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a Bioheat and Mass Transfer Laboratory, Department of Mechanical Engineering,
b Department of Cell Biology and Neuroanatomy,
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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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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During freezing of cell suspensions, ice nucleates first in the extracellular space causing an osmotic gradient to be set up across the intracellular isotonic solution and the freeze concentrated extracellular solution [5]. Depending on whether the cooling rate is low or high, the intracellular water permeates across the cell membrane and joins the extracellular ice phase or freezes and forms ice inside of the cell, respectively. In most cases, cells undergoing intracellular ice formation (IIF) are rendered osmotically inactive (lysed), due to the loss of cell membrane integrity [6]. Similarly cells that experience a severe loss of intracellular water are also rendered osmotically inactive [7]. Both IIF and long exposures to high solute concentrations are lethal to cells, which means that cooling rates that are either "too high" or "too low" can kill cells; therefore an "optimal" cooling rate should and does exist between the high and low. This has been confirmed experimentally for a variety of cells, and 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 probability of IIF result in different optimal cooling rates for different cells. Therefore, to optimize a cryopreservation protocol, it is important to measure the cell membrane's permeability to water. There are currently no experimental techniques that yield data on how sperm cells either dehydrate or form IIF during freezing in the presence of extracellular ice [4]. Currently available cryomicroscopy techniques are limited 1) by the resolution of the light microscope, which is close to or equal to some of the morphological dimensions of the sperm cell [9], and 2) by the fact that measured changes in 2-dimensional areas can be translated to 3-dimensional volumetric changes only for geometric figures like spheres, discs, cylinders, etc. Thus, the small radial dimensions and irregular (nonspherical) shapes of the sperm cells do not allow the observation and reduction of meaningful biophysical data through the cryomicroscope.
This study reports the use of a shape-independent differential scanning calorimeter (DSC) technique [10, 11] to measure the membrane permeability parameters of mouse sperm cells during freezing. The DSC is an instrument that measures heat releases during phase change processes as a function of time and temperature. In the DSC technique, two heat releases from the same cell suspension (or tissue system) are measured 1) during freezing of osmotically active (live) cells in media (where the intracellular water is being transported across the membrane to freeze in the extracellular space) and 2) during freezing of osmotically inactive (dead) cells in media. The difference in heat release measured between the two cooling runs is correlated to water transport. This has been demonstrated in a variety of cellular systems including Epstein Barr Virus Transformed (EBVT) human lymphocyte cell suspensions [10], normal rat liver tissue slices [11], the liver tissue slices of a freeze-tolerant wood frog, Rana sylvatica [12, 13]. Because the DSC technique is independent of the size and shape of the cells being observed, it is used in the present study to measure the membrane permeability parameters of mouse sperm cells at two different cooling rates (5 and 20°C/min) in the presence of extracellular ice and cryoprotective agents (CPAs). Numerical simulations of water transport in mouse sperm cells are then performed under a variety of cooling rates (5–100°C/min) using the experimentally determined membrane permeability parameters. 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 "optimal cooling rates" for mouse sperm cryopreservation. As an additional test of the predicted range of optimal cooling rates, the percentage of viable and motile sperm cells were obtained after freezing at two different cooling rates (slow = 5°C/min; fast = 20°C/min) in two different media (low and high CPA).
A Model Of Water Transport During Freezing
In this section we present the mathematical equations and the membrane permeability parameters used to model water transport during freezing in the presence of extracellular ice and cryoprotective agents (CPAs) in a cell suspension system. Kedem and Katchalsky [14] 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 two differential equations that describe the water and CPA flux across the membrane [14]. If the flux of CPA is negligible in comparison to the water flux [15, 16], then the Kedem-Katchalsky model reduces to a model that assumes only water transport, as proposed by Mazur [5] and later modified by Levin et al. [17]. The various assumptions made in the development of Mazur's model of water transport are discussed in detail elsewhere [18, 19]. The water transport model of Mazur was further modified to incorporate the presence of CPAs on the volumetric shrinkage response of cells during freezing as [20, 21],
with Lp, the sperm cell membrane permeability to water defined by Levin et al. [17] 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 cell volume at temperature, T (K); Ac is the effective membrane surface area for water transport, assumed to be constant during the freezing process; Vo and Vb are the isotonic (initial) and osmotically inactive sperm cell volumes, respectively. In this study, the mouse sperm cell is modeled as a long cylinder with length (L) of 122 µm and a radius (ro) of 0.46 µm, which translates to Vo ~81 µm3 and Ac ~353 µm2 as reported by Du et al. [22]. The osmotically inactive cell volume, Vb, was assumed to be 0.61Vo as reported by Willoughby et al. [23]; 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 salt; vcpa is the molar volume of CPA (73.3 x 1012 µm3/mole); vw is the molar volume of water (18 x 1012 µm3/mole); 
