The effect of extracellular ice and cryoprotective agents on the water permeability parameters of human sperm plasma membrane during freezing

Ramachandra V. Devireddy1, David J. Swanlund1, Kenneth P. Roberts2,3, Jon L. Pryor2,3 and John C. Bischof1,2,4

1 Bioheat and Mass Transfer Laboratory, Department of Mechanical Engineering, 2 Department of Urologic Surgery and 3 Department of Obstetrics and Gynecology, University of Minnesota, Minneapolis, MN 55455, USA


    Abstract
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
A firm biophysical basis for the cryopreservation of human spermatozoa is limited by a lack of knowledge regarding the water permeability characteristics during freezing in the presence of extracellular ice and cryoprotective agents (CPA). Cryomicroscopy cannot be used to measure dehydration during freezing in human spermatozoa because of their highly non-spherical shape and their small dimensions which are at the limits of light microscopic resolution. Using a new shape-independent differential scanning calorimeter (DSC) technique, volumetric shrinkage during freezing of human sperm cell suspensions was obtained at cooling rates of 5 and 10°C/min in the presence of extracellular ice and CPA. Using previously published data, the human sperm cell was modelled as a cylinder of length 40.2 µm and a radius of 0.42 µm with an osmotically inactive cell volume, Vb, of 0.23Vo, where Vo is the isotonic cell volume. By fitting a model of water transport to the experimentally obtained volumetric shrinkage data, the best fit membrane permeability parameters (Lpg and ELp) were determined. The `combined best fit' membrane permeability parameters at 5 and 10°C/min for human sperm cells in modified media are: Lpg = 2.4x10–14 m3/Ns (0.14 µm/min-atm) and ELp = 357.7 kJ/mol (85.5 kcal/mol) (R2 = 0.98), and in CPA media (with 6% glycerol and 10% egg yolk) are Lpg[cpa] = 0.67x10–14 m3/Ns (0.04 µm/min-atm) and ELp[cpa] = 138.9 kJ/mol (33.2 kcal/mol) (R2 = 0.98). These parameters are significantly different from previously published parameters for human spermatozoa obtained at suprazero temperatures and at subzero temperatures in the absence of extracellular ice. The parameters obtained in this study also suggest that damaging intracellular ice formation (IIF) could occur in human sperm cells at cooling rates as low as 25–45°C/min, depending on the concentrations of the CPA. This may help to explain the discrepancy between the empirically determined optimal cryopreservation cooling rates (<100°C/min) and the numerically predicted optimal cooling rates (>7000°C/min) obtained using previously published suprazero human sperm permeability parameters which do not account for the presence of extracellular ice.

Key words: cryopreservation/differential scanning calorimetry/human spermatozoa/membrane permeability/water transport


    Introduction
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
From the earliest reported experiments of freezing of human spermatozoa (Spallanzani, 1776Go; Davenport, 1897Go; Parkes, 1945Go), there have been many improvements in the methodology of human sperm cryopreservation. Some of these improvements include the use of cryoprotectants (e.g. glycerol; Polge et al., 1949); the use of glycerol–egg yolk–citrate media for sperm isolation; the use of ampoules, straws and pellets; and various freezing and thawing techniques (Storey et al., 1998; also see review by Brotherton, 1990). In addition, several improvements have been reported on the assessment of human sperm motility, viability, energy status, damage to the plasma membrane or to the subcellular elements, chromatin stability and chromosomal damage (Watson, 1995Go; Royere et al., 1996Go). Both the ability to freeze and the possibility of pregnancy following intrauterine insemination (IUI) have been reported as early as 1953 (Bunge and Sherman, 1953Go). However, the bulk of our understanding on the effect of freezing human spermatozoa is still empirical in nature since the unique size and shape of human spermatozoa limit the applicability of traditional techniques, such as cryomicroscopy, to measure the state of intracellular water during freezing (Gao et al., 1997Go). Further improvement and increased acceptance of human sperm cryopreservation protocols necessitates a more fundamental understanding of the freezing processes in human sperm cell suspensions.

