Effect of cryoprotectant concentration on bovine oocyte permeability and comparison of two membrane permeability modelling approaches

The plasma membrane permeability to water and cryoprotectant (CPA) significantly impacts vitrification efficiency of bovine oocytes. Our study was designed to determine the concentration-dependent permeability characteristics for immature (GV) and mature (MII) bovine oocytes in the presence of ethylene glycol (EG) and dimethyl sulphoxide (Me2SO), and to compare two different modeling approaches: the two parameter (2P) model and a nondilute transport model. Membrane permeability parameters were determined by consecutively exposing oocytes to increasing concentrations of Me2SO or EG. Higher water permeability was observed for MII oocytes than GV oocytes in the presence of both Me2SO and EG, and in all cases the water permeability was observed to decrease as CPA concentration increased. At high CPA concentrations, the CPA permeability was similar for Me2SO and EG, for both MII and GV oocytes, but at low concentrations the EG permeability of GV oocytes was substantially higher. Predictions of cell volume changes during CPA addition and removal indicate that accounting for the concentration dependence of permeability only has a modest effect, but there were substantial differences between the 2P model and the nondilute model during CPA removal, which may have implications for design of improved methods for bovine oocyte vitrification.


Results
Permeability parameters estimation. To determine concentration-dependent permeability characteristics for GV and MII bovine oocytes, cells were sequentially exposed to a series of increasing CPA concentrations, as illustrated in Fig. 1. When cells were transferred from an isotonic solution into a hypertonic CPA solution they immediately dehydrated and shrank in response to the higher solution osmolality, and then slowly re-gained iso-osmotic volume as the solute and water permeated the cell to maintain osmotic equilibrium with the extracellular medium. The rate of this shrink-swell response is a measure of the permeability of the cell membrane to the solute and water 3 . As shown in Fig. 1, model predictions are in good agreement with the experimental cell volume measurements.
We first examined the potential differences in permeability values between GV and MII oocytes for exposure to EG and Me 2 SO. The resulting best-fit water and CPA permeability values from the 2P model are shown in Fig. 2 and Table 1. Overall, the water permeability was about two-fold higher for MII oocytes than GV oocytes. This was true for the water permeability in the presence of both Me 2 SO and EG, and the effect was statistically significant (p < 0.05). The CPA permeability was similar for Me 2 SO and EG, for both MII and GV oocytes, with the exception of the EG permeability for GV oocytes, which was substantially higher at low EG concentrations.
We next examined the potential effects of CPA concentration on the permeability values. Results indicate that CPA concentration had a statistically significant effect on the water permeability in all cases (p < 0.05), and, in general, the water permeability decreased by about a factor of two as the CPA concentration increased from 0.3 mol/L to 3.5 mol/L (Table 1).
Only GV oocytes exposed to EG exhibited a continuous decrease in CPA permeability with increasing CPA concentration (Table 1). In this case, the effect of CPA concentration was statistically significant (p = 0.002), and the CPA permeability decreased by more than threefold from 1.31 µm/s at 0.3 mol/L EG to 0.35 µm/s at 3.5 mol/L EG. The effect of CPA concentration was also significant for MII oocytes exposed to Me 2 SO (p = 0.014), but in this case, the CPA permeability did not exhibit a clear trend: the lowest permeability was 0.38 µm/s at 0.68 mol/L and the highest was 0.68 µm/s at 1.55 mol/L.