s is the disassociation constant for salt (= 2); ns is the number of moles of salt (= Ci x (Vo - Vb), where Ci is the initial cell osmolality, 0.285 M); 
Hf is the latent heat of fusion of water (335 mJ/mg); 
is the density of water (1000 kg/m3). Note that when ncpa is zero (i.e., no CPA is present), equations 1 and 2 reduce to the "water transport" model as described by Mazur [5] and Levin et al. [17] and Lp is an Arrhenius function of Lpg and ELp. The two unknown membrane permeability parameters of the model, either Lpg[cpa] and ELp[cpa] in the presence of CPA or Lpg and ELp in the absence of CPA, are 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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Cauda epididymal sperm were obtained from 4- to 8-mo-old ICR mice (Harlan, Indianapolis, IN). After cervical dislocation, pairs of cauda epididymides were excised from 2 mice and placed in a 1.5-ml microfuge tube containing either 500 µl of 37°C Dulbecco's Phosphate Buffered Saline Solution (D-PBS; Life Technologies, Grand Island, NY), pH 7.2, overlaid with 50 µl of mineral oil or the same buffer containing 15% egg yolk. D-PBS was chosen as the basal physiological buffer in these experiments because it has been used routinely by several groups as a component of mouse sperm isolation media [4]. The temperature/time variables at which sperm were collected for our use was fixed at 37°C for 10 min. Egg yolk was prepared from chicken eggs obtained at a local grocery, as described elsewhere [24], and stored in aliquots as a 15% solution (v:v) in D-PBS at -20°C prior to use. Caudae epididymides were cut several times with an iris scissors to allow sperm to swim-out into the media, and cell suspensions were recovered after a 10-min incubation at 37°C. Aliquots were examined microscopically to determine cell concentration and percentage motility/viability. Samples with excessive red blood cells (RBCs) contamination or that were less than 45% motile were discarded. For DSC experiments in the absence of CPA, sperm were concentrated by gentle centrifugation (300 x g, room temperature) for 5 min followed by resuspension to a concentration of 50–200 x 107 cells/ml in room temperature D-PBS or 15% egg yolk/D-PBS. For DSC experiments in the presence of CPA, prior to centrifugation, cells were diluted into CPA as described below and aliquots were removed for freeze-thaw experiments.
Preparation of Sperm: In CPA Media Solutions
DSC experiments were also conducted in the presence of a permeating CPA (glycerol, v:v ratio) and an impermeant CPA (raffinose, w:v ratio) at two different concentrations, which we termed low and high. The low CPA media consisted of 1% glycerol (Life Technologies), 6% raffinose (Life Technologies), and 15% egg yolk in D-PBS solution. The high CPA media consisted of 4% glycerol, 16% raffinose, and 15% egg yolk in D-PBS solution. Using freezing point osmometry, the low CPA media was found to be 0.135 M glycerol and 0.13 M raffinose in the isotonic (~0.285 M) buffer solution (D-PBS with 15% egg yolk), while the high CPA was ~0.54 M glycerol and ~0.26 M raffinose in the isotonic buffer solution. Note that egg yolk was found to have no colloid osmotic pressure. Step-wise addition of CPAs was performed to ensure that the volumetric excursions of the cells were within the osmotic tolerance limits of the mouse sperm cells, i.e., ~0.9Vo to 1.03Vo to maintain > 90% motility [23]. At room temperature, a double-strength stock of low CPA was added to sperm suspensions in 4 equal volume steps at 2-min intervals to achieve a final single-strength CPA solution. For high CPA experiments, an 8% glycerol solution was added to sperm suspensions in 4 equal volume steps at 2-min intervals to achieve a final single-strength CPA solution, followed by a 2:1 dilution in 2 steps with 24% raffinose, 4% glycerol. After the addition of CPAs, the samples were concentrated by gentle centrifugation (as described earlier), and water transport (DSC) experiments were completed within 3 h of sperm isolation.
DSC Experiments
To ensure the accuracy and repeatability of the experimental data, the limitations of the DSC-Pyris 1 (Perkin Elmer Corporation, Norwalk, CT) machine were studied, and a set of calibration and control experiments were performed as detailed previously for a DSC-7 (Perkin Elmer Corporation) machine [10]. These included 1) calibration and minimization of the thermal lag and 2) baseline determination of the thermogram (a sigmoidal baseline was used). In addition, the DSC technique presented in this study is relatively insensitive to the baseline used because the heat releases are "differences" and not "absolute" values, so calibration and controls experiments also included 3) effect of Pseudomonas syringae on DSC heat release readings; 4) experiments with osmotically inactive (lysed) sperm cells (qdsc = 0); and 5) error due to noise in the DSC readings (less than 4% of qdsc). It should be noted that the total volume of cell water in the DSC sample (V) = number of cells x water volume in a single sperm cell = ~109 (cells) x 80(µm3/cell) x 0.4(cell water fraction) x 10-18 (m3/µm3) = 32 x 10-9 (m3). Assuming that the cell water has a density of 1000 kg/m3, this translates to 0.032 mg of cell water per mg of total sample. Thus, the expected value of qdsc per mg of DSC sample = mass of cell water per mg of total sample x latent heat of fusion of water = 0.032(mg) x 335(mJ/mg) = 10.72 mJ/mg of total sample (which agrees quite closely with the measured values ranging from 9 to 11 mJ/mg). Noting that the DSC has a noise of ~0.24 mJ/mg [10], the error due to noise in the DSC reading of interest (qdsc) is less than 4%.
To perform the DSC dynamic cooling experiments, the mouse sperm samples (7–9 mg) were placed in standard aluminum sample pans (Perkin Elmer Corporation), and a natural ice nucleator P. syringae (ATCC, Rockville, MD) was added (0.5–1 mg) before the pans were sealed. The ice-nucleating agent P. syringae always nucleated the extracellular space at temperatures 
-4°C. The DSC pans were reweighed to measure the total sample weight (< 10 mg), and the DSC experiments were performed using the dynamic cooling protocol, outlined below.