During freezing of cell suspensions, ice nucleates first in the extracellular space causing an osmotic gradient to be set up across the membrane, i.e. between the intracellular isotonic solution and the freeze-concentrated extracellular solution (Mazur, 1963Go). Depending on whether the cooling rate is `low' or `high', the intracellular water moves across the cell membrane and joins the extracellular ice phase, or freezes and forms ice inside 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 (Mazur, 1984Go). Similarly, cells which experience a severe loss of intracellular water are also rendered osmotically inactive (Lovelock, 1953Go). Both IIF and long exposures to high solute concentrations are lethal to cells; thus, cooling rates which are either `too high' or `too low' can kill cells. Therefore, the `optimal' cooling rate should and does exist between the `high' and `low' freezing rates. 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 (Mazur et al., 1972Go). 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. In general, the `optimal' cooling rate is defined as that cooling rate which minimizes both the slow cooling and IIF injury, i.e. cool as fast as possible without forming damaging intracellular ice. Therefore, to optimize a cryopreservation protocol it is important to measure the permeability of the cell membrane to water. There are currently no experimental techniques which yield data on how sperm cells either dehydrate or form IIF during freezing in the presence of extracellular ice (Gao et al., 1997Go). Currently available cryomicroscopy techniques are limited: (i) by the resolution of the light microscope, which is close to or equal to some of the morphological dimensions of the sperm cell; and (ii) by the fact that they rely on the translation of projected two-dimensional area measurements to infer three-dimensional volumetric changes. Thus, the small radial dimensions and irregular (non-spherical) 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 to measure the membrane permeability parameters of human sperm cells during freezing. The principle of the DSC technique can be stated as follows. During dehydration (water transport) of intact cells in the absence of intracellular freezing, the concentrations of intracellular impermeant electrolytes, substrates, cofactors, proteins, etc. increase as essentially pure water is transported across the plasma membrane into the medium where it freezes, releasing heat of fusion proportional to the amount of water removed from the cell. The cells are then lysed, and the DSC measurement then repeated exactly as before; the resulting heat released is lower because the water transport no longer functions; the difference in heat release so measured ({Delta}qdsc) is used to calculate the cell water that has permeated across the plasma membrane, from which one can deduce the cell volume (V) as a function of subzero temperature (T). The DSC technique has been applied to measure the membrane permeability parameters in a variety of biological systems, including Epstein–Barr virus transformed (EBVT) human lymphocyte cell suspensions (Devireddy et al., 1998Go), in a normal mammalian (rat) liver tissue system (Devireddy and Bischof, 1998Go), in Dunning AT-1 rat prostate tumour tissue (Devireddy et al., 1999aGo), in liver tissue slices of a freeze-tolerant wood frog, Rana sylvatica (Barratt et al., 1998Go; Devireddy et al., 1999bGo,cGo), as well as in mouse sperm cell suspensions (Devireddy et al., 1999dGo). The DSC technique is independent of the size and shape of the cells being observed, and is used in this study to measure the membrane permeability parameters of human sperm cells at two different cooling rates (5 and 10°C/min; the reasons for the choice of these cooling rates will be discussed later) in the presence of extracellular ice and cryoprotective agents (CPA). Numerical simulations of water transport in human sperm cells are then performed under a variety of cooling rates (5 to 100°C/min) using the experimentally determined membrane permeability parameters. The simulation results were analysed to predict the amount of water left in the cell after dehydration ceases, in the absence of IIF, and the `optimal cooling rates' for human sperm cryopreservation.


    Materials and methods
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Mathematical modelling of water transport during freezing
In this section the mathematical equations and the membrane permeability parameters used to model water transport during freezing in the presence of extracellular ice and CPA in a cell suspension system are presented. A model has been proposed for water and solute transport in response to chemical potential gradients based on irreversible thermodynamics (Kedem and Katchalsky, 1958Go). The Kedem–Katchalsky model consisted of two differential equations which describe the water and CPA flux across the membrane. If the flux of CPA is negligible in comparison to the water flux (McCaa et al., 1991Go; Gilmore et al., 1995Go), then the Kedem–Katchalsky model reduces to a model which assumes only water transport, as proposed originally (Mazur, 1963Go) and later modified (Levin et al., 1976Go). The various assumptions made in the development of Mazur's model of water transport are discussed in detail elsewhere (McGrath, 1988Go). The water transport model of Mazur was further modified (Karlsson et al., 1993Go) to incorporate the presence of CPA on the volumetric shrinkage response of cells during freezing as:

with Lp, the sperm cell membrane permeability to water defined (Levin et al., 1976Go) 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 a subzero 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 human sperm cell was modelled as a long cylinder with length (L) 40.2 µm and a radius (ro) of 0.42 µm, which translates to Vo ~22.2 µm3 and Ac ~106 µm2 as reported in the literature (Curry et al., 1996Go). The value of Vb was assumed to be 0.23Vo (Noiles et al., 1993Go). 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 or CPA in solution; vcpa is the molar volume of CPA (73.3x1012 µm3/mol); vw is the molar volume of water (18x1012 µm3/mol); [openphi]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 mol/l); {Delta}Hf is the latent heat of fusion of water (335 mJ/mg); {rho} is the density of water (1000 kg/m3). Note that when ncpa is zero (i.e. no CPA is present), equations [1] and [2]GoGo reduce to the `water transport' model as described earlier (Mazur, 1963Go; Levin et al., 1976Go), 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.

Isolation of human spermatozoa
Human semen samples were obtained from men seeking initial or follow-up evaluation for infertility at the Men's Reproductive Health Center at the University of Minnesota. Semen was collected by masturbation after 2–3 days abstinence and standard semen analyses were performed (WHO, 1999). Ejaculates with total progressive motility counts of <106 cells, or ejaculates that were positive for antisperm antibodies, were not used in this study. Additional semen samples were obtained from donors of unknown fertility status, as well as known fertile men. Within 4 h of collection, samples (usually two to four) were pooled and concentrated to 0.5–1 ml by centrifugation at 400 g for 10 min at room temperature. The concentrated sperm suspension was then re-centrifuged at 300 g for 25 min at room temperature through 2 ml of Isolate, a 90% density gradient medium (Irvine Scientific, Santa Ana, CA, USA), which removed most non-motile cells and seminal fluid debris. The resulting sperm pellet was resuspended to a volume of 300–500 µl in modified Biggers, Whitten and Whittingham media (modified BWW media, 282 mOsm; Irvine Scientific) and aliquots were assayed for percent viability.

