{"paper_id":"0d129c17-e1ee-4c2a-aab8-749c4b856511","body_text":"Water and cryoprotectant permeability of mature equine oocytes: experimental measurements and in silico predictions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Water and cryoprotectant permeability of mature equine oocytes: experimental measurements and in silico predictions Sonia Gago, Tania García-Martínez, Judith Diaz-Muñoz, Mónica Acacio, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9031036/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Vitrification of equine oocytes is an essential practice for advancing assisted reproductive technologies however, its efficiency remains limited due to the lack of stage and species-specific information on membrane permeability parameters. In this study, water ( L p ) and CPA permeability ( P s ) for dimethyl sulfoxide (Me₂SO) and ethylene glycol (EG) were measured in in vitro matured (MII) equine oocytes. Cumulus oocyte complexes were obtained from abattoir ovaries or by ovum pick-up and matured in vitro for 30h at 6% CO 2 . Oocytes followed ideal osmometer behavior principles, with an osmotically inactive volume of 27%. L p increased with temperature from 0.941 ± 0.082 µmmin⁻¹atm⁻¹ at 25°C to 1.462 ± 0.084 µmmin⁻¹atm⁻¹ in Me₂SO, and from 0.889 ± 0.094 to 1.613 ± 0.066 µmmin⁻¹ atm⁻¹ in EG. P s also increased significantly with temperature: P sMe₂SO rose from 0.175 ± 0.024 µm/s to 0.353 ± 0.022 µm/s and P sEG from 0.138 ± 0.020 µm/s to 0.349 ± 0.014 µm/s. Activation energies (E a ) were 6.03 and 8.15 kcal/mol for L p , and 9.60 and 12.69 kcal/mol for P s for Me₂SO and EG, respectively. In silico predictions closely matched in vitro observations. Simulations predicted that oocytes recovered their original volume after 7min 42s at 38.5°C and at 25°C after 17min 8s. This study provides the first stage and species-specific permeability values for MII equine oocytes, supporting improved vitrification modeling. Biological sciences/Biochemistry Biological sciences/Biotechnology Biological sciences/Physiology Vitrification osmotic response membrane transport activation energy assisted reproduction Figures Figure 1 Figure 2 Figure 3 1. INTRODUCTION Cryopreservation of mammalian oocytes and embryos have progressed considerably during the last decades, becoming an essential part of assisted reproductive technologies due to the increasing number of pregnanci es and live births reported in several species 1 , 2 . Among the different cryopreservation techniques, vitrification is currently the most widely adopted method in many domestic species, including the horse. This technique relies on extremely rapid cooling rates combined with high concentrations of cryoprotectant agents (CPAs) to avoid ice crystal formation and the structural damage associated with it 3–5 . In the equine species, the possibility to cryopreserve oocytes offers several practical and genetic advantages that are highly relevant for both research and breeding programs. Cryopreservation allows reproductive decisions to be postponed and it also facilitates the storage of oocytes outside the natural breeding season. In addition, cryopreserved oocytes can be used to create oocyte banks, increasing genetic diversity in endangered breeds and populations with narrow genetic bases. Additionally, the distribution of cryopreserved oocytes and embryos offers a practical alternative to the transportation of live animals, reducing the risk of disease transmission and mitigating carbon emissions 3 . Despite these benefits, the efficiency of equine oocyte cryopreservation remains low compared to other species and outcomes are still inconsistent across laboratories. This situation highlights the urgent need for standardized and optimized vitrification protocols 6 . The success of vitrification depends on multiple interacting factors including the develomental stage of the oocyte, the specific vitrification protocol, CPA the type and concentration and the duration of the exposure to this solutions 7 , 8 . Because these variables influence both osmotic responses and CPA toxicity, empirical approaches often lead to suboptimal results. Therefore, quantitative tools capable of predicting oocyte behavior during CPA loading and removal are essential to move beyond trial‑and‑error strategies. In addition, mathematical approaches can reduce CPA toxicity by optimizing the timing and concentration of CPA exposure 9 . However, the application of these models to improve vitrification of in vitro matured equine oocytes has not yet been fully explored. Mathematical models, such as the two-parameter (2P) formalism, simulate the transport of water and CPAs across the oocyte membrane and predict changes in oocyte volume and intracellular CPA concentrations during exposure to CPA solutions 10 . These models help identify exposure conditions that mantain oocyte volume within osmotic tolerance limits, preventing excessive shrinkage or swelling that may cause irreversible damage 11 . In addition, mathematical approaches can reduce CPA toxicity by optimizing timing and concentration of CPA exposure 9 . However, the application of these models to improve vitrification of equine in vitro matured oocyte has not yet fully explored. A major limitation is that stage‑specific membrane permeability data for equine oocytes is still very limited. Permeability values obtained from other species cannot be directly extrapolated, as oocyte membrane properties vary considerably across species and developmental stages. Even within the same species, immature and mature oocytes may require different CPA loading and removal procedures due to differences in membrane composition 12 – 15 . For this reason, permeability values previously reported for immature equine oocytes cannot be applied to metaphase II (MII) oocytes 16 . These limitations emphasize the need for direct, stage- and species-specific measurements of water and CPA permeability in MII equine oocytes 11 . The aim of the present study was to address this knowledge gap by experimentally determining water ( L p ) and CPA permeability ( P s ) parameters in MII equine oocytes and by characterizing their osmotic behavior under controlled conditions. By providing the first permeability values specific to this developmental stage, our work establishes a foundation for the development of more accurate mathematical models of membrane transport. These data may contribute to refining vitrification protocols, improving CPA exposure strategies, and ultimately enhancing oocyte survival and developmental competence in equine ART. 2. RESULTS 2.1. Equine in vitro matured oocyte characteristics Equine in vitro matured oocytes have a mean cytoplasm oocyte diameter (without zona pellucida) of 106.1 ± 0.5 µm, corresponding to an average radius of 53.0 ± 0.3 µm (mean ± SEM). Based on these measurements, the initial surface area (A o ) was calculated to be 35,430 ± 350 µm², and the initial volume (V o ) was 629,400 ± 9,200 µm³. The A o /V o ratio exhibited a mean value of 0.057 ± 0.000 µm − 1 , indicating minimal variability across the samples (see Table 1 ). These geometric parameters provide a precise baseline characterization of the oocyte size and structural properties at the onset of the experiments. Table 1 Measurements of diameter, radius, surface area, and volume of in vitro matured equine oocytes. Mean d (µm) r (µm) Ao (µm 2 ) Vo (µm 3 ) A o /V o (µm − 1 ) 106.066 53.033 35429.213 629363.118 0.057 SEM 0.519 0.259 346.691 9245.445 0.000 d: Diameter (𝜇m); r: Radius (µm); Ao: Surface área (𝜇m 2 ); Vo: Volume (µm 3 ); Ao/Vo ratio (µm −1 ). Values are given as Mean ± SEM. 2.2. Boyle-van ′ t Hoff, osmotically inactive volume of in vitro matured equine oocytes We tested whether in vitro matured equine oocytes behaved as ideal osmometers, which would show a linear Boyle–van ’t Hoff relationship between cell volume and the inverse of the medium osmolality. Oocyte volumes were measured under isotonic conditions (HM; 292 mOsm kg − 1 ) and in a series of hypo- and hypertonic solutions (ranging between 234 and1903 mOsm kg − 1 ). After 10 min of equilibration at 38.5°C in the different solutions, volumes were recorded and normalized to the original isotonic value. Thirty-five oocytes with a spherical morphology (≥ 5 per condition) were analyzed, and normalized volumes were plotted against the reciprocal of the solution osmolality. Our results showed a strong goodness of fit (R 2 = 0.9483), as MII equine oocytes conformed to the predicted behavior, acting as ideal osmometers across the tested osmolality range (234–1903 mOsm) (see Fig. 1 ). The osmotically inactive volume (V b ) was calculated as 27% of the isotonic cell volume for MII equine oocytes. 2.3. Modeling membrane permeability of equine MII oocytes 2.3.1. Membrane permeability parameters Water permeability ( L p ) and solute permeability ( P s ) of MII equine oocytes in the presence of 1.55M EG or Me 2 SO at 25°C or 38.5°C are described in Table 2 . Overall, L p values varied significantly between the temperatures for each CPA ( L p Me2SO : 0.941 ± 0.082 at 25°C and 1.462 ± 0.084 at 38.5°C (p = 0.0012) ; L p EG : 0.889 ± 0.094 at 25°C and 1.613 ± 0.066 at 38.5°C ( P < 0.0001)). P s also increased significantly when the temperature increased from 25°C to 38.5°C ( P s Me2SO : 0.175 ± 0.024 at 25°C and 0.353 ± 0.022 at 38.5°C ( P < 0.0001); P s EG : 0.138 ± 0.020 at 25°C and 0.349 ± 0.014 at 38.5°C ( P < 0.0001). In contrast, no differences in water permeability nor solute permeability were detected between the CPAs at the same temperature ( P > 0.05). Table 2 Water permeability ( L p ) and solute permeability ( P s ) of equine in vitro matured oocytes exposed to 1.55 M Me 2 SO or 1.55M EG at 25°C or 38.5°C. CPA Temperature Membrane permeability parameters L p (µm atm − 1 min − 1 ) P s (µm sec − 1 ) Me 2 SO 25°C 0.941 ± 0.082 a,1 0.175 ± 0.024 a, 1 38.5°C 1.462 ± 0.084 b,2 0.353 ± 0.022 b, 2 EG 25°C 0.889 ± 0.094 a, 1 0.138 ± 0.020 a, 1 38.5°C 1.613 ± 0.066 b,2 0.349 ± 0.014 b, 2 Data are given as mean ± SEM. a,b Different superscript letters indicate significant differences between temperatures for the same CPA ( P < 0.05). 1,2 Different superscript numbers indicate significant differences in L p or P s between CPAs for the same temperature ( P < 0.05). Me 2 SO, dimethyl sulfoxide; EG, ethylene glycol. 2.3.2. Activation Energy of Membrane Permeability in in vitro Matured Equine Oocytes Activation energy (E a ) of L p and P s was estimated from mean permeability values measured at 25°C and 38.5°C. As individual oocytes were not measured at both temperatures, E a calculations reflect the average temperature sensitivity across the cohort of MII oocytes. E a L p values were 6.03 kcal mol − 1 for Me 2 SO and 8.15 kcal mol − 1 for EG (see Table 3 ). In contrast, E a P s values of 9.60 kcal mol − 1 for Me 2 SO and 12.69 kcal mol − 1 for EG. Table 3 Activation energy of water (E a L p ) and cryoprotective agents (E a P s ) membrane permeability. CPA E a L p (kcal mol − 1 ) E a P s (kcal mol − 1 ) Me 2 SO 6.03 9.60 EG 8.15 12.69 2.3.3. In silico predictions versus in vitro observations For our comparison of the effects of temperature on cell osmotic response, MII equine oocytes were exposed to an ES containing 7.5% Me₂SO and 7.5% EG at two temperatures (25°C and 38.5°C). Because these CPAs are permeable, water moves in response to the osmotic gradient while CPAs enter the cell along their concentration gradient, causing changes in cell volume. Permeability parameters previously determined using single-CPA solutions (either Me₂SO or EG) enabled us to predict oocyte responses during exposure to the ES. Model predictions of relative cell volume over time for oocytes exposed to ES at 25°C or 38.5°C are shown in Fig. 2 A and 2 B. Our model predictions show that oocytes exposed to ES shrink to a minimum of 46% of their isotonic volume after 8 s of exposure at 38.5°C whereas at 25°C the oocytes are predicted to shrink to a mínimum of 44% within 15s. Moreover, simulations predict that oocytes at 38.5°C swell back to their isotonic volume faster than at 25°C, recovering their original volume after 7min 43s or 17min 8s, respectively. The in vitro oocyte osmotic response of equine MII oocytes exposed to ES showed that they recover their initial volume at 6 min 31 s at 38.5°C and 19min 8s at 25°C for OPU derived oocytes and 9min 6s at 38.5°C and 18min 53s at 25°C for slaughterhouse oocytes. Despite these differences, both values of area under the curve (AUC) from slaughterhouse and OPU derived oocytes did not present any statistical differences with the simulation group. As expected, oocytes in all groups initially decreased in volume due to water efflux. Following this shrinkage phase, the cells began to swell as CPA entered across the membrane, driven by the concentration gradient. These relative volume changes were temperature dependent and closely aligned with the model predictions, as no significant differences in AUC values were observed between groups ( P > 0.05). Overall, these low RMSE values across temperatures and oocyte sources indicate strong agreement between the in silico predictions and the observed volume responses. These values are described in Table 4 . Table 4 Root mean square error (RMSE) for predicted versus observed oocyte volume changes in slaughterhouse-derived and ovum pick-up (OPU)-derived oocytes at 25°C and 38.5°C. See corresponding columns in the table. In silico 25°C – Slaughterhouse In silico 25°C - OPU In silico 38.5°C - Slaughterhouse In silico 38.5°C - OPU RMSE 0.083 0.047 0.092 0.071 3. DISCUSSION This study provides a quantitative characterization of the osmotic behavior and membrane transport properties of in vitro matured equine oocytes, offering new information that is essential for improving vitrification strategies in this species. The measurements obtained here confirm that equine MII oocytes belong to the group of relatively large mammalian gametes, with a mean cytoplasmic diameter of 106.66 ± 0.52 µm. This value is consistent with previously reported measurements in equine GV oocytes, which are around 105 µm in diameter. This similarity between GV and MII oocytes suggests that cytoplasmic size remains relatively stable during maturation in equine species 16 . When compared with other mammals, equine oocytes are larger than mouse GV oocytes (70–80 µm) 17 , similar to human MII oocytes (103–119 µm) 18 , and slightly smaller than porcine GV oocytes (around 120 µm) 17 . These interspecies differences are relevant because oocyte size directly influences osmotic behavior, CPA permeation kinetics, and overall response to cryopreservation. The osmotically inactive volume (V b ) of MII equine oocytes was estimated at 27% of the isotonic volume, a value that falls within the range reported for other mammalian species. For example, bovine oocytes show a V b of approximtelly 26.1% 19 while rabbit, human, and mouse oocytes exhibit values around 20%, 19%, and 21%, respectively 20 – 22 . These differences likely reflect species-specific variations in cellular composition, organelle density, and membrane characteristics that define the fraction of volume resistant to osmotic perturbation. Interestingly, the equine V b value obtained in our study is also close to the 31% previosly reported for equine GV oocytes, suggesting that the osmotically inactive fraction does not undergo major changes during maturation under the experimental conditions used 16 . This stability supports the use of a single V b parameter in mathematical models for equine oocytes, although permeability parameters must still be determined specifically for each developmental stage. Hydraulic ( L p ) and solute ( P s ) permeabilities of oocytes are critical determinants of oocyte response during CPA loading and removal, and they are known to vary widely between species, temperatures, and maturarion stages (GV vs MII) 11 . For equine GV oocytes at 22°C, previously reported L p values are around 0.6284 µm min⁻¹ atm⁻¹ when exposed to 1.5M EG or 0.57 µm min⁻¹ atm⁻¹ when exposed to 1.5 M Me₂SO, while P s for ethylene glycol (P sEG ) and dimethyl sulfoxide (P sMe2SO ) are 0.3394 µm s⁻¹ 16 and 