**Assessment of human sperm membrane integrity**

A methodology for the assessment of sperm membrane integrity, using dual florescent staining and flow cytometric analysis, has been developed by Garner et al. (1986) and previously validated in our laboratory (Gao et al., 1992, 1993; Noilles et al., 1993). Propidium iodide (catalogue no. P4170; Sigma Chemical Co., St Louis MO, USA) is a bright red, nucleic acid-specific fluorophore which permeates poorly into spermatozoa with intact plasma

Prevention of Lethal Osmotic Injury to Cells

independently), the value of

**Addition of glycerol** 

value was used in the present example.

During Addition and Removal of Cryoprotective Agents: Theory and Technology 107

ln *e i ei <sup>s</sup> M M M MM s s ss*

Since human spermatozoa behave as ideal osmometer (Du et al., 1993), intracellular concentrations of impermeable solute (salt) and permeable solute (cryoprotective agent) can

*i i b ss n n i*

Where *Vb*= osmotically inactive cell volume (um3), and 0=initial condition (t=0). Initial conditions for V(0), 0 *<sup>i</sup> Mn* , 0 *<sup>i</sup> Ms* , 0 *<sup>i</sup> Ns* are known based on each experimental condition or protocol. In the computer simulations, it was assumed that extracellular concentrations of permeating or non-permeating solutes were constant, and that the mixture of solutions during

Human sperm volume, surface area, vb, water and glycerol permeability coefficients have been determined and previously published (Gao et al., 1992; Kleinhans et al., 1992; Noiles et al., 1993; Du et al., 1994). The values of these parameters are shown in Table 1. Assuming that there is no interaction between water and glycerol during their transport through the sperm membrane (or in other words, water and glycerol penetrate the cell membrane

calculated. From this equation and the data in Table 1, σ was calculated to be 0.99. This

**Surface area** (A) 120μm2 Kleinhans et al (1992) **Volume** (V) 34μm3 (Kleinhans et al. (1992) **Osmotically inactive volume** (Vb) 16.6μm3 Kleinhans et al. (1992)

**Water permeability coefficient** (Lp) 2.4μm/min/atm Noiles et al. (1993) **Glycerol permeability coefficient** (Ps) 1.68×10-3cm/min Gao et al. (1993)

Using equations [4-7] kinetics of glycerol/water transport across the sperm plasma membrane as well as the cell volume excursion during different glycerol addition and removal procedures were calculated using a commercial differential equation solver, SLAB (Civilized Software, Inc., Bethesda, MD, USA). The sperm volume excursion and water transport through the membrane of cells in anisosmotic solution without glycerol were

A final 1.00 M glycerol in sperm suspension was achieved by 1:1 (v/v) mixing of the original, isotonic sperm suspension with 2.0M glycerol solution which contains an isotonic

*i s s i*

0

 0 0

*V t V VN t* 

*V V VN*

*b ss*

*i*

*N t*

*V t V VN t* 

*b ss*

*i*

1 *PV RTL s s <sup>p</sup>* (Kedem and Katchalsky, 1958), can be

(6)

(7)

Du et al. (1993)

be calculated as previously described (Mazur and Schneider, 1984).

*Mt M*

*M t*

the glycerol addition and removal was instantaneous, i.e. the mixing time =0.

Table 1. Characteristic of human spermatozoa at 22°C

calculated using equation [4] and [5] with *M*s=0 and *N*s=0.

membrane, but is able to diffuse readily in to spermatozoa with a damaged membrane. 6- Carboxyfluoroscein diacetate (CFDA; Sigma, Catalog #C5041) is a membrane- permeable compound. After penetrating into cells, it is hydrolysed by intracellular esterase to 6 carboxyfluoroscein which is a bright green, membrane-impermeable fluorophore (Garner et al., 1986). When CFDA is added into the cell suspension with membrane-intact spermatozoa, the cells fluoresce bright green (Garner et al., 1986). Thus 5 ul CFDA (0.25 mg/ml DMSO) and 5 up propidium iodide (1 mg/ml water) stock solutions were added to each o.5ml of the treated sperm suspensions. A total of 1×105 spermatozoa per treatment were analyzed using a FACStar Plus Flow cytometer (Becton Dickinson, Rutherford, NJ, USA). The cells with CFDA staining and without propidium iodide staining were considered as intact cells. The percentage of intact cells was determined for each treatment.