Viability assay
Subsamples (~25 µl) were assayed for plasma membrane integrity by dual fluorescent dye labelling using a LIVE/DEAD Sperm Viability Kit (Molecular Probes, Eugene, OR, USA) according to the instructions provided. Briefly, SYBR-14 (live cell stain) and propidium iodide (dead cell stain) were prepared fresh daily in HEPES-buffered saline and used at final concentrations of 100 nmol/l and 600 nmol/l respectively (Garner and Johnson, 1995Go). Cells were first exposed to SYBR-14 for 15–30 min at 37°C followed by a 5- to 10-min incubation with propidium iodide. Between 100–300 cells from each sample were counted at 200x magnification using a BX-50 fluorescence-equipped light microscope (Olympus, Tokyo, Japan) and the appropriate filters. The mean (± SD) percentage of spermatozoa with intact plasma membranes in the pools (n = 9) was 84.0 ± 14.9.

DSC dynamic cooling experiments
For DSC experiments in the absence of CPA, sperm suspensions were concentrated a final time by centrifugation at 300 g for 5 min, resuspended to 1–200 µl in modified BWW media and placed on ice. Sperm cell concentrations were determined using a haemocytometer. All samples used in the DSC experiments had concentrations of viable cells ranging from 80x107 to 500x107 cells/ml. For DSC experiments in the presence of CPA, cells were treated in an identical manner as above except that stock CPA (48% TES–Tris, 30% citrate solution with 20% egg yolk/12% glycerol; Irvine Scientific) was added dropwise to achieve a 1:1 v/v CPA:modified BWW ratio just before the final centrifugation step (Graham et al., 1972Go; Weidel and Prins, 1987Go). Dropwise addition of CPA was performed to minimize osmotic injury effects (Gao et al., 1995Go; Gilmore et al., 1997Go). Thus the final concentration of CPA media was 10% egg yolk and 6% glycerol in TES–Tris–citrate solution and modified BWW media. Osmolarity of the CPA media was calculated to be 1113 mOsm, which includes ~790 mOsm of glycerol. This value is supported by the osmolarity of the CPA media obtained using a vapour pressure osmometer, ~1134 ± 57 mOsm.

To ensure the accuracy and repeatability of the experimental data, the limitations of the DSC-Pyris 1 (Perkin Elmer Corporation, Norwalk, CT, USA) machine were studied, and a set of calibration and control experiments were performed as detailed previously for a DSC-7 machine (Devireddy et al., 1998Go). These included: (i) calibration and minimization of the thermal lag; (ii) baseline determination of the thermogram (a sigmoidal baseline was used); (iii) effect of Pseudomonas syringae on DSC heat release readings; (iv) experiments with osmotically inactive (lysed) sperm cells ({Delta}qdsc = 0); and (v) error due to noise in the DSC readings (less than 5% of {Delta}qdsc). The DSC technique presented in this study was relatively insensitive to the choice of baseline used since the heat releases were `differences' and not `absolute' values. In addition, the measured value of {Delta}qdsc (• in Figure 1Go) was shown to be proportional to the initial concentration of viable cells in the DSC sample and also agreed quite closely with the predicted value of {Delta}qdsc (---- in Figure 1Go).



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Figure 1. Plot of {Delta}qdsc as a function of initial concentration of viable cells in the differential scanning calorimeter (DSC) sample. The measured values of {Delta}qdsc are shown (•), along with the predicted value of {Delta}qdsc (----). Note that the measured values of {Delta}qdsc are in close agreement with the predicted value. The error bars represent the standard deviation in the data, i.e. the measured values of {Delta}qdsc.

 
To perform the DSC dynamic cooling experiments, the human sperm samples (7–9 mg) were placed in standard aluminium sample pans (Perkin Elmer) and a natural ice nucleator P.syringae (ATCC, Rockville, MD, USA) was added (0.5–1 mg) before the pans were sealed. The ice nucleating agent P.syringae always nucleated the extracellular space at temperatures >= –5°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 and described in detail elsewhere (Devireddy et al., 1998Go, 1999dGo).