0.5575 µm s⁻¹ 23 , respectively. In our study, MII oocytes at 25°C showed a modest increase in L p (0.889 ± 0.094 µm min⁻¹ atm⁻¹ for EG and 0.941 ± 0.082 µm min⁻¹ atm⁻¹ for Me2SO), whereas P sEG and P sMe2SO were considerable lower to 0.138 ± 0.020 µm s⁻¹ and 0.175 ± 0.024 µm s⁻¹, respectively). This pattern, relatively preserved or slightly increased water permeability accompanied by reduced CPA permeability, is consistent with observations in bovine and rat oocytes, where maturation from the GV to the MII stage is associated with a decline in P s values 13 , 24 . Such changes are generally attributed to maturation-associated remodeling of the plasma membrane, including modification in lipid composition, cholesterol content, and the distribution or regulation of aquaporins and other channels 25 , 26 . Functionally, a lower P s in MII oocytes may help limit the rate of CPA entry, potentially reducing acute toxicity, but it also implies that longer or more concentrated CPA exposures may be required to achieve adequate intracellular CPA levels. Temperature is another major factor influencing membrane permeability. Although no previous measurements of L p or P s values at 38.5°C have been reported for equine, studies in other species have shown that CPA permeation is markely influenced by temperature, with higher temperatures resulting in faster solute permeation 27 , 28 . Our results confirm this trend: increasing the temperature from 25°C to 38.5°C led to a statistically significant increase in both P sEG and P sMe2SO values. These findings indicate that both oocyte maturation and temperature induce structural and functional modifications of the plasma membrane that differentially affect water and cryoprotectant transport. Activation energies (E a ) provide additional insight into the temperature sensitivity of membrane transport. In our study, the E a values calculated for MII equine oocytes were 6.03 kcal mol⁻¹ for L p and 9.60 kcal mol⁻¹ for P s in Me₂SO, and 8.15 kcal mol⁻¹ for L p and 12.69 kcal mol⁻¹ for P s in EG. These values are lower than those previously reported for equine GV oocytes 16 , where E a L p reached 11.19 kcal mol⁻¹ and E a P s for EG was 15.81 kcal mol⁻¹, suggesting that the membranes of mature oocytes may require less energy to increase permeability with temperature. Although individual oocytes were not measured at both temperatures, a limitation that should be addressed in future studies, the E a values obtained here still offer a useful approximation of the temperature dependence of water and CPA transport in equine MII oocytes. The in silico predictions obtained using the two-parameter (2P) model, parameterized with our experimentally derived L p and P s values, showed strong agreement with the in vitro volume changes of equine MII oocytes exposed to an equilibration solution (ES) containing 7.5% Me₂SO and 7.5% EG. At both 25°C and 38.5°C, the model accurately reproduced the characteristic biphasic osmotic response: an initial rapid shrinkage due to water efflux, followed by a gradual swelling as CPAs permeate the membrane and the intracellular osmolality increases. Predicted recovery times to isotonic volume (approximately 7 min 43 s at 38.5°C and 17 min 8 s at 25°C) were close to the experimental observations for both slaughterhouse- and ovum pick-up (OPU)-derived oocytes, and the area under the curve values did not differ significantly between simulations and empirical data. The low root mean square error (RMSE) values across conditions further support the suitability of the 2P model for capturing the osmotic behavior of MII equine oocytes under the tested CPA conditions. These findings are consistent with reports in bovine oocytes, where 2P-based models have successfully described volumetric responses and supported the design of CPA loading schemes 10 . Our study also provides insight into the influence of oocyte origin on osmotic behavior. Although slaughterhouse and OPU derived MII oocytes were obtained under different conditions and may represent distinct physiological backgrounds, their volume responses to the equilibration solution were similar and closely matched model predictions, indicating that the main biophysical parameters governing water and CPA transport are comparable between sources and supporting the use of abattoir-derived oocytes as a practical model for method development. Several limitations should nevertheless be considered such as technical factors, including potential mechanical effects associated with pipetting 16 , that may have contributed to minor deviations between predicted and observed volume trajectories. Even so, the close agreement between experimental data and simulations across temperatures and oocyte sources supports the robustness of the permeability parameters obtained in our study and their utility for guiding the optimization of vitrification protocols 11 . Further studies are now needed to validate these permeability data and in silico predictions, particularly by assessing developmental competence after vitrification using model‑guided protocols. The high concordance between experimental and simulated volume profiles has several important implications for equine oocyte vitrification. First, it demonstrates that stage‑ and species‑specific permeability parameters can be reliably integrated into mathematical models to predict water and CPA fluxes under clinically relevant conditions. Similar modelling approaches have successfully guided CPA loading strategies in human oocytes 29 and have been shown to improve the prediction of osmotic responses in bovine oocytes 27 . In the equine species, previous studies on GV‑stage oocytes have already highlighted the value of combining experimental permeability measurements with computational simulations to optimize CPA exposure and reduce osmotic injury 16 , 23 . Our results extend this modelling framework to MII oocytes, showing that accurate permeability parameters allow the rational design of CPA exposure protocols that maintain volume excursions within osmotic tolerance limits and minimize mechanical and biochemical stress. Second, the temperature-dependent differences observed in both L p / P s and the resulting volume dynamics suggest that performing equilibration at 38.5°C may shorten the time oocytes spend outside their physiological volume range compared with 25°C. Similar temperature-dependent increases in water and CPA fluxes have already reported in other species 27 , 30 , indicating that higher temperatures can facilitate faster osmotic equilibration. This reduction in the duration of extreme shrinkage or swelling could be advantageous for preserving membrane integrity and cytoskeletal organization 27 . However, studies in marine oocytes also highlight that elevated temperatures may increase CPA toxicity and metabolic activity 30 , meaning that the optimal balance between osmotic safety and toxicity risk must still be empirically determined for equine oocytes. CONCLUSIONS In summary, this study provides the first detailed characterization of water ( L p ) and cryoprotectant ( P s ) permeability parameters, activation energies (E a ), and osmotic behavior of in vitro matured equine oocytes, and demonstrates that these data can be effectively incorporated into a two-parameter transport model. Our results show that equine oocytes behave as ideal osmometers with an osmotically inactive volume of 27%, exhibit maturation and temperature dependent changes in water and solute permeabilities, and display volume responses to equilibration solutions that are accurately predicted by in silico simulations. These findings underscore the need for stage and species specific biophysical data when designing vitrification protocols, as extrapolation from other species or developmental stages may lead to suboptimal CPA exposure conditions. By providing experimentally validated permeability parameters for equine MII oocytes, our work establishes a quantitative basis for rational, model-guided optimization of CPA loading and unloading schemes, with the ultimate goal of improving oocyte survival, preserving cellular function, and enhancing developmental competence in equine assisted reproduction. 4. METHODOLOGY 4.1. Chemicals and suppliers All chemicals and reagents employed in this study were obtained from Sigma Chemical Co. (St. Louis, MO, USA), unless otherwise stated. 4.2. Oocyte collection and in vitro maturation (IVM) Ovaries from mares were collected at two different local abattoirs (Escorxador Sabadell, Sabadell, Spain; and Viñals Soler, Argentona, Spain) and were transported to the laboratory in pre-warmed water (35–37°C) within 4–6 h. Upon arrival at the laboratory, ovaries were cleaned with saline solution (0.9% sodium chloride (NaCl; 35–37°C). Cumulus–oocyte complexes (COCs) were recovered from each follicle by initially incising the follicular wall with a scalpel to allow the release of follicular fluid. Subsequently, the internal walls of the follicle were carefully scraped using a sharp-edged curette to detach any remaining COCs. All contents were collected into tubes containing EquiPlus medium (Minitube, ref. 19982/2281). To maximize recovery, each follicle was additionally rinsed twice with EquiPlus medium and COCs were then collected under a stereomicroscope. Recovered COCs were kept overnight (approximately 17–18 h) at room temperature in holding medium (HM) consisting of TCM-199 Hanks–HEPES, TCM-199 Earle’s, fetal bovine serum (FBS), sodium pyruvate and gentamicin to facilitate a better synchronization of the experimental set-up. The following day, oocytes were transferred to maturation medium containing TCM-199 Earle’s, FBS, epidermal growth factor (EGF), and follicle-stimulating hormone (FSH), placed in four-well plates, and cultured for an additional 30 h at 38.5°C in a 6% CO₂ atmosphere. 4.3. Transvaginal Ultrasound-Guided Follicular Aspiration for Oocyte Retrieval OPU sesions were performed in 2 mares aged 10 and 15 years. Mares were evaluated by routine transrectal ultrasound scanning to find a good population of follicles between 1 and 2 cm in diameter for aspiration. Before follicular aspiration, preventive antibiotic therapy was administrated, as well as sedation, anesthesia, and antispasmodic treatment. For this purpose it was administered gentamycin sulfate (Genta equine®, 6.6 mg/kg, iv, Dechra Veterinary Products, Aulendorf, Germany), flunixin meglumine (Flunixin inyectable ®, 1.1 mg/kg, iv, Norbrook, Newry, UK), detomidine hydrochloride (Domidine® 0.02 mg/kg, iv, Dechra Veterinary Products, Aulendorf, Germany), butorphanol tartrate (Torbugesic® 0.03 mg/kg, iv, Pfizer, New York, USA) and butylscopolamine (Buscapina®, 0.12 mg/kg, iv, Boehringer Ingelheim, Ingelheim am Rhein, Germany). The vulva and perineum were washed three times with a neutral soap, and the bladder was emptied using a urinary catheter. OPU was performed by transvaginal ultrasound guided follicle aspiration/flushing using a 12-gauge double-lumen needle attached to a double vacuum pump (Minitüb, Tiefenbach, Germany) and a sectorial probe (SE3123, MyLabGamma, Esaote®, Genova, Italy). All follicles between 1 to 2 cm were punctured and washed with flushing medium (Equiflush®, Minitüb, Tiefenbach, Germany) supplemented with 1000 UI/L of sodium heparin (Heparina sodica®, ROVI, Madrid, Spain). Recovered fluid was collected into pre-warmed 250 mL tubes (37°C, REF: 23362/0251), filtered through a sterile 70 µm embryo filter (EmCon®, IMV Technologies, France), and the contents were examined in a 120 mm Petri dish to identify COCs under a stereomicroscope. A total of 22 oocytes were recovered from three OPU sessions (3 replicates). The protocol was approved by the Ethics Committee on Animal and Human Experimentation (CEEAH) of the Universitat Autonoma de Barcelona (CEEAH 1424) and all experiments were performed in accordance with relevant guidelines and regulations. Animals were maintained in paddocks, fed with grain, forage, straw, and hay, with ad libitum access to water, and housed at the Equine Reproduction Service of the Universitat Autònoma de Barcelona (Bellaterra, Cerdanyola del Vallès, Spain), which operates under strict health and animal welfare standards. 4.4. Measurement of oocyte volumetric changes After 30 hours of in vitro maturation (IVM), oocytes were denuded of cumulus cells with the help of 10 mg mL − 1 hyaluronidase (HYA). Only matured oocytes showing a normal appearance and a visible first polar body were used for subsequent experiments. An oocyte was placed in a 25 µL drop of HM covered with mineral oil, and held with a holding pipette (outer diameter, 100 µm) connected to a micromanipulator on an inverted microscope (Zeiss Axio Vert A1, Germany). An initial photograph was taken to calculate the initial volume of the oocyte using a time-lapse video recorder (Zeiss Zen imaging software/Axiocam ERc 5s). The oocyte was then covered with another pipette of larger inner diameter (600 µm) connected to a different micromanipulator. By sliding the dish, the oocyte was introduced into a 25 µL drop containing different treatment solutions and left to equilibrate for 20 or 10 min at 25°C or 38.5°C respectively (see Fig. 3 ). Images were taken every 5 s using a time-lapse video recorder with a camera mounted on an inverted light microscope. Their cross-sectional areas were quantified with the image analysis software ImageJ v1.54 (National Institutes of Health, Bethesda, MD, USA) as described in García-Martínez et al. 27 . From the measured area, the oocyte radius (r) was determined, which was then used to calculate the cell volume (V o ) and surface area (A o ). Oocytes that failed to exhibit the expected shrinkage or swelling behavior were classified as damaged and were excluded from the analysis. 4.5. Estimation of the Osmotically Inactive Volume Using Boyle–van ’t Hoff Analysis For the correct application of cell membrane transport models, it was assumed that oocytes behave as ideal osmometers. Accordingly, they were expected to follow the Boyle–van ’t Hoff relationship, displaying a linear correlation between cell volume and the inverse of the medium osmolality 31 . To verify that in vitro matured equine oocytes followed this behavior, their osmotic response was assessed by measuring volume changes in both hypotonic and hypertonic solutions. We used holding medium (HM; 80% TCM-199 + 20% FBS) as an isotonic condition and the osmolality of the solution was verified to be 292 ± 0.003 mOsm kg − 1 (mean ± standard error of mean (SEM)) using a cryoscopic osmometer (Osmomat 030, Gonotec). The osmolality of the treatment solutions was then adjusted by adding calculated amounts of Milli-Q water (hypotonic) or sucrose (hypertonic), resulting in final solution osmolalities ranging from 234 ± 0.001 mOsm/kg to 1903 ± 0.013 mOsm kg − 1 . For each oocyte, an initial volume measurement in HM was obtained as a control prior to exposure to the different media. Subsequently, the oocyte was transferred into the treatment solutions and left to equilibrate for 10 min at 38.5°C before recording the volume again. A total of 35 MII equine oocytes that remained close to spherical in shape were individually analyzed (with a minimum of five oocytes per condition). Cell volume measurements in each solution were first normalized to the reference volume under isotonic conditions. These normalized values were then plotted as a function of the reciprocal of the osmolality of the treatment solutions. 