The flow cytometer settings used for the experiments were (i) the gates were set using forward and 90° light scatter signals at acquisition to exclude debris and aggregates; (ii) instrument alignment was performed daily with fluorescent microbead standards to standardize sensitivity and setup; (iii) photomultiplier settings were adjusted with unstained overlap with individually stained cells; (iv) excitation was at 488 nm from a 4 W argon laser operating at 200 mW. Fluorescein emission intensity was measured using a 530/30 nm bandpass filter, and propidium iodide intensity using a 630/22 m bandpass filter.

#### **Determination of osmotic injury as a function of sperm volume excursion in anisosmotic solutions of nonpermeating solutes**

The anisosmotic solutions, ranging from 40 to 1500 mOsmol, were prepared as follows: hypo-osmotic solutions were made osmotic solutions were made by adding sucrose to TALP medium (sucrose and the solutes in TALP medium are essentially membraneimpermeable compounds). The final osmolality of each solution was measured and checked using a freezing-point depression osmometer (Adanced DigiMate Osmometer, Model 3D2; Advanced Instrument, Inc., Needham Heights, MA, USA). The osmotic tolerance of human spermatozoa was evaluated by exposing the cells to the anisosmotic solutions. A 10ul volume of isotonic cell suspension (286 mOsmol, 1×109 cells/ml) was mixed with 150μl of each anisosmotic solution. After 1 s to 30 min, spermatozoa in each anisosmotic solution were returned to near isotonic conditions (272-343 mOsmol) by adding 1500 μl isotonic TALP medium to 100 μl of each anisosmotic cell suspension. Sperm motility and plasma membrane integrity were measured by CASA and CFDA-propidium iodide dual fluorescent staining techniques respectively before and after the anisosmotic exposure. The centrifugal force used in sample preparation was 400 g for 7 min. All experiments were conducted at 22°C.

#### **Thermodynamic modeling and mathematical formulation for glycerol and water permeating across the human sperm membrane**

The next step was to compute the osmotic cell volume excursions associated with the addition and removal of hyperosmotic solutions of the permeating cryoprotectant glycerol to suspensions of human spermatozoa in isotonic saline. The classical KK formalism (shown as equations (4) and (5)) is used here and for the case of a solution consisting of a single permeable solute (e.g. glycerol) the average of extracellular and intracellular cryoprotective agent concentrations (osmolality) can be given as

membrane, but is able to diffuse readily in to spermatozoa with a damaged membrane. 6- Carboxyfluoroscein diacetate (CFDA; Sigma, Catalog #C5041) is a membrane- permeable compound. After penetrating into cells, it is hydrolysed by intracellular esterase to 6 carboxyfluoroscein which is a bright green, membrane-impermeable fluorophore (Garner et al., 1986). When CFDA is added into the cell suspension with membrane-intact spermatozoa, the cells fluoresce bright green (Garner et al., 1986). Thus 5 ul CFDA (0.25 mg/ml DMSO) and 5 up propidium iodide (1 mg/ml water) stock solutions were added to each o.5ml of the treated sperm suspensions. A total of 1×105 spermatozoa per treatment were analyzed using a FACStar Plus Flow cytometer (Becton Dickinson, Rutherford, NJ, USA). The cells with CFDA staining and without propidium iodide staining were considered as intact cells. The percentage of intact cells was determined for each treatment. The flow cytometer settings used for the experiments were (i) the gates were set using forward and 90° light scatter signals at acquisition to exclude debris and aggregates; (ii) instrument alignment was performed daily with fluorescent microbead standards to standardize sensitivity and setup; (iii) photomultiplier settings were adjusted with unstained overlap with individually stained cells; (iv) excitation was at 488 nm from a 4 W argon laser operating at 200 mW. Fluorescein emission intensity was measured using a 530/30 nm bandpass filter, and propidium iodide intensity using a 630/22 m bandpass

