Measurement and simulation of water and methanol transport in algal cells

BACKGROUND: Experimental data and a complementary biophysical model are presented to describe the dynamic response of a unicellular microalga to osmotic processes encountered during cryopreservation. METHOD OF APPROACH: Chlorococcum texanum (C. texanum) were mounted on a cryoperfusion microscope stage and exposed sequentially to various solutions of sucrose and methanol. Transient volumetric excursions were determined by capturing images of cells in real time and utilizing image analysis software to calculate cell volumes. A biophysical model was applied to the data via inverse analysis in order to determine the plasma membrane permeability to water and to methanol. The data were also used to determine the elastic modulus of the cell wall and its effect on cell volume. A three-parameter (hydraulic conductivity (Lp), solute permeability; (omega), and reflection coefficient, (sigma)) membrane transport model was fit to data obtained during methanol perfusion to obtain constitutive property values. These results were compared with the property values obtained for a two coefficient (Lp and omega) model. RESULTS: The three-parameter model gave a value for sigma not consistent with practical physical interpretation. Thus, the two-coefficient model is the preferred approach for describing simultaneous water and methanol transport. The rate of both water and methanol transport were strongly dependent on temperature over the measured temperature range (25 degrees C to -5 degrees C) and cells were appreciably more permeable to methanol than to water at all measured temperatures. CONCLUSION: These results may explain in part why methanol is an effective cryoprotective agent for microalgae.     

Membrane transport properties of equine and macaque ovarian tissues frozen in mixtures of dimethylsulfoxide and ethylene glycol

The rate at which equine and macaque ovarian tissue sections are first cooled from +25 degrees C to +4 degrees C has a significant effect on the measured water transport when the tissues are subsequently frozen in 0.85 M solutions of glycerol, dimethylsulfoxide (DMSO), or ethylene glycol (EG). To determine whether the response of ovarian tissues is altered if they are suspended in mixtures of cryoprotective agents (CPAs), rather than in solutions of a single CPA, we have now measured the subzero water transport from ovarian tissues that were suspended in mixtures of DMSO and EG. Sections of freshly collected equine and macaque ovaries were suspended either in a mixture of 0.9 M EG plus 0.7 M DMSO (equivalent to a mixture of approximately 5% vv of EG and DMSO) or in a 1.6M solution of only DMSO or only EG. The tissue sections were cooled from +25 degrees C to +4 degrees C and then frozen to subzero temperatures at 5 degrees C/min. As the tissues were being frozen, a shape-independent differential scanning calorimeter technique was used to measure water loss from the tissues and, consequently, the best fit membrane permeability parameters (L(pg) and E(Lp)) of ovarian tissues during freezing. In the mixture of DMSO+EG, the respective values of L(pg) and E(Lp) for equine tissue first cooled at 40 degrees C/min between +25 degrees C and +4 degrees C before being frozen were 0.15 microm/min atm and 7.6 kcal/mole. The corresponding L(pg) and E(Lp) values for equine tissue suspended in 1.6M DMSO were 0.12 microm/min atm and 27.2 kcal/mole; in 1.6M EG, the values were 0.06 microm/min atm and 21.9 kcal/mole, respectively. For macaque ovarian tissues suspended in the mixture of DMSO+EG, the respective values of L(pg) and E(Lp) were 0.26 microm/min atm and 26.2 kcal/mole. Similarly, the corresponding L(Lg) and E(Lp) values for macaque tissue suspended in 1.6M DMSO were 0.22 microm/min atm and 31.4 kcal/mole; in 1.6 M EG, the values were 0.20 microm/min atm and 27.9 kcal/mole. The parameters for both equine and macaque tissue samples suspended in the DMSO+EG mixture and first cooled at 0.5 degrees C/min between +25 degrees C and +4 degrees C were very similar to the corresponding values for samples cooled at 40 degrees C/min. In contrast, the membrane parameters of equine and macaque samples first cooled at 0.5 degrees C/min in single-component solutions were significantly different from the corresponding values for samples cooled at 40 degrees C/min. These results show that the membrane properties of ovarian cells from two species are different, and that the membrane properties are significantly affected both by the solution in which the tissue is suspended and by the rate at which the tissue is cooled from +25 degrees C to +4 degrees C before being frozen. These observations suggest that these variables ought to be considered in the derivation of methods to cryopreserve ovarian tissues.     