4.6. Membrane permeability parameters A two-parameter transport model was used to describe how water and permeating solutes move across the cell membrane over time, using two coupled differential equations and assuming no interaction between water and the permeating solutes within the membrane. This model allowed us to determine the permeability of equine IVM oocytes to water ( L p ) and to CPAs ( P s ). Water flux into the cell over time is expressed as (1): $$\\left(1\\right)\\frac{d{V}_{w}}{dt}=-{L}_{p}ART\\left(Me-Mi\\right)$$ where V w is the cell water volume, L p is the membrane permeability to water (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 the CPA transport is given by (2): $$\\left(2\\right)\\frac{d{N}_{s}}{dt}={P}_{s}A\\left({M}_{s}^{e}-{M}_{s}^{i}\\right)$$ where N s is the intracellular moles of CPA, P s is CPA permeability and M i s −1 and M e s −1 are the intracellular and extracellular CPA molalities, respectively. In order to determine L p and P s for each CPA and temperature the image analysis data obtained from each oocyte was fitted to the 2P model as previously described by García Martínez et al. 27 . The equations for water and CPA transport were solved numerically using the ode15s function in Matlab software. Model predictions were fitted to the data to estimate permeabilities by minimizing the sum error squared in Matlab using the fminsearch function, which implements the Nelder-mead simplex algorithm 32 . An average of eight oocytes per condition that remained close to spherical in shape were used. Parameters are described in Table 5 . Table 5 Thermodynamic and Volume Parameters Used for Modeling Water and CPA Transport Description Values Symbol Universal gas constant 8.314 m 3 PA K − 1 mol − 1 R Absolute temperature 298 K (25°C) or 311 K (38.5°C) T Molar volume of water 18.02*10 12 µM mol − 1 V w Molar volume of CPA 55.8*10 − 6 m 3 mol − 1 EG 33 V s1 71.3*10 − 6 m 3 mol − 1 Me 2 SO 33 V s2 4.7. Mathematical in silico predictions To predict cell volume response and intracellular CPA concentration when MII equine oocytes were exposed to equilibration solution (ES; HM supplemented with 7.5% (v/v) Me 2 SO and 7.5% (v/v) EG) two solute transport equations were defined, one for Me 2 SO and another for EG. For this purpose, a system of three ordinary differential equations was solved for the three variables (V w , 𝑁 Me2SO and 𝑁 EG ) in Matlab software using the ode15s function, which implements an explicit Runge-Kutta formula 34 , 35 . The rate of Me 2 SO transport is given by (3): (3) \\(\\frac{dNM{e}_{2}SO}{dt}=PM{e}_{2}SOA\\left({M}_{M{e}_{2}SO}^{e}-{M}_{M{e}_{2}SO}^{i}\\right)\\) And the rate of EG transport is given by (4): (4) \\(\\frac{dNEG}{dt}=PEGA\\left({M}_{EG}^{e}-{M}_{EG}^{i}\\right)\\) In silico predictions for the ES exposure were performed at 25°C or 38.5°C using water and solute permeability values estimated in the experiments described above. Water permeability was assumed to be the mean L p value at the given temperature, obtained by averaging the individual measurements for MII oocytes exposed to 1.55 M Me 2 SO or 1.55 M EG. 4.8. Determination of activation Energy of Membrane Permeability in in vitro Matured Equine Oocytes The permeability of the plasma membrane to water ( L p ) and cryoprotective agents ( P s ) in MII equine oocytes was measured at two temperatures; 25°C and 38.5°C. As the same oocytes were not measured at both temperatures, activation energies (E a ) were estimated using the mean L p and P s values for each temperature. Experimental values were converted to Kelvin and linearized using the Arrhenius Eq. (5) 36 : $$\\left(5\\right)\\text{ln}\\left(k\\right)=\\text{ln}\\left(k0\\right)-\\frac{Ea}{RT}$$ where k represents L p or P s , R is the gas constant (1.987 cal·mol⁻¹·K⁻¹), E a is the activation energy, and k 0 is the pre-exponential factor. E a was calculated from the slope of ln(k) versus 1/T, and k 0 from the intercept. Although individual oocyte measurements at both temperatures were not available, the resulting E a values reflect the average temperature sensitivity of membrane water and cryoprotectant transport. All calculations were performed in Microsoft Excel. 4.9. In vitro osmotic behaviour following ES exposure at 25°C and 38.5°C To assess the accuracy of the model predictions, the in silico values generated by the theoretical models were compared with in vitro measurements of the osmotic response of equine MII oocytes exposed to the equilibration solution (ES; 7.5% (v/v) EG and 7.5% (v/v) Me₂SO in TCM-199 HEPES) at the designated temperatures (25°C or 38.5°C). For each temperature, an average of 10 MII equine oocytes, each maintaining an approximately spherical shape, were individually analyzed. To further evaluate whether oocytes recovered via OPU exhibit similar behavior, an additional experimental group was included. 4.10. Statistical analysis Statistical analyses were performed using GraphPad Prism (version 9.3.1). To determine the osmotic inactive volume of MII equine oocytes, data were fitted to the Boyle–van’t Hoff equation. A linear least squares approach was applied to fit the data, and linear regression was used to extrapolate the relationship, allowing estimation of the cell volume at infinite osmolality (V b ). Permeability parameters ( L p and P s ) were assessed using the Shapiro–Wilk test to evaluate normality, followed by a one-way ANOVA with multiple comparisons to assess differences between CPAs and temperatures. To evaluate the agreement between model predictions and in vitro measurements as an integrative descriptor of the overall volumetric response the area under the curve (AUC) was calculated for each oocyte 37 , and either a Kruskal–Wallis test or an ordinary one-way ANOVA with multiple comparisons was performed depending on data normality. In addition, the root mean squared error (RMSE) was calculated. A significance level of P < 0.05 was considered statistically significant for all analyses. Declarations Competing interests The author(s) declare no competing interests. Funding This study was supported by research project PID2024-160962OB-I00 (funded by MCIN/AEI/ 10.13039/501100011033/ ) and Project 2021 SGR 00900 (Generalitat de Catalunya) to TM. Mrs. Gago is funded by a predoctoral grant from Generalitat de Catalunya (DI00002), and Ms. Díaz-Muñoz holds a predoctoral scholarship PRE2021-098675 (funded by MCIN/AEI/ 10.13039/501100011033/ ). Author Contribution SG: Writing original draft, Visualization, Validation, Investigation, Formal analysis, Data curation. TGM: Visualization, Supervision, Validation. JDM: Investigation. MA: Investigation. JC: Investigation. JM: Investigation. AZH: Investigation, Supervision. NCB: Investigation, Supervision, Project administration, Funding. TM: Writing review & editing, Validation, Supervision, Project administration, Funding, Investigation, Data curation. Acknowledgement We thank the staff at Escorxador Sabadell S.L. and Argentona (SVO. Viñals Soler) slaughterhouses for kindly providing access to ovarian samples essential for this study. We thank BioRender.com for providing the platform used to create the Figure 1. Data Availability All data supporting the findings of this study are available within the paper References Bosch, E., De Vos, M. & Humaidan, P. The Future of Cryopreservation in Assisted Reproductive Technologies. Front. Endocrinol. 11 , 67 (2020). Parmegiani, L. et al. Blastocyst formation, pregnancy, and birth derived from human oocytes cryopreserved for 5 years. Fertility and Sterility 90, 2014.e7-2014.e10 (2008). De Coster, T., Velez, D. A., Van Soom, A., Woelders, H. & Smits, K. Cryopreservation of equine oocytes: looking into the crystal ball. Reprod. Fertil. Dev. 32 , 453 (2020). Son, W. Y. & Tan, S. L. Comparison between slow freezing and vitrification for human embryos. Expert Rev. Med. Dev. 6 , 1–7 (2009). Maclellan, L. J. et al. Pregnancies from vitrified equine oocytes collected from super-stimulated and non-stimulated mares. Theriogenology 58 , 911–919 (2002). Angel-Velez, D. et al. New Alternative Mixtures of Cryoprotectants for Equine Immature Oocyte Vitrification. Animals 11 , 3077 (2021). Angel, D. et al. Embryo development after vitrification of immature and in vitro-matured equine oocytes. Cryobiology 92 , 251–254 (2020). Du, M. et al. Optimization of vitrification methods for equine oocytes. Tissue Cell. 91 , 102632 (2024). Benson, J. D., Kearsley, A. J. & Higgins, A. Z. Mathematical optimization of procedures for cryoprotectant equilibration using a toxicity cost function. Cryobiology 64 , 144–151 (2012). García-Martínez, T. et al. Effect of cryoprotectant concentration on bovine oocyte permeability and comparison of two membrane permeability modelling approaches. Sci. Rep. 11 , 15387 (2021). Caliskan, S., Liu, D., Oldenhof, H., Sieme, H. & Wolkers, W. F. Use of membrane transport models to design cryopreservation procedures for oocytes. Anim. Reprod. Sci. 267 , 107536 (2024). Edashige, K. Permeability of the plasma membrane to water and cryoprotectants in mammalian oocytes and embryos: Its relevance to vitrification. Reprod. Med. Biol. 16 , 36–39 (2017). Agca, Y., Liu, J., Peter, A. T., Critser, E. S. & Critser, J. K. Effect of developmental stage on bovine oocyte plasma membrane water and cryoprotectant permeability characteristics. Mol. Reprod. Dev. 49 , 408–415 (1998). Fahy, G. M., Wowk, B., Wu, J. & Paynter, S. Improved vitrification solutions based on the predictability of vitrification solution toxicity. Cryobiology 48 , 22–35 (2004). Gandhi, G., Kuwayama, M., Kagalwala, S., Pangerkar, P. & Appendix, A. Cryotech® Vitrification Thawing. in Cryopreservation of Mammalian Gametes and Embryos (eds Nagy, Z. P., Varghese, A. C. & Agarwal, A.) vol. 1568 281–295 (Springer New York, New York, NY, (2017). Içli, S. et al. Loading equine oocytes with cryoprotective agents captured with a finite element method model. Sci. Rep. 11 , 19812 (2021). Wang, Z. W., Zhang, G. L., Schatten, H., Carroll, J. & Sun, Q. Y. Cytoplasmic Determination of Meiotic Spindle Size Revealed by a Unique Inter-Species Germinal Vesicle Transfer Model. Sci. Rep. 6 , 19827 (2016). Kitasaka, H., Konuma, Y., Tokoro, M., Fukunaga, N. & Asada, Y. Oocyte cytoplasmic diameter of ≥ 130 µm can be used to determine human giant oocytes. F&S Sci. 3 , 10–17 (2022). Wang, X., Al Naib, A., Sun, D. W. & Lonergan, P. Membrane permeability characteristics of bovine oocytes and development of a step-wise cryoprotectant adding and diluting protocol. Cryobiology 61 , 58–65 (2010). Liu, J., Mullen, S., Meng, Q., Critser, J. & Dinnyes, A. Determination of oocyte membrane permeability coefficients and their application to cryopreservation in a rabbit model. Cryobiology 59 , 127–134 (2009). Newton, H., Pegg, D. E., Barrass, R. & Gosden, R. G. Osmotically inactive volume, hydraulic conductivity, and permeability to dimethyl sulphoxide of human mature oocytes. Reproduction 117 , 27–33 (1999). Toner, M., Cravalho, E. G. & Armant, D. R. Water transport and estimated transmembrane potential during freezing of mouse oocytes. J. Membrain Biol. 115 , 261–272 (1990). Lotz, J. et al. Transport processes in equine oocytes and ovarian tissue during loading with cryoprotective solutions. Biochimica et Biophysica Acta (BBA). - Gen. Subj. 1865 , 129797 (2021). Agca, Y., Liu, J., Critser, E. S. & Critser, J. K. Fundamental cryobiology of rat immature and mature oocytes: Hydraulic conductivity in the presence of Me2SO, Me2SO permeability, and their activation energies. J. Exp. Zool. 286 , 523–533 (2000). Arcarons, N. et al. Cholesterol added prior to vitrification on the cryotolerance of immature and in vitro matured bovine oocytes. PLoS ONE . 12 , e0184714 (2017). Ribeiro, J. C., Carrageta, D. F., Bernardino, R. L., Alves, M. G. & Oliveira, P. F. Aquaporins and Animal Gamete Cryopreservation: Advances and Future Challenges. Animals 12 , 359 (2022). García-Martínez, T. et al. Impact of equilibration duration combined with temperature on the outcome of bovine oocyte vitrification. Theriogenology 184 , 110–123 (2022). Kasai, M. Advances in the cryopreservation of mammalian oocytes and embryos: Development of ultrarapid vitrification. Reprod. Med. Biology . 1 , 1–9 (2002). Davidson, A. F., Benson, J. D. & Higgins, A. Z. Mathematically optimized cryoprotectant equilibration procedures for cryopreservation of human oocytes. Theor. Biol. Med. Model. 11 , 13 (2014). Olver, D. J., Heres, P., Paredes, E. & Benson, J. D. Rational synthesis of total damage during cryoprotectant equilibration: modelling and experimental validation of osmomechanical, temperature, and cytotoxic damage in sea urchin (Paracentrotus lividus) oocytes. PeerJ 11 , e15539 (2023). Kleinhans, F. W. Membrane Permeability Modeling: Kedem–Katchalsky vs a Two-Parameter Formalism. Cryobiology 37 , 271–289 (1998). Lagariasy, J. C., Reedsz, J. A., Wrightx, M. H., Wright, P. E. & Lagarias, Jeffrey, C. Convergence properties of the Nelder mead simplex method in low dimensions. Soc. Industrial Appl. Math. 9 , 112–147 (1998). Vian, A. M. & Higgins, A. Z. Membrane permeability of the human granulocyte to water, dimethyl sulfoxide, glycerol, propylene glycol and ethylene glycol. Cryobiology 68 , 35–42 (2014). Dormand, J. R. & Prince, P. J. A family of embedded Runge-Kutta formulae. J. Comput. Appl. Math. 6 , 19–26 (1980). Shampine, L. F. & Reichelt, M. W. The MATLAB ODE Suite. SIAM J. Sci. Comput. 18 , 1–22 (1997). Hunter, J. E., Bernard, A., Fuller, B. J., McGrath, J. J. & Shaw, R. W. Measurements of the membrane water permeability (Lp) and its temperature dependence (activation energy) in human fresh and failed-to-fertilize oocytes and mouse oocyte. Cryobiology 29 , 240–249 (1992). Scheff, J. D., Almon, R. R., DuBois, D. C., Jusko, W. J. & Androulakis, I. P. Assessment of Pharmacologic Area Under the Curve When Baselines are Variable. Pharm. Res. 28 , 1081–1089 (2011). Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-9031036\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":608199415,\"identity\":\"7a69af23-b1d5-43d5-872b-8b0edf391f49\",\"order_by\":0,\"name\":\"Sonia Gago\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Autonomous University of Barcelona\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Sonia\",\"middleName\":\"\",\"lastName\":\"Gago\",\"suffix\":\"\"},{\"id\":608199416,\"identity\":\"bac08dc2-3ae8-407f-9efb-171adeca51bc\",\"order_by\":1,\"name\":\"Tania García-Martínez\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Hospital Universitario Son Espases\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Tania\",\"middleName\":\"\",\"lastName\":\"García-Martínez\",\"suffix\":\"\"},{\"id\":608199417,\"identity\":\"112db1e9-02a8-4982-b5cf-290984ab064a\",\"order_by\":2,\"name\":\"Judith Diaz-Muñoz\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Autonomous University of Barcelona\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Judith\",\"middleName\":\"\",\"lastName\":\"Diaz-Muñoz\",\"suffix\":\"\"},{\"id\":608199418,\"identity\":\"05c10cf7-44cf-48c0-af5e-b80397a5cbf8\",\"order_by\":3,\"name\":\"Mónica Acacio\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Embryotools R\\u0026D Centre\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Mónica\",\"middleName\":\"\",\"lastName\":\"Acacio\",\"suffix\":\"\"},{\"id\":608199419,\"identity\":\"2fa94a6a-f322-4034-8879-5f2e3b107141\",\"order_by\":4,\"name\":\"Jaime Catalán\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Institute of Food and Agricultural Technology\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Jaime\",\"middleName\":\"\",\"lastName\":\"Catalán\",\"suffix\":\"\"},{\"id\":608199420,\"identity\":\"afc4ac01-d2ea-4be3-9d1a-3b10ca5ec538\",\"order_by\":5,\"name\":\"Jordi Miró\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Autonomous University of Barcelona\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Jordi\",\"middleName\":\"\",\"lastName\":\"Miró\",\"suffix\":\"\"},{\"id\":608199421,\"identity\":\"b82dc09f-bdcf-4c42-9fee-0e1c01cc9f1a\",\"order_by\":6,\"name\":\"Adam Zachary Higgins\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Oregon State University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Adam\",\"middleName\":\"Zachary\",\"lastName\":\"Higgins\",\"suffix\":\"\"},{\"id\":608199422,\"identity\":\"417aeb2d-b4d6-4d26-9f07-60cf89ca831a\",\"order_by\":7,\"name\":\"Nuno Costa-Borges\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Embryotools R\\u0026D Centre\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Nuno\",\"middleName\":\"\",\"lastName\":\"Costa-Borges\",\"suffix\":\"\"},{\"id\":608199423,\"identity\":\"b2e15e44-3514-4939-8fe1-5e5e47b7062e\",\"order_by\":8,\"name\":\"Teresa Mogas\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA40lEQVRIiWNgGAWjYNCDDwwMCQQV8SBzGGdAtDA2EK2FmYcYLfbsvQ8f/qhhiObnX/z4s22bXR4D++HnD/DawnPc2JjnGEPuzBnPzKRz25KLGXjSDPE7TCKNTZqBjSF3w40DZsy5bcyJDRIMBLTIP2P/+eMfSMvxz58t2+qBWtg/ErCFjY2Btw2o5XyPgTRj22GgFh4CtpxJY5bm7ZMA+oWnTLLn3PFiNp6cwhn4tLC3H2P8+OObTW4///HNH36UVefxsx/f8AGfFiiQAKIECJONCOVQwH+AeLWjYBSMglEwsgAAjFhGRKazKQYAAAAASUVORK5CYII=\",\"orcid\":\"\",\"institution\":\"Autonomous University of Barcelona\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Teresa\",\"middleName\":\"\",\"lastName\":\"Mogas\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2026-03-04 13:53:31\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-9031036/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-9031036/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":104980692,\"identity\":\"10771d12-6d73-4115-a5f8-38701faacee4\",\"added_by\":\"auto\",\"created_at\":\"2026-03-19 13:13:41\",\"extension\":\"jpg\",\"order_by\":1,\"title\":\"Figure 1\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":30886,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eBoyle van’t Hoff plot for \\u003cem\\u003ein vitro\\u003c/em\\u003e matured equine oocytes. Solutions with osmolalities of 234, 292, 505, 886, 1056, 1333 and 1903 mOsm kg\\u003csup\\u003e-1\\u003c/sup\\u003e were used. The regression calculation yields the value for the osmotically inactive fraction of 27% of isotonic volume with R\\u003csup\\u003e2\\u003c/sup\\u003e=0.9483. Error bars indicate the standard error of mean (SEM) above and below the mean.