury, respectively. This drop in viability at 2°C/min and 200°C/min is significant at the >0.95 confidence level when compared with the viability data at 20°C/min and 50°C/min. However, the drop is not significant when compared with the viability obtained at 70°C/min and 130°C/min. These results confirm that there is a relatively large range of optimal cooling rates for equine sperm in the presence of CPAs, consistent with the results predicted from the measured water transport data. However, the use of only 3 stallions in this study may somewhat limit the application of the results to sperm samples from other stallions. A more detailed examination of the freezing rates and conditions (flat straws, tubes, cell concentrations) on the postthaw viability of equine sperm is currently being performed.
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Effect of Cooling Rate on Membrane Permeability Parameters
There is a significant decrease of 30%–60% in the predicted value of the activation energy, ELp, between the 5°C/min and 20°C/min DSC water transport data (Table 2). It might be that the sperm cooled at 20°C/min undergo incomplete dehydration and the final end volume is significantly higher than the osmotically inactive cell volume of 0.6Vo. It might also be that the equine sperm experience IIF when cooled at 20°C/min. Unfortunately, we currently have no independent means of verifying the end volumes or the biophysical response for equine sperm at a given cooling rate. The observed change in the activation energy is assumed to be intrinsic to the water transport data; more information is contained in data from cooling rates further away from equilibrium cooling, i.e., water transport data from 20°C/min contain more dynamic information than do data from 5°C/min, as noted previously [11, 12, 29, 30, 34]. A similar drop in predicted value of the activation energy (ELp) was found in normal rat hepatocytes, both in the presence and absence of the CPA dimethylsulfoxide (DMSO), using standard cellular cryomicroscopy [34] and in Dunning AT-1 rat prostate tumor tissue using the DSC technique [30]. A similar result was also obtained in both mouse [11] and human [12] sperm suspension studies. The assumption that water transport is still the dominant biophysical response in equine sperm cooled at 20°C/min in the Kenney extender and CPA medium is further supported by the following observations: 1) the magnitude of the DSC-measured difference in heat release (qdsc) was constant between 5°C/min and 20°C/min, and 2) no secondary heat release was observed at 5°C/min or 20°C/min to suggest incomplete dehydration, as was the case for Epstein-Barr virus transformed lymphocytes [9]. Therefore, for the purpose of this study it was assumed that the sperm experience complete dehydration to the osmotically inactive cell volume of 0.6Vo at a cooling rate of 20°C/min.
Effect of Extracellular Ice and CPAs on Membrane Permeability Parameters
Other than the DSC technique used here, there are currently no experimental techniques that yield data on how sperm either dehydrate or form intracellular ice during freezing in the presence of extracellular ice [21]. However, there are a few techniques, such as the time-to-lysis method [36, 37] and the Coulter counter technique, that can be used to measure the volumetric response of sperm to external changes in osmolarity at temperatures above 0°C [15]. The results obtained using these techniques for mammalian sperm are essentially in agreement with each other. The suprazero membrane permeability, Lp 0.5–10 µm min-1 atm-1, and the activation energy at suprazero temperatures, Ea 3–14 kcal/mol, provide a good understanding of suprazero water (and CPA) transport response for a variety of mammalian sperm, including human, ram, bull, rabbit, and mouse [21]. However, these techniques have not as yet been applied to equine sperm, and there is a paucity of suprazero permeability parameters for stallion sperm. There is 1 report of a suprazero membrane permeability (Lp) of 26.0 µm min-1 atm-1 at 22°C for equine sperm [38].
The best-fit parameters obtained in this study using the DSC water transport data (Table 2) during freezing of equine sperm are significantly lower than the reported suprazero permeability value [38]. A similar discrepancy was also found for human and mouse sperm membrane permeability values [11, 12]. This discrepancy between membrane permeabilities may be associated with changes in the sperm plasma membrane during suprazero cooling. These changes could include either a lipid phase transition between 0°C and 4°C [39] or cold shock or chilling injury during cooling [2–4, 24, 25]. The presence of extracellular ice further alters the cell membrane transport properties. In general, for mammalian cells the average activation energy obtained in the presence of extracellular ice is approximately twice as large as that for unfrozen solutions at suprazero temperatures [17]; more specifically, it is 3 times as large in human granulocytes [40]. These changes in membrane transport properties might be associated with a variety of thermotropic (temperature dependent) phase phenomena. For example, the temperature reduction that induces solidification in the extracellular medium may lead to lyotropic (i.e., independent of cooling rate) membrane phase change(s) and corresponding alterations of membrane permeability [41–44] and membrane fluidity [45]. Clearly, the relative importance of temperature and the effect of extracellular ice on the predicted membrane permeability parameters (Lpg and ELp) is dependent on the cell type.