DSC Dynamic Cooling Protocol
The DSC dynamic cooling protocol developed to measure water transport out of sperm cells at a cooling rate of 5 (or 20)°C/min is explained below and is identical to the protocol developed for a cell suspension system described in detail by Devireddy et al. [10].
Step 1: The sample (sperm cell suspension either in the D-PBS solution or in the high or low CPA solutions), plus 0.5 to 1 mg of P. syringae bacteria initially at 4°C, was cooled at 5 (or 20)°C/min until the extracellular ice nucleated (~-3.5°C in D-PBS and ~-4.5 to -5.5°C in the CPA solutions). Step 2: After nucleation, the sample was thawed at a warming rate (10°C/min) such that Tph (either -0.53°C, -1.1°C, -2.4°C for the different media solutions of isotonic D-PBS with 15% egg yolk, low CPA, and high CPA, respectively) was reached (but not overshot) and ice remained in the extracellular solution. (Isothermal equilibrium at the phase change temperature [Tph] will permit the ice nuclei to exist but not grow into ice crystals, minimizing the osmotic shrinkage of the cells. Step 3: The sample was then cooled to -50°C at 5 (or 20)°C/min causing the sperm cells to undergo cellular dehydration. The lower curve in Figure 1A corresponds to the heat release associated with dehydration and the total area is represented by qinitial. Step 4: The sample was reequilibrated at Tph by thawing at 100°C/min. Step 5: To differentiate between the heat released by the media and the intracellular fluid in step 3, the sample was cooled at a high cooling rate (200°C/min) down to -100°C. This causes all the sperm cells to lyse and become osmotically inactive. Step 6: Step 4 was repeated. Since all the sperm cells have compromised membranes, the intracellular water, proteins, and salts now are continuous (no membrane barriers exist) as previously suggested by Kö;t1rber et al. [25]. Step 7: The sample was then cooled to -50°C at 5 (or 20)°C/min to measure the final heat release due to lysed or osmotically inactive sperm cells mixed with media. The upper curve in Figure 1A corresponds to this heat release and the total area is represented by qfinal.
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The heat release measured during the final cooling run, qfinal, was compared with the DSC measured heat release from a separate control experiment composed of only osmotically inactive (or lysed) mouse sperm cells, and the magnitude of the heat releases were found to be within ± 1%. This suggests that the fast cooling run in step 5 (200°C/min to -100°C) compromised the membrane integrity of all the mouse sperm cells in the sample. Further support of this observation was obtained when ~99.7% of mouse sperm cells cooled at 130°C/min to -100°C on a Linkam stage (Linkam Scientific, Surrey, UK) stained with propidium iodide (PI, dead cell stain) and ~0.3% stained with SYBR-14 (live cell stain).
Translation of Heat Release to Cell Volume Data for Dynamic Cooling
The heat release measurements of interest are qdsc and q(T)dsc, which are the total and fractional difference between the heat releases measured by integration of the heat flows in steps 3 and 7, respectively, using the DSC-Pyris 1 software. The total difference in the integrated heat release between the baseline (constant and sigmoidal) and the actual thermogram in the two cooling runs (step 3 and step 7) is denoted as qdsc (= qinitial - qfinal) and is shown in Figure 1A. The fractional difference in the integrated heat release from Tph down to a subzero temperature, T, is denoted by q(T)dsc = q(T)initial - q(T)final and is shown in Figure 1B. This difference in heat release has been shown to be related to cell volume changes in cell suspensions [10], in normal rat liver tissue systems [11] and in the liver tissue of wood frog R. sylvatica [12] as,
We can rearrange this equation to measure water transport data from the DSC measured heat releases q(T)dsc and qdsc as,
Note that the DSC measured heat release readings q(T)dsc and qdsc are obtained separately at 5°C/min (shown in Fig. 1 for sperm cells suspended in D-PBS with 15% egg yolk) and at 20°C/min (data not shown) both in the absence and presence of CPAs. The DSC water transport data obtained using equation 4 was shown to generate statistically similar data (> 95% confidence level using the Student's t-test) to that obtained using a standard cellular cryomicroscopy technique with a spherical cell system [10] and also to the water transport data obtained using the low temperature microscopy method in a normal rat liver tissue system [11]. Since the use of equation 4 to generate water transport data from DSC measured heat release readings has been validated in both cell and tissue systems, it is reasonable to presume that it can be used to generate the water transport data in a sperm cell suspension system as well. The unknowns needed in equation 4 apart from the DSC heat release readings are Vi (the initial cell volume) and Vb (the osmotically inactive cell volume). The initial volume of the sperm cells in the D-PBS solution was assumed to be the isotonic cell volume, Vo (~81 µm3) as reported by Du et al. [22] and from this the initial cell volume, Vi, was calculated to be 0.91Vo and 0.88Vo in the low and high CPA media, respectively. Note that the initial volumes of the sperm cells in the CPA media, Vi, are lower than the isotonic cell volume, Vo, since the nonpermeating CPA (in this case raffinose) increases the osmotic pressure of the extracellular media, leading to an efflux of the intracellular water into the extracellular media. The osmotically inactive cell volume, Vb, was assumed in all cases to be 0.61Vo as obtained by Willoughby et al. [23].