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"1.jpg\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-9031036/v1/8cf894e16f9a2343627fdc40.jpg\"},{\"id\":104980691,\"identity\":\"ee4e3e59-2ee2-4f1a-abff-9dbc43649fea\",\"added_by\":\"auto\",\"created_at\":\"2026-03-19 13:13:41\",\"extension\":\"jpg\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":63143,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003e(a) Comparison between model predictions and \\u003cem\\u003ein vitro\\u003c/em\\u003e resultsobtained in equine \\u003cem\\u003ein vitro\\u003c/em\\u003e-matured oocytes (slaughterhouse-derived or OPU) exposed for 20 min to ES (ES: 7.5% Me₂SO and 7.5% EG) at 25°C. Data are the means of relative volumes ± SEM. (b) Comparison between model predictions and \\u003cem\\u003ein vitro \\u003c/em\\u003eresults obtained in equine MII oocytes (slaughterhouse or OPU) exposed for 10 min to ES at 38.5°C. Data are the means of relative volumes ± SEM. The agreement between the model predictions and the \\u003cem\\u003ein vitro\\u003c/em\\u003emeasurements was quantified additionally using the root mean square error (RMSE).\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"2.jpg\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-9031036/v1/2cda3d2a6a08a19b6d6ed0a1.jpg\"},{\"id\":104980693,\"identity\":\"bde3e2d3-9dc5-41f2-b318-9a39526b89e6\",\"added_by\":\"auto\",\"created_at\":\"2026-03-19 13:13:42\",\"extension\":\"jpg\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":70889,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eSchematic representation of the 60 mm Petri dish used in the experimental set-up for analyzing volume changes in \\u003cem\\u003ein vitro\\u003c/em\\u003e matured equine oocytes.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"3.jpg\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-9031036/v1/00bad7bb6205dd8300f2b4e0.jpg\"},{\"id\":105562576,\"identity\":\"8ad9032d-23dd-4fb8-955d-4925e25fc6e1\",\"added_by\":\"auto\",\"created_at\":\"2026-03-27 12:43:07\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1390122,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-9031036/v1/b448aed1-8b30-48bd-bb76-77ba937900d3.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Water and cryoprotectant permeability of mature equine oocytes: experimental measurements and in silico predictions\",\"fulltext\":[{\"header\":\"1. INTRODUCTION\",\"content\":\"\\u003cp\\u003eCryopreservation of mammalian oocytes and embryos have progressed considerably during the last decades, becoming an essential part of assisted reproductive technologies due to the increasing number of pregnanci es and live births reported in several species \\u003csup\\u003e\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e1\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2\\u003c/span\\u003e\\u003c/sup\\u003e. Among the different cryopreservation techniques, vitrification is currently the most widely adopted method in many domestic species, including the horse. This technique relies on extremely rapid cooling rates combined with high concentrations of cryoprotectant agents (CPAs) to avoid ice crystal formation and the structural damage associated with it \\u003csup\\u003e3\\u0026ndash;5\\u003c/sup\\u003e.\\u003c/p\\u003e \\u003cp\\u003eIn the equine species, the possibility to cryopreserve oocytes offers several practical and genetic advantages that are highly relevant for both research and breeding programs. Cryopreservation allows reproductive decisions to be postponed and it also facilitates the storage of oocytes outside the natural breeding season. In addition, cryopreserved oocytes can be used to create oocyte banks, increasing genetic diversity in endangered breeds and populations with narrow genetic bases. Additionally, the distribution of cryopreserved oocytes and embryos offers a practical alternative to the transportation of live animals, reducing the risk of disease transmission and mitigating carbon emissions \\u003csup\\u003e\\u003cspan citationid=\\\"CR3\\\" class=\\\"CitationRef\\\"\\u003e3\\u003c/span\\u003e\\u003c/sup\\u003e. Despite these benefits, the efficiency of equine oocyte cryopreservation remains low compared to other species and outcomes are still inconsistent across laboratories. This situation highlights the urgent need for standardized and optimized vitrification protocols \\u003csup\\u003e\\u003cspan citationid=\\\"CR6\\\" class=\\\"CitationRef\\\"\\u003e6\\u003c/span\\u003e\\u003c/sup\\u003e.\\u003c/p\\u003e \\u003cp\\u003eThe success of vitrification depends on multiple interacting factors including the develomental stage of the oocyte, the specific vitrification protocol, CPA the type and concentration and the duration of the exposure to this solutions \\u003csup\\u003e\\u003cspan citationid=\\\"CR7\\\" class=\\\"CitationRef\\\"\\u003e7\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR8\\\" class=\\\"CitationRef\\\"\\u003e8\\u003c/span\\u003e\\u003c/sup\\u003e. Because these variables influence both osmotic responses and CPA toxicity, empirical approaches often lead to suboptimal results. Therefore, quantitative tools capable of predicting oocyte behavior during CPA loading and removal are essential to move beyond trial‑and‑error strategies. In addition, mathematical approaches can reduce CPA toxicity by optimizing the timing and concentration of CPA exposure \\u003csup\\u003e\\u003cspan citationid=\\\"CR9\\\" class=\\\"CitationRef\\\"\\u003e9\\u003c/span\\u003e\\u003c/sup\\u003e. However, the application of these models to improve vitrification of \\u003cem\\u003ein vitro\\u003c/em\\u003e matured equine oocytes has not yet been fully explored.\\u003c/p\\u003e \\u003cp\\u003eMathematical models, such as the two-parameter (2P) formalism, simulate the transport of water and CPAs across the oocyte membrane and predict changes in oocyte volume and intracellular CPA concentrations during exposure to CPA solutions \\u003csup\\u003e\\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e10\\u003c/span\\u003e\\u003c/sup\\u003e. These models help identify exposure conditions that mantain oocyte volume within osmotic tolerance limits, preventing excessive shrinkage or swelling that may cause irreversible damage \\u003csup\\u003e\\u003cspan citationid=\\\"CR11\\\" class=\\\"CitationRef\\\"\\u003e11\\u003c/span\\u003e\\u003c/sup\\u003e. In addition, mathematical approaches can reduce CPA toxicity by optimizing timing and concentration of CPA exposure \\u003csup\\u003e\\u003cspan citationid=\\\"CR9\\\" class=\\\"CitationRef\\\"\\u003e9\\u003c/span\\u003e\\u003c/sup\\u003e. However, the application of these models to improve vitrification of equine \\u003cem\\u003ein vitro\\u003c/em\\u003e matured oocyte has not yet fully explored.\\u003c/p\\u003e \\u003cp\\u003eA major limitation is that stage‑specific membrane permeability data for equine oocytes is still very limited. Permeability values obtained from other species cannot be directly extrapolated, as oocyte membrane properties vary considerably across species and developmental stages. Even within the same species, immature and mature oocytes may require different CPA loading and removal procedures due to differences in membrane composition \\u003csup\\u003e\\u003cspan additionalcitationids=\\\"CR13 CR14\\\" citationid=\\\"CR12\\\" class=\\\"CitationRef\\\"\\u003e12\\u003c/span\\u003e\\u0026ndash;\\u003cspan citationid=\\\"CR15\\\" class=\\\"CitationRef\\\"\\u003e15\\u003c/span\\u003e\\u003c/sup\\u003e. For this reason, permeability values previously reported for immature equine oocytes cannot be applied to metaphase II (MII) oocytes \\u003csup\\u003e\\u003cspan citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e16\\u003c/span\\u003e\\u003c/sup\\u003e. These limitations emphasize the need for direct, stage- and species-specific measurements of water and CPA permeability in MII equine oocytes \\u003csup\\u003e\\u003cspan citationid=\\\"CR11\\\" class=\\\"CitationRef\\\"\\u003e11\\u003c/span\\u003e\\u003c/sup\\u003e. The aim of the present study was to address this knowledge gap by experimentally determining water (\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e) and CPA permeability (\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e) parameters in MII equine oocytes and by characterizing their osmotic behavior under controlled conditions. By providing the first permeability values specific to this developmental stage, our work establishes a foundation for the development of more accurate mathematical models of membrane transport. These data may contribute to refining vitrification protocols, improving CPA exposure strategies, and ultimately enhancing oocyte survival and developmental competence in equine ART.\\u003c/p\\u003e\"},{\"header\":\"2. RESULTS\",\"content\":\"\\u003cdiv id=\\\"Sec3\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.1. Equine \\u003cem\\u003ein vitro\\u003c/em\\u003e matured oocyte characteristics\\u003c/h2\\u003e \\u003cp\\u003eEquine \\u003cem\\u003ein vitro\\u003c/em\\u003e matured oocytes have a mean cytoplasm oocyte diameter (without zona pellucida) of 106.1\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.5 \\u0026micro;m, corresponding to an average radius of 53.0\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.3 \\u0026micro;m (mean\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;SEM). Based on these measurements, the initial surface area (A\\u003csub\\u003eo\\u003c/sub\\u003e) was calculated to be 35,430\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;350 \\u0026micro;m\\u0026sup2;, and the initial volume (V\\u003csub\\u003eo\\u003c/sub\\u003e) was 629,400\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;9,200 \\u0026micro;m\\u0026sup3;. The A\\u003csub\\u003eo\\u003c/sub\\u003e/V\\u003csub\\u003eo\\u003c/sub\\u003e ratio exhibited a mean value of 0.057\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.000 \\u0026micro;m\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e, indicating minimal variability across the samples (see Table\\u0026nbsp;\\u003cspan refid=\\\"Tab1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e). These geometric parameters provide a precise baseline characterization of the oocyte size and structural properties at the onset of the experiments.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab1\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 1\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eMeasurements of diameter, radius, surface area, and volume of \\u003cem\\u003ein vitro\\u003c/em\\u003e matured equine oocytes.\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"6\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c6\\\" colnum=\\\"6\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"1\\\" rowspan=\\\"2\\\"\\u003e \\u003cp\\u003eMean\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003ed (\\u0026micro;m)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003er (\\u0026micro;m)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003eAo (\\u0026micro;m\\u003csup\\u003e2\\u003c/sup\\u003e)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003eVo (\\u0026micro;m\\u003csup\\u003e3\\u003c/sup\\u003e)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003eA\\u003csub\\u003eo\\u003c/sub\\u003e/V\\u003csub\\u003eo\\u003c/sub\\u003e (\\u0026micro;m\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e)\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e106.066\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e53.033\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e35429.213\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e629363.118\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.057\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eSEM\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.519\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.259\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e346.691\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e9245.445\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e \\u003cp\\u003e0.000\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003ed: Diameter (\\u0026#120583;m); r: Radius (\\u0026micro;m); Ao: Surface \\u0026aacute;rea (\\u0026#120583;m\\u003csup\\u003e2\\u003c/sup\\u003e); Vo: Volume (\\u0026micro;m\\u003csup\\u003e3\\u003c/sup\\u003e); Ao/Vo ratio (\\u0026micro;m\\u003csup\\u003e\\u0026minus;1\\u003c/sup\\u003e). Values are given as Mean \\u0026plusmn; SEM.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec4\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.2. Boyle-van \\u0026prime; t Hoff, osmotically inactive volume of \\u003cem\\u003ein vitro\\u003c/em\\u003e matured equine oocytes\\u003c/h2\\u003e \\u003cp\\u003eWe tested whether \\u003cem\\u003ein vitro\\u003c/em\\u003e matured equine oocytes behaved as ideal osmometers, which would show a linear Boyle\\u0026ndash;van \\u0026rsquo;t Hoff relationship between cell volume and the inverse of the medium osmolality. Oocyte volumes were measured under isotonic conditions (HM; 292 mOsm kg\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e) and in a series of hypo- and hypertonic solutions (ranging between 234 and1903 mOsm kg\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e). After 10 min of equilibration at 38.5\\u0026deg;C in the different solutions, volumes were recorded and normalized to the original isotonic value. Thirty-five oocytes with a spherical morphology (\\u0026ge;\\u0026thinsp;5 per condition) were analyzed, and normalized volumes were plotted against the reciprocal of the solution osmolality. Our results showed a strong goodness of fit (R\\u003csup\\u003e2\\u003c/sup\\u003e\\u0026thinsp;=\\u0026thinsp;0.9483), as MII equine oocytes conformed to the predicted behavior, acting as ideal osmometers across the tested osmolality range (234\\u0026ndash;1903 mOsm) (see Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e). The osmotically inactive volume (V\\u003csub\\u003eb\\u003c/sub\\u003e) was calculated as 27% of the isotonic cell volume for MII equine oocytes.