Cryomicroscope investigation and thermodynamic modeling of the freezing of unfertilized hamster ova

Thermodynamic computer modeling was used to predict the freezing response of single-celled unfertilized hamster ova. The cell membrane transport characteristics were investigated, using a microscope diffusion chamber system. The mean osmotically inactive cell volume was determined to be 21.6% of the initial cell volume. An overall mean value of 0.8 +/- 0.1 micron3/micron2.min.atm (= 18 +/- 2.5 micron/sec) was determined for the membrane hydraulic coefficient, Lp. The effect of the extracellular solute concentration on Lp was determined at room temperature (approximately 23 degrees C). A thermodynamic computer model was used to predict the cell response to freezing. The predicted response was compared to the actual volumetric response observed during freezing on a temperature-controlled cryomicroscope conduction stage. The effect of the cooling rate on the nucleation temperature of unprotected ova and protected ova suspended in a 1.5 M DMSO solution was investigated. Overall mean nucleation temperatures of -13 and -57.1 degrees C were observed for unprotected and protected ova, respectively, where the mean nucleation temperature for protected ova was strongly cooling rate dependent.     

Studies on membrane permeability of zebrafish (Danio rerio) oocytes in the presence of different cryoprotectants

Investigation into fish oocyte membrane permeability is essential for developing successful protocols for their cryopreservation. The aim of the present work was to study the permeability of the zebrafish (Danio rerio) oocyte membrane to water and cryoprotectants before cryopreservation protocol design. The study was conducted on stage III and stage V zebrafish oocytes. Volumetric changes of stage III oocytes in different concentrations of sucrose were measured after 20 min exposure at 22 degrees C and the osmotically inactive volume of the oocytes (Vb) was determined using the Boyle-van't Hoff relationship. Volumetric changes of oocytes during exposure to different cryoprotectant solutions were also measured. Oocytes were exposed to 2 M dimethyl sulphoxide (DMSO), propylene glycol (PG), and methanol for 40 min at 22 degrees C. Stage III oocytes were also exposed to 2 M DMSO at 0 degrees C. Oocyte images were captured on an Olympus BX51 cryomicroscope using Linkham software for image recording. Scion Image was used for image analysis and diameter measurement. The experimental data were fitted to a two-parameter model using Berkeley Madonna 8.0.1 software. Hydraulic conductivity (L(p)) and solute (cryoprotectant) permeability (Ps) were estimated using the model. The osmotically inactive volume of stage III zebrafish oocytes was found to be 69.5%. The mean values+/-SE of Lp were found to be 0.169+/-0.02 and 0.196+/-0.01 microm/min/atm in the presence of DMSO and PG, respectively, at 22 degrees C, assuming an internal isosmotic value for the oocyte of 272 mOsm. The Ps values were 0.000948+/-0.00015 and 0.000933+/-0.00005 cm/min for DMSO and PG, respectively. It was also shown that the membrane permeability of stage III oocytes decreased significantly with temperature. No significant changes in cell volume during methanol treatment were observed. Fish oocyte membrane permeability parameters are reported here for the first time. The Lp and Ps values obtained for stage III zebrafish oocytes are generally lower than those obtained from successfully cryopreserved mammalian oocytes and higher than those obtained with fish embryos and sea urchin eggs. It was not possible to estimate membrane permeability parameters for stage V oocytes using the methods employed in this study because stage V oocytes experienced the separation of outer oolemma membrane from inner vitelline during exposure to cryoprotectants.     

Permeation of glycerol and propane-1,2-diol into human platelets

The permeability of human platelets to glycerol (GLY) and propane-1,2-diol (propylene glycol, PG) has been determined by measuring the time course of their change in volume following abrupt immersion in solutions of these solutes. A simple light-scattering method, and its calibration to measure mean platelet volume is described. The data are analyzed by means of the Kedem-Katchalsky (K-K) equations, modified to take into account the nonideal behavior of both intracellular and extracellular solutes. The values of the K-K parameters at 2, 21, and 37 degrees C, respectively, were as follows: the hydraulic conductivities (Lp) were 1 x 10(-7), 7 x 10(-7) and 3 x 10(-6) cm.sec-1.atm-1; the solute permeabilities for PG (omega RTPG) were 1.9 x 10(-6), 2.8 x 10(-5), and 1.3 x 10(-4) cm.sec-1; the solute permeabilities for GLY (omega RTGLY), at 21 and 37 degrees C only, were 2.6 x 10(-7) and 1.4 x 10(-6) cm.sec-1. The reflection coefficient (sigma) was 1 throughout. The relevant activation energies were -Lp, 16.5 kcal.mol-1; omega RTPG, 20.5 kcal.mol-1; and omega RTGLY, 17.9 kcal.mol-1. The use of these data is illustrated by computing schedules for the addition and removal of GLY and PG so that the amplitudes of changes in platelet volume are held within predetermined limits.     