Step 1: The sample (sperm cell suspension either in modified BWW media or in the CPA media) + 0.5–1 mg of P.syringae bacteria initially at 4°C, was cooled at 5 (or 10) °C/min until the extracellular ice nucleated (~–3.5°C in modified BWW media and ~–4.5°C in the CPA media). Step 2: After nucleation, the sample was thawed at a warming rate (10°C/min) such that phase change temperature, Tph (–0.53°C and –2.1°C for the isotonic modified BWW media and CPA media respectively) was reached (but not overshot) and ice remained in the extracellular solution. Equilibrium at 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 10) °C/min, which caused the sperm cells to undergo cellular dehydration. The lower curve in Figure 2AGo corresponded to the heat release associated with dehydration, and the total area is represented by qinitial. Step 4: The sample was re-equilibrated at Tph by thawing at 50°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 caused all the sperm cells to lyse and become osmotically inactive. Step 6: Step 4 was repeated. Since all the sperm cells had compromised membranes, the intracellular water, proteins and salts were now continuous (no membrane barriers existed) as previously suggested (Körber et al., 1991Go).Step 7: The sample was then cooled to –50°C at 5 (or 10) °C/min to measure the final heat release due to lysed or osmotically inactive sperm cells mixed with media. The upper curve in Figure 2AGo corresponded to this heat release, and the total area was represented by qfinal.



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Figure 2. Superimposed heat flow thermograms obtained during the first (Step 3) and last (Step 7) of the DSC cooling protocol for human sperm cell suspension system, shown for a cooling rate of 5°C/min. The negative axis for the heat flow on the y-axis implies an exothermic heat release in the DSC sample. (A) Total difference between the initial (Step 3, lower curve) and the final cooling run (Step 7, upper curve) of the DSC dynamic cooling protocol. The total difference between qinitial (Step 3) and qfinal (Step 7) is denoted as {Delta}qdsc. (B) Fractional difference between the initial (Step 3, lower curve) and the final cooling run (Step 7, upper curve) of the DSC dynamic cooling protocol down to a subzero temperature, T. The fractional heat release difference between the first cooling run (Step 3), q(T)initial, and during the last (Step 7) cooling run, q(T)final is denoted as {Delta}q(T)dsc.

 
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) human sperm cells, and the magnitude of the heat releases were found to be within ±1%. In addition, >98% of human sperm cells were found to stain with propidium iodide (dead cell stain) when the DSC pans were forced open after the fast cooling run (Step 5). This suggested that the fast cooling run in Step 5 (200°C/min to –100°C) compromised the membrane integrity of all the human sperm cells in the DSC sample.

Translation of DSC-measured heat release to dynamic cell volume data
The heat release measurements of interest were {Delta}qdsc and {Delta}q(T)dsc, which were the total and fractional differences between the heat releases measured by integration of the heat flows in Steps 3 and 7 respectively using the DSC Pyris 1 software (Perkin-Elmer Corp., Norwalk, CT, USA). 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) was denoted as {Delta}qdsc (= qinitialqfinal) and is shown in Figure 2AGo. The fractional difference in the integrated heat release from Tph down to a subzero temperature, T, is denoted by {Delta}q(T)dsc (= q(T)initialq(T)final) and is shown in Figure 2BGo. This difference in heat release has been shown to be related to cell volume changes in cell suspensions (Devireddy et al., 1998Go), in several tissue systems (Devireddy and Bischof, 1998Go; Devireddy et al., 1999aGo,bGo), and in mouse sperm cell suspensions (Devireddy et al., 1999dGo) as:

This equation can be rearranged to measure water transport data from the DSC measured heat releases {Delta}q(T)dsc and {Delta}qdsc as:

Note that the DSC-measured heat release readings {Delta}q(T)dsc and {Delta}qdsc are obtained separately at 5°C/min (shown in Figure 2Go for sperm cells suspended in modified BWW media) and at 10°C/min (data not shown) both in the absence and presence of CPA. The DSC water transport data obtained using equation [4]Go were shown to generate statistically similar data [statistically insignificant differences (P > 0.05) by Student's t-test] to those obtained using a standard cellular cryomicroscopy technique with a spherical cell system (Devireddy et al., 1998Go), and also to the water transport data obtained using the low-temperature microscopy method in a normal rat liver tissue system (Devireddy and Bischof, 1998Go). Since the use of equation [4]Go 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 also be used to generate the water transport data in a sperm cell suspension system. The unknowns needed in equation [4]Go, 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 both modified BWW media and the CPA media was assumed to be the isotonic cell volume, Vo (~22.2 µm3) as reported earlier (Curry et al., 1996Go). As stated above, the osmotically inactive cell volume, Vb, was assumed to be 0.23Vo in modified BWW media, while in the CPA media the presence of glycerol in the intracellular compartment increased the osmotically inactive cell volume to ~0.32Vo.

Numerical methods
A non-linear 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 (Bevington and Robinson, 1992Go). The optimal fit of equation [1]Go to the experimental data was obtained by selecting a set of parameters which minimized the residual variance, {chi}2, and maximized a goodness of fit parameter, R2 (Montgomery and Runger, 1994Go). 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 non-linear curve fitting code was slightly modified such that R2 was minimized by one set of parameters for all cooling rates as described previously (Smith et al., 1998Go). All the curve fitting results presented have an R2 value greater than or equal to 0.97, 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]GoGo), which was then numerically solved using a fourth-order Runge–Kutta method using a FORTRAN code on a SGI (SGI, Mountain View, CA, USA) workstation (Pazhayannur and Bischof, 1997Go).