We also fit the data to the non-dilute model and analyzed the resulting best-fit permeability parameters. As shown in Fig. 3 and Table 2, the trends for the non-dilute model were nearly identical to those observed for the 2P model. Similar to the water permeability from the 2P model, the best-fit water permeability values from the non-dilute model decreased by a more than a factor of two as the CPA concentration increased from 0.3 mol/L to 3.5 mol/L, and the effect of CPA concentration on the water permeability was statistically significant in all cases (p < 0.004). For the non-dilute model, only the CPA permeability parameter for GV oocytes exposed to EG showed a continuous decrease with increasing concentration, which is consistent with the results for the 2P model. However, there was an even more substantial decrease in the CPA permeability parameter for the non-dilute model, which yielded a CPA permeability parameter at 3.5 mol/L that was about six times lower than the permeability parameter at 0.3 mol/L. Only the oocytes at the GV stage exposed to Me 2 SO showed apparent constant permeability to that cryoprotectant across all concentrations. The oocytes in the other categories did exhibit apparent changes to CPA permeability between different concentrations, but the trend was not consistent. www.nature.com/scientificreports/ To account for the effects of CPA concentration on water and CPA permeability, we fit the permeability data to a concentration-dependent model 25 . This model is consistent with a transport mechanism that is limited by binding of CPA to a transporter protein such as an aquaporin. The resulting model fits are shown as lines in Figs. 2 and 3, and the best-fit equations are provided in Tables 1 and 2. The concentration dependent model fits are in reasonable agreement with the permeability data.

Model comparison.
To examine the potential practical implications of different modeling approaches, we simulated the cell volume response of both GV and MII bovine oocytes during CPA addition and removal fol- and their corresponding theoretical fitting curves (solid line) obtained with the 2P model. Exposure to 0.3 mol/L EG starts at t = 0, and the change every 5 min to subsequent increasing EG concentrations is demarcated in the X-axis with a vertical dotted line. (B) An example of the oocyte's morphology at relevant timeframes (at the minimal volume) is shown below each graphic (magnification 20x). Note shrinkage in response to increasing EG concentration. QR code links to a representative video time-lapse for an MII oocyte exposed to increasing EG concentrations. The most common approach for predicting cell volume changes during CPA addition and removal is to use the 2P model with constant water and CPA permeability values. This baseline case is shown by the solid black lines in Figs. 4 and 5. For comparison, the dotted black lines show predictions for the 2P model using concentration dependent permeability values. The two modeling approaches yield nearly identical predictions, and the slight differences are small and not likely to have practical significance. The non-dilute model predictions are also similar to the 2P model baseline case, with the exception of the first step of CPA removal. The non-dilute model exhibits less swelling and faster equilibration during the first step of CPA removal than the 2P model.

Discussion
The development of a reliable method for the cryopreservation of mammalian oocytes is crucial for assisted reproduction in both human and domestic species [31][32][33] . However, in bovine species, the success rates are still limited due to the oocytes' unique structure and sensitivity to cooling 4,34 . One of the most important cryobiological properties that affects the survival of a cell after vitrification is the permeability of the plasma membrane to water and CPA 35 . These permeability values determine the extent of cell volume changes and the time required for CPA equilibration. Therefore, knowledge of these permeability parameters is useful for predicting the likely optimal conditions during CPA addition and removal. Typically cell membrane permeability parameters are determined for exposure to a single CPA concentration 3,6,36 . However, oocytes are exposed to various CPA concentrations during the vitrification process, and previous studies suggest that the water and CPA permeability may be concentration dependent 25 . Therefore, in this study, we examined the potential effects of CPA concentration on the membrane permeability parameters and the implications for bovine oocyte vitrification. Table 3 shows the water and CPA permeability values for bovine oocytes determined in previous studies 3,6,36 . In these studies, the permeability parameters were estimated by measuring cell volume changes after exposure to a single CPA concentration ranging between 1.2 mol/L and 1.8 mol/L. In the current study, we measured the www.nature.com/scientificreports/ permeability for various CPA concentrations by sequentially exposing oocytes to increasing concentrations, but the most appropriate concentration for direct comparison to previous studies is 1.55 mol/L (see Table 1). Overall, our results are consistent with the trends observed in previous studies: the water permeability of MII oocytes was nearly twofold higher than that of GV oocytes, and the CPA permeability was similar for EG and Me 2 SO and for GV and MII oocytes. However, the water permeability values determined in this study were higher than previous studies. The reason for this discrepancy is unclear but may be related to differences in the methods used to determine the permeability values 37,38 .