Predicted permeability parameters of human ovarian tissue cells to various cryoprotectants and water

This study presents a generic numerical model to simulate the coupled solute and solvent transport in human ovarian tissue sections during addition and removal of chemical additives or cryoprotective agents (CPA). The model accounts for the axial and radial diffusion of the solute (CPA) as well as axial convection of the CPA, and a variable vascular surface area (A) during the transport process. In addition, the model also accounts for the radial movement of the solvent (water) into and out of the vascular spaces. Osmotic responses of various cells within an human ovarian tissue section are predicted by the numerical model with three model parameters: permeability of the tissue cell membrane to water (L(p)), permeability of the tissue cell membrane to the solute or CPA (omega) and the diffusion coefficient of the solute or CPA in the vascular space (D). By fitting the model results with published experimental data on solute/water concentrations within an human ovarian tissue section, I was able to determine the permeability parameters of ovarian tissue cells in the presence of 1.5M solutions of each of the following: dimethyl sulphoxide (DMSO), propylene glycol (PROH), ethylene glycol (EG), and glycerol (GLY), at two temperatures (4 degrees C and 27 degrees C). Modeling Approach 1: Assuming a constant value of solute diffusivity (D = 1.0 x 10(-9) m(2)/sec), the best fit values of L(p) ranged from 0.35 x 10(-14) to 1.43 x 10(-14) m(3)/N-sec while omega ranged from 2.57 x 10(-14) to 70.5 x 10(-14) mol/N-sec. Based on these values of L(p) and omega, the solute reflection coefficient, sigma defined as sigma = 1-omega v(CPA)/L(P) ranged from 0.9961 to 0.9996. Modeling Approach 2: The relative values of omega and sigma from our initial modeling suggest that the embedded ovarian tissue cells are relatively impermeable to all the CPAs investigated (or omega approximately 0 and sigma approximately 1.0). Consequently the model was modified and used to predict the values of L(p) and D assuming omega = 0 and sigma = 1.0. The best fit values of L(p) ranged from 0.44 x 10(-14) to 1.2 x 10(-14) m(3)/N-sec while D ranged from 0.85 x 10(-9) to 2.08 x 10(-9) m(2)/sec. Modeling Approach 3: Finally, the best fit values of D from modeling approach 2 were incorporated into model 1 to re-predict the values of L(p) and omega. It is hoped that the ovarian tissue cell parameters reported here will help to optimize chemical loading and unloading procedures for whole ovarian tissue sections and consequently, tissue cryopreservation procedures.     

Freezing response and optimal cooling rates for cryopreserving sperm cells of striped bass, Morone saxatilis

This study explored the optimization of techniques for sperm cryopreservation of an economically important fish species, the striped bass Morone saxatilis. The volumetric shrinkage or the water transport response during freezing of sperm cells was obtained using a differential scanning calorimeter (DSC) technique. Water transport was obtained in the presence of extracellular ice at a cooling rate of 20 degrees C/min in two different media: (1) without cryoprotective agents (CPAs), and (2) with 5% (v/v) dimethyl sulfoxide (DMSO). The sperm cell was modeled as a cylinder of length of 22.8 microm and diameter 0.288 microm and was assumed to have an osmotically inactive cell volume (V(b)) of 0.6 V(0), where V(0) is the isotonic or initial cell volume. By fitting a model of water transport to the experimentally determined water transport data, the best fit membrane permeability parameters (reference membrane permeability to water, L(pg) or L(pg)[cpa] and the activation energy, E(Lp) or E(Lp)[cpa]) were determined and ranged from L(pg)=0.011-0.001 microm/min-atm, and E(Lp)=40.2-9.2 kcal/mol). The parameters obtained in this study suggested that the optimal rate of cooling for striped bass sperm cells in the presence and absence of DMSO range from 14 to 20 degrees C/min. These theoretically predicted rates of optimally freezing M. saxatilis sperm compared quite closely with independent and experimentally determined optimal rates of cooling striped bass sperm.     

