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Materials and methods
- Cryoprotective agent and temperature effects on human sperm membrane permeabilities: convergence of theoretical and empirical approaches for optimal cryopreservation methods


The base medium used was isosmotic Tyrode's lactate HEPES (TL HEPES)-buffered solution (285 ± 5 mOsm/kg) (Bavister et al., 1983Go). Osmolality was determined using a freezing-point depression osmometer (Model 3D2; Advanced Instruments, Needham Heights, MA, USA). The cryoprotectant treatment solutions were prepared by mixing glycerol, DMSO, PG or EG with isosmotic TL HEPES to yield final CPA concentrations of 1 mol/l (glycerol, DMSO and PG) and 2 mol/l (EG). Those concentrations were chosen to ensure accurate permeability estimates from the electronic particle counter (EPC). All media components used in the experiments were obtained from Sigma Chemical Company (St Louis, MO, USA).

Human spermatozoa preparation
Semen samples were obtained from healthy donors by masturbation, after informed consent. The samples were obtained after a minimum of 48 h of sexual abstinence. A minimum concentration of 2x107 spermatozoa per ml, with at least 40% motility, was required for the samples to be included in the study. The ejaculates were allowed to liquefy in an incubator (5% CO2/95% air, 37°C, and high humidity) for 30 min. Samples were layered on a discontinuous (90 and 47%) Percoll gradient to select for motile cells and then washed with TL HEPES supplemented with pyruvate (0.01 mg/ml) and resuspended to ~2.5 ml final sample volume. A fraction of the sample (5 µl) was analysed using computer-assisted semen analysis (CASA) (Cell Soft, Version 3.2/C; CRYOResources, Ltd, Montgomery, NY, USA). Subsequent CASA analysis was done at the completion of each experiment.

Electronic particle counter
An EPC (ZM model; Coulter Electronics, Inc., Hialeah, FL, USA) with a standard 50 µm aperture tube was used for all measurements. Volumes (V) were calibrated via spherical styrene beads (Duke Scientific Corporation, Palo Alto, CA, USA) with a diameter of 3.98 ± 0.03 µm (V = 33.1 µm3) at 22, 11 and 0°C. The relationship between conductivity and styrene bead volume was assumed to be the same as the relationship between conductivity and sperm volume.

Temperature control
Experiments were conducted using a cooled methanol circulating bath. Experimental temperatures were measured using a thermocouple, directly before and after each experimental run and kept within ±2°C (room temperature at 22°C, and a cooling bath at 11 and 0°C). At each experimental temperature, the experimental media, the cell sample, the aperture tube, the calibration beads and the pipette tips were pre-equilibrated to the experimental temperature.

Data analysis
Statistical analysis
Data were analysed using standard analysis of variance and multiple range test approaches with the SAS® General Linear Models program (SAS Institute Inc., Cary, NC, USA).

Determination of membrane permeability coefficients
A pair of coupled non-linear equations (Kedem and Katchalsky, 1958Go) was used as the theoretical model for analysis of cell membrane permeability in a ternary solution consisting of a permeable solute (cryoprotectant, subscript `s') and an impermeable solute (NaCl, subscript `n') and water. The cell volume and amount of intracellular solute concentration as functions of time are presented as:


where V is cell volume, Vb is osmotically inactive cell volume and mis is the molal concentration of CPA inside the cell, and

The superscripts `i' and `e' refer to the intra- and extracellular compartments respectively. The terms LpCPA, PCPA and {sigma} are parameters for the hydraulic conductivity of water in the presence of CPA, the permeability coefficient of the CPA and the reflection coefficient, respectively. The temperature and universal gas constant are given by T and R, respectively. For the impermeable solute (NaCl), the intracellular osmolality is given by:

where Vs = Nis· is the CPA volume ( is the partial molar volume of the CPA). The superscript `(o)' represents the initial values at t = 0. A fixed value of Vb (Gilmore et al., 1995Go) was used in the analysis.

Evaluation of fitting calculation
The curve-fitting procedure was used to find parameter values that made the theoretical curve most resemble the plot of experimental data using the least-sum-of-squares method. The sum-of-squares (S) can be considered a function of the parameters S(P1, P2....Pm) in an (m + 1)-dimensional space. For the transport parameters LpCPA and PCPA the sum-of-squares is given by:

where Xthi represents theoretical data calculated from the modified KK equations and X expi represents experimental data. The values of S(LpCPA, PCPA) serve as the criteria for estimating the best fit parameters. In order to evaluate the fitting calculation, the numerical values of sum-of-squares at different values of LpCPA and PCPA, varying from –50% to +50% of the best fitted LpCPA and PCPA estimates were calculated. These values were then plotted in three-dimensional space. The fitting calculation was very sensitive to the PCPA value; even very slight changes in PCPA estimates (5%) resulted in significant changes in values of the sum-of-squares. The sensitivity of the calculation to the value of LpCPA was much less; however, it was sufficient to determine a minimum sum-of-squares and therefore a robust estimate of LpCPA.

Activation energies for parameters LpCPA and PCPA The Arrhenius relationship was used to determine the Ea of the parameters LpCPA and PCPA (Levin et al., 1976Go). The permeability value (LpCPA or PCPA) at any temperature T can be plotted as ln[Pa(T)] versus 1/T (Arrhenius plot):

where Ea is the activation energy for the process, expressed in kcal/mol, which can be determined by linear regression calculation of the slope of the Arrhenius plot as:

Simulation of intracellular water volume during freezing and thawing.
The changes of intracellular water volume and the mol number of intracellular CPA during temperature change of rate B can be calculated using the following coupled equations (Liu et al., 1997Go):


(W is the weight of a substance). The terms Vw and A are cell water volume and surface area of a cell, and nis is the number of mol of CPA inside the cell (see Table IGo for a complete listing of symbols and abbreviations). The temperature and universal gas constant are given by T and R respectively. C is the total solute concentration in g/100 g, MW is the molecular weight, and v10 is the molar volume of water. The value of parameters Lp (T) and PCPA (T) can be calculated with the Arrhenius relationships, using Ea for Lp and PCPA, respectively.  
The extracellular solute concentration, C = C(T, Rt), at temperature T can be determined by solving the following equation of the melting point for CPA/NaCl/water ternary solution:

where coefficients A1, B1, and C1 are functions of Rt. The coefficients for DMSO and glycerol have been determined (Pegg, 1983Go, 1986Go). The coefficients for EG have been determined recently (Woods et al., 1999Go). Definitions of all major symbols presented in the equations, along with corresponding units and values are given in Table IGo.

Data acquisition.
The EPC was interfaced to a microcomputer using a CSA-1 interface (The Great Canadian Computer Company, Edmonton, Alberta, Canada). Aliquots of 100 µl of 2 mol/l glycerol, 2 mol/l DMSO, 2 mol/l PG, or 4 mol/l EG were added dropwise over 60 s to 100 µl of cell suspension, yielding final CPA concentrations of 1 and 2 mol/l, respectively. Cells were allowed to equilibrate for ~3 min, at which time they return to near normal volumes, before all 200 µl were returned to isosmotic media. The cells abruptly swell upon return to isosmotic conditions due to the influx of water (determined predominantly by LpCPA) and then return at a lower rate to normal volumes as CPA diffuses out (determined predominantly by PCPA). The resulting changes in cell volume were measured over time. A total of three donors were used and the experiments were performed at 22, 11 and 0°C. Data were analysed using a two parameter fitting method as previously described (Gilmore et al., 1998Go).

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