    Results
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Dynamic cooling response and membrane permeability parameters
Water transport data and simulation using best fit parameters in equation [1]Go at cooling rates of 5 and 10°C/min in modified BWW media are shown in Figure 3AGo. The dynamic portion of the cooling curve was between –0.53°C and –10°C at these cooling rates. Water transport cessation was 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 2Go. The best fit of equation [1]Go to the 5°C/min water transport data was obtained for membrane permeability parameter values of Lpg = 3.7x10–14 m3Ns (0.22 µm/min-atm) and ELp = 391.2 kJ/mol (93.5 kcal/mol) with an R2 value of 0.99, while the corresponding values for the 10°C/min data were Lpg = 1.9x10–14 m3/Ns (0.11 µm/min-atm) and ELp = 312.5 kJ/mol (74.7 kcal/mol) with an R2 value of 0.99 (Table IGo). The model simulated equilibrium cooling response [equilibrium was achieved at each temperature when the internal and external osmotic pressures were equal (i.e. {pi}i = {pi}o)] was generated by setting the left-hand side of equation [1]Go = 0 and balancing the intracellular and extracellular unfrozen chemical activity of water on the right-hand side at a particular subzero temperature.



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Figure 3. Volumetric response of human spermatozoa as a function of subzero temperatures obtained using the DSC technique in (A) modified BWW media and (B) CPA media. The open ({circ},{square}) and closed (•,{blacksquare}) symbols represent the 5 and 10°C/min data respectively. The model simulated equilibrium cooling response is shown as a dotted line in both figures. The model simulated dynamic cooling response at 5 and 10°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 Table IGo, in the water transport equation (equations [1] and [2]GoGo).

 

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Table I. Predicted subzero membrane permeability parameters for human sperm cells in the presence of extracellular ice and cryoprotective agents (CPA), assuming Vb = 0.23Vo
 
Water transport data and simulation using best fit parameters in equation [1]Go at cooling rates of 5 and 10°C/min in the CPA media (as described earlier) are shown in Figure 3BGo. The dynamic portion of the cooling curve was between –0.53°C and –15°C at these cooling rates. The best fit of equation [1]Go to the 5°C/min water transport data was obtained for membrane permeability parameter values of Lpg[cpa] = 1.01x10–14 m3/Ns (0.06 µm/min-atm) and ELp[cpa] = 194.6 kJ/mol (46.5 kcal/mol) with an R2 value of 0.99, while the corresponding values for the 10°C/min data were Lpg[cpa] = 0.67x10–14 m3/Ns (0.04 µm/min-atm) and ELp[cpa] = 131.8 kJ/mol (31.5 kcal/mol) with an R2 value of 0.99 (Table IGo).

Statistical analysis
The differences in the water transport data between the 5 and 10°C/min rates shown in Figure 3A and BGo were not statistically significant. However, the differences between the data obtained in the presence and absence of CPA were statistically significant in the dynamic part of the cooling curve (>80% confidence level using Student's t-test). The 10°C/min dynamic data were statistically significant from the equilibrium cooling response, both in the presence and absence of CPA (with >90% confidence level). However, the differences between the 5°C/min data and the equilibrium cooling response were not statistically significant.

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 modified BWW media and in the CPA media, as shown in Table IGo. The `combined best fit' membrane permeability parameters maximized the goodness of fit parameter, R2, for the 5 and 10°C/min water transport data concurrently. The contour plots of the goodness of fit parameter, R2 (= 0.98) in the Lpg and ELp (or Lpg[cpa] and ELp[cpa]) space that `fit' the water transport data at 5 and 10°C/min in modified BWW media and in the CPA media, are shown in Figure 4A and BGo 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 >0.98. An interesting observation was the `serrations' on the y-axis in Figure 4AGo, which corresponded to the contour space that fitted the water transport data at 5°C/min. These `serrations' showed that combinations of ELp ~0.0 and Lpg ranging from 3.5 to 8x10–14 m3/Ns (~0.2 to 0.5 µm/min-atm) can also simulate the 5°C/min data in the absence of CPA with a goodness of fit parameter, R2 >0.98. Note that the contour space that fitted the water transport data in the presence of CPA (Figure 4BGo) was significantly smaller than in the absence of CPA (Figure 4AGo), suggesting that a smaller set of parameters could predict the water transport response in the presence of CPA.



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Figure 4. Contour plots of the goodness of fit parameter R2 (= 0.98) for water transport response in human spermatozoa in (A) modified BWW media and (B) CPA media. The common region corresponds to the range of parameters that `fit' the water transport data at both the cooling rate (either 5 or 10°C/min) with R2 >= 0.98. Note that the `combined best fit' parameters are represented by `*' in both the figures, while the `x' represent the `best fit' parameters at either 5 or 10°C/min.