Plasma membrane water permeabilities of human oocytes: the temperature dependence of water movement in individual cells.

Membrane water permeability values were measured in individual fresh human pre-ovulatory oocytes using real time microscopy in a microscope diffusion chamber. The cells were exposed to anisosmotic conditions, their volume responses measured, and from these data the Lp values were computed employing the Kedem-Katchalsky analyses of irreversible thermodynamics. Lp values were measured at four temperatures for each oocyte between 37 degrees C and 10 degrees C, and the temperature-related Arrhenius activation energy (Ea) calculated. It was apparent that individual oocytes exhibited a wide range of Lp values; at 37 degrees C Lp values ranged between 0.33 and 1.80 microns/atm/min. However, each oocyte exhibited the expected inverse linear correlation between Lp and temperature, with high linear correlations (R2 values between 0.73 and 0.96). A mean value for Ea of 8.61 +/- 5.11 Kcal/mol was computed. It is apparent that pre-ovulatory human oocytes express a range of biological diversity in terms of membrane water transport, and this fact needs to be considered when attempting to formulate cryopreservation protocols for storage of these oocytes.     

Measurements of the membrane water permeability (Lp) and its temperature dependence (activation energy) in human fresh and failed-to-fertilize oocytes and mouse oocyte.

The volumetric response of oocytes during rapid alterations of the extracellular osmotic environment were recorded using video microscopy. From these observations, the kinetics of water loss for human and mouse oocytes were determined over the temperature range 37 to 10 degrees C, including 37, 30, 20, and 10 degrees C. The changes in diameter of oocytes were measured over a 5-min period and a computer model was used to derive values for membrane water permeability (Lp) and inactive volume (Vb) and to compare the experimental data to the predicted values. The results for the mouse oocyte Lp were comparable to values determined by other methods. However the human data, for both failed-to-fertilize and fresh oocytes, have a wide range of values with large standard deviations. The Lp values at the various temperatures were used to calculate the Arrhenius activation energy (Ea). An Ea value of 9.48 kcal/mol was found for the fresh mouse oocyte, whereas the activation energy for human oocytes was extremely low, 3.73 kcal/mol for fresh oocytes and 1.93 kcal/mol for failed-to-fertilize oocytes.     

Permeability of cultured megakaryocytopoietic cells of the rat to dimethyl sulfoxide

The permeability of the membrane of the rat megakaryocytopoietic cell to dimethyl sulfoxide was measured to assess its availability to the intracellular compartment. The method used was osmotic, and measured the initial loss of cell water followed by a reswelling to isotonic volume when cells were placed in culture media containing 0.6 M DMSO. Values for the hydraulic coefficient, Lp, the permeability of the membrane to DMSO, wRT , and the reflection coefficient were calculated from the equations of Kedem and Katchalsky . The average value at 25 degrees C for Lp was 0.46 micron min-1 atm1 ; wRT was 9.3 micron min-1, and the reflection coefficient was 0.65. At these cell volumes, 50% equilibration occurred in 5 sec. Cells equilibrated in 0.6 M DMSO increased their volume of osmotically inactive water. Coupled with this phenomenon of stabilization of water was a reduction in the hydraulic coefficient by 50%. These findings are discussed in the context of current hypotheses about cellular viability during freezing and thawing in the presence and absence of cryoprotectants.     

Development of a novel microperfusion chamber for determination of cell membrane transport properties.