**Determination of osmotic injury as a function of sperm volume excursion in anisosmotic** 

The anisosmotic solutions, ranging from 40 to 1500 mOsmol, were prepared as follows: hypo-osmotic solutions were made osmotic solutions were made by adding sucrose to TALP medium (sucrose and the solutes in TALP medium are essentially membraneimpermeable compounds). The final osmolality of each solution was measured and checked using a freezing-point depression osmometer (Adanced DigiMate Osmometer, Model 3D2; Advanced Instrument, Inc., Needham Heights, MA, USA). The osmotic tolerance of human spermatozoa was evaluated by exposing the cells to the anisosmotic solutions. A 10ul volume of isotonic cell suspension (286 mOsmol, 1×109 cells/ml) was mixed with 150μl of each anisosmotic solution. After 1 s to 30 min, spermatozoa in each anisosmotic solution were returned to near isotonic conditions (272-343 mOsmol) by adding 1500 μl isotonic TALP medium to 100 μl of each anisosmotic cell suspension. Sperm motility and plasma membrane integrity were measured by CASA and CFDA-propidium iodide dual fluorescent staining techniques respectively before and after the anisosmotic exposure. The centrifugal force used in sample preparation was 400 g for 7 min. All experiments were conducted at

**Thermodynamic modeling and mathematical formulation for glycerol and water** 

The next step was to compute the osmotic cell volume excursions associated with the addition and removal of hyperosmotic solutions of the permeating cryoprotectant glycerol to suspensions of human spermatozoa in isotonic saline. The classical KK formalism (shown as equations (4) and (5)) is used here and for the case of a solution consisting of a single permeable solute (e.g. glycerol) the average of extracellular and intracellular cryoprotective

filter.

22°C.

**solutions of nonpermeating solutes** 

**permeating across the human sperm membrane** 

agent concentrations (osmolality) can be given as

$$\overline{\boldsymbol{M}}\_{s} = \left(\boldsymbol{M}\_{s}^{e} - \boldsymbol{M}\_{s}^{i}\right) \Big/ \left[\ln\left(\boldsymbol{M}\_{s}^{e} \Big/ \boldsymbol{M}\_{s}^{i}\right)\right]$$

Since human spermatozoa behave as ideal osmometer (Du et al., 1993), intracellular concentrations of impermeable solute (salt) and permeable solute (cryoprotective agent) can be calculated as previously described (Mazur and Schneider, 1984).

$$M\_n^i\left(t\right) = M\_n^i\left(0\right) \left(\frac{V\left(0\right) - V\_b - \overline{V}\_s N\_s^i\left(0\right)}{V\left(t\right) - V\_b - \overline{V}\_s N\_s^i\left(t\right)}\right) \tag{6}$$

$$M\_s^i(t) = \left(\frac{N\_s^i(t)}{V(t) - V\_b - \overline{V}\_s N\_s^i(t)}\right) \tag{7}$$

Where *Vb*= osmotically inactive cell volume (um3), and 0=initial condition (t=0). Initial conditions for V(0), 0 *<sup>i</sup> Mn* , 0 *<sup>i</sup> Ms* , 0 *<sup>i</sup> Ns* are known based on each experimental condition or protocol. In the computer simulations, it was assumed that extracellular concentrations of permeating or non-permeating solutes were constant, and that the mixture of solutions during the glycerol addition and removal was instantaneous, i.e. the mixing time =0.

Human sperm volume, surface area, vb, water and glycerol permeability coefficients have been determined and previously published (Gao et al., 1992; Kleinhans et al., 1992; Noiles et al., 1993; Du et al., 1994). The values of these parameters are shown in Table 1. Assuming that there is no interaction between water and glycerol during their transport through the sperm membrane (or in other words, water and glycerol penetrate the cell membrane independently), the value of 1 *PV RTL s s <sup>p</sup>* (Kedem and Katchalsky, 1958), can be calculated. From this equation and the data in Table 1, σ was calculated to be 0.99. This value was used in the present example.


