**2.1 Materials and methods**

104 Current Frontiers in Cryobiology

The two-parameter model was firstly presented by Jacob (1932-1933), and further developed by Kleinhans (1998), Katkov (2000) recently. The model utilizes the parameters *Lp* and *Ps* (CPA solute permeability) to characterize membrane permeability when water, a permeable

> *w e i p c dV L A RT M M*

*s e i sc s s dN PA M M*

where *Ns* is the number of osmoles of solute inside cell, *R* is the universal gas constant, *T* is the absolute temperature, *Mi* and *Me* are the intracellular and extracellular osmolality, respectively. The subscript 's' refers to permeable solute, and remaining symbols are as

The classical formulation of coupled, passive membrane transport was developed by Kedem and Katchalshy (1958) using the theory of linear irreversible thermodynamics. The formulation includes two coupled first-order non-linear ordinary equations which describe the total transmembrane volume flux and the transmembrane permeable solute flux

In the model (so called Kedem-Katchalssky transport formalism or KK formalism), a reflection coefficient (σ) was introduced with Lp and Ps to describe water and solute (CPA)

> *<sup>c</sup> ei ei pc n n s s*

*s c e i*

Where *Vc* is cell volume, *Ms* is the average osmolality of intracellular and extracellular

The KK formalism used to be the most general of the three mentioned. However, more recent literature suggests that aquaporins in cell membrane are highly selective, with nonionic solute transport occurring mainly through the lipid bilayer or through other channels that are distinct from the aquaporins (Gilmore et al, 1995; Preston et al, 1992). In this case, the estimation of σ as independent parameter may be inappropriate and may not be relevant from a biological stand point (Kleinhans, 1998). By assuming that there is no interaction between water and solute during their transport through the membrane, the value of σ can be determined as 1 *PV RTL s s <sup>p</sup>* , where *Vs* = partial molar volume of permeating solute. In this manner, the KK formalism can still get correct result as two

*dN dV <sup>M</sup> PA M M*

1

*s sc s s*

(4)

(5)

*dV L A RT M M M M*

*i*

*i*

*dt* (2)

*dt* (3)

ii. Two-parameter model

previously defined.

respectively.

parameter model.

iii. Three-parameter model

transport across the plasma membrane:

*dt*

*i*

*dt dt*

solution, and the subscript '*n*' refers to nonpermeable solute, respectively.

solute and a nonpermeable solute are present:

### **Preparation of sperm suspension**

Human semen samples were obtained by masturbation from healthy donors after at least 2 days of sexual abstinence. Samples were allowed to liquefy in an incubator (5% CO2, 95% air, 37C, and high humidity) for ~1h. A total of 5 ul of the liquefied semen were used for a computer-assisted semen analysis (CASA) using CellSoft (Version 3.2/C, CRYO Resources, Ltd, Montgomery, NY, USA) (Jequier and Crich, 1986; Crister et al., 1988b). A swim-up procedure was performed to separate motile form immotile cells [layering 500ul of modified Tyrode's medium (TALP: Bavister et al., 1983) over 250 ul of semen, incubating for ~1 h in the incubator and carefully aspirating 400 ul of the supernatant in which >95% of spermatozoa were motile]. The motile cell suspensions were centrifuged at 400g for 7min and resuspended in the TALP medium (286~290 Osmol) supplemented with pyruvate (0.01 mg/ml) and bovine serum albumin (4 mg/ml), at a cell concentration of 1×109 cell/ml.