A novel microperfusion chamber was developed to measure kinetic cell volume changes under various extracellular conditions and to quantitatively determine cell membrane transport properties. This device eliminates modeling ambiguities and limitations inherent in the use of the microdiffusion chamber and the micropipette perfusion technique, both of which have been previously validated and are closely related optical technologies using light microscopy and image analysis. The resultant simplicity should prove to be especially valuable for study of the coupled transport of water and permeating solutes through cell membranes. Using the microperfusion chamber, water and dimethylsulfoxide (DMSO) permeability coefficients of mouse oocytes as well as the water permeability coefficient of golden hamster pancreatic islet cells were determined. In these experiments, the individual cells were held in the chamber and perfused at 22 degrees C with hyperosmotic media, with or without DMSO (1.5 M). The cell volume change was videotaped and quantified by image analysis. Based on the experimental data and irreversible thermodynamics theory for the coupled mass transfer across the cell membrane, the water permeability coefficient of the oocytes was determined to be 0.47 micron. min-1. atm-1 in the absence of DMSO and 0.65 microns. min-1. atm-1 in the presence of DMSO. The DMSO permeability coefficient of the oocyte membrane and associated membrane reflection coefficient to DMSO were determined to be 0.23 and 0.85 micron/s, respectively. These values are consistent with those determined using the micropipette perfusion and microdiffusion chamber techniques. The water permeability coefficient of the golden hamster pancreatic islet cells was determined to be 0.27 microns. min-1. atm-1, which agrees well with a value previously determined using an electronic sizing (Coulter counter) technique. The use of the microperfusion chamber has the following major advantages: 1) This method allows the extracellular condition(s) to be readily changed by perfusing a single cell or group of cells with a prepared medium (cells can be reperfused with a different medium to study the response of the same cell to different osmotic conditions). 2) The short mixing time of cells and perfusion medium allows for accurate control of the extracellular osmolality and ensures accuracy of the corresponding mathematical formulation (modeling). 3) This technique has wide applicability in studying the cell osmotic response and in determining cell membrane transport properties.     

Subzero water permeability parameters and optimal freezing rates for sperm cells of the southern platyfish, Xiphophorus maculatus

This study reports the subzero water transport characteristics (and empirically determined optimal rates for freezing) of sperm cells of live-bearing fishes of the genus Xiphophorus, specifically those of the southern platyfish Xiphophorus maculatus. These fishes are valuable models for biomedical research and are commercially raised as ornamental fish for use in aquariums. Water transport during freezing of X. maculatus sperm cell suspensions was obtained using a shape-independent differential scanning calorimeter technique in the presence of extracellular ice at a cooling rate of 20 degrees C/min in three different media: (1) Hanks' balanced salt solution (HBSS) without cryoprotective agents (CPAs); (2) HBSS with 14% (v/v) glycerol, and (3) HBSS with 10% (v/v) dimethyl sulfoxide (DMSO). The sperm cell was modeled as a cylinder with a length of 52.35 microm and a diameter of 0.66 microm with an osmotically inactive cell volume (Vb) of 0.6 V0, where V0 is the isotonic or initial cell volume. This translates to a surface area, SA to initial water volume, WV ratio of 15.15 microm(-1). By fitting a model of water transport to the experimentally determined volumetric shrinkage data, the best fit membrane permeability parameters (reference membrane permeability to water at 0 degrees C, Lpg or Lpg [cpa] and the activation energy, E(Lp) or E(Lp) [cpa]) were found to range from: Lpg or Lpg [cpa] = 0.0053-0.0093 microm/minatm; E(Lp) or E(Lp) [cpa] = 9.79-29.00 kcal/mol. By incorporating these membrane permeability parameters in a recently developed generic optimal cooling rate equation (optimal cooling rate, [Formula: see text] where the units of B(opt) are degrees C/min, E(Lp) or E(Lp) [cpa] are kcal/mol, L(pg) or L(pg) [cpa] are microm/minatm and SA/WV are microm(-1)), we determined the optimal rates of freezing X. maculatus sperm cells to be 28 degrees C/min (in HBSS), 47 degrees C/min (in HBSS+14% glycerol) and 36 degrees C/min (in HBSS+10% DMSO). Preliminary empirical experiments suggest that the optimal rate of freezing X. maculatus sperm in the presence of 14% glycerol to be approximately 25 degrees C/min. Possible reasons for the observed discrepancy between the theoretically predicted and experimentally determined optimal rates of freezing X. maculatus sperm cells are discussed.     

Cryoprotectant permeability parameters for cells used in a bioengineered human corneal equivalent and applications for cryopreservation