 
In Figure 4A and BGo, the `combined best fit' parameters compared quite closely with the parameters obtained at the higher cooling rate of 10°C/min, presumably due to the fact that the 10°C/min water transport data were farther away from equilibrium than the 5°C/min data. This suggested that the membrane permeability parameters obtained using the 10°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 was not true. This suggestion was clearly supported by the contours shown in Figure 4BGo, where the contour for 10°C/min data was almost completely enclosed by the contour for 5°C/min. Therefore, in order to obtain the membrane permeability parameters that `best predict' the behaviour of a biological system, water transport data need to be obtained at the highest possible cooling rate at which dehydration occurs exclusively, as noted earlier (Smith et al., 1998Go; Devireddy et al., 1999aGo,dGo).

Simulations of water transport
Water transport simulations obtained using the `combined best fit' parameters in equation [1]Go are shown for a variety of cooling rates (5–100°C/min) in Figure 5Go. In Figure 5A and BGo, the numerically simulated non-dimensional 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 modified BWW media and in the CPA media respectively. The non-dimensional cellular volume (V/Vo), which decreased due to dehydration during freezing, was plotted on the y-axis, while the subzero temperatures were 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 homogeneous or volume-catalysed nucleation (Toner, 1993Go) to the initial sperm water volume, [(V–Vb)/(Vo–Vb)] as described earlier for a rat liver tissue system (Pazhayannur and Bischof, 1997Go). Note that V was the end volume after water transport ceased (at ~–30°C), and Vo and Vb were the initial (isotonic) and final (osmotically inactive) sperm cell volumes respectively. In modified BWW media, for cooling rates of <=10, 20, 40, 50 and 100°C/min, the trapped water volume was <=1.2, 22.2, 52.7, 60.1 and 79.1% of initial osmotically active water volume respectively, and the corresponding end volumes were <=0.24Vo, 0.4Vo, 0.64Vo, 0.7Vo and 0.84Vo respectively (Figure 5AGo). In the CPA media (Figure 5BGo), for cooling rates of <=10, 20, 40, 50 and 100°C/min, the trapped water volume was <=2.4, 6.7, 30.2, 40.3 and 66.2% of initial osmotically active water volume respectively. Therefore, depending on the concentrations of the CPA, the water transport simulations (Figure 5Go) showed that cooling rates as low as 20°C/min could cause intracellular water to be trapped within the human sperm cells. With sufficient supercooling, this trapped water would ultimately form intracellular ice.



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Figure 5. Volumetric response of human spermatozoa at various cooling rates as a function of subzero temperatures using the `combined best fit' membrane permeability parameters (shown in Table IGo) in (A) modified BWW media and (B) CPA media. The water transport curves (solid lines) represent the model simulated response for different cooling rates (from left to right: 5, 10, 20, 40, 50 and 100°C/min). The model simulated equilibrium cooling response is also shown in both figures as a dotted line.

 
As described earlier (see Introduction), the cooling rate which optimizes the freeze–thaw response of any cellular system can be defined as the fastest cooling rate in a given media without forming damaging IIF (Mazur et al., 1972Go). IIF was defined as damaging and lethal for embryos if >10–15% of the initial intracellular water was involved (Mazur, 1990Go). We defined the `optimal cooling rate' as the cooling rate at which ~5% of the initial osmotically active water volume was trapped inside the cells at temperature, T ~–30°C. The simulations (shown in Figure 5Go) showed that the `optimal cooling rate' in modified BWW media and in the CPA media were ~14 and ~16°C/min respectively. Note, that if IIF occurred by a heterogeneous or a surface-catalysed nucleation mechanism (Toner, 1993Go) (generally between –5 and –20°C for a variety of single cells)–which our model does not predict–then potentially even more water would 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 an overestimation.


    Discussion
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
Parameter sensitivity analysis: effect of varying the osmotically inactive cell volume (Vb)
The value of the osmotically inactive cell volume of human sperm cells has been reported to range from 0.23Vo (the value used in this study; Noiles et al., 1993Go) to ~0.5Vo (Gilmore et al., 1995Go). 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 0.5Vo. The DSC data were correspondingly modified (using equation [4]Go) and the modified DSC water transport data were curve-fitted to the water transport model (equations [1] and [2]GoGo) using the non-linear least squares curve fitting technique as described previously. The predicted values of the membrane permeability parameters (Lpg and ELp), using a value of Vb = 0.5Vo, are shown in Table IIGo. An increase of ~117% in the value of Vb from 0.23Vo to 0.5Vo resulted in the model-predicted membrane permeability parameters being within 30% of the each other (as shown in Tables I and IIGoGo). This lack of sensitivity in the membrane permeability parameters to the value of the osmotically inactive cell volume has been reported in the literature for a variety of cell and tissue systems (Pazhayannur and Bischof, 1997Go; Devireddy et al., 1998Go, 1999aGo). Thus, errors in the estimated value of Vb can alter the model predicted membrane permeability parameters (Lpg and ELp), but the trends remain the same.