Numerical Methods
A nonlinear least-squares curve fitting technique was implemented using a computer program to calculate the membrane permeability parameters (Lpg and ELp) that best fit the volumetric shrinkage data as previously described by Bevington and Robinson [26]. The optimal fit of equation 1 to the experimental data was obtained by selecting a set of parameters that minimized the residual variance, 
2, and maximized a goodness of fit parameter, R2 [27]. In order to predict the membrane permeability parameters that produced a "combined best fit" to the experimental water transport data at two or more cooling rates, the nonlinear curve fitting code was slightly modified such that R2 was minimized by one set of parameters for all cooling rates as previously described [28, 29]. All the curve fitting results presented have an R2 value greater than or equal to 0.93, indicating that there was a good agreement between the experimental data points and the fit calculated using the estimated membrane permeability parameters. To simulate the biophysical response of a sperm cell under a variety of cooling rates, the best-fit parameters were substituted in the water transport equation (equations 1 and 2), which was then numerically solved using a 4th order Runge-Kutta method using a FORTRAN code on an SGI (SGI, Mountain View, CA) workstation [28–30].
Freeze/Thaw Experiments
As an independent verification of the range of cooling rates appropriate for cryopreservation, mouse sperm cells were frozen and thawed using a -80°C freezer. At room temperature, 50-µl aliquots of sperm suspensions in high or low CPA were transferred to 0.6-ml microtubes and placed in either an open plastic rack (fast cooling rates) or in a styrofoam box (slow cooling rates). Both the rack and the box were placed in a -80°C freezer for 1 h, after which samples were transferred to LN2 for storage. Cooling rates of samples, either in the open rack or in the styrofoam box, when placed in the -80°C freezer were measured using type T thermocouples (Omega Tech. Corp., Stamford, CT). The thermocouple voltages were read by a Fluke Hydra DataLogger (Dytec Instruments, Bloomington, MN), saved digitally, and transferred to a personal computer for further data reduction and analysis. In the open plastic rack, the thermocouple readings translated to a cooling rate of ~35°C/min until ice nucleated in the sample at ~-8.5°C and ~20°C/min from ~-2°C to -80°C. In the styrofoam box, the corresponding cooling rates were ~6°C/min until ice nucleated at ~-7.4°C and 5°C/min from ~-2°C to -80°C. Samples in LN2 were thawed (~200°C/min) by holding each tube in air for 5 sec and then swirling in a 37°C water bath for 45 sec. Tubes were placed in a room temperature rack for 3 min before beginning CPA dilution. All samples in CPA were diluted 1:10 with 1% bovine serum albumin/Hepes buffered saline solution (BSA/HBS; Life Technologies), pH 7.4 at room temperature. Step-wise dilution of CPAs was performed to ensure that, during the removal of CPAs, the volumetric excursions of the cells were within the osmotic tolerance limits reported for mouse sperm cells [23, 31]. For samples in low CPA, 4 steps of 60 mOsm reductions at 1.5-min intervals were used. For samples in high CPA, 11 dilution steps at 1.5-min intervals were used: 3 steps of 100 mOsm each, 2 steps of 75 mOsm each, 5 steps of 50 mOsm each, and a final 20 mOsm reduction.
Motility and Viability Assays
Prefreeze motility and viability estimates were obtained after a 1:10 dilution into 1% BSA/HBS. Postthaw motility and viability were assessed after diluting CPA loaded samples 1:10 into 1% BSA/HBS. Sperm viability was determined using 2 fluorescent nucleic acid dyes obtained from Molecular Probes (Eugene, OR) in kit form according to the instructions supplied. SYBR-14 (live cell stain) and propidium iodide (PI; dead cell stain) were prepared fresh daily in HBS and used at final concentrations of 100 nM and 600 nM, respectively. The use of SYBR-14/PI to assess sperm viability has been validated for a number of mammalian sperm including mouse and human [32–34]. Between 100–300 cells/sample were scored in each assay using an Olympus BX-50 microscope at x200 magnification and Nomarski DIC optics (motility) or FITC and Texas Red filter cubes (viability). Motility estimates are reported as "total motile" (i.e., all cells that show some motility), however, it was our observation that at least 75% of the motile cell population were highly progressive.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Initial experiments were performed to establish a simple and reproducible mouse sperm isolation protocol that would result in a sufficiently viable and motile population of cells for use in water transport and freeze/thaw experiments. Isolation of sperm in D-PBS with a mineral oil overlay showed consistently higher initial motility (~50% vs. ~19%) and viability (~48% vs. ~29%) than preparations without oil (as shown in Table 1; differences are significant with a confidence level 95% using a Student's t-test). Therefore, in the absence of CPAs and egg yolk, all DSC experiments used sperm collected in D-PBS with a mineral oil overlay. Given that sperm precooled to a temperature near 4°C (as required for DSC experiments) will experience significant chilling injury or cold shock [35–37], we determined if the addition of 15% egg yolk to D-PBS would minimize this effect and, if so, whether membrane permeability parameters would be affected. Sperm were isolated with and without the addition of 15% egg yolk to D-PBS and motility measured. The results demonstrated that including egg yolk in the isolation buffer significantly increases the motile population of cells after up to 3 h incubation on ice. However, sperm cell viability was less significantly affected by cooling to 4°C (data not shown). These data are in agreement with Songsasen and Leibo [24], who showed a nearly 4-fold drop in cell survival after cooling to -4°C in PBS without egg yolk. However, our DSC data in the presence and absence of 15% egg yolk indicates that sperm cells in either media produced essentially identical water transport results (n = 6, > 99% confidence level with Student's t-test).