Table 1. Characteristic of human spermatozoa at 22°C

Using equations [4-7] kinetics of glycerol/water transport across the sperm plasma membrane as well as the cell volume excursion during different glycerol addition and removal procedures were calculated using a commercial differential equation solver, SLAB (Civilized Software, Inc., Bethesda, MD, USA). The sperm volume excursion and water transport through the membrane of cells in anisosmotic solution without glycerol were calculated using equation [4] and [5] with *M*s=0 and *N*s=0.

#### **Addition of glycerol**

A final 1.00 M glycerol in sperm suspension was achieved by 1:1 (v/v) mixing of the original, isotonic sperm suspension with 2.0M glycerol solution which contains an isotonic

Prevention of Lethal Osmotic Injury to Cells

**Removal of glycerol** 

*Approach 1*: FVS dilution

*Approach 2*: FMS dilution

follows:

During Addition and Removal of Cryoprotective Agents: Theory and Technology 109

*Mf <sup>M</sup> n*

Where Mf = the final cryoprotective agent concentration in the cell suspension (molarity), Mo = cryoprotective agent concentration in the original stock cryoprotective agent medium (molarity), n= total number of steps, *i* =*i*th-step addition, *V*o= the original volume of isotonic cell suspension (ml), ∆M= increment of glycerol molarity in cell suspension after each step of glycerol addition, \* *Vi*1 = the total volume of cell suspension before the *i*th-step addition, *Vi*= volume of cryoprotective agent stock medium added to cell suspension at the *i*th step.

To dilute the concentrated glycerol in the sperm suspension and remove glycerol from the cells, an isotonic without glycerol was added stepwise to the suspension. The FVS approach,

Given the volume of the sperm suspension (*Vo*) with an initial cryoprotective agent concentration (*Mo*), the total volume of isotonic solution required to dilute the cryoprotective

Using the FVS approach, the volume of isotonic solution which needs to be added to be cell suspension at the ith-step during the first n-1 steps (n steps in total) can be calculated as

> 1 1 *o o <sup>i</sup>*

where Ms = cryoprotective agent concentration in the cell suspension (molarity) after *n*-1 step dilutions, *M*o =cryoprotective agent concentration initial sperm suspension (molarity), *n*= total number of steps, *i*=the *i*th-step addition, *V*o= original volume of cell suspension (ml) and *Vi*= volume of isotonic solution added into cell suspension at the *i*th step. After n-1 steps of addition of isotonic solution into the cell suspension, the diluted sperm suspension was centrifuged (400 g for 5-7 min), and then the sperm pellet was resuspended in an isotonic

Concentrated glycerol in the sperm suspension was diluted stepwise by addition of an isotonic solution. The decrement in the molarity of glycerol after each step dilution was fixed. In the general case, the following equation can be used to calculate the volume of isotonic solution

> *<sup>M</sup> Mo n*

*<sup>V</sup> V M <sup>V</sup> n nM* 

solution, which results in the last (*n*th) step removal of glycerol from the cells.

added to cell suspension at the ith step during the first n-1 step (n steps in total):

1 *<sup>o</sup> s*

1

*s*

FMS approach, and a two-step osmotic buffer approach were used for the dilution.

agent concentration from Mo to Ms can be calculated by the following equation:

*<sup>M</sup> <sup>V</sup> M* 

(13)

(14)

(15)

(16)

(non –permeating solute) salt concentration. Two approaches for mixing the 2.0 M glycerol solution with the sperm suspension were used, i.e. a fixed-volume-step (FVS) approach and a fixed –molarity-step (FMS) approach:

#### *Approach 1:* fixed-volume-step addition

A 2.0 M glycerol solution was added stepwise to the sperm suspension, and the volume of the 2.0 M glycerol solution added in each step was constant. For example, to make a four step addition of 1ml of 2.0 M glycerol solution to a 1 ml isotonic sperm sample, 0.25 ml of 2.0 M glycerol solution would be added four times to the isotonic sperm suspension. The time interval between any two steps was 0.5-1 min.