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec5\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e2.3. Modeling membrane permeability of equine MII oocytes\\u003c/h2\\u003e \\u003cdiv id=\\\"Sec6\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.1. Membrane permeability parameters\\u003c/h2\\u003e \\u003cp\\u003eWater permeability (\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e) and solute permeability (\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e) of MII equine oocytes in the presence of 1.55M EG or Me\\u003csub\\u003e2\\u003c/sub\\u003eSO at 25\\u0026deg;C or 38.5\\u0026deg;C are described in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e. Overall, \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e values varied significantly between the temperatures for each CPA (\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep Me2SO\\u003c/sub\\u003e: 0.941\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.082 at 25\\u0026deg;C and 1.462\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.084 at 38.5\\u0026deg;C (p\\u0026thinsp;=\\u0026thinsp;0.0012) ; \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep EG\\u003c/sub\\u003e: 0.889\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.094 at 25\\u0026deg;C and 1.613\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.066 at 38.5\\u0026deg;C (\\u003cem\\u003eP\\u003c/em\\u003e\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.0001)). \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e also increased significantly when the temperature increased from 25\\u0026deg;C to 38.5\\u0026deg;C (\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es Me2SO\\u003c/sub\\u003e: 0.175\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.024 at 25\\u0026deg;C and 0.353\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.022 at 38.5\\u0026deg;C (\\u003cem\\u003eP\\u003c/em\\u003e\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.0001); \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es EG\\u003c/sub\\u003e: 0.138\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.020 at 25\\u0026deg;C and 0.349\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.014 at 38.5\\u0026deg;C (\\u003cem\\u003eP\\u003c/em\\u003e\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.0001). In contrast, no differences in water permeability nor solute permeability were detected between the CPAs at the same temperature (\\u003cem\\u003eP\\u003c/em\\u003e\\u0026thinsp;\\u0026gt;\\u0026thinsp;0.05).\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab2\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 2\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eWater permeability (\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e) and solute permeability (\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e) of equine \\u003cem\\u003ein vitro\\u003c/em\\u003e matured oocytes exposed to 1.55 M Me\\u003csub\\u003e2\\u003c/sub\\u003eSO or 1.55M EG at 25\\u0026deg;C or 38.5\\u0026deg;C.\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"4\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"1\\\" rowspan=\\\"2\\\"\\u003e \\u003cp\\u003eCPA\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\" morerows=\\\"1\\\" rowspan=\\\"2\\\"\\u003e \\u003cp\\u003eTemperature\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e \\u003cp\\u003eMembrane permeability parameters\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e (\\u0026micro;m atm\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e min\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e (\\u0026micro;m sec\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e)\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eMe\\u003csub\\u003e2\\u003c/sub\\u003eSO\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e25\\u0026deg;C\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.941\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.082 \\u003csup\\u003ea,1\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e0.175\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.024 \\u003csup\\u003ea,\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e1\\u003c/span\\u003e\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e38.5\\u0026deg;C\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e1.462\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.084 \\u003csup\\u003eb,2\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e0.353\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.022 \\u003csup\\u003eb,\\u003cspan citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2\\u003c/span\\u003e\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eEG\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e25\\u0026deg;C\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.889\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.094 \\u003csup\\u003ea,\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e1\\u003c/span\\u003e\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e0.138\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.020 \\u003csup\\u003ea,\\u003cspan citationid=\\\"CR1\\\" class=\\\"CitationRef\\\"\\u003e1\\u003c/span\\u003e\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e38.5\\u0026deg;C\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e1.613\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.066 \\u003csup\\u003eb,2\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e0.349\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.014 \\u003csup\\u003eb,\\u003cspan citationid=\\\"CR2\\\" class=\\\"CitationRef\\\"\\u003e2\\u003c/span\\u003e\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003cp\\u003eData are given as mean\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;SEM. \\u003csup\\u003ea,b\\u003c/sup\\u003e Different superscript letters indicate significant differences between temperatures for the same CPA (\\u003cem\\u003eP\\u003c/em\\u003e\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.05). \\u003csup\\u003e1,2\\u003c/sup\\u003e Different superscript numbers indicate significant differences in \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e or \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e between CPAs for the same temperature (\\u003cem\\u003eP\\u003c/em\\u003e\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.05). Me\\u003csub\\u003e2\\u003c/sub\\u003eSO, dimethyl sulfoxide; EG, ethylene glycol.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec7\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.2. Activation Energy of Membrane Permeability in \\u003cem\\u003ein vitro\\u003c/em\\u003e Matured Equine Oocytes\\u003c/h2\\u003e \\u003cp\\u003eActivation energy (E\\u003csub\\u003ea\\u003c/sub\\u003e) of \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e and \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e was estimated from mean permeability values measured at 25\\u0026deg;C and 38.5\\u0026deg;C. As individual oocytes were not measured at both temperatures, E\\u003csub\\u003ea\\u003c/sub\\u003e calculations reflect the average temperature sensitivity across the cohort of MII oocytes. E\\u003csub\\u003ea\\u003c/sub\\u003eL\\u003csub\\u003ep\\u003c/sub\\u003e values were 6.03 kcal mol\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e for Me\\u003csub\\u003e2\\u003c/sub\\u003eSO and 8.15 kcal mol\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e for EG (see Table\\u0026nbsp;\\u003cspan refid=\\\"Tab3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e). In contrast, E\\u003csub\\u003ea\\u003c/sub\\u003eP\\u003csub\\u003es\\u003c/sub\\u003e values of 9.60 kcal mol\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e for Me\\u003csub\\u003e2\\u003c/sub\\u003eSO and 12.69 kcal mol\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e for EG.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab3\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 3\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eActivation energy of water (E\\u003csub\\u003ea\\u003c/sub\\u003e \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e) and cryoprotective agents (E\\u003csub\\u003ea\\u003c/sub\\u003e \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e) membrane permeability.\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"3\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eCPA\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eE\\u003csub\\u003ea\\u003c/sub\\u003e \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e (kcal mol\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e)\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eE\\u003csub\\u003ea\\u003c/sub\\u003e \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e (kcal mol\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e)\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eMe\\u003csub\\u003e2\\u003c/sub\\u003eSO\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e6.03\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e9.60\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eEG\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e8.15\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e12.69\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec8\\\" class=\\\"Section3\\\"\\u003e \\u003ch2\\u003e2.3.3. \\u003cem\\u003eIn silico\\u003c/em\\u003e predictions versus \\u003cem\\u003ein vitro\\u003c/em\\u003e observations\\u003c/h2\\u003e \\u003cp\\u003eFor our comparison of the effects of temperature on cell osmotic response, MII equine oocytes were exposed to an ES containing 7.5% Me₂SO and 7.5% EG at two temperatures (25\\u0026deg;C and 38.5\\u0026deg;C). Because these CPAs are permeable, water moves in response to the osmotic gradient while CPAs enter the cell along their concentration gradient, causing changes in cell volume. Permeability parameters previously determined using single-CPA solutions (either Me₂SO or EG) enabled us to predict oocyte responses during exposure to the ES. Model predictions of relative cell volume over time for oocytes exposed to ES at 25\\u0026deg;C or 38.5\\u0026deg;C are shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003eA and \\u003cspan refid=\\\"Fig2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003eB. Our model predictions show that oocytes exposed to ES shrink to a minimum of 46% of their isotonic volume after 8 s of exposure at 38.5\\u0026deg;C whereas at 25\\u0026deg;C the oocytes are predicted to shrink to a m\\u0026iacute;nimum of 44% within 15s. Moreover, simulations predict that oocytes at 38.5\\u0026deg;C swell back to their isotonic volume faster than at 25\\u0026deg;C, recovering their original volume after 7min 43s or 17min 8s, respectively. The \\u003cem\\u003ein vitro\\u003c/em\\u003e oocyte osmotic response of equine MII oocytes exposed to ES showed that they recover their initial volume at 6 min 31 s at 38.5\\u0026deg;C and 19min 8s at 25\\u0026deg;C for OPU derived oocytes and 9min 6s at 38.5\\u0026deg;C and 18min 53s at 25\\u0026deg;C for slaughterhouse oocytes. Despite these differences, both values of area under the curve (AUC) from slaughterhouse and OPU derived oocytes did not present any statistical differences with the simulation group. As expected, oocytes in all groups initially decreased in volume due to water efflux. Following this shrinkage phase, the cells began to swell as CPA entered across the membrane, driven by the concentration gradient. These relative volume changes were temperature dependent and closely aligned with the model predictions, as no significant differences in AUC values were observed between groups (\\u003cem\\u003eP\\u003c/em\\u003e\\u0026thinsp;\\u0026gt;\\u0026thinsp;0.05).\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003cp\\u003eOverall, these low RMSE values across temperatures and oocyte sources indicate strong agreement between the in silico predictions and the observed volume responses. These values are described in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab4\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab4\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 4\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eRoot mean square error (RMSE) for predicted versus observed oocyte volume changes in slaughterhouse-derived and ovum pick-up (OPU)-derived oocytes at 25\\u0026deg;C and 38.5\\u0026deg;C. See corresponding columns in the table.\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"5\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e\\u003cem\\u003eIn silico\\u003c/em\\u003e 25\\u0026deg;C \\u0026ndash; Slaughterhouse\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e\\u003cem\\u003eIn silico\\u003c/em\\u003e 25\\u0026deg;C - OPU\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e\\u003cem\\u003eIn silico\\u003c/em\\u003e 38.5\\u0026deg;C - Slaughterhouse\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e\\u003cem\\u003eIn silico\\u003c/em\\u003e 38.5\\u0026deg;C - OPU\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eRMSE\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e0.083\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003e0.047\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e \\u003cp\\u003e0.092\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e \\u003cp\\u003e0.071\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003c/div\\u003e\"},{\"header\":\"3. DISCUSSION\",\"content\":\"\\u003cp\\u003eThis study provides a quantitative characterization of the osmotic behavior and membrane transport properties of \\u003cem\\u003ein vitro\\u003c/em\\u003e matured equine oocytes, offering new information that is essential for improving vitrification strategies in this species. The measurements obtained here confirm that equine MII oocytes belong to the group of relatively large mammalian gametes, with a mean cytoplasmic diameter of 106.66\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.52 \\u0026micro;m. This value is consistent with previously reported measurements in equine GV oocytes, which are around 105 \\u0026micro;m in diameter. This similarity between GV and MII oocytes suggests that cytoplasmic size remains relatively stable during maturation in equine species \\u003csup\\u003e\\u003cspan citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e16\\u003c/span\\u003e\\u003c/sup\\u003e. When compared with other mammals, equine oocytes are larger than mouse GV oocytes (70\\u0026ndash;80 \\u0026micro;m) \\u003csup\\u003e\\u003cspan citationid=\\\"CR17\\\" class=\\\"CitationRef\\\"\\u003e17\\u003c/span\\u003e\\u003c/sup\\u003e, similar to human MII oocytes (103\\u0026ndash;119 \\u0026micro;m) \\u003csup\\u003e\\u003cspan citationid=\\\"CR18\\\" class=\\\"CitationRef\\\"\\u003e18\\u003c/span\\u003e\\u003c/sup\\u003e, and slightly smaller than porcine GV oocytes (around 120 \\u0026micro;m) \\u003csup\\u003e\\u003cspan citationid=\\\"CR17\\\" class=\\\"CitationRef\\\"\\u003e17\\u003c/span\\u003e\\u003c/sup\\u003e. These interspecies differences are relevant because oocyte size directly influences osmotic behavior, CPA permeation kinetics, and overall response to cryopreservation.\\u003c/p\\u003e \\u003cp\\u003eThe osmotically inactive volume (V\\u003csub\\u003eb\\u003c/sub\\u003e) of MII equine oocytes was estimated at 27% of the isotonic volume, a value that falls within the range reported for other mammalian species. For example, bovine oocytes show a V\\u003csub\\u003eb\\u003c/sub\\u003e of approximtelly 26.1% \\u003csup\\u003e19\\u003c/sup\\u003e while rabbit, human, and mouse oocytes exhibit values around 20%, 19%, and 21%, respectively \\u003csup\\u003e\\u003cspan additionalcitationids=\\\"CR21\\\" citationid=\\\"CR20\\\" class=\\\"CitationRef\\\"\\u003e20\\u003c/span\\u003e\\u0026ndash;\\u003cspan citationid=\\\"CR22\\\" class=\\\"CitationRef\\\"\\u003e22\\u003c/span\\u003e\\u003c/sup\\u003e. These differences likely reflect species-specific variations in cellular composition, organelle density, and membrane characteristics that define the fraction of volume resistant to osmotic perturbation. Interestingly, the equine V\\u003csub\\u003eb\\u003c/sub\\u003e value obtained in our study is also close to the 31% previosly reported for equine GV oocytes, suggesting that the osmotically inactive fraction does not undergo major changes during maturation under the experimental conditions used \\u003csup\\u003e\\u003cspan citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e16\\u003c/span\\u003e\\u003c/sup\\u003e. This stability supports the use of a single V\\u003csub\\u003eb\\u003c/sub\\u003e parameter in mathematical models for equine oocytes, although permeability parameters must still be determined specifically for each developmental stage.