Our results demonstrate that the water permeability of bovine oocytes decreases as the CPA concentration increases. This trend has been observed previously for various other cell types 25,39,40 , and has been explained in terms of steric hindrance caused by CPA binding to water-transporting channels 41 . Bovine oocytes are known to express aquaporins 36,42 and the observation that water permeability decreases as CPA concentration increases is consistent with such a mechanism. For some cell types, including mouse oocytes, the water permeability has been observed to increase as CPA concentration increases 37,38 . The reason for this trend is unclear, but it does not appear to be relevant to bovine oocytes.
Our results also show that the EG permeability of bovine GV oocytes decreases as EG concentration increases. Bovine oocytes express both aquaporin 3 and aquaporin 7 42 . These aquaglyceroporins have been shown to transport glycerol, ethylene glycol and possibly other CPAs 36 and are postulated to transport these molecules via successive binding to various sites on the aquaporin protein 43,44 . These binding sites can become saturated at high CPA concentrations, leading to slower CPA transport 43,44 . In contrast to glycerol and ethylene glycol, there is evidence that Me 2 SO transport through aquaporin 3 is negligible in mammalian oocytes 35 , which may explain why we did not observe a concentration dependence for the Me 2 SO permeability. We also did not observe a concentration dependence of the EG permeability for MII oocytes, suggesting that changes in aquaporin expression or membrane composition during oocyte development may have impacted the EG transport mechanism 45 .
One potential explanation for the observed effects of CPA concentration on the permeability parameters is the use of the 2P model for making predictions under non-dilute conditions. It has been suggested that the non-dilute transport model (Eqs. 5 and 6) can provide more accurate predictions, particularly at high CPA concentrations 29 . Therefore, we also analyzed the permeability parameters for GV and MII bovine oocytes with the non-dilute transport model 29 . Our results show nearly identical tendencies with both mathematical models: the water permeability decreases as EG or Me 2 SO concentration increases in both GV and MII oocytes, and the EG permeability decreases as EG concentration increases in GV oocytes (see Tables 1 and 2). Elmoazzen et al. 29 argued that when the permeability coefficient P is divided by concentration (as we have done in Table 2), the resulting ratio should not be dependent on CPA concentration. Nevertheless, our results indicate that GV oocytes exposed to EG exhibit a substantial decrease in the value of this ratio as the EG concentration increases. This indicates that the observed decreases in water and CPA permeability with increasing CPA concentration cannot be attributed only to use of the 2P model under non-dilute conditions, suggesting a physical transport process that is CPA concentration dependent.
Cell membrane transport predictions such as those shown in Fig. 5 can be useful for evaluating the potential for damage during CPA addition and removal and for design of less damaging methods. Many cell types have limited tolerance for changes in cell volume, with increasing volume changes causing additional loss of cell Table 2. Bovine oocyte plasma membrane water permeability (L), solute permeability (P) of immature (GV) and mature (MII) oocytes in the presence of increasing CPA (EG or Me 2 SO) concentrations. Permeability parameters obtained from 0.3, 0.68, 1.55 and 3.5 mol/L EG or Me 2 SO data fit with the nondilute model. The equation represents the best-fit model curve for each stage and CPA. Unless indicated otherwise, data are given as the mean ± s.e.m. Different superscript letters indicate significant differences between different molarities within the same CPA and nuclear stage (P < 0.05). Different superscript numbers indicate significant differences in water or solute permeability between GV and MII stage within the same CPA (P < 0.05). * In this case the fitting algorithm was unable to converge because the value of b was so large that the 1 in the denominator became negligible. This results in a constant ratio a/b, which can be satisfied using various combinations of a and b. The values of a and b in Table 2 46 demonstrated that MII spindle damage in bovine