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Research Papers

# Effect of Hydroxyapatite Nanoparticles on Biotransport Phenomena in Freezing HeLa CellsOPEN ACCESS

[+] Author and Article Information
Jingru Yi

Department of Electronic Science and Technology,
University of Science and Technology of China,
Hefei 230027, China

Gang Zhao

Department of Electronic Science and Technology,
University of Science and Technology of China,
Hefei 230027, China
Anhui Provincial Engineering Technology
Research Center for Biopreservation and
Artificial Organs,
Hefei 230027, China
e-mail: zhaog@ustc.edu.cn

1Corresponding author.

Manuscript received July 25, 2014; final manuscript received November 26, 2014; published online June 16, 2015. Assoc. Editor: Jianping Fu.

J. Nanotechnol. Eng. Med 5(4), 040904 (Nov 01, 2014) (7 pages) Paper No: NANO-14-1050; doi: 10.1115/1.4029331 History: Received July 25, 2014; Revised November 26, 2014; Online June 16, 2015

## Abstract

The effect of nanoparticles on subzero biotransport phenomena of living cells is very rare in the literature, although the information is of great importance for the application of nanotechnology in the field of cryobiology. In this study, subzero water transport phenomena in freezing HeLa cells in 1 × phosphate buffered saline (PBS) containing 0%, 0.05%, and 0.1% (w/w) hydroxyapatite (HA) nanoparticles with and without pre-incubation at 37 °C was quantitatively investigated. The results reveal that the presence of HA nanoparticles slightly facilitates the subzero water transport of HeLa cells.

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## Introduction

Cryopreservation and cryotherapy are two biomedical applications in cryogenics. Cryopreservation is a way to achieve long-term banking of cells, tissues or organs [1,2]. Cryotherapy, which is also called cryosurgery or cryoablation, is a way to destroy undesired tissues by freezing [3,4,5-3,4,5]. During typical freezing, two biophysical processes can cause damages to cells: intracellular ice formation (IIF) and excessive cell dehydration [6]. Both of the two events are closely associated with the subzero water transport across the cell membrane: on the one hand, a higher than optimal cooling rate stops the intracellular water flux out of the cell and then causes IIF [7]; on the other hand, a suboptimum cooling rate allows enough time for cells to lose water but could cause injury due to severe cell dehydration [1]. Therefore, investigation of subzero water transport of living cells are of great importance to optimize both cryopreservation and cryotherapy procedures.

Nanoparticles have long been used to solve challenges emerged in diagnosis and treatment fields, such as cancer destruction [8,9,10,11-8,9,10,11] and tumor cryoablation [5,12]. Recently, it is reported that the presence of nanoparticles changes the thermal conductivities and the kinetics of ice nucleation and growth in solutions during freezing [10,13,14,15-13,14,15]. For example, incorporating HA nanoparticles to glycerol and PEG-600 solutions has been proven to significantly affect the solutions' behavior of devitrification and recrystallization upon warming [14]. Also, palmitoyl nanogold particles are reported to have a complex effect on homogeneous nucleation temperature and phase change temperature of the dimethyl sulfoxide solutions [16]. These findings suggest that it is possible to apply nanotechnology in the field of cryopreservation in order to improve the cryopreservation outcome by modulating the thermophysical properties of the cryopreservation solutions.

Therefore, we are motivated to find out if nanotechnology could also be used to modulate the water transport across living cells during freezing since the typical cryopreservation methods are facing many challenges [17], such as chemical toxicity of cryoprotective agents (CPAs). However, to the best of our knowledge, the effect of nanoparticles on subzero biotransport of living cells remains unexplored although the information is of importance for applying nanotechnology to the field of cryobiology.

In this study, the influence of nanoparticles on subzero water transport of HeLa cells in 1 × PBS solutions during freezing with and without pre-incubation at 37 °C was quantitatively studied. The aim of pre-incubation before experiments was to determine whether or not the incubation can facilitate the uptake of the nanoparticles by cells, which might change the water transport across the cells. HA [Ca10(OH)2(PH4)6)] nanoparticles were utilized because of their excellent biocompatibility and absorbability [18,19]. Microscopic topography of cell membrane surface was studied using scanning electron microscopy (SEM).

## Materials and Methods

###### Reagents and Cells.

HeLa cells were obtained from Longping Wen (USTC, China) as a gift. Dulbecco's modified eagle's medium (DMEM), fetal bovine serum (FBS), and penicillin G and streptomycin were obtained from Hyclone (Thermo Fisher Scientific, Inc., Waltham, MA). DMEM was supplemented with penicillin G (100 U L-1) and streptomycin (100 U L-1). Trypsin was obtained from Biosharp (Biosharp Co., China).