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Table II. Predicted sub-zero membrane permeability parameters for human sperm cells in the presence of extracellular ice and cryoprotective agents (CPA), assuming Vb = 0.5Vo
 
The effect of varying the osmotically inactive cell volume on the model-simulated value of trapped water (or a lower bound on intracellular ice) was also investigated. This was done by performing additional water transport simulations using the `combined best fit' parameters shown in Table IIGo. When the value of Vb was assumed to be 0.5Vo, in modified BWW media, for cooling rates of <=10, 20, 40, 50 and 100°C/min, the trapped water volume was <=1.9, 28.2, 56.5, 66.4 and 82.3% of initial osmotically active cell volume respectively. The corresponding values in the CPA media were <=2.1, 9.2, 29.2, 41.3 and 65.1% of initial osmotically active cell volume respectively. These values were comparable with those obtained earlier using a Vb value of 0.23Vo. Thus, the variation in the value of Vb does not significantly alter the model predictions and, as noted earlier depending on the concentration of CPA, cooling rates as low as 20°C/min can cause significant amounts of intracellular water to be trapped inside human spermatozoa.

Experiments at higher cooling rates
As noted earlier and in other studies, it is essential that water transport parameters be obtained at the highest possible cooling rate at which dehydration occurs exclusively (Smith et al., 1998Go; Devireddy et al., 1999aGo,dGo). One of the main disadvantages of the DSC technique is that it cannot distinguish between the heat releases obtained during water transport and IIF. So, a correlative method is needed to determine that the biophysical response is in fact water transport and not IIF (Devireddy and Bischof, 1998Go; Devireddy et al., 1998Go). Since standard cellular cryomicroscopy cannot be used to determine the biophysical response during freezing in human spermatozoa, an indirect methodology was used to determine the maximum cooling rate at which water transport occurred exclusively in human spermatozoa. It has been reported (Henry et al., 1993Go) that the plot of motility, plasma membrane integrity and mitochondrial function versus cooling rate resembles an inverted `U' curve with an optimal cooling rate of 10°C/min (with rapid thawing rate) in the presence of 0.85 mol/l glycerol. These data suggest that the loss of motility, plasma membrane integrity and mitochondrial function at cooling rates >10°C/min are due to the formation of IIF. Thus, the highest cooling rate which causes water transport to occur exclusively in human spermatozoa in the presence of 0.85 mol/l glycerol (which is very close to the concentration of glycerol used in this study, 0.79 mol/l) is ~10°C/min, and hence DSC experiments were not performed at higher cooling rates. It is possible that in the absence of CPA, some IIF may occur at 10°C/min. However, for the purpose of this study this possibility was considered negligible.

Membrane transport parameters in the absence of extracellular ice
As mentioned earlier, there are currently no experimental techniques which yield data on how sperm cells either dehydrate or form intracellular ice during freezing in the presence of extracellular ice (Gao et al., 1997Go). However, there exist a few techniques such as the `time to lysis' method (Noiles et al., 1993Go; Watson, 1995Go) and the `Coulter counter' technique (Gilmore et al., 1995Go) to measure the volumetric response of sperm cells to external changes in osmolarity at suprazero temperatures. The parameters obtained using these techniques, suprazero membrane permeability, Lp ~0.85–5.1x10–13m3/Ns (0.5–3 µm/min-atm) and activation energy at suprazero temperatures, Ea ~12–30 kJ/mol (3–7 kcal/mol), serve to provide a good understanding of suprazero water transport response for human sperm cells (Gao et al., 1997Go). The suprazero membrane permeability, Lp of human sperm cells is higher than that of other mammalian cells [with the possible exception of red blood cells (RBC) and hepatocytes] and activation energies, Ea are low in comparison with other mammalian cells (Curry et al., 1994Go; Gao et al., 1997Go). One reason for the high permeability values might be the presence of channel-forming proteins selective to water in the sperm plasma cell membrane. For example, the high membrane permeability value reported for human RBC is due to the presence of CHIP28, a channel-forming protein. It has been shown (Liu et al., 1995Go) that CHIP28 does not mediate the water transport process in human sperm cells. However, the presence of an analogue to CHIP28 in the sperm cell plasma membrane cannot be ruled out (Hasegawa et al., 1994Go; Gilmore et al., 1995Go). It should also be noted that water-transporting proteins (water channels, aquaporins) were identified in several parts of the reproductive system, including the testis efferent ductules, seminal vesicles, prostate, uterus and placenta (see review by Verkman et al., 1996).

Suprazero permeability parameters cannot 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 (Curry et al., 1994Go). This conclusion is based on the fact that water permeabilities predicted on the basis of the above-mentioned techniques suggest that human sperm cells should be able to dehydrate at cooling rates up to 7000°C/min during freezing, when in fact experiments show that the `optimal cooling rate' for human sperm cells is <100°C/min depending on the concentrations of CPA in the extracellular milieu (Henry et al., 1993Go; Curry et al., 1994Go). One reason for this discrepancy may be that the values of membrane permeability parameters at subzero temperatures in the presence of extracellular ice are markedly different than those reported in the 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 an order of magnitude than the corresponding Ea at suprazero temperatures, then the discrepancy between numerical simulations and experimental data can be reconciled (Gao et al., 1997Go). The best fit parameters obtained in this study using the DSC water transport data (shown in Tables I and IIGoGo) during freezing of human spermatozoa, confirm that this is indeed the case; Lpg ~3.7–0.5x10–14 m3/Ns (0.22–0.03 µm/min-atm) and ELp ~130–503 kJ/mol (31–120 kcal/mol).