\\u003c/p\\u003e \\u003cp\\u003eHydraulic (\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e) and solute (\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e) permeabilities of oocytes are critical determinants of oocyte response during CPA loading and removal, and they are known to vary widely between species, temperatures, and maturarion stages (GV vs MII) \\u003csup\\u003e\\u003cspan citationid=\\\"CR11\\\" class=\\\"CitationRef\\\"\\u003e11\\u003c/span\\u003e\\u003c/sup\\u003e. For equine GV oocytes at 22\\u0026deg;C, previously reported \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e values are around 0.6284 \\u0026micro;m min⁻\\u0026sup1; atm⁻\\u0026sup1; when exposed to 1.5M EG or 0.57 \\u0026micro;m min⁻\\u0026sup1; atm⁻\\u0026sup1; when exposed to 1.5 M Me₂SO, while \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e for ethylene glycol (P\\u003csub\\u003esEG\\u003c/sub\\u003e) and dimethyl sulfoxide (P\\u003csub\\u003esMe2SO\\u003c/sub\\u003e) are 0.3394 \\u0026micro;m s⁻\\u0026sup1; \\u003csup\\u003e16\\u003c/sup\\u003e and 0.5575 \\u0026micro;m s⁻\\u0026sup1; \\u003csup\\u003e23\\u003c/sup\\u003e, respectively. In our study, MII oocytes at 25\\u0026deg;C showed a modest increase in \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e (0.889\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.094 \\u0026micro;m min⁻\\u0026sup1; atm⁻\\u0026sup1; for EG and 0.941\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.082 \\u0026micro;m min⁻\\u0026sup1; atm⁻\\u0026sup1; for Me2SO), whereas \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003esEG\\u003c/sub\\u003e and \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003esMe2SO\\u003c/sub\\u003e were considerable lower to 0.138\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.020 \\u0026micro;m s⁻\\u0026sup1; and 0.175\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.024 \\u0026micro;m s⁻\\u0026sup1;, respectively). This pattern, relatively preserved or slightly increased water permeability accompanied by reduced CPA permeability, is consistent with observations in bovine and rat oocytes, where maturation from the GV to the MII stage is associated with a decline in \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e values \\u003csup\\u003e\\u003cspan citationid=\\\"CR13\\\" class=\\\"CitationRef\\\"\\u003e13\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR24\\\" class=\\\"CitationRef\\\"\\u003e24\\u003c/span\\u003e\\u003c/sup\\u003e. Such changes are generally attributed to maturation-associated remodeling of the plasma membrane, including modification in lipid composition, cholesterol content, and the distribution or regulation of aquaporins and other channels \\u003csup\\u003e\\u003cspan citationid=\\\"CR25\\\" class=\\\"CitationRef\\\"\\u003e25\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR26\\\" class=\\\"CitationRef\\\"\\u003e26\\u003c/span\\u003e\\u003c/sup\\u003e. Functionally, a lower \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e in MII oocytes may help limit the rate of CPA entry, potentially reducing acute toxicity, but it also implies that longer or more concentrated CPA exposures may be required to achieve adequate intracellular CPA levels.\\u003c/p\\u003e \\u003cp\\u003eTemperature is another major factor influencing membrane permeability. Although no previous measurements of \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e or \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e values at 38.5\\u0026deg;C have been reported for equine, studies in other species have shown that CPA permeation is markely influenced by temperature, with higher temperatures resulting in faster solute permeation \\u003csup\\u003e\\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e27\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR28\\\" class=\\\"CitationRef\\\"\\u003e28\\u003c/span\\u003e\\u003c/sup\\u003e. Our results confirm this trend: increasing the temperature from 25\\u0026deg;C to 38.5\\u0026deg;C led to a statistically significant increase in both P\\u003csub\\u003esEG\\u003c/sub\\u003e and P\\u003csub\\u003esMe2SO\\u003c/sub\\u003e values. These findings indicate that both oocyte maturation and temperature induce structural and functional modifications of the plasma membrane that differentially affect water and cryoprotectant transport.\\u003c/p\\u003e \\u003cp\\u003eActivation energies (E\\u003csub\\u003ea\\u003c/sub\\u003e) provide additional insight into the temperature sensitivity of membrane transport. In our study, the E\\u003csub\\u003ea\\u003c/sub\\u003e values calculated for MII equine oocytes were 6.03 kcal mol⁻\\u0026sup1; for \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e and 9.60 kcal mol⁻\\u0026sup1; for \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e in Me₂SO, and 8.15 kcal mol⁻\\u0026sup1; for \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e and 12.69 kcal mol⁻\\u0026sup1; for \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e in EG. These values are lower than those previously reported for equine GV oocytes \\u003csup\\u003e\\u003cspan citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e16\\u003c/span\\u003e\\u003c/sup\\u003e, where E\\u003csub\\u003ea\\u003c/sub\\u003e \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e reached 11.19 kcal mol⁻\\u0026sup1; and E\\u003csub\\u003ea\\u003c/sub\\u003e \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e for EG was 15.81 kcal mol⁻\\u0026sup1;, suggesting that the membranes of mature oocytes may require less energy to increase permeability with temperature. Although individual oocytes were not measured at both temperatures, a limitation that should be addressed in future studies, the E\\u003csub\\u003ea\\u003c/sub\\u003e values obtained here still offer a useful approximation of the temperature dependence of water and CPA transport in equine MII oocytes.\\u003c/p\\u003e \\u003cp\\u003eThe \\u003cem\\u003ein silico\\u003c/em\\u003e predictions obtained using the two-parameter (2P) model, parameterized with our experimentally derived \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e and \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e values, showed strong agreement with the \\u003cem\\u003ein vitro\\u003c/em\\u003e volume changes of equine MII oocytes exposed to an equilibration solution (ES) containing 7.5% Me₂SO and 7.5% EG. At both 25\\u0026deg;C and 38.5\\u0026deg;C, the model accurately reproduced the characteristic biphasic osmotic response: an initial rapid shrinkage due to water efflux, followed by a gradual swelling as CPAs permeate the membrane and the intracellular osmolality increases. Predicted recovery times to isotonic volume (approximately 7 min 43 s at 38.5\\u0026deg;C and 17 min 8 s at 25\\u0026deg;C) were close to the experimental observations for both slaughterhouse- and ovum pick-up (OPU)-derived oocytes, and the area under the curve values did not differ significantly between simulations and empirical data. The low root mean square error (RMSE) values across conditions further support the suitability of the 2P model for capturing the osmotic behavior of MII equine oocytes under the tested CPA conditions. These findings are consistent with reports in bovine oocytes, where 2P-based models have successfully described volumetric responses and supported the design of CPA loading schemes \\u003csup\\u003e\\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e10\\u003c/span\\u003e\\u003c/sup\\u003e.\\u003c/p\\u003e \\u003cp\\u003eOur study also provides insight into the influence of oocyte origin on osmotic behavior. Although slaughterhouse and OPU derived MII oocytes were obtained under different conditions and may represent distinct physiological backgrounds, their volume responses to the equilibration solution were similar and closely matched model predictions, indicating that the main biophysical parameters governing water and CPA transport are comparable between sources and supporting the use of abattoir-derived oocytes as a practical model for method development. Several limitations should nevertheless be considered such as technical factors, including potential mechanical effects associated with pipetting \\u003csup\\u003e\\u003cspan citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e16\\u003c/span\\u003e\\u003c/sup\\u003e, that may have contributed to minor deviations between predicted and observed volume trajectories. Even so, the close agreement between experimental data and simulations across temperatures and oocyte sources supports the robustness of the permeability parameters obtained in our study and their utility for guiding the optimization of vitrification protocols \\u003csup\\u003e\\u003cspan citationid=\\\"CR11\\\" class=\\\"CitationRef\\\"\\u003e11\\u003c/span\\u003e\\u003c/sup\\u003e. Further studies are now needed to validate these permeability data and \\u003cem\\u003ein silico\\u003c/em\\u003e predictions, particularly by assessing developmental competence after vitrification using model‑guided protocols.\\u003c/p\\u003e \\u003cp\\u003eThe high concordance between experimental and simulated volume profiles has several important implications for equine oocyte vitrification. First, it demonstrates that stage‑ and species‑specific permeability parameters can be reliably integrated into mathematical models to predict water and CPA fluxes under clinically relevant conditions. Similar modelling approaches have successfully guided CPA loading strategies in human oocytes\\u003csup\\u003e\\u003cspan citationid=\\\"CR29\\\" class=\\\"CitationRef\\\"\\u003e29\\u003c/span\\u003e\\u003c/sup\\u003e and have been shown to improve the prediction of osmotic responses in bovine oocytes\\u003csup\\u003e\\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e27\\u003c/span\\u003e\\u003c/sup\\u003e. In the equine species, previous studies on GV‑stage oocytes have already highlighted the value of combining experimental permeability measurements with computational simulations to optimize CPA exposure and reduce osmotic injury \\u003csup\\u003e\\u003cspan citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e16\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR23\\\" class=\\\"CitationRef\\\"\\u003e23\\u003c/span\\u003e\\u003c/sup\\u003e. Our results extend this modelling framework to MII oocytes, showing that accurate permeability parameters allow the rational design of CPA exposure protocols that maintain volume excursions within osmotic tolerance limits and minimize mechanical and biochemical stress. Second, the temperature-dependent differences observed in both \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e/\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e and the resulting volume dynamics suggest that performing equilibration at 38.5\\u0026deg;C may shorten the time oocytes spend outside their physiological volume range compared with 25\\u0026deg;C. Similar temperature-dependent increases in water and CPA fluxes have already reported in other species \\u003csup\\u003e\\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e27\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR30\\\" class=\\\"CitationRef\\\"\\u003e30\\u003c/span\\u003e\\u003c/sup\\u003e, indicating that higher temperatures can facilitate faster osmotic equilibration. This reduction in the duration of extreme shrinkage or swelling could be advantageous for preserving membrane integrity and cytoskeletal organization \\u003csup\\u003e\\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e27\\u003c/span\\u003e\\u003c/sup\\u003e. However, studies in marine oocytes also highlight that elevated temperatures may increase CPA toxicity and metabolic activity \\u003csup\\u003e\\u003cspan citationid=\\\"CR30\\\" class=\\\"CitationRef\\\"\\u003e30\\u003c/span\\u003e\\u003c/sup\\u003e, meaning that the optimal balance between osmotic safety and toxicity risk must still be empirically determined for equine oocytes.\\u003c/p\\u003e\"},{\"header\":\"CONCLUSIONS\",\"content\":\"\\u003cp\\u003eIn summary, this study provides the first detailed characterization of water (\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e) and cryoprotectant (\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e) permeability parameters, activation energies (E\\u003csub\\u003ea\\u003c/sub\\u003e), and osmotic behavior of \\u003cem\\u003ein vitro\\u003c/em\\u003e matured equine oocytes, and demonstrates that these data can be effectively incorporated into a two-parameter transport model. Our results show that equine oocytes behave as ideal osmometers with an osmotically inactive volume of 27%, exhibit maturation and temperature dependent changes in water and solute permeabilities, and display volume responses to equilibration solutions that are accurately predicted by \\u003cem\\u003ein silico\\u003c/em\\u003e simulations. These findings underscore the need for stage and species specific biophysical data when designing vitrification protocols, as extrapolation from other species or developmental stages may lead to suboptimal CPA exposure conditions.\\u003c/p\\u003e \\u003cp\\u003eBy providing experimentally validated permeability parameters for equine MII oocytes, our work establishes a quantitative basis for rational, model-guided optimization of CPA loading and unloading schemes, with the ultimate goal of improving oocyte survival, preserving cellular function, and enhancing developmental competence in equine assisted reproduction.\\u003c/p\\u003e\"},{\"header\":\"4. METHODOLOGY\",\"content\":\"\\u003cdiv id=\\\"Sec12\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.1. Chemicals and suppliers\\u003c/h2\\u003e \\u003cp\\u003eAll chemicals and reagents employed in this study were obtained from Sigma Chemical Co. (St. Louis, MO, USA), unless otherwise stated.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec13\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.2. Oocyte collection and \\u003cem\\u003ein vitro\\u003c/em\\u003e maturation (IVM)\\u003c/h2\\u003e \\u003cp\\u003eOvaries from mares were collected at two different local abattoirs (Escorxador Sabadell, Sabadell, Spain; and Vi\\u0026ntilde;als Soler, Argentona, Spain) and were transported to the laboratory in pre-warmed water (35\\u0026ndash;37\\u0026deg;C) within 4\\u0026ndash;6 h. Upon arrival at the laboratory, ovaries were cleaned with saline solution (0.9% sodium chloride (NaCl; 35\\u0026ndash;37\\u0026deg;C). Cumulus\\u0026ndash;oocyte complexes (COCs) were recovered from each follicle by initially incising the follicular wall with a scalpel to allow the release of follicular fluid. Subsequently, the internal walls of the follicle were carefully scraped using a sharp-edged curette to detach any remaining COCs. All contents were collected into tubes containing EquiPlus medium (Minitube, ref. 19982/2281). To maximize recovery, each follicle was additionally rinsed twice with EquiPlus medium and COCs were then collected under a stereomicroscope. Recovered COCs were kept overnight (approximately 17\\u0026ndash;18 h) at room temperature in holding medium (HM) consisting of TCM-199 Hanks\\u0026ndash;HEPES, TCM-199 Earle\\u0026rsquo;s, fetal bovine serum (FBS), sodium pyruvate and gentamicin to facilitate a better synchronization of the experimental set-up. The following day, oocytes were transferred to maturation medium containing TCM-199 Earle\\u0026rsquo;s, FBS, epidermal growth factor (EGF), and follicle-stimulating hormone (FSH), placed in four-well plates, and cultured for an additional 30 h at 38.5\\u0026deg;C in a 6% CO₂ atmosphere.