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Dynamic Cooling Response and Membrane Permeability Parameters
Figure 2A shows the water transport data and simulation using best-fit parameters in equations 1 and 2 at cooling rates of 5 and 20°C/min in the D-PBS solution (and in D-PBS with 15% egg yolk). The open and filled circles represent the DSC water transport (volumetric shrinkage) data at the cooling rate of 5 and 20°C/min, respectively. The dynamic portion of the cooling curve is between -0.53°C to -8°C at these cooling rates. Water transport cessation is observed in the DSC heat release data as an overlap of the thermograms from the first (step 3) and last (step 7) run as seen in Figure 1. The best fit of equation 1 to the 5°C/min water transport data was obtained for membrane permeability parameter values of Lpg = 1.7 x 10-15 m3/Ns (0.01 µm/min-atm) and ELp = 211.5 kJ/mole (50.6 kcal/mole) with an R2 value of 0.98, while the corresponding values for the 20°C/min data are Lpg = 1.7 x 10-15 m3/Ns (0.01 µm/min-atm) and ELp = 85.7 kJ/mole (20.5 kcal/mole) with an R2 value of 0.95 (Table 2). The fits generated by these parameters are shown in Figure 2A as solid lines. The model-simulated equilibrium cooling response (equilibrium is achieved at each temperature when the internal and external osmotic pressures are equal [i.e., 
i = o]) is also shown for reference as dotted lines and is generated by setting the left hand side (LHS) of equation 1 = 0 and balancing the intracellular and extracellular unfrozen chemical activity of water on the right hand side (RHS) at a particular subzero temperature.
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Figure 2B shows the water transport data and simulation using best-fit parameters in equations 1 and 2 at cooling rates of 5 and 20°C/min in the low CPA media (as described earlier). The open and filled squares represent water transport data in the low CPA media at the cooling rates of 5 and 20°C/min, respectively. The dynamic portion of the cooling curve is between -0.53°C to -10°C at these cooling rates. The best fit of equation 1 to the 5°C/min water transport data was obtained for membrane permeability parameter values of Lpg[cpa] = 1.36 x 10-15 m3/Ns (0.008 µm/min-atm) and ELp[cpa] = 143.5 kJ/mole (34.3 kcal/mole) with an R2 value of 0.99, while the corresponding values for the 20°C/min data are Lpg[cpa] = 1.53 x 10-15 m3/Ns (0.009 µm/min-atm) and ELp[cpa] = 112.6 kJ/mole (26.9 kcal/mole) with an R2 value of 0.99 (Table 2). The fits generated by these parameters are shown in Figure 2B as solid lines, and the model-simulated equilibrium cooling response is also shown for reference as dotted lines.
Figure 2C shows the water transport data and simulation using best-fit parameters in equations 1 and 2 at cooling rates of 5 and 20°C/min in the high CPA media (as described earlier). The open and filled triangles represent water transport data in the high CPA media at the cooling rates of 5 and 20°C/min, respectively. The dynamic portion of the cooling curve is between -0.53°C to -10°C at these cooling rates. The best fit of equation 1 to the 5°C/min water transport data was obtained for membrane permeability parameter values of Lpg[cpa] = 0.68 x 10-15 m3/Ns (0.004 µm/min-atm) and ELp[cpa] = 83.7 kJ/mole (20 kcal/mole) with an R2 value of 0.99, while the corresponding values for the 20°C/min data are Lpg[cpa] = 0.68 x 10-15 m3/Ns (0.004 µm/min-atm) and ELp[cpa] = 50.6 kJ/mole (12.1 kcal/mole) with an R2 value of 0.99 (Table 2). The fits generated by these parameters are shown in Figure 2C as solid lines, and the model-simulated equilibrium cooling response is also shown for reference as dotted lines.
Combined Best-Fit Parameters
A new set of membrane permeability parameters (Lpg and ELp or Lpg[cpa] and ELp[cpa]) were obtained that produced a combined best fit to the experimentally determined water transport data in D-PBS and in the low and high CPA media solutions, as shown in Table 2. The combined best-fit membrane permeability parameters maximized the goodness of fit parameter, R2, for the 5 and 20°C/min water transport data concurrently. Figure 3 shows the contour plots of the goodness of fit parameter, R2 (= 0.90) in the Lpg and ELp (or Lpg[cpa] and ELp[cpa]) space that "fit" the water transport data at 5 and 20°C/min in the D-PBS (Fig. 3A) and in the low (Fig. 3B) and high (Fig. 3C) CPA media solutions, respectively. Any combination of Lpg and ELp (or Lpg[cpa] and ELp[cpa]) shown to be within the contour will fit the water transport data at that cooling rate with an R2 value > 0.90. The predicted "best-fit" parameters are denoted by a star (*) and fall close to (Fig. 3A) or within (Figs. 3, B and C) the overlap of the two contours. The combined best-fit parameters compare quite closely with the parameters obtained at the higher cooling rate of 20°C/min, presumably due to the fact that the 20°C/min water transport data is farther away from equilibrium than the 5°C/min data. This suggests that the membrane permeability parameters obtained using the 20°C/min water transport data could predict the volumetric response of the sperm cell at the lower cooling rate of 5°C/min quite accurately, while the converse is not true. Therefore, to obtain the membrane permeability parameters that "best predict" the behavior of a biological system, water transport data needs to be obtained at the highest possible cooling rate at which dehydration occurs exclusively, as noted earlier [28, 29].