HA nanoparticles, short rodlike (20 nm in diameter and 100 nm long), were purchased from Nanjing Emperor Nano Material Co., Ltd. (Nanjing, China). Sodium hexametaphosphate [Na6(PO3)6] was purchased from Sangon Biotech Co., Ltd. (Shanghai, China).

###### Determination of the Necessary Amount of Sodium Hexametaphosphate as Dispersant.

Sodium hexametaphosphate [Na6(PO3)6] (Sangon Biotech Co., Ltd., China) was used as dispersant to prevent nanoparticles from aggregating in the solution based on the electrostatic repulsion and steric hindrance effects [20]. In order to minimize the amount of Na6(PO3)6 in cell suspensions because excessive Na6(PO3)6 may impede the differentiation of living cells [20], we needed to find out if a small amount of Na6(PO3)6 could be adopted while it was still efficient in dispersing the HA nanoparticles in the solution. According to the fact that nanoparticles' aggregation enlarges the particle radius, the particle radius of the solution was then regarded as the indication of its dispersion degree.

The particle radii at different weight ratio of Na6(PO3)6 to HA measured by a DYNAPRO-99 (Wyatt Technology Corp., Santa Barbara, CA) dynamic light scattering instrument are shown in Fig. 1. It can be seen from the figure that is less aggregated with the increase of Na6(PO3)6. However, particle radius at 0.05 weight ratio of Na6(PO3)6 to HA (119.8 nm) is relatively small, suggesting the solution at such weight ratio is also highly dispersed. Therefore, we decided to use a weight ratio of 0.05 for further studies.

We also conducted the sedimentation experiments to make sure that such small amount of Na6(PO3)6 can make the nanoparticle suspension highly dispersed throughout our entire experiments. Solutions containing 0.1% HA nanoparticle with and without Na6(PO3)6 were used to make the comparison. Note that solutions without nanoparticles were transparent at first. After adding HA nanoparticles and subsequently dispersing the nanoparticle suspensions by using an ultrasonic cleaner (Shanghai KUDOS Ultrasonic Instrument Co., Ltd., China), the solution became turbid and appeared milky (Fig. 2). It can be seen from Fig. 2 that at 0 h, the two suspensions were both homogeneous (indicated by milky color). However, after 0.5 h, the HA nanoparticles in the solutions without Na6(PO3)6 began to aggregate and sink to the bottom (indicated by arrows) whereas the solutions with Na6(PO3)6 stayed homogeneous. Considering the experiment only lasted no more than half an hour, the small amount of Na6(PO3)6 was considered to be sufficient for our experiment.

###### Preparation of HA Nanoparticle Suspensions.

The HA nanoparticle suspensions were prepared by mixing HA nanoparticles and Na6(PO3)6 in 1 × PBS solutions. The HA concentrations were 0%, 0.05%, and 0.1% (w/w). The weight of Na6(PO3)6 was 0.05 of that of HA. The osmolality of the nanoparticle suspensions with HA concentration of 0%, 0.05%, and 0.1% were all measured to be 290 mOsm using a Fiske Micro-Osmometer (Model 216, Advanced Instruments, Inc., Norwood, MA).

###### Preparation of Cell Suspension.

HeLa cells were cultured in DMEM supplemented with 10% FBS in a humidified atmosphere of 5% CO2 at 37 °C. The cells were detached using 20% Trypsin at up to 90% confluence. The harvested cells were then centrifuged at 100 × g for 5 min and resuspended in the prepared HA nanoparticle suspensions. Half of the cell suspensions were then put back to the incubator for 10 min of incubation at 37 °C.

Finally, five cell suspensions were investigated: cells in 1 × PBS and cells in 0.05%, 0.1% HA nanoparticle suspensions with and without incubation. We took these five cell suspensions as five different experimental groups.

###### Subzero Water Transport Experiments.

Experiments were conducted using an Olympus BX53 microscope (Olympus Corp., Tokyo, Japan) with a 50 × objective and an FDCS196 cryostage (Linkam Scientific Instruments Ltd., UK). A Qimaging MicroPublisher 5.0 RTV CCD camera (Survey, BC, Canada) was utilized for real-time monitoring and recording of experimental processes.

Each group of cell suspensions (10 μl) was first pipetted onto the coverslip (18 mm diameter) on the cryostage and then be gently covered with another coverslip. Ice-seeding was carried out at −1 °C. Samples were warmed to −0.5 °C and equilibrated for 3 min for better visualization [6]. Although equilibrium freezing point was −0.52 °C [21] or −0.53 °C [22], 3 min of equilibrium at −0.5 °C was not enough for completely melting extracellular ice because ice can still be observed in the field of microscope.

After equilibrium, cell