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec14\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.3. Transvaginal Ultrasound-Guided Follicular Aspiration for Oocyte Retrieval\\u003c/h2\\u003e \\u003cp\\u003eOPU sesions were performed in 2 mares aged 10 and 15 years. Mares were evaluated by routine transrectal ultrasound scanning to find a good population of follicles between 1 and 2 cm in diameter for aspiration. Before follicular aspiration, preventive antibiotic therapy was administrated, as well as sedation, anesthesia, and antispasmodic treatment. For this purpose it was administered gentamycin sulfate (Genta equine\\u0026reg;, 6.6 mg/kg, iv, Dechra Veterinary Products, Aulendorf, Germany), flunixin meglumine (Flunixin inyectable \\u0026reg;, 1.1 mg/kg, iv, Norbrook, Newry, UK), detomidine hydrochloride (Domidine\\u0026reg; 0.02 mg/kg, iv, Dechra Veterinary Products, Aulendorf, Germany), butorphanol tartrate (Torbugesic\\u0026reg; 0.03 mg/kg, iv, Pfizer, New York, USA) and butylscopolamine (Buscapina\\u0026reg;, 0.12 mg/kg, iv, Boehringer Ingelheim, Ingelheim am Rhein, Germany). The vulva and perineum were washed three times with a neutral soap, and the bladder was emptied using a urinary catheter. OPU was performed by transvaginal ultrasound guided follicle aspiration/flushing using a 12-gauge double-lumen needle attached to a double vacuum pump (Minit\\u0026uuml;b, Tiefenbach, Germany) and a sectorial probe (SE3123, MyLabGamma, Esaote\\u0026reg;, Genova, Italy). All follicles between 1 to 2 cm were punctured and washed with flushing medium (Equiflush\\u0026reg;, Minit\\u0026uuml;b, Tiefenbach, Germany) supplemented with 1000 UI/L of sodium heparin (Heparina sodica\\u0026reg;, ROVI, Madrid, Spain). Recovered fluid was collected into pre-warmed 250 mL tubes (37\\u0026deg;C, REF: 23362/0251), filtered through a sterile 70 \\u0026micro;m embryo filter (EmCon\\u0026reg;, IMV Technologies, France), and the contents were examined in a 120 mm Petri dish to identify COCs under a stereomicroscope. A total of 22 oocytes were recovered from three OPU sessions (3 replicates).\\u003c/p\\u003e \\u003cp\\u003eThe protocol was approved by the Ethics Committee on Animal and Human Experimentation (CEEAH) of the Universitat Autonoma de Barcelona (CEEAH 1424) and all experiments were performed in accordance with relevant guidelines and regulations. Animals were maintained in paddocks, fed with grain, forage, straw, and hay, with ad libitum access to water, and housed at the Equine Reproduction Service of the Universitat Aut\\u0026ograve;noma de Barcelona (Bellaterra, Cerdanyola del Vall\\u0026egrave;s, Spain), which operates under strict health and animal welfare standards.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec15\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.4. Measurement of oocyte volumetric changes\\u003c/h2\\u003e \\u003cp\\u003eAfter 30 hours of \\u003cem\\u003ein vitro\\u003c/em\\u003e maturation (IVM), oocytes were denuded of cumulus cells with the help of 10 mg mL\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e hyaluronidase (HYA). Only matured oocytes showing a normal appearance and a visible first polar body were used for subsequent experiments. An oocyte was placed in a 25 \\u0026micro;L drop of HM covered with mineral oil, and held with a holding pipette (outer diameter, 100 \\u0026micro;m) connected to a micromanipulator on an inverted microscope (Zeiss Axio Vert A1, Germany). An initial photograph was taken to calculate the initial volume of the oocyte using a time-lapse video recorder (Zeiss Zen imaging software/Axiocam ERc 5s). The oocyte was then covered with another pipette of larger inner diameter (600 \\u0026micro;m) connected to a different micromanipulator. By sliding the dish, the oocyte was introduced into a 25 \\u0026micro;L drop containing different treatment solutions and left to equilibrate for 20 or 10 min at 25\\u0026deg;C or 38.5\\u0026deg;C respectively (see Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e). Images were taken every 5 s using a time-lapse video recorder with a camera mounted on an inverted light microscope. Their cross-sectional areas were quantified with the image analysis software ImageJ v1.54 (National Institutes of Health, Bethesda, MD, USA) as described in Garc\\u0026iacute;a-Mart\\u0026iacute;nez \\u003cem\\u003eet al.\\u003c/em\\u003e \\u003csup\\u003e27\\u003c/sup\\u003e. From the measured area, the oocyte radius (r) was determined, which was then used to calculate the cell volume (V\\u003csub\\u003eo\\u003c/sub\\u003e) and surface area (A\\u003csub\\u003eo\\u003c/sub\\u003e). Oocytes that failed to exhibit the expected shrinkage or swelling behavior were classified as damaged and were excluded from the analysis.\\u003c/p\\u003e \\u003cp\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec16\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.5. Estimation of the Osmotically Inactive Volume Using Boyle\\u0026ndash;van \\u0026rsquo;t Hoff Analysis\\u003c/h2\\u003e \\u003cp\\u003eFor the correct application of cell membrane transport models, it was assumed that oocytes behave as ideal osmometers. Accordingly, they were expected to follow the Boyle\\u0026ndash;van \\u0026rsquo;t Hoff relationship, displaying a linear correlation between cell volume and the inverse of the medium osmolality\\u003csup\\u003e\\u003cspan citationid=\\\"CR31\\\" class=\\\"CitationRef\\\"\\u003e31\\u003c/span\\u003e\\u003c/sup\\u003e. To verify that \\u003cem\\u003ein vitro\\u003c/em\\u003e matured equine oocytes followed this behavior, their osmotic response was assessed by measuring volume changes in both hypotonic and hypertonic solutions. We used holding medium (HM; 80% TCM-199\\u0026thinsp;+\\u0026thinsp;20% FBS) as an isotonic condition and the osmolality of the solution was verified to be 292\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.003 mOsm kg\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e (mean\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;standard error of mean (SEM)) using a cryoscopic osmometer (Osmomat 030, Gonotec). The osmolality of the treatment solutions was then adjusted by adding calculated amounts of Milli-Q water (hypotonic) or sucrose (hypertonic), resulting in final solution osmolalities ranging from 234\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.001 mOsm/kg to 1903\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.013 mOsm kg\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e. For each oocyte, an initial volume measurement in HM was obtained as a control prior to exposure to the different media. Subsequently, the oocyte was transferred into the treatment solutions and left to equilibrate for 10 min at 38.5\\u0026deg;C before recording the volume again. A total of 35 MII equine oocytes that remained close to spherical in shape were individually analyzed (with a minimum of five oocytes per condition). Cell volume measurements in each solution were first normalized to the reference volume under isotonic conditions. These normalized values were then plotted as a function of the reciprocal of the osmolality of the treatment solutions.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec17\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.6. Membrane permeability parameters\\u003c/h2\\u003e \\u003cp\\u003eA two-parameter transport model was used to describe how water and permeating solutes move across the cell membrane over time, using two coupled differential equations and assuming no interaction between water and the permeating solutes within the membrane. This model allowed us to determine the permeability of equine IVM oocytes to water (\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e) and to CPAs (\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e). Water flux into the cell over time is expressed as (1):\\u003cdiv id=\\\"Equa\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equa\\\" name=\\\"EquationSource\\\"\\u003e\\n$$\\\\left(1\\\\right)\\\\frac{d{V}_{w}}{dt}=-{L}_{p}ART\\\\left(Me-Mi\\\\right)$$\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere V\\u003csub\\u003ew\\u003c/sub\\u003e is the cell water volume, \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e is the membrane permeability to water (hydraulic conductivity), A is the area of the plasma membrane, R is the universal gas constant, T is the absolute temperature, and M\\u003csub\\u003ee\\u003c/sub\\u003e and M\\u003csub\\u003ei\\u003c/sub\\u003e are the total external and internal osmolalities, respectively. The rate of the CPA transport is given by (2):\\u003cdiv id=\\\"Equb\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equb\\\" name=\\\"EquationSource\\\"\\u003e\\n$$\\\\left(2\\\\right)\\\\frac{d{N}_{s}}{dt}={P}_{s}A\\\\left({M}_{s}^{e}-{M}_{s}^{i}\\\\right)$$\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere N\\u003csub\\u003es\\u003c/sub\\u003e is the intracellular moles of CPA, \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e is CPA permeability and M\\u003csub\\u003ei s\\u003c/sub\\u003e\\u003csup\\u003e\\u0026minus;1\\u003c/sup\\u003e and M\\u003csub\\u003ee s\\u003c/sub\\u003e\\u003csup\\u003e\\u0026minus;1\\u003c/sup\\u003e are the intracellular and extracellular CPA molalities, respectively. In order to determine \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e and \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e for each CPA and temperature the image analysis data obtained from each oocyte was fitted to the 2P model as previously described by Garc\\u0026iacute;a Mart\\u0026iacute;nez \\u003cem\\u003eet al.\\u003c/em\\u003e\\u003csup\\u003e27\\u003c/sup\\u003e. The equations for water and CPA transport were solved numerically using the ode15s function in Matlab software. Model predictions were fitted to the data to estimate permeabilities by minimizing the sum error squared in Matlab using the fminsearch function, which implements the Nelder-mead simplex algorithm \\u003csup\\u003e\\u003cspan citationid=\\\"CR32\\\" class=\\\"CitationRef\\\"\\u003e32\\u003c/span\\u003e\\u003c/sup\\u003e. An average of eight oocytes per condition that remained close to spherical in shape were used. Parameters are described in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab5\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e.\\u003c/p\\u003e \\u003cp\\u003e \\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab5\\\" border=\\\"1\\\"\\u003e \\u003ccaption language=\\\"En\\\"\\u003e \\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 5\\u003c/div\\u003e \\u003cdiv class=\\\"CaptionContent\\\"\\u003e \\u003cp\\u003eThermodynamic and Volume Parameters Used for Modeling Water and CPA Transport\\u003c/p\\u003e \\u003c/div\\u003e \\u003c/caption\\u003e \\u003ccolgroup cols=\\\"4\\\"\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e \\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e \\u003cthead\\u003e \\u003ctr\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eDescription\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003eValues\\u003c/p\\u003e \\u003c/th\\u003e \\u003cth align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e \\u003cp\\u003eSymbol\\u003c/p\\u003e \\u003c/th\\u003e \\u003c/tr\\u003e \\u003c/thead\\u003e \\u003ctbody\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eUniversal gas constant\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e8.314 m\\u003csup\\u003e3\\u003c/sup\\u003e PA K\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e mol\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e \\u003cp\\u003eR\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eAbsolute temperature\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e298 K (25\\u0026deg;C) or 311 K (38.5\\u0026deg;C)\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eT\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colspan=\\\"1\\\" nameend=\\\"c4\\\" namest=\\\"c4\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eMolar volume of water\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e18.02*10\\u003csup\\u003e12\\u003c/sup\\u003e \\u0026micro;M mol\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eV\\u003csub\\u003ew\\u003c/sub\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colspan=\\\"1\\\" nameend=\\\"c4\\\" namest=\\\"c4\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e \\u003cp\\u003eMolar volume of CPA\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e55.8*10\\u003csup\\u003e\\u0026minus;\\u0026thinsp;6\\u003c/sup\\u003e m\\u003csup\\u003e3\\u003c/sup\\u003e mol\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e EG \\u003csup\\u003e33\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e \\u003cp\\u003eV\\u003csub\\u003es1\\u003c/sub\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colspan=\\\"1\\\" nameend=\\\"c4\\\" namest=\\\"c4\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003c/tr\\u003e \\u003ctr\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u0026nbsp;\\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e \\u003cp\\u003e71.3*10\\u003csup\\u003e\\u0026minus;\\u0026thinsp;6\\u003c/sup\\u003e m\\u003csup\\u003e3\\u003c/sup\\u003e mol\\u003csup\\u003e\\u0026minus;\\u0026thinsp;1\\u003c/sup\\u003e Me\\u003csub\\u003e2\\u003c/sub\\u003eSO \\u003csup\\u003e\\u003cspan citationid=\\\"CR33\\\" class=\\\"CitationRef\\\"\\u003e33\\u003c/span\\u003e\\u003c/sup\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003ctd align=\\\"left\\\" colspan=\\\"2\\\" nameend=\\\"c4\\\" namest=\\\"c3\\\"\\u003e \\u003cp\\u003eV\\u003csub\\u003es2\\u003c/sub\\u003e\\u003c/p\\u003e \\u003c/td\\u003e \\u003c/tr\\u003e \\u003c/tbody\\u003e \\u003c/colgroup\\u003e \\u003c/table\\u003e\\u003c/div\\u003e \\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec18\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.7. Mathematical \\u003cem\\u003ein silico\\u003c/em\\u003e predictions\\u003c/h2\\u003e \\u003cp\\u003eTo predict cell volume response and intracellular CPA concentration when MII equine oocytes were exposed to equilibration solution (ES; HM supplemented with 7.5% (v/v) Me\\u003csub\\u003e2\\u003c/sub\\u003eSO and 7.5% (v/v) EG) two solute transport equations were defined, one for Me\\u003csub\\u003e2\\u003c/sub\\u003eSO and another for EG. For this purpose, a system of three ordinary differential equations was solved for the three variables (V\\u003csub\\u003ew\\u003c/sub\\u003e, \\u0026#119873;\\u003csub\\u003eMe2SO\\u003c/sub\\u003e and \\u0026#119873;\\u003csub\\u003eEG\\u003c/sub\\u003e) in Matlab software using the ode15s function, which implements an explicit Runge-Kutta formula \\u003csup\\u003e\\u003cspan citationid=\\\"CR34\\\" class=\\\"CitationRef\\\"\\u003e34\\u003c/span\\u003e,\\u003cspan citationid=\\\"CR35\\\" class=\\\"CitationRef\\\"\\u003e35\\u003c/span\\u003e\\u003c/sup\\u003e.\\u003c/p\\u003e \\u003cp\\u003eThe rate of Me\\u003csub\\u003e2\\u003c/sub\\u003eSO transport is given by (3):\\u003c/p\\u003e \\u003cp\\u003e(3) \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\frac{dNM{e}_{2}SO}{dt}=PM{e}_{2}SOA\\\\left({M}_{M{e}_{2}SO}^{e}-{M}_{M{e}_{2}SO}^{i}\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/p\\u003e \\u003cp\\u003eAnd the rate of EG transport is given by (4):\\u003c/p\\u003e \\u003cp\\u003e(4) \\u003cspan class=\\\"InlineEquation\\\"\\u003e\\u003cspan class=\\\"mathinline\\\"\\u003e\\\\(\\\\frac{dNEG}{dt}=PEGA\\\\left({M}_{EG}^{e}-{M}_{EG}^{i}\\\\right)\\\\)\\u003c/span\\u003e\\u003c/span\\u003e\\u003c/p\\u003e \\u003cp\\u003e \\u003cem\\u003eIn silico\\u003c/em\\u003e predictions for the ES exposure were performed at 25\\u0026deg;C or 38.5\\u0026deg;C using water and solute permeability values estimated in the experiments described above. Water permeability was assumed to be the mean \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e value at the given temperature, obtained by averaging the individual measurements for MII oocytes exposed to 1.55 M Me\\u003csub\\u003e2\\u003c/sub\\u003eSO or 1.55 M EG.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec19\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.8. Determination of activation Energy of Membrane Permeability in \\u003cem\\u003ein vitro\\u003c/em\\u003e Matured Equine Oocytes\\u003c/h2\\u003e \\u003cp\\u003eThe permeability of the plasma membrane to water (\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e) and cryoprotective agents (\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e) in MII equine oocytes was measured at two temperatures; 25\\u0026deg;C and 38.5\\u0026deg;C. As the same oocytes were not measured at both temperatures, activation energies (E\\u003csub\\u003ea\\u003c/sub\\u003e) were estimated using the mean \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e and \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e values for each temperature. Experimental values were converted to Kelvin and linearized using the Arrhenius Eq.