Effect of CPAs on Membrane Transport Parameters
The DSC technique was used to obtain water transport data and values for water permeability parameters (Lpg[cpa] and ELp[cpa]) of equine sperm in the presence of CPAs (Table 2). Although the exact mechanism by which the presence of CPAs modifies the water permeability parameters is as yet unknown, several studies have shown that the presence of CPAs tends to reduce these membrane permeability parameter values (Lpg[cpa] and ELp[cpa]). An increase in the concentration of solutes in the extracellular medium decreased the predicted value of reference membrane permeability of equine sperm (Lpg) from 0.02 µm min-1 atm-1 in Kenney extender to an Lpg[cpa] of 0.008 µm min-1 atm-1 in the CPA medium. This trend is consistent with results reported in previous studies on membrane permeability parameters of ova and embryos by Mazur [35]. Gilmore et al. [15] demonstrated that the value of Lp[cpa] obtained in the presence of various CPAs (1 M glycerol, 1 M propylene glycol, 1 M DMSO, and 2 M ethylene glycol) is lower by 30%–60% than that obtained in the absence of CPAs for human sperm at suprazero temperatures (i.e., Lp[cpa] < Lp). Smith et al. [34], using standard cellular cryomicroscopy, also reported a similar decrease in the value of Lpg[cpa] in isolated rat hepatocytes in the presence of 1 M and 2 M DMSO during freezing. Mazur [35] stated that ELp remained unaltered because of changes in the extracellular concentration (i.e., ELp[cpa] ELp), Gilmore et al. [15], using a Coulter counter technique, measured an increase in the value of the Ea[cpa] for human sperm (i.e., Ea[cpa] > Ea), and Smith et al. [34] found a decrease in the value of ELp[cpa] with increasing concentrations of DMSO for isolated rat hepatocytes (i.e., ELp[cpa] < ELp). Similarly, the activation energies determined in the present study (Table 2) also showed a decrease between Kenney extender and the CPA medium. Thus, the effect of CPAs on the activation energy (ELp) is still not entirely clear. However, there is a general consensus in the published literature that both the overall hydraulic permeability (Lp) and the reference membrane permeability (Lpg) tend to decrease in the presence of CPAs. Further studies are clearly needed.
Stallion vs. Mouse and Human Sperm Water Transport Parameters
The DSC technique has been used to obtain water transport parameter values in the presence of extracellular ice and CPAs for mouse and human sperm suspensions [11, 12]. A comparison of the equine sperm membrane permeability parameter values obtained in the present study with those of mouse and human sperm reveals differences in both the predicted water transport values and the optimal cooling rates. The reference membrane permeability is 0.04 µm min-1 atm-1 for human, 0.008 µm min-1 atm-1 for stallion, and 0.007 µm min-1 atm-1 for mouse sperm suspensions. Similarly, the activation energy is 33.2 kcal/mol for human, 12.1 kcal/mol for equine, and 22.2 kcal/mol for mouse sperm suspensions. These differences in membrane permeability parameters translate into the predicted optimal cooling rates in CPA medium of 16°C/min for human, 60°C/min for stallion, and 35°C/min for mouse sperm suspensions. However, the equine sperm seem to have a much larger range of optimal cooling rates (20–100°C/min) than either mouse (20–50°C/min) or human (10–22°C/min) sperm.
Conclusion
The volumetric shrinkage response during freezing and the subzero water transport parameter values for sperm suspensions from 3 stallions were obtained in this study. The subzero water transport parameters are significantly different from those reported for equine and other mammalian sperm parameters determined in the absence of extracellular ice. The parameters obtained in the present study suggest that the optimal cooling rate for equine sperm in the absence of any CPA is 29°C/min and is 60°C/min with CPAs. Numerical simulations also showed that there is a much narrower range of optimal cooling rates in the absence of CPAs (27–31°C/min) than in the CPA medium (20–100°C/min). This prediction was verified independently by measuring the percentage of viable equine sperm after freezing to -80°C in the CPA medium at various cooling rates ranging from 2°C/min to 200°C/min. The experimentally determined water transport data and modeling made available in the current study should improve our understanding of how to optimize equine sperm cryopreservation protocols based firm biophysical principles.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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1 This work was supported by a grant from the Academic Health Center, University of Minnesota, Minneapolis, MN. 
2 Correspondence: K.P. Roberts, Department of Urologic Surgery, University of Minnesota, 420 Delaware Street S.E., Minneapolis, MN 55455. FAX: 612 626 0428; roberts{at}med.umn.edu
3 Current address: Department of Mechanical Engineering, Louisiana State University, Baton Rouge, LA 70803.
Accepted: August 28, 2001.
Received: June 25, 2001.
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), Legionnaire (
), and Rooster (
) for a cooling rate of 20°C/min in the absence of CPAs. The model-simulated dynamic cooling response for the 3 horses is also shown as solid lines and was obtained by using the best-fit membrane permeability parameters (Lpg and ELp) shown in 
) symbols represent the 5°C/min and 20°C/min data, respectively. The model-simulated equilibrium cooling response is shown as a dotted line. The model-simulated dynamic cooling response at 5°C/min and 20°C/min is shown as a solid line and was obtained by using the best-fit membrane permeability parameters (Lpg and ELp or Lpg[cpa] and ELp[cpa]) shown in 