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Statistical Analysis
The DSC water transport data at 5 and 20°C/min were found to be statistically significantly different from one another with 95% confidence level (in the dynamic part of the cooling curve, ~-0.53 to -10°C) in D-PBS (with and without 15% egg yolk) as well as in the low and high CPA solutions. However, the differences in the water transport data between the low and high CPA medium were found to be statistically significant only with 80% confidence level (at both 5 and 20°C/min, in the dynamic part of the cooling curve, ~-0.53 to -10°C). And finally, the differences in the water transport data between the D-PBS and in the CPA solutions were found to be statistically significant with a confidence level 95% (in the dynamic part of the cooling curve, ~-0.53 to -10°C).
Water Transport Simulations
Water transport simulations obtained using the combined best-fit parameters in equation 1 are shown for a variety of cooling rates (5–100°C/min) in Figure 4. In Figure 4, A–C, the numerically simulated nondimensional cellular volume (V/Vo) obtained using these combined best-fit parameters is shown for a variety of cooling rates (at 5, 10, 20, 40, 50, and 100°C/min) in the D-PBS solution, and in the high and low CPA media, respectively. The nondimensional cellular volume (V/Vo), which decreases due to dehydration during freezing, is plotted on the y-axis while 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 cell at the temperature, T (~-30°C) where intracellular ice formation can occur by a homogenous or volume catalyzed nucleation [19] to the initial sperm water volume, [(V - Vb)/(Vo - Vb)] as described earlier for a rat liver tissue system [30] (where V is the end volume after water transport ceases [at ~-30°C], and Vo and Vb are the initial [isotonic] and final [osmotically inactive] sperm cell volumes, respectively). In the D-PBS solution, for cooling rates of 
20, 40, 50, and 100°C/min, the trapped water volume was 2.6%, 5.1%, 20.5%, and 56.4% of initial osmotically active water volume, respectively, and the corresponding end volumes were 0.62Vo, 0.63Vo, 0.69Vo, and 0.83Vo, respectively (Fig. 4A). In the low CPA media (Fig. 4B), for cooling rates of 20, 40, 50, and 100°C/min, the trapped water volume was 1%, 21.3%, 30.8%, and 51.8% of initial osmotically active water volume, respectively, and the corresponding values in the high CPA media (Fig. 4C), were 1.3%, 4.3%, 16.6%, and 40.2%. Therefore, depending on the concentrations of the CPAs, the water transport simulations (Fig. 4) show that cooling rates as low as 25–45°C/min can cause intracellular water to be trapped within the mouse sperm cells. This trapped water will ultimately form intracellular ice with sufficient supercooling.
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As described earlier (see Introduction), the cooling rate that optimizes the freeze/thaw response of any cellular system can be defined as the fastest cooling rate in a given media without forming damaging intracellular ice (IIF) [8]. Mazur [38] defines IIF in embryos as damaging and lethal if > 10–15% of the initial intracellular water is involved. 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 temperature, T ~-30°C. The simulations (shown in Fig. 4) show that the optimal cooling rates in D-PBS and in low and high CPA media solutions are ~39, ~26, and ~44°C/min, respectively. Note, that if IIF occurs by a heterogeneous or a surface catalyzed nucleation mechanism [19] (generally between -5 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 cells than predicted by water transport alone (i.e., the lower bound of intracellular ice discussed above). Thus, the optimal cooling rates (stated above) based on the lower bound of intracellular ice are probably over estimated.
Motility and Viability Results
Results of freeze/thaw experiments normalized to prefreeze controls in both the high and low CPA media are shown in Figure 5 (prefreeze controls are shown in Table 1). In all the panels (Fig. 5, A–D), cooling rate is shown on the x-axis as slow (5°C/min) vs. fast (20°C/min), and either percentage viability or motility is shown on the y-axis. Figure 5, A and B, show the postthaw behavior in high CPA media (4% glycerol and 16% raffinose with 15% egg yolk in D-PBS), while Figure 5, C and D, show the postthaw behavior in low CPA media (1% glycerol and 6% raffinose with 15% egg yolk in D-PBS). Figure 5A shows that the high CPA media had a deleterious effect at both the slow and fast cooling rates, with motility being less than 10%. The percentage of motile sperm in low CPA media are significantly higher (by a factor of four) at both the slow and fast cooling rates, as shown in Figure 5C. In comparison, the viability differences between the frozen/thawed sperm cells in the high vs. low CPA media are less extreme. The slow cooling rate viability for high and low CPA media (Fig. 5, B and D, respectively) are essentially identical (~31–33%). However, there is a significant improvement (almost double) in postthaw viability for the fast cooling rate with low CPA media (Fig. 5D) vs. high CPA media (Fig. 5B). These preliminary results clearly show that the cooling rate and media component composition can dramatically impact the cryopreservation of mouse sperm. In summary, we found the greatest quantitative and qualitative success in preserving sperm morphology, motility, and membrane integrity with the low CPA media and fast cooling conditions, i.e., a relatively low concentration of cryoprotectant, and a cooling rate of 20°C/min.