\\u0026nbsp;(5) \\u003csup\\u003e36\\u003c/sup\\u003e:\\u003cdiv id=\\\"Equc\\\" class=\\\"Equation\\\"\\u003e\\u003cdiv format=\\\"TEX\\\" class=\\\"mathdisplay\\\" id=\\\"FileID_Equc\\\" name=\\\"EquationSource\\\"\\u003e\\n$$\\\\left(5\\\\right)\\\\text{ln}\\\\left(k\\\\right)=\\\\text{ln}\\\\left(k0\\\\right)-\\\\frac{Ea}{RT}$$\\u003c/div\\u003e\\u003c/div\\u003e\\u003c/p\\u003e \\u003cp\\u003ewhere k represents \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e or \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e, R is the gas constant (1.987 cal\\u0026middot;mol⁻\\u0026sup1;\\u0026middot;K⁻\\u0026sup1;), E\\u003csub\\u003ea\\u003c/sub\\u003e is the activation energy, and k\\u003csub\\u003e0\\u003c/sub\\u003e is the pre-exponential factor. E\\u003csub\\u003ea\\u003c/sub\\u003e was calculated from the slope of ln(k) versus 1/T, and k\\u003csub\\u003e0\\u003c/sub\\u003e from the intercept. Although individual oocyte measurements at both temperatures were not available, the resulting E\\u003csub\\u003ea\\u003c/sub\\u003e values reflect the average temperature sensitivity of membrane water and cryoprotectant transport. All calculations were performed in Microsoft Excel.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec20\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.9. \\u003cem\\u003eIn vitro\\u003c/em\\u003e osmotic behaviour following ES exposure at 25\\u0026deg;C and 38.5\\u0026deg;C\\u003c/h2\\u003e \\u003cp\\u003eTo assess the accuracy of the model predictions, the \\u003cem\\u003ein silico\\u003c/em\\u003e values generated by the theoretical models were compared with \\u003cem\\u003ein vitro\\u003c/em\\u003e measurements of the osmotic response of equine MII oocytes exposed to the equilibration solution (ES; 7.5% (v/v) EG and 7.5% (v/v) Me₂SO in TCM-199 HEPES) at the designated temperatures (25\\u0026deg;C or 38.5\\u0026deg;C). For each temperature, an average of 10 MII equine oocytes, each maintaining an approximately spherical shape, were individually analyzed. To further evaluate whether oocytes recovered via OPU exhibit similar behavior, an additional experimental group was included.\\u003c/p\\u003e \\u003c/div\\u003e \\u003cdiv id=\\\"Sec21\\\" class=\\\"Section2\\\"\\u003e \\u003ch2\\u003e4.10. Statistical analysis\\u003c/h2\\u003e \\u003cp\\u003eStatistical analyses were performed using GraphPad Prism (version 9.3.1). To determine the osmotic inactive volume of MII equine oocytes, data were fitted to the Boyle\\u0026ndash;van\\u0026rsquo;t Hoff equation. A linear least squares approach was applied to fit the data, and linear regression was used to extrapolate the relationship, allowing estimation of the cell volume at infinite osmolality (V\\u003csub\\u003eb\\u003c/sub\\u003e). Permeability parameters (\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e and \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e) were assessed using the Shapiro\\u0026ndash;Wilk test to evaluate normality, followed by a one-way ANOVA with multiple comparisons to assess differences between CPAs and temperatures.\\u003c/p\\u003e \\u003cp\\u003eTo evaluate the agreement between model predictions and \\u003cem\\u003ein vitro\\u003c/em\\u003e measurements as an integrative descriptor of the overall volumetric response the area under the curve (AUC) was calculated for each oocyte \\u003csup\\u003e\\u003cspan citationid=\\\"CR37\\\" class=\\\"CitationRef\\\"\\u003e37\\u003c/span\\u003e\\u003c/sup\\u003e, and either a Kruskal\\u0026ndash;Wallis test or an ordinary one-way ANOVA with multiple comparisons was performed depending on data normality. In addition, the root mean squared error (RMSE) was calculated. A significance level of \\u003cem\\u003eP\\u003c/em\\u003e\\u0026thinsp;\\u0026lt;\\u0026thinsp;0.05 was considered statistically significant for all analyses.\\u003c/p\\u003e \\u003c/div\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003e \\u003ch2\\u003eCompeting interests\\u003c/h2\\u003e \\u003cp\\u003eThe author(s) declare no competing interests.\\u003c/p\\u003e \\u003c/p\\u003e\\u003ch2\\u003eFunding\\u003c/h2\\u003e \\u003cp\\u003eThis study was supported by research project PID2024-160962OB-I00 (funded by MCIN/AEI/\\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003e10.13039/501100011033/\\u003c/span\\u003e\\u003cspan address=\\\"10.13039/501100011033/\\\" targettype=\\\"DOI\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e) and Project 2021 SGR 00900 (Generalitat de Catalunya) to TM. Mrs. Gago is funded by a predoctoral grant from Generalitat de Catalunya (DI00002), and Ms. D\\u0026iacute;az-Mu\\u0026ntilde;oz holds a predoctoral scholarship PRE2021-098675 (funded by MCIN/AEI/\\u003cspan class=\\\"ExternalRef\\\"\\u003e\\u003cspan class=\\\"RefSource\\\"\\u003e10.13039/501100011033/\\u003c/span\\u003e\\u003cspan address=\\\"10.13039/501100011033/\\\" targettype=\\\"DOI\\\" class=\\\"RefTarget\\\"\\u003e\\u003c/span\\u003e\\u003c/span\\u003e).\\u003c/p\\u003e\\u003ch2\\u003eAuthor Contribution\\u003c/h2\\u003e\\u003cp\\u003eSG: Writing original draft, Visualization, Validation, Investigation, Formal analysis, Data curation. TGM: Visualization, Supervision, Validation. JDM: Investigation. MA: Investigation. JC: Investigation. JM: Investigation. AZH: Investigation, Supervision. NCB: Investigation, Supervision, Project administration, Funding. TM: Writing review \\u0026amp; editing, Validation, Supervision, Project administration, Funding, Investigation, Data curation.\\u003c/p\\u003e\\u003ch2\\u003eAcknowledgement\\u003c/h2\\u003e\\u003cp\\u003eWe thank the staff at Escorxador Sabadell S.L. and Argentona (SVO. Vi\\u0026ntilde;als Soler) slaughterhouses for kindly providing access to ovarian samples essential for this study. We thank BioRender.com for providing the platform used to create the Figure 1.\\u003c/p\\u003e\\u003ch2\\u003eData Availability\\u003c/h2\\u003e\\u003cp\\u003eAll data supporting the findings of this study are available within the paper\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\u003cli\\u003e\\u003cspan\\u003eBosch, E., De Vos, M. \\u0026amp; Humaidan, P. The Future of Cryopreservation in Assisted Reproductive Technologies. \\u003cem\\u003eFront. Endocrinol.\\u003c/em\\u003e \\u003cb\\u003e11\\u003c/b\\u003e, 67 (2020).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eParmegiani, L. et al. Blastocyst formation, pregnancy, and birth derived from human oocytes cryopreserved for 5 years. Fertility and Sterility 90, 2014.e7-2014.e10 (2008).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eDe Coster, T., Velez, D. A., Van Soom, A., Woelders, H. \\u0026amp; Smits, K. Cryopreservation of equine oocytes: looking into the crystal ball. \\u003cem\\u003eReprod. Fertil. Dev.\\u003c/em\\u003e \\u003cb\\u003e32\\u003c/b\\u003e, 453 (2020).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eSon, W. Y. \\u0026amp; Tan, S. L. Comparison between slow freezing and vitrification for human embryos. \\u003cem\\u003eExpert Rev. Med. Dev.\\u003c/em\\u003e \\u003cb\\u003e6\\u003c/b\\u003e, 1\\u0026ndash;7 (2009).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eMaclellan, L. J. et al. Pregnancies from vitrified equine oocytes collected from super-stimulated and non-stimulated mares. \\u003cem\\u003eTheriogenology\\u003c/em\\u003e \\u003cb\\u003e58\\u003c/b\\u003e, 911\\u0026ndash;919 (2002).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eAngel-Velez, D. et al. New Alternative Mixtures of Cryoprotectants for Equine Immature Oocyte Vitrification. \\u003cem\\u003eAnimals\\u003c/em\\u003e \\u003cb\\u003e11\\u003c/b\\u003e, 3077 (2021).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eAngel, D. et al. Embryo development after vitrification of immature and in vitro-matured equine oocytes. \\u003cem\\u003eCryobiology\\u003c/em\\u003e \\u003cb\\u003e92\\u003c/b\\u003e, 251\\u0026ndash;254 (2020).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eDu, M. et al. Optimization of vitrification methods for equine oocytes. \\u003cem\\u003eTissue Cell.\\u003c/em\\u003e \\u003cb\\u003e91\\u003c/b\\u003e, 102632 (2024).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eBenson, J. D., Kearsley, A. J. \\u0026amp; Higgins, A. Z. Mathematical optimization of procedures for cryoprotectant equilibration using a toxicity cost function. \\u003cem\\u003eCryobiology\\u003c/em\\u003e \\u003cb\\u003e64\\u003c/b\\u003e, 144\\u0026ndash;151 (2012).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eGarc\\u0026iacute;a-Mart\\u0026iacute;nez, T. et al. 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S. \\u0026amp; Critser, J. K. Effect of developmental stage on bovine oocyte plasma membrane water and cryoprotectant permeability characteristics. \\u003cem\\u003eMol. Reprod. Dev.\\u003c/em\\u003e \\u003cb\\u003e49\\u003c/b\\u003e, 408\\u0026ndash;415 (1998).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eFahy, G. M., Wowk, B., Wu, J. \\u0026amp; Paynter, S. Improved vitrification solutions based on the predictability of vitrification solution toxicity. \\u003cem\\u003eCryobiology\\u003c/em\\u003e \\u003cb\\u003e48\\u003c/b\\u003e, 22\\u0026ndash;35 (2004).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eGandhi, G., Kuwayama, M., Kagalwala, S., Pangerkar, P. \\u0026amp; Appendix, A. Cryotech\\u0026reg; Vitrification Thawing. in Cryopreservation of Mammalian Gametes and Embryos (eds Nagy, Z. P., Varghese, A. 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Advances in the cryopreservation of mammalian oocytes and embryos: Development of ultrarapid vitrification. \\u003cem\\u003eReprod. Med. Biology\\u003c/em\\u003e. \\u003cb\\u003e1\\u003c/b\\u003e, 1\\u0026ndash;9 (2002).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eDavidson, A. F., Benson, J. D. \\u0026amp; Higgins, A. Z. Mathematically optimized cryoprotectant equilibration procedures for cryopreservation of human oocytes. \\u003cem\\u003eTheor. Biol. Med. Model.\\u003c/em\\u003e \\u003cb\\u003e11\\u003c/b\\u003e, 13 (2014).\\u003c/span\\u003e\\u003c/li\\u003e \\u003cli\\u003e\\u003cspan\\u003eOlver, D. J., Heres, P., Paredes, E. \\u0026amp; Benson, J. D. 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Res.\\u003c/em\\u003e \\u003cb\\u003e28\\u003c/b\\u003e, 1081\\u0026ndash;1089 (2011).\\u003c/span\\u003e\\u003c/li\\u003e\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"scientific-reports\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"scirep\",\"sideBox\":\"Learn more about [Scientific Reports](http://www.nature.com/srep/)\",\"snPcode\":\"\",\"submissionUrl\":\"\",\"title\":\"Scientific Reports\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Scientific Reports\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Vitrification, osmotic response, membrane transport, activation energy, assisted reproduction\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-9031036/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-9031036/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eVitrification of equine oocytes is an essential practice for advancing assisted reproductive technologies however, its efficiency remains limited due to the lack of stage and species-specific information on membrane permeability parameters. In this study, water (\\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e) and CPA permeability (\\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e) for dimethyl sulfoxide (Me₂SO) and ethylene glycol (EG) were measured in \\u003cem\\u003ein vitro\\u003c/em\\u003e matured (MII) equine oocytes. Cumulus oocyte complexes were obtained from abattoir ovaries or by ovum pick-up and matured \\u003cem\\u003ein vitro\\u003c/em\\u003e for 30h at 6% CO\\u003csub\\u003e2\\u003c/sub\\u003e. Oocytes followed ideal osmometer behavior principles, with an osmotically inactive volume of 27%. \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e increased with temperature from 0.941\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.082 \\u0026micro;mmin⁻\\u0026sup1;atm⁻\\u0026sup1; at 25\\u0026deg;C to 1.462\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.084 \\u0026micro;mmin⁻\\u0026sup1;atm⁻\\u0026sup1; in Me₂SO, and from 0.889\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.094 to 1.613\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.066 \\u0026micro;mmin⁻\\u0026sup1; atm⁻\\u0026sup1; in EG. \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e also increased significantly with temperature: \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003esMe₂SO\\u003c/em\\u003e\\u003c/sub\\u003e rose from 0.175\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.024 \\u0026micro;m/s to 0.353\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.022 \\u0026micro;m/s and \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003esEG\\u003c/em\\u003e\\u003c/sub\\u003e from 0.138\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.020 \\u0026micro;m/s to 0.349\\u0026thinsp;\\u0026plusmn;\\u0026thinsp;0.014 \\u0026micro;m/s. Activation energies (E\\u003csub\\u003ea\\u003c/sub\\u003e) were 6.03 and 8.15 kcal/mol for \\u003cem\\u003eL\\u003c/em\\u003e\\u003csub\\u003ep\\u003c/sub\\u003e, and 9.60 and 12.69 kcal/mol for \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003es\\u003c/sub\\u003e for Me₂SO and EG, respectively. \\u003cem\\u003eIn silico\\u003c/em\\u003e predictions closely matched \\u003cem\\u003ein vitro\\u003c/em\\u003e observations. Simulations predicted that oocytes recovered their original volume after 7min 42s at 38.5\\u0026deg;C and at 25\\u0026deg;C after 17min 8s. This study provides the first stage and species-specific permeability values for MII equine oocytes, supporting improved vitrification modeling.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Water and cryoprotectant permeability of mature equine oocytes: experimental measurements and in silico predictions\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2026-03-19 13:13:37\",\"doi\":\"10.21203/rs.3.rs-9031036/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Revision requested\",\"date\":\"2026-04-10T11:41:09+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2026-04-10T04:43:12+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2026-04-07T16:44:08+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2026-03-26T17:44:33+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"293372994881323349423191125171454564947\",\"date\":\"2026-03-19T16:39:10+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"3187810705322216401574214355482373164\",\"date\":\"2026-03-18T10:41:00+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"41893653900483954111008569973937281127\",\"date\":\"2026-03-18T02:51:28+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2026-03-17T08:23:56+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvited\",\"content\":\"\",\"date\":\"2026-03-09T12:48:17+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2026-03-05T06:29:13+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"checksComplete\",\"content\":\"\",\"date\":\"2026-03-05T06:25:34+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Scientific Reports\",\"date\":\"2026-03-04T13:46:39+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"scientific-reports\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"scirep\",\"sideBox\":\"Learn more about [Scientific Reports](http://www.nature.com/srep/)\",\"snPcode\":\"\",\"submissionUrl\":\"\",\"title\":\"Scientific Reports\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Scientific Reports\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"dfc91603-ee0d-41ac-8283-10fb4f6b17e4\",\"owner\":[],\"postedDate\":\"March 19th, 2026\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"under-review\",\"subjectAreas\":[{\"id\":64718626,\"name\":\"Biological sciences/Biochemistry\"},{\"id\":64718627,\"name\":\"Biological sciences/Biotechnology\"},{\"id\":64718628,\"name\":\"Biological sciences/Physiology\"}],\"tags\":[],\"updatedAt\":\"2026-05-18T12:55:51+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2026-03-19 13:13:37\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-9031036\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-9031036\",\"identity\":\"rs-9031036\",\"version\":[\"v1\"]},\"buildId\":\"XKTyCvWXoU3ODBz1xrDgd\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}