A human corneal equivalent is being developed with applications in pharmaceutical testing and biomedical research, but the distribution of this engineered tissue, depends on successful cryopreservation. Cryopreservation of tissues depends on the presence of cryoprotectants, their addition and removal, and exposure to conditions during freezing and thawing, all of which depend on cellular membrane permeabilities to water and cryoprotectant. This study defines the permeability properties that define the rate of water and cryoprotectant movement across the plasma membrane of isolated human corneal endothelial, keratocyte, and epithelial cells. Cells were transferred from isotonic conditions (300 mosm/kg) to 0.5, 1, or 2 M dimethyl sulfoxide and propylene glycol solutions at constant temperature, and cell volumes monitored using an electronic particle counter. Histograms describing cell volume changes over time after cryoprotectant exposure allowed calculation of hydraulic conductivity (Lp), cryoprotectant permeability (Ps), and the reflection coefficient (sigma). Experimental values for Lp and Ps at 4, 13, 22, and 37 degrees C were used to determine the Arrhenius activation energy (Ea). Defining the permeability parameters and temperature dependencies allows simulation of responses of human corneal cells to addition and removal of cryoprotectants and to freezing conditions, allowing amount of supercooling, intracellular electrolyte concentration, and intracellular cryoprotectant concentration to be calculated. Simulations also show that the constituent cells in the bioengineered cornea respond differently to addition and removal of cryoprotectants and to freezing. This study has defined the requirements during cryopreservation for the corneal cells; future work will define the matrix requirements which will allow the development of a cryopreservation protocol.     

Reflection coefficients of permeant molecules in human red cell suspensions

The Staverman reflection coefficient, sigma for several permeant molecules was determined in human red cell suspensions with a Durrum stopped-flow spectrophotometer. This procedure was first used with dog, cat, and beef red cells and with human red cells. The stopped-flow technique used was similar to the rapid-flow method used by those who originally reported sigma measurements in human red cells for molecules which rapidly penetrate the red cell membrane. The sigma values we obtained agreed with those previously reported for most of the slow penetrants, except malonamide, but disagreed with all the sigma values previously reported for the rapid penetrants. We were unable to calculate an "equivalent pore radius" with our sigma data. The advantages of our equipment and our experimental procedure are discussed. Our sigma data suggest that sigma is indirectly proportional to the log of the nonelectrolyte permeability coefficient, omega. Since a similar trend has been previously shown for log omega and molar volume of the permeant molecules, a correlatioo was shown between sigma and molar volume suggesting the membrane acts as a sieve.     

Determination of bull sperm membrane permeability to water and cryoprotectants using a concentration-dependent self-quenching fluorophore

The objective of this study was to determine the membrane permeability characteristics of bovine spermatozoa. These included the hydraulic conductivity (Lp), the permeability coefficients (Ps) of four common cryoprotective agents (CPAs) and the associated reflection coefficients (sigma). Stopped-flow fluorometry was applied in order to capture rapid cell volume changes under anisosmotic conditions in the absence or presence of permeant solutes (CPAs). This technique utilizes a concentration-dependent self-quenching entrapped fluorophore. The resulting cell volume changes were used in three-parameter fitting calculations to compute Lp in the absence of permeant solutes and Ps and Lp in the presence of permeating solutes (CPAs) at 22 degrees C. The hydraulic conductivity in the absence of permeating solutes was estimated to be 0.68+/-0.05 microm/min/atm (mean+/-SEM). Hydraulic conductivity (Lp) in the presence of CPAs was 0.91+/-0.27 (mean+/-SEM), 0.29+/-0.04, 0.42+/-0.05, and 0.39+/-0.03 microm/min/atm in the presence of dimethylsulfoxide (Me(2)SO), glycerol, propylene glycol (PG), and ethylene glycol (EG), respectively. The values for Ps were estimated to be 1.72+/-0.36, 1.75+/-0.03, 2.47+/-0.24, and 1.49+/-0.33 x 10(-3)cm/min for Me(2)SO, glycerol, PG, and EG, respectively. The data were used to simulate volume excursions during addition and removal of CPA, to predict the different effects of the four CPAs.     

The effect of dimethylsulfoxide on the water transport response of rat hepatocytes during freezing.