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DISCUSSION |
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There is a significant decrease (~20–50%) in the predicted value of the activation energy, ELp (or ELp[cpa]) between the 5 and 20°C/min DSC water transport data (Table 2). It might be that the sperm cells cooled at 20°C/min undergo incomplete dehydration and the final end volume is significantly higher than the osmotically inactive cell volume of 0.61Vo, or that the sperm cells experience IIF when cooled at 20°C/min. Unfortunately, at the present time, we have no independent means of verifying the end volumes for mouse sperm cells cooled at 20°C/min to -20°C. However, it should be pointed out that a similar drop in predicted value of the activation energy, ELp (or ELp[cpa]) was also found in normal rat hepatocyte cells both in the presence and absence of CPA (DMSO) using standard cellular cryomicroscopy [28] and also in Dunning AT-1 rat prostate tumor tissue using the DSC technique [29]. In addition, the viability/motility results obtained in this study (Fig. 5) suggest that significant IIF is not occurring at 20°C/min, as the percentage viability/motility increases or remains constant between the slow (5°C/min) and fast (20°C/min) cooling rate in both in the high and low CPA media (i.e., reflects "solute effects" as the dominant mechanism of freezing injury and not IIF). This suggests that water transport is still the dominant biophysical response in mouse sperm cells cooled at 20°C/min. This is further supported by the observation that 1) the magnitude of the DSC measured difference in heat release, qdsc, was found to be constant between 5 and 20°C/min and 2) no secondary heat release was observed at 20°C/min to suggest incomplete dehydration, as was the case for EBVT lymphocytes [10]. Therefore, for the purpose of this study it was assumed that the sperm cells undergo complete dehydration to the osmotically inactive cell volume of 0.61Vo at a cooling rate of 20°C/min (in D-PBS as well as in the low and high CPA media solutions). The observed change in the activation energy is assumed to be intrinsic to the water transport data itself, where more information is contained in data from cooling rates further away from equilibrium cooling, i.e., 20°C/min water transport data contains more dynamic information than at 5°C/min, as noted earlier [28, 29].
Suprazero Membrane Transport Parameters: Absence of Extracellular Ice
As mentioned earlier, there are currently no experimental techniques that yield data on how sperm cells either dehydrate or form intracellular ice during freezing in the presence of extracellular ice [4]. However, there exist a few techniques like the Time to Lysis method and Coulter counter technique to measure the volumetric response of sperm cells to external changes in osmolarity, at suprazero temperatures. Briefly, the Time to Lysis method involves exposing cells to a hypotonic solution containing only nonpermeating solutes and determining the time to lysis that is proportional to the permeability of the cell membrane to water [39–42]. The Coulter counter technique uses a particle counter and sizer to measure volumetric changes in a population of cells over time after initiation of an osmotic stress [16, 23]. The range of parameters obtained using these techniques are essentially in agreement; suprazero membrane permeability, Lp ~0.85–17 x 10-13 m3/Ns (0.5–10 µm/min-atm) and activation energy at suprazero temperatures, Ea ~12–60 kJ/mol (3–14 kcal/mol) and serve to provide a good understanding of suprazero water (and CPA) transport response for a variety of mammalian sperm cells, including human, ram, bull, rabbit, and mouse [4]. More specifically, Noiles et al. [42] have reported a temperature dependence of Lp for mouse sperm cells that drops from ~10 µm/min-atm at 37°C to ~0.4 µm/min-atm at -3°C and an activation energy of ~11–14 kcal/mol in the absence of extracellular ice.
The suprazero membrane permeability, Lp, of sperm cells is higher than other mammalian cells (with the possible exception of red blood cells, RBCs, and liver hepatocyte cells) and activation energies, Ea, are low in comparison to other mammalian cells [4]. One reason for the high permeability values might be due to the presence of channel-forming proteins selective to water in the sperm plasma cell membrane. For example, the high permeability values in human RBCs is due to the presence of CHIP28, a channel-forming protein. Liu et al. [43] have shown that CHIP28 does not mediate the water transport process in human sperm cells. However the presence of an analog to CHIP28 in the sperm cell plasma membrane cannot be ruled out [44].
Inability of Suprazero Permeability Parameters to Predict Subzero Response
The extrapolation of the suprazero permeability data obtained in the absence of extracellular ice using the techniques described above to subzero temperatures in the presence of extracellular ice has not been successful [45]. This conclusion is based on the fact that water permeabilities predicted on the basis of the above-mentioned techniques suggest that mouse sperm cells should be able to dehydrate at rates up to 5000°C/min during freezing when, in fact, experiments show that the optimal cooling rate for mouse sperm cells is between 10–40°C/min depending on the concentrations of CPAs in the extracellular milieu [46–48]. One way to account for this discrepancy is that the values of membrane permeability parameters at subzero temperatures in the presence of extracellular ice are markedly different from those reported in literature at suprazero temperatures. In particular, if Lpg at subzero temperatures is lower by at least an order of magnitude than Lp at suprazero temperatures and ELp at subzero temperatures is higher by at least a factor of two than the corresponding Ea at suprazero temperatures, then the discrepancy between numerical simulations and experimental data can be reconciled [4]. The best-fit parameters obtained in this study using the DSC water transport data (shown in Table 2), during freezing of mouse sperm, confirm that this is indeed the case: Lpg ~1.7–0.68 x 10-15 m3/Ns (0.01–0.004 µm/min-atm) and ELp ~64–209 kJ/mole (15–50 kcal/mole).