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 and/or a cold shock damage or `chilling' injury during cooling (Watson, 1981Go; Drobnis et al., 1993Go). The presence of extracellular ice further alters the cell membrane transport properties, as measured using cryomicroscopy for a variety of cells. 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 (McGrath, 1988Go). It has been found that for human granulocytes the activation energy is dramatically higher (~3 times) and membrane permeability is dramatically lower (~10–15 times) at subzero temperatures in the presence of extracellular ice, when compared with activation energy at suprazero temperatures in the absence of extracellular ice (Schwartz and Diller, 1983Go). This trend is consistent with the results obtained in this study for human sperm cells and in a previous study of mouse sperm cells (Devireddy et al., 1999dGo). 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 which 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 (Steponkus, 1984Go; Caffrey, 1987Go). The relative importance of temperature and the effect of extracellular ice on the membrane permeability Lp, is dependent on the cell type. The present study shows that human sperm cells have dramatically different membrane permeabilities at subzero temperatures in the presence of extracellular ice as compared with previously published values at suprazero temperatures.

Membrane transport parameters in the presence of CPA
The DSC technique was used to obtain water transport data and water permeability parameters (Lpg[cpa] and ELp[cpa]) of human sperm cells in the presence of extracellular ice and CPA. Although the exact mechanism by which the presence of CPA modifies the water permeability parameters is as yet unknown, several studies have shown that the presence of CPA tends to reduce the membrane permeability parameters, Lpg[cpa] and ELp[cpa]. A similar trend is seen in the data shown in Tables I and IIGoGo, where an increase in the concentration of solutes in the extracellular medium is shown to decrease the predicted value of reference membrane permeability of human sperm cells, Lpg from 2.4x10–14 m3/Ns (0.14 µm/min-atm) in modified BWW media to Lpg[cpa] of 0.67x10–14m3/Ns (0.04 µm/min-atm) in CPA media. This trend is consistent with results reported in previous studies on membrane permeability parameters of ova and embryos (Mazur, 1990Go). It was demonstrated that the value of Lp[cpa] obtained in the presence of various CPA [1 mol/l glycerol; 1 mol/l propylene glycol; 1 mol/l dimethylsulphoxide (DMSO) and 2 mol/l ethylene glycol] was lower by 30–60% than that obtained in their absence for human sperm cells at suprazero temperatures (i.e. Lp[cpa] < Lp) (Gilmore et al., 1995Go). A similar decrease was also reported in the value Lpg[cpa] in isolated rat hepatocytes in the presence of 1 mol/l and 2 mol/l DMSO using standard cellular cryomicroscopy (Smith et al., 1998Go). Earlier, it was stated (Mazur, 1990Go) that ELp remains unaltered due to changes in the extracellular concentration (i.e. ELp[cpa] ~ ELp), while others (Gilmore et al., 1995Go) measured an increase (by a factor of 2 to 3) in the value of the Ea[cpa] for human sperm cells (i.e. Ea[cpa] > Ea) using a Coulter counter technique. A reduction (by ~40–60%) was also found in the value of ELp[cpa] with increasing concentrations of DMSO for isolated rat hepatocytes (i.e. ELp[cpa] < ELp) (Smith et al., 1998Go).

To conclude, a new shape-independent differential scanning calorimeter (DSC) technique was used in this study to obtain the volumetric shrinkage during freezing of human sperm cell suspensions in the presence of extracellular ice and CPA at two different cooling rates (5 and 10°C/min). By fitting a model of water transport to the experimentally obtained volumetric shrinkage data, the best fit membrane permeability parameters (Lpg and ELp) were determined. The parameters obtained in this study (Lpg ~0.22 to 0.03 µm/min-atm and ELp ~30 to 120 kcal/mol, with and without the presence of CPA respectively) were significantly different from the membrane permeability parameters reported in the literature for human spermatozoa in the absence of extracellular ice at suprazero (and subzero) temperatures (Lp ~0.5–3.0 µm/min-atm and Ea ~3.0–7.0 kcal/mol, with and without the presence of CPA respectively). The new parameters obtained in this study help to explain the discrepancy in the predicted optimal cooling rates based on suprazero permeability parameters (~7000°C/min) and the experimentally determined optimal cooling rates (<100°C/min). It is hoped that the experimentally determined water transport data and modelling made available by the new DSC technique will lead to an understanding of how to optimize human sperm cryopreservation protocols on a firm biophysical basis.


    Acknowledgments
 
This work was supported by NSF-BES # 9703326 and a grant from Reproductive Health Associates (RHA), St Paul, Minnesota, USA.


    Notes
 
1 To whom correspondence should be addressed Back


    References
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 References
 
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Submitted on November 8, 1999; accepted on February 10, 2000.