Successful improvement of cryopreservation protocols for cells in suspension requires knowledge of how such cells respond to the biophysical stresses of freezing (intracellular ice formation, water transport) while in the presence of a cryoprotective agent (CPA). This work investigates the biophysical water transport response in a clinically important cell type--isolated hepatocytes--during freezing in the presence of dimethylsulfoxide (DMSO). Sprague-Dawley rat liver hepatocytes were frozen in Williams E media supplemented with 0, 1, and 2 M DMSO, at rates of 5, 10, and 50 degrees C/min. The water transport was measured by cell volumetric changes as assessed by cryomicroscopy and image analysis. Assuming that water is the only species transported under these conditions, a water transport model of the form dV/dT = f(Lpg([CPA]), ELp([CPA]), T(t)) was curve-fit to the experimental data to obtain the biophysical parameters of water transport--the reference hydraulic permeability (Lpg) and activation energy of water transport (ELp)--for each DMSO concentration. These parameters were estimated two ways: (1) by curve-fitting the model to the average volume of the pooled cell data, and (2) by curve-fitting individual cell volume data and averaging the resulting parameters. The experimental data showed that less dehydration occurs during freezing at a given rate in the presence of DMSO at temperatures between 0 and -10 degrees C. However, dehydration was able to continue at lower temperatures (< -10 degrees C) in the presence of DMSO. The values of Lpg and ELp obtained using the individual cell volume data both decreased from their non-CPA values--4.33 x 10(-13) m3/N-s (2.69 microns/min-atm) and 317 kJ/mol (75.9 kcal/mol), respectively--to 0.873 x 10(-13) m3/N-s (0.542 micron/min-atm) and 137 kJ/mol (32.8 kcal/mol), respectively, in 1 M DMSO and 0.715 x 10(-13) m3/N-s (0.444 micron/min-atm) and 107 kJ/mol (25.7 kcal/mol), respectively, in 2 M DMSO. The trends in the pooled volume values for Lpg and ELp were very similar, but the overall fit was considered worse than for the individual volume parameters. A unique way of presenting the curve-fitting results supports a clear trend of reduction of both biophysical parameters in the presence of DMSO, and no clear trend in cooling rate dependence of the biophysical parameters. In addition, these results suggest that close proximity of the experimental cell volume data to the equilibrium volume curve may significantly reduce the efficiency of the curve-fitting process.     

A theoretically estimated optimal cooling rate for the cryopreservation of sperm cells from a live-bearing fish, the green swordtail Xiphophorus helleri

Sperm cryopreservation of live-bearing fishes, such as those of the genus Xiphophorus is only beginning to be studied, although these fishes are valuable models for biomedical research and are commercially raised as ornamental fish for use in aquariums. To explore optimization of techniques for sperm cryopreservation of these fishes, this study measured the volumetric shrinkage response during freezing of sperm cells of Xiphophorus helleri by use of a shape-independent differential scanning calorimeter (DSC) technique. Volumetric shrinkage during freezing of X. helleri sperm cell suspensions was obtained in the presence of extracellular ice at a cooling rate of 20 degrees C/min in three different media: (1) Hanks' balanced salt solution (HBSS) without cryoprotective agents (CPAs); (2) HBSS with 14% (v/v) glycerol; and (3) HBSS with 10% (v/v) dimethyl sulfoxide (DMSO). The sperm cell was modeled as a cylinder of 33.3 microm in length and 0.59 microm in diameter with an osmotically inactive cell volume (V(b)) of 0.6V(o), where V(o) is the isotonic or initial cell volume. By fitting a model of water transport to the experimentally determined volumetric shrinkage data, the best-fit membrane permeability parameters (reference membrane permeability to water, L(pg) or L(pg)[cpa] and the activation energy, E(Lp) or E(Lp)[cpa]) of the Xiphophorus helleri sperm cell membrane were determined. The best-fit membrane permeability parameters at 20 degrees C/min in the absence of CPAs were: L(pg)=0.776 x 10(-15)m3/Ns (0.0046 microm/min atm), and E(Lp)=50.1 kJ/mol (11.97 kcal/mol) (R2=0.997). The corresponding parameters in the presence of 14% glycerol were L(pg)[cpa]=1.063 x 10(-15)m3/Ns (0.0063 microm/min atm), and E(Lp)[cpa]=83.81 kJ/mol (20.04 kcal/mol) (R2=0.997). The parameters in the presence of 10% DMSO were L(pg)[cpa]=1.4 x 10(-15)m3/Ns (0.0083 microm/min atm), and E(Lp)[cpa]=90.96 kJ/mol (21.75 kcal/mol) (R2=0.996). Parameters obtained in this study suggested that the optimal rate of cooling for X. helleri sperm cells in the presence of CPAs ranged from 20 to 35 degrees C/min and were in close agreement with recently published, empirically determined optimal cooling rates.     