oocyte occurs more frequently as the extracellular solution concentrations diverge from isosmotic. Moreover, they estimated that to prevent osmotic damage to the MII spindle with a probability of 90%, it is necessary to use CPA addition and removal procedure which maintains the cells within a volume range of 1.1 to 0.52 times the isotonic volume. Therefore, using the Kuwayama protocol 30 for bovine oocytes is not expected to cause very much osmotic damage to the spindle during CPA loading based on predictions using any of the modeling approaches that we investigated (see Fig. 5). However, during CPA removal, the non-dilute model predicts that GV and MII oocytes will shrink to an equilibrium value much faster than the 2P model predicts, which involves maintaining the cells in a more prolonged state of osmotic stress. Based on the osmotic damage model developed by Mullen et al. 46 , maintenance of the oocytes at a volume of 38% relative to isotonic is expected to cause about 35% of oocytes to experience osmotic damage to the spindle. Exposure to CPA can also cause cell damage due to toxicity. Although toxicity is expected to be less of a problem during CPA removal, it is still important to design removal procedures with toxicity in mind. Benson et al. 47 demonstrated that inducing swelling is beneficial because it decreases the intracellular CPA concentration www.nature.com/scientificreports/ and its associated toxicity. Human oocytes swell to more than their isotonic volume during the first step of the CPA removal process after vitrification 48 . In contrast, bovine oocytes are predicted to exhibit much less swelling (Figs. 4 and 5), especially for the non-dilute model, which may increase CPA toxicity. Overall, the predictions presented in Fig. 5 suggest that modifying the first step of the CPA removal process may reduce damage to bovine oocytes. In particular, we observed that the non-dilute model predicts that the amount of osmotic swelling after vitrification relative to the starting (shrunken) volume is minor compared to the dilute model. To our knowledge, we are the first to demonstrate that the non-dilute model and dilute model predict such different volume responses during CPA removal, highlighting the need for future studies to examine the relative accuracy of the two different modeling approaches. If the non-dilute model predictions turn out to be more accurate than those from the dilute model, this suggests that a very different protocol for CPA removal should be well tolerated (a lot less sucrose would be needed as an osmotic buffer in step 1). By reducing the amount of sucrose in the medium the oocytes would not be expected to shrink as much, keeping them within osmotic tolerance limits. This is expected to cause much less damage than the original protocol 48 .

Conclusions
Historically, cell permeabilities to water and CPA were assumed to be independent of CPA concentration. This is likely due to the predominance of slow cooling methods employed for cellular cryopreservation for the last half century, where a single concentration of CPA was used. In recent years, vitrification has become the preferred method for mammalian oocyte cryopreservation, requiring reconsideration of this assumption. In this study, we have examined the effects of CPA concentration on water and CPA membrane permeability for bovine oocytes. We have shown that water permeability is inversely related to CPA concentration. Furthermore, CPA concentration also affects membrane CPA permeability, with differential effects depending upon the maturation stage of the oocyte and the specific CPA type. Although both the water and CPA permeability change with concentration, accounting for the concentration dependence of permeability only had a slight effect on cell volume predictions during CPA addition and removal, suggesting that the typical assumption that permeability is independent of concentration is reasonable. We have also investigated two modeling approaches, one using dilute solution assumptions, and another that is not restricted to those assumptions. The results suggest that only slight differences exist in the predictions during the CPA loading steps of the procedure, but a greater difference was noted between the two models' predictions during the first stage of CPA removal. This may have important implications for developing improved procedures for the vitrification of mammalian oocytes.