The discrepancy between the membrane permeabilities determined in this study and the suprazero permeabilities reported in previous studies may be associated with possible changes in the sperm cell plasma membrane during cooling. These changes could include either a lipid phase transition between 0 and 4°C [42] and/or a cold shock damage or "chilling" injury during cooling [35, 36]. 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 studies conducted in unfrozen solutions at higher temperatures [18]. Schwartz and Diller [49] found that for human granulocytes, the activation energy is dramatically higher (~3 times; Lp drops by about 10–15 times) at subzero temperatures in the presence of extracellular ice, when compared to activation energy at suprazero temperatures in the absence of extracellular ice. This trend is consistent with the results obtained in this study for mouse sperm cells and also in liposomes [50]. These changes in membrane transport properties at lower temperatures 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 changes and corresponding alterations of membrane permeability [51, 52]. The relative importance of temperature and the effect of extracellular ice on the membrane permeability, Lp, is dependent on the cell type. This study shows that mouse sperm cells have dramatically different water transport properties at suprazero temperatures in the absence of extracellular ice and at subzero temperatures in the presence of extracellular ice.
Effect of CPAs on Membrane Transport Parameters
The DSC technique was used to obtain water transport data and water permeability parameters (Lpg[cpa] and ELp[cpa]) of mouse sperm cells in the presence of CPAs (as shown in 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 the membrane permeability parameters, Lpg[cpa] and ELp[cpa]. This is at least partially the case with the data shown in Table 2, where an increase in the concentration of solutes in the extracellular medium is shown to decrease the predicted value of reference membrane permeability of mouse sperm cells, Lpg from 1.7 x 10-15 m3/Ns (0.01 µm/min-atm) in D-PBS (with 15% egg yolk) to Lpg[cpa] of 0.68 x 10-15 m3/Ns (0.004 µm/min-atm) in high CPA media. This trend is consistent with results reported by Mazur in previous studies [38] on membrane permeability parameters of ova and embryos. Gilmore et al. [16] 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 their absence for human sperm cells at suprazero temperatures (i.e., Lp[cpa] < Lp). Smith et al. [28] also report a similar decrease in the value Lpg[cpa] in isolated rat hepatocytes in the presence of 1 M and 2 M DMSO using standard cellular cryomicroscopy. Mazur [38] states that ELp remains unaltered due to changes in the extracellular concentration (i.e., ELp[cpa] ~ ELp); Gilmore et al. [16] measured an increase in the value of the Ea[cpa] for human sperm cells (i.e., Ea[cpa] > Ea) using a Coulter counter technique; Smith et al. [28] found a decrease in the value of ELp[cpa] with increasing concentrations of DMSO for isolated rat hepatocytes (i.e., ELp[cpa] < ELp). The activation energies found in this study (Table 2) show an increase between D-PBS and low CPA media (at 20°C/min) and a decrease between D-PBS and high CPA media. Thus, no firm conclusions can be drawn as to the effect of CPAs on activation energies based on experimental data reported in the literature and in this study. Further studies are clearly needed.
Viability Results: Compared to Literature
The motility and viability results presented in this study (see Table 1 and Fig. 5) for frozen/thawed mouse sperm cells are comparable to values reported in literature [46,48, 53]. For example, Songsasen et al. [53] report that ~30% (normalized to prefreeze control) of the frozen/thawed mouse (B6D2F1 strain) sperm cells had intact cell membranes when cooled at 20°C/min in a solution containing 0.3 M raffinose and 0.2 M glycerol in D-PBS supplemented with 3 mg/ml of BSA. In the same study [53], the inclusion of 16.7% egg yolk instead of BSA was found to increase the percentage of sperm cells with intact membranes to ~40% (normalized to prefreeze control). Some of the highest motility was reported by Tada et al. [47], who found that 56 ± 8% of the frozen/thawed mouse (ICR) sperm cells were motile when frozen (at an uncontrolled cooling rate) and thawed in a solution containing 1.75% glycerol with 18% raffinose in a physiological saline solution (0.86% NaCl). Thus, our motility/viability results are comparable to other published values performed under similar conditions.
Correlation of Motility/Viability to Water Transport Response
The water transport simulations (see Results; Fig. 4) suggest that the optimal cooling rate for high and low CPA media is ~44 and ~26°C/min. Note that for the low CPA media, the simulated optimal cooling rate is quite close to the measured fast cooled (20°C/min) freeze/thaw experiments, which show the greatest quantitative success in preserving frozen/thawed sperm. This result conforms to the idea that the optimal freeze/thaw response in any cellular system will be obtained when the system is cooled at the fastest cooling rate in a given media (CPA) without forming damaging intracellular ice. In fact, the motility/viability results shown in Figure 5 resemble the "left side" (slow cooling) of the inverted U curve, implying that solute-effects injury is the predominant damage mechanism at the cooling rates tested in the freeze/thaw experiments. It may of course, be possible, by freezing mouse sperm cells in the high CPA media at the optimal cooling rate of ~44°C/min, to achieve an even higher percentage of viable sperm cells than the optimal values obtained with the low CPA media at fast (20°C/min) cooling conditions. However, this will not be possible until the significant loss of motility in the high CPA media in comparison to the low CPA media (comparing Fig. 5, A and C), can be addressed.
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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2 Correspondence: John C. Bischof, Bioheat and Mass Transfer Laboratory, Department of Mechanical Engineering, University of Minnesota, 111 Church Street S.E., Minneapolis, MN 55455. FAX: 612 624 1398; bischof{at}maroon.tc.umn.edu
Accepted: April 22, 1999.
Received: January 11, 1999.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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