In the general case, the volume of cryoprotective agent stock medium added to cell suspension in each step can be calculated by the following equation:

$$V\_i = \frac{M\_f \times V\_o}{M\_o - M\_f} \times \frac{1}{n} \tag{8}$$

Where *Mf*= the final CPA concentration (molarity) in the cell suspension, Mo = cryoprotective agent concentration (molarity) in the original stock cryoprotective agent medium, *n*= total number of steps, *i*=*i*th step addition, Vo= the original volume of isotonic cell suspension, and *Vi*= the volume of CPA stock medium added into cell suspension at the *i*th step.

#### *Approach 2:* fixed-molarity-step addition

Glycerol-containing medium was added stepwise into the cell suspension in such a way that the glycerol molar concentration in the cell suspension was increased by a fixed amount after each step of addition. For example, to increase the molarity by 0.25 M in each of four steps, 0.14, 0.19, 0.27 and 0.4 ml of 2.0 M glycerol stock solution should be added (step by step, four steps in total) to 1 ml of the sperm suspension. The time interval between any two steps was 0.5-1min.

In the general case, the volume of cryoprotective agent stock medium added to cell suspension at the *i*th step can be calculated by the following equation:

$$V\_i = \frac{M\_f \times V\_o \times n \times M\_o}{\left(nM\_o - iM\_f\right)\left[nM\_o - \left(i - 1\right)M\_f\right]}\quad\text{where }i = 1, \dots, n\tag{9}$$

$$V\_i = \frac{1}{\lambda n \left(V\_o \Big/ V\_{i-1}^\*\right) - 1} \times V\_{i-1}^\* \tag{10}$$

$$V\_{i-1}^\* = V\_o + \sum V\_k \quad \text{where } k = 1, \dots, i-1 \tag{11}$$

$$
\mathcal{A} = \frac{\mathcal{M}\_o}{\mathcal{M}\_f} \tag{12}
$$

$$
\Delta M = \frac{M\_f}{n} \tag{13}
$$

Where Mf = the final cryoprotective agent concentration in the cell suspension (molarity), Mo = cryoprotective agent concentration in the original stock cryoprotective agent medium (molarity), n= total number of steps, *i* =*i*th-step addition, *V*o= the original volume of isotonic cell suspension (ml), ∆M= increment of glycerol molarity in cell suspension after each step of glycerol addition, \* *Vi*1 = the total volume of cell suspension before the *i*th-step addition, *Vi*= volume of cryoprotective agent stock medium added to cell suspension at the *i*th step.

#### **Removal of glycerol**

108 Current Frontiers in Cryobiology

(non –permeating solute) salt concentration. Two approaches for mixing the 2.0 M glycerol solution with the sperm suspension were used, i.e. a fixed-volume-step (FVS) approach and

A 2.0 M glycerol solution was added stepwise to the sperm suspension, and the volume of the 2.0 M glycerol solution added in each step was constant. For example, to make a four step addition of 1ml of 2.0 M glycerol solution to a 1 ml isotonic sperm sample, 0.25 ml of 2.0 M glycerol solution would be added four times to the isotonic sperm suspension. The time

In the general case, the volume of cryoprotective agent stock medium added to cell

*f o* 1

(8)

where i=1, …, n (9)

(10)

(12)

\* *VV V io k* <sup>1</sup> where *k*=1, …, i-1 (11)

*o f M V*

Where *Mf*= the final CPA concentration (molarity) in the cell suspension, Mo = cryoprotective agent concentration (molarity) in the original stock cryoprotective agent medium, *n*= total number of steps, *i*=*i*th step addition, Vo= the original volume of isotonic cell suspension, and *Vi*= the volume of CPA stock medium added into cell suspension at the

Glycerol-containing medium was added stepwise into the cell suspension in such a way that the glycerol molar concentration in the cell suspension was increased by a fixed amount after each step of addition. For example, to increase the molarity by 0.25 M in each of four steps, 0.14, 0.19, 0.27 and 0.4 ml of 2.0 M glycerol stock solution should be added (step by step, four steps in total) to 1 ml of the sperm suspension. The time interval between any two

In the general case, the volume of cryoprotective agent stock medium added to cell

 \* 1 \*

*o f M M* 

1

*nV V* 

1 <sup>1</sup> *i i o i V V*

*M M n*

a fixed –molarity-step (FMS) approach: *Approach 1:* fixed-volume-step addition

interval between any two steps was 0.5-1 min.