Material and method
Reagents. Unless otherwise specified, all chemicals and reagents were purchased from Sigma Chemical Co Oocyte collection and in vitro maturation. The in vitro maturation (IVM) procedure followed has been described previously 49 . Briefly, ovaries from slaughtered postpubertal heifers (12-18 months old) were transported from a local slaughterhouse to the laboratory in saline solution (0.9% NaCl) at 35-37 °C within 2 h. Immature cumulus-oocyte complexes (COCs) were aspirated from 3 to 8 mm follicles using an 18-gauge needle attached to a 5 mL syringe. COCs with more than three layers of cumulus cells and a homogeneous cytoplasm were selected and washed three times in modified Dulbecco's PBS (PBS supplemented with 36 µg/mL pyruvate, 50 µg/mL gentamicin and 0.5 mg/mL bovine serum albumin). Groups of 40-50 COCs were placed in 500 µL of maturation medium covered with mineral oil in four-well plate and cultured for 24 h at 38.5 °C in a 5% CO 2 humidified air atmosphere. The maturation medium (IVM medium) was tissue culture medium (TCM-199) supplemented with 10% (v/v) fetal bovine serum (FBS), 10 ng/mL epidermal growth factor and 50 µg/mL gentamicin.
Measurement of oocyte volumetric changes following increasing CPA exposure. GV bovine oocytes at time 0 h or MII bovine oocytes after 24 h of IVM were denuded of cumulus cells by gentle pipetting. Only GV showing a normal appearance and metaphase II oocytes with a normal appearance and a visible first polar body were used. An oocyte was placed in a 25 µl drop of holding medium (HM: TCM199-Hepes supplemented with 20% (v/v) FBS) covered with mineral oil, and was held with a holding pipette (outer diameter, 95-120 µm; MPH-MED-30, Origio, Denmark) connected to a micromanipulator on an inverted microscope (Zeiss Axio Vert A1, Germany). An initial photograph was taken of the oocyte in order to calculate the initial volume. The oocyte was then covered with another pipette with a larger inner diameter (600-µm diameter) (G-1 Narishigue, Tokyo, Japan) connected to a different micromanipulator. Then, by sliding the dish the oocyte was exposed consecutively to 25 µl drops containing increasing CPA concentrations at 25 °C, as illustrated in Fig. 6. Each oocyte was exposed consecutively to CPA concentrations of 0.30 mol/L, 0.68 mol/L, 1.55 mol/L, and 3.5 mol/L. These concentrations were chosen because they are expected to generate similar cell volume changes for each change in CPA concentration. In addition, the gradual increase in CPA concentration prevents excessive shrinkage which may result in osmotic damage. For the exposure times at each concentration it was considered the time needed for the oocyte to recover the isotonic cell volume and was set at 5 min for EG and 7 min for www.nature.com/scientificreports/ Me 2 SO. CPA solutions consisted of EG or Me 2 SO diluted in HM. The cell volume response of the oocyte during the experiments was recorded every 3.5 s with a time-lapse video recorder (Zeiss Zen imaging software/Axiocam ERc 5 s). The volume of the oocyte in each image was calculated from the area of the cross section using ImageJ software. Only those immature oocytes (EG: n = 6; Me 2 SO: n = 5) and mature oocytes (EG: n = 5; Me 2 SO: n = 7) that remained spherical on shrinkage were individually analyzed and used for calculation of permeability coefficients, with several oocytes in each group being discarded.

Membrane transport models. Dilute solution model (two-parameter transport formalism). The 2P
model, which has its roots in work by Jacobs and Stewart 27,28 , provides a description of the osmotic responses of cells in solutions with both permeating and nonpermeating solutes. In this formalism, the water flux into the cell over time is expressed as: where V w is the cell water volume, L p is the membrane hydraulic conductivity, A is the area of the plasma membrane, R is the universal gas constant, T is the absolute temperature, and M e and M i are the total external and internal osmolalities, respectively. The rate of CPA transport is given by: where N s is the intracellular moles of CPA, P s is the CPA permeability, M i s and M e s are the intracellular and extracellular CPA molality, respectively. To obtain the intracellular CPA volume, it is necessary to multiply by the partial molar volume of the CPA, υ s , resulting in Estimation of cell membrane permeability parameters. A randomized block design was used for this experiment, with the oocyte being the blocking factor 50 . Each oocyte was used in the entire series of solutions for a single CPA. In other words, an oocyte was used to estimate the permeability of the CPA at each concentration, but for only one of the two CPAs. Volumetric data for each oocyte at each concentration was assessed as described and the first 3 min were fitted to the 2P and nondilute solution models to determine the water permeability (L p and L, respectively) and CPA permeability (P CPA and P, respectively). This was performed for both GV and MII oocytes. The differential equations (Eqs. 1 and 2) for the 2P model; Eqs. (5) and (6) for the nondilute solution model) were solved in Matlab software using the ode45 function, which implements an explicit Runge-Kutta formula 51,52 . To estimate the permeability values, model predictions were fit to the data by minimizing the sum of the error squared in Matlab using the fminsearch function, which implements the Nelder-Mead simplex algorithm 53 . For the first CPA concentration, the initial state was assumed to be the normal physiological state for oocytes in equilibrium with isotonic solution. For subsequent CPA concentrations, the initial state was assumed to be equal to the final state from model predictions for the previous CPA concentration. The concentrations used in these experiments are given in Table 4 in units of molarity, molality and mole fraction. The constants used for model predictions are given in Table 5.