Kinetics of water loss and the likelihood of intracellular freezing in mouse ova. Influence of the method of calculating the temperature dependence of water permeability

To avoid intracellular freezing and its usually lethal consequences, cells must lose their freezable water before reaching their ice-nucleation temperature. One major factor determining the rate of water loss is the temperature dependence of the water permeability, Lp (hydraulic conductivity). Because of the paucity of water permeability measurements at subzero temperatures, that temperature dependence has usually been extrapolated from above-zero measurements. The extrapolation has often been based on an exponential dependence of Lp on temperature. This paper compares the kinetics of water loss based on that extrapolation with that based on an Arrhenius relation between Lp and temperature, and finds substantial differences below -20 to -25 degrees C. Since the ice-nucleation temperature of mouse ova in the cryoprotectants DMSO and glycerol is usually below -30 degrees C, the Arrhenius form of the water-loss equation was used to compute the extent of supercooling in ova cooled at rates between 1 and 8 degrees C/min and the consequent likelihood of intracellular freezing. The predicted likelihood agrees well with that previously observed. The water-loss equation was also used to compute the volumes of ova as a function of cooling rate and temperature. The computed cell volumes agree qualitatively with previously observed volumes, but differ quantitatively.     

Subfreezing volumetric behavior and stochastic modeling of intracellular ice formation in Drosophila melanogaster embryos

Cryomicroscopic observations were made of the volumetric behavior and kinetics of intracellular ice formation (IIF) in Drosophila melanogaster embryos in a modified cell culture medium (BD.20) or BD.20 + 2 M ethylene glycol. After rapid cooling to a given temperature, transient volumetric contraction of the embryos during the isothermal period was quantified by computerized video image analysis. Fitting these data to the numerical solution of the volume flux equation yielded estimates of the hydraulic permeability coefficient (Lp) for individual embryos at various subfreezing temperatures. Lp approximately followed an Arrhenius relation between -2 and -9 degrees C, with a value of 0.168 microns/(min-atm) extrapolated to 0 degrees C and an apparent activation energy delta E of 38.9 kcal/mol. IIF during an isothermal period occurred at random times whose characteristic temperature range and kinetics were affected by the presence of ethylene glycol. A stochastic process model developed to fit these data indicated the influence of both time-dependent and instantaneous components of IIF, presumed to be the result of seeding and heterogeneous nucleation, respectively. The presence of 2 M ethylene glycol depressed the characteristic temperature of instantaneous IIF by about 12 degrees C and reduced the rate constant for time-dependent IIF. Comparison with observed incidences of IIF yielded an estimate of the supercooling tolerance of 3 to 5 degrees C.     

Suprazero cooling conditions significantly influence subzero permeability parameters of mammalian ovarian tissue

To model the cryobiological responses of cells and tissues, permeability characteristics are often measured at suprazero temperatures and the measured values are used to predict the responses at subzero temperatures. The purpose of the present study was to determine whether the rate of cooling from +25 to +4 degrees C influenced the measured water transport response of ovarian tissue at subzero temperatures in the presence or absence of cryoprotective agents (CPAs). Sections of freshly collected equine ovarian tissue were first cooled either at 40 degrees C/min or at 0.5 degrees C/min from 25 to 4 degrees C, and then cooled to subzero temperatures. A shape-independent differential scanning calorimeter (DSC) technique was used to measure the volumetric shrinkage during freezing of equine ovarian tissue sections. After ice was induced to form in the extracellular fluid within the specimen, the sample was frozen from the phase change temperature to -50 degrees C at 5 degrees C/min. Replicate samples were frozen in isotonic medium alone or in medium containing 0.85 M glycerol or 0.85 M dimethylsulfoxide. The water transport response of ovarian tissue samples cooled at 40 degrees C/min from 25 to 4 degrees C was significantly different (confidence level >95%) from that of tissue samples cooled at 0.5 degrees C/min, whether in the presence or absence of CPAs. We fitted a model of water transport to the experimentally-derived volumetric shrinkage data and determined the best-fit membrane permeability parameters (L(pg) and E(Lp)) of equine ovarian tissue during freezing. Subzero water transport parameters of ovarian tissue samples cooled at 0.5 degrees C/min from 25 to 4 degrees C ranged from: L(pg) = 0.06 to 0.73 microm/min.atm and E(Lp) = 6.1 to 20.5 kcal/mol. The corresponding parameters of samples cooled at 40 degrees C/min from 25 to 4 degrees C ranged from: L(pg) = 0.04 to 0.61 microm/min.atm and E(Lp) = 8.2 to 54.2 kcal/mol. Calculations made of the theoretical response of tissue at subzero temperatures suggest that the optimal cooling rates to cryopreserve ovarian tissue are significantly dependent upon suprazero cooling conditions.