*Approach 2:* fixed-molarity-step addition

*i*

*V*

*i*th step.

steps was 0.5-1min.

suspension in each step can be calculated by the following equation:

suspension at the *i*th step can be calculated by the following equation:

 1) *fo o*

*nM iM nM i M*

*M V nM*

*of o f*

*i*

*V*

To dilute the concentrated glycerol in the sperm suspension and remove glycerol from the cells, an isotonic without glycerol was added stepwise to the suspension. The FVS approach, FMS approach, and a two-step osmotic buffer approach were used for the dilution.

#### *Approach 1*: FVS dilution

Given the volume of the sperm suspension (*Vo*) with an initial cryoprotective agent concentration (*Mo*), the total volume of isotonic solution required to dilute the cryoprotective agent concentration from Mo to Ms can be calculated by the following equation:

$$V = \left\lfloor \frac{M\_o}{M\_s} - \mathbf{1} \right\rfloor \tag{14}$$

Using the FVS approach, the volume of isotonic solution which needs to be added to be cell suspension at the ith-step during the first n-1 steps (n steps in total) can be calculated as follows:

$$V\_i = \frac{V}{n-1} = \frac{V\_o}{n-1} \left[\frac{M\_o}{M\_s} - 1\right] \tag{15}$$

where Ms = cryoprotective agent concentration in the cell suspension (molarity) after *n*-1 step dilutions, *M*o =cryoprotective agent concentration initial sperm suspension (molarity), *n*= total number of steps, *i*=the *i*th-step addition, *V*o= original volume of cell suspension (ml) and *Vi*= volume of isotonic solution added into cell suspension at the *i*th step. After n-1 steps of addition of isotonic solution into the cell suspension, the diluted sperm suspension was centrifuged (400 g for 5-7 min), and then the sperm pellet was resuspended in an isotonic solution, which results in the last (*n*th) step removal of glycerol from the cells.

#### *Approach 2*: FMS dilution

Concentrated glycerol in the sperm suspension was diluted stepwise by addition of an isotonic solution. The decrement in the molarity of glycerol after each step dilution was fixed. In the general case, the following equation can be used to calculate the volume of isotonic solution added to cell suspension at the ith step during the first n-1 step (n steps in total):

$$
\Delta M = \frac{M\_o}{n} \tag{16}
$$

Prevention of Lethal Osmotic Injury to Cells

Mazur and Leibo, 1977; Leibo, 1981).

**glycerol** 

**Statistical analysis** 

data are so presented.

**2.2 Result** 

mOsmol.

min.

During Addition and Removal of Cryoprotective Agents: Theory and Technology 111

buffer were directly transferred to an isotonic solution (TALP), (Table 3) (Rowe et al, 1968;

Medium (TALP) with 2.0M glycerol was added either in one step or stepwise (using FVS or FMS approaches) to an equal volume of the isotonic sperm suspension to achieve a final 1.0 M glycerol concentration at 22°C. The glycerol in the spermatozoa was removed/diluted by a one-step or stepwise addition (using FVS or FMS approaches) of TALP medium, with or without an osmotic buffer (sucrose), to the cell suspension. Some detailed procedures for the removal of glycerol are described in Table 2 and 3. Sperm motility and plasma membrane integrity were measured before and after the different glycerol addition and removal procedures by CASA and the dual staining technique and flow cytometry respectively.

Data were analyzed using standard analysis of variance approaches with the General Linear Models procedure of the Statistical Analysis System (Spector et al., 1985). Comparisons were

The percentage of spermatozoa which maintained motility or plasma membrane integrity after each treatment was normalized to that of untreated, isotonic control samples and the

Human spermatozoa were exposed for 5min to hyper- or hypo-osmotic solutions of sucrose and TALP salts ranging in concentration from 60 to 1200 mOsmol, and their motilities were then determined by CASA while still in those solutions. Figure 3 shows that sperm motilities dropped significantly when the osmolality was >50 mOsmol above or below isotonic (286 mOsmol). Motilities approached zero when the osmolalities were <200 or >600

The next step was to compare these motilities with those observed after spermatozoa were transferred from these anisosmotic solutions back to near isotonic solutions. Figures 4 and 5 show the motilities as a function of time after transfer from hyperosmotic or from hypoosmotic exposures respectively. In both cases, the more the initial exposure departed from isotonicity, the greater the damage upon return to isotonicty. Most, or all, of the damage was evident in the first 30 s after the return, although in the case of transfer from hypertonic solutions to near isotonic, there was a further slight and gradual decline over the ensuing 30

Figure 6 compares sperm motilities after a 5 min exposure to the various anisosmotic solutions before and after the return to near isotonic conditions. The reduction in the motilities of spermatozoa exposed to hypo-osmotic media was not affected by the return to isotonic media, but most of the apparent loss of motility of spermatozoa in hyperosmotic media of between 286 and 600 mOsmol was reversed when spermatozoa were returned to near isotonic. For example, although only 10% of spermatozoa were motile in 600 mOsmol

conducted using a protected LSD (least significant difference) approach (Zar, 1984).

**Determination of osmotic injury as a function of sperm volume excursion** 

**Experimental examination of the predicted osmotic injury during addition /removal of** 

$$V\_i = \frac{1}{n\left(V\_o \Big/ V\_{i-1}^\*\right) - 1} \times V\_{i-1}^\* \quad \text{where } i = 1, \dots, n - 1 \tag{17}$$

$$V\_{i-1}^{\*} = V\_o + \sum V\_k \quad \text{where } k = 1, \dots, i-1 \tag{18}$$

where ∆*M*= the decrement in the glycerol molarity in the spermatozoa after each stepwise addition of the isotonic solution, *M*o = cryoprotective agent concentration (molarity) in the initial sperm suspension, n= total number of steps, *i*=*i*th-step addition, *V*o=original volume of cell suspension, \* *Vi*<sup>1</sup> = the total volume of cell suspension before the *i*th-step addition and *Vi*= volume of isotonic solution added into cell suspension at *it*h step. After n-1 step of addition , the cryoprotective agent concentration in the cell was diluted to ∆M. Then spermatozoa were transferred to isotonic conditions, which is the last (the nth) step removal of glycerol, see Table 2 fore examples.

*Approach 3*: Two-step dilution with an osmotic buffer


Add 2000 μl of isotonic solution directly to 100 μl of cell suspension with 1.0 M glycerol

Table 2. Procedures used in one-step and eight-step removal of 1.0 M glycerol from human spermatozoa


Table 3. Procedures used in the two-step removal of 1.0 M glycerol from spermatozoa using sucrose as an osmotic buffer

In the first step, glycerol was directly removed by transferring cells to a hyperosmotic medium (osmotic buffer, TALP with sucrose) containing no glycerol but only nonpermeating solutes (salts and sucrose), and in the second step spermatozoa in the osmotic buffer were directly transferred to an isotonic solution (TALP), (Table 3) (Rowe et al, 1968; Mazur and Leibo, 1977; Leibo, 1981).

## **Experimental examination of the predicted osmotic injury during addition /removal of glycerol**

Medium (TALP) with 2.0M glycerol was added either in one step or stepwise (using FVS or FMS approaches) to an equal volume of the isotonic sperm suspension to achieve a final 1.0 M glycerol concentration at 22°C. The glycerol in the spermatozoa was removed/diluted by a one-step or stepwise addition (using FVS or FMS approaches) of TALP medium, with or without an osmotic buffer (sucrose), to the cell suspension. Some detailed procedures for the removal of glycerol are described in Table 2 and 3. Sperm motility and plasma membrane integrity were measured before and after the different glycerol addition and removal procedures by CASA and the dual staining technique and flow cytometry respectively.