To characterize the effects of CPA concentration, the permeability data was fit to the following concentrationdependent permeability models 25 www.nature.com/scientificreports/ where a and b are best-fit constants. In Eq. (10), we use the ratio of the non-dilute model permeability coefficient P to the CPA molality M s , for the reasons described in Elmoazzen et al. 29 . In particular, Elmoazzen et al. 29 show that the nondilute model reduces to the 2P model under dilute conditions, where the parameter ratio P/M CPA is proportional to the 2P model permeability P CPA .
Prediction of cell volume changes during bovine oocyte vitrification. The following Kuwayama protocol 30 for CPA addition and removal for vitrification of oocytes was used to predict the response of oocytes and compare different modeling approaches: Two steps for loading CPA: Step 1 10 min in 1.6 mol/L EG in TCM199 medium at 22°C.
Three steps for removal CPA: Step 1 1 min in 1.0 mol/L of sucrose in TCM199 medium at 37°C.
We compared volume excursion predictions during CPA addition and removal using four different modeling approaches: 1. Dilute (2P) model with constant water and CPA permeability. 2. Dilute (2P) model with water and CPA permeability changed with CPA concentration according to equations (7) and (8). 3. Nondilute model with constant water and CPA permeability. 4. Nondilute model with water and CPA permeability changed with CPA concentration according to equations (9) and (10).
Predictions for the CPA addition and removal process following these 4 conditions were carried out by numerically solving the model equations in Matlab as described above. To obtain predictions with constant permeability values, we used the permeability to water and EG obtained at 1.55 mol/L. This represents a baseline case that is consistent with the typical approach of estimating permeability for exposure to 1-2 mol/L CPA. To make predictions using concentration dependent permeability values, we used a different approach during CPA (10) P M s = a bM s + 1 www.nature.com/scientificreports/ addition and removal. For CPA addition, we used the external CPA concentration in Eqs. (7)(8)(9)(10) to estimate the permeability values. For CPA removal, we used the intracellular CPA concentration to estimate the permeability values. In order to simulate the cell volume response of the vitrification and warming Kuwayama's protocol, information on the isotonic cell volume of bovine oocytes at different developmental stages is required. The mean cell volumes for GV and MII bovine oocytes in isotonic medium were 8.17 × 10 5 and 7.40 × 10 5 μm 3 , respectively; accordingly, the surface area was 4.22 × 10 4 and 3.95 × 10 4 μm 2 .
Statistical analysis. Statistical tests were performed using the statistical package R, Version R 3.4.4. The normality of data distribution was checked using the Shapiro-Wilk test and homogeneity of variances through the Levene test. When required, data were linearly transformed into √ x, arcsin √ x or log(x) prior to running statistical tests. An one-way analysis of variance (ANOVA) followed by a pairwise comparison test (Tukey-Kramer adjustment) was used to assess differences molarities within the same CPA and nuclear stage and differences in water or solute permeability between GV and MII stage within the same CPA. Significance was set at p ≤ 0.05.