Current mammalian oocyte and embryo cryopreservation protocols have evolved from methods that have been successful with mouse and cattle embryos [1]. The basic strategy typically employed involves the use of a two-step, or interrupted slow freezing (ISF) procedure, which is now a common procedure to cryopreserve many different cell and tissue types [2]. In general, this procedure consists of an initial slow cooling period followed by rapid cooling as the sample is plunged into liquid nitrogen (LN2) for final storage. In the initial slow cooling step, extracellular ice is induced at a temperature just below the solution freezing point, and slow cooling is continued (at a given rate defined as B1) in the presence of this growing ice phase, which raises the extracellular solute concentration in the unfrozen fraction and results in water exiting the cell via exosmosmosis. (Table 1 contains a description of terms and abbreviations.) Permeating cryoprotective agents (CPAs) such as glycerol, dimethyl sulfoxide (DMSO), ethylene glycol (EG), or propylene glycol (PG) are typically included in the suspension medium to protect cells against injury from the high concentrations of electrolytes (so-called solution effects) that develop as water exits the solution as ice. These CPAs become increasingly concentrated intracellularly as a cell dehydrates.
As this ISF procedure continues, the slow cooling step is terminated at an intermediate temperature at which plunging occurs (Tp), and is followed by a rapid cooling step (at a given rate defined as B2). If the initial cooling step is conducted in a way that allows formation of a critical concentration ([CPA]c) of intracellular solute ([S]i; in the present study defined as CPA + NaCl), then the CPA will interact with the remaining water in the cell, which results in the formation of a glass-like structure (vitrification) by the intracellular solution, and prevention of damaging intracellular ice formation (IIF). The concentration of CPA required to achieve intracellular vitrification during the subsequent rapid cooling (and to maintain the vitrified state during warming) is dependent upon the nature of the solute, the rate of rapid cooling during the plunge into LN2, and the rate of warming during subsequent thawing [3].
The Tp at which the [CPA]c is attained during the slow cooling phase of ISF depends on the initial concentration of CPA present in a cell (at the onset of the slow freezing step) and the initial slow cooling rate. For a given [CPA]c, this temperature could be theoretically determined for a specific initial concentration of CPA loaded into cells prior to freezing and a specific cooling rate. This suggests that theoretical determination of an ISF cryopreservation protocol is possible, if the [CPA]c is known.
Therefore, in the context of ISF protocol development, the goal is to determine the best selection of the initial CPA concentration ([CPA]0), B1, and Tp that will allow [S]i to reach [CPA]c. These determinations can be achieved by experimental and theoretical approaches. The procedures usually involve defining ranges of prospective selections of [CPA]0 and B1 for a given cell and CPA type, followed by evaluation of these ranges to determine which will yield optimal results as judged by experimental or established theoretical criteria. Many models have been proposed to integrate these aspects (to differing extents) in an attempt to quantitatively examine the biophysical events that occur during cryopreservation. Mazur [4, 5] first introduced a model that allowed examination of the kinetics of water loss from cells at subzero temperatures, relating it to the effects of cooling and warming velocity on cryosurvival. Liu et al. [6] established a theoretical model that incorporates the transmembrane movement of cryoprotectant at low temperatures and the DMSO/NaCl/water ternary phase diagram. Karlsson et al. [7] conducted a comprehensive study in which a coupled mechanistic model was used to design and optimize a two-step cryopreservation protocol for mouse oocytes. Briefly, their method consisted of fixing a given CPA concentration (1.5 M), then optimizing the cryopreservation protocol by 1) minimizing the time taken to reach the final temperature (to reduce injury by solution effects) and 2) avoiding IIF. The optimization process developed by Karlsson et al. [7] involved defining a cost-function equivalent to the duration of the freezing protocol. The protocol was then theoretically optimized by using a sequential simplex algorithm to minimize the cost function, subject to the constraint that the predicted incidence of IIF remains below 5% [7].
The objective of the present study was to theoretically optimize an ISF protocol to cryopreserve rat zygotes. In this study, DMSO was chosen as the permeable CPA because the most complete set of information exists for solutions of this permeating cryoprotectant; specifically, critical concentrations/cooling and warming rates necessary for vitrification and ternary solution phase diagram information [3, 8, 9]. The basic phenomenological strategy employed in the current model was similar to the studies by Karlsson et al. [7, 10] in that the consequences of the duration of slow cooling and the probability of IIF were considered; however, the current strategy employed a different theoretical method. Specifically, the current model assumed, first, that the cell membrane was permeable to CPA at any temperature (with permeability being calculated using the Arrhenius relationship); second, that the actual ternary solution phase diagram was used instead of the more general Clausius-Clapeyron equation; and third, that a simplified model was used to predict IIF. Essentially, development of the model followed three steps: 1) an initial range of DMSO concentrations from 0 to 4 molal, and a range of cooling rates from 0 to 2.5°C/min were evaluated theoretically to determine the selections of [CPA]0 and B1 that would allow the [S]i to reach the [CPA]c; 2) using Mazur's IIF model [11], the selections that could result in IIF were eliminated; and 3) the associated plunging temperatures for the combinations of [CPA]0 and B1 ranges were then calculated. The optimum set of conditions from the final range was then selected based on minimum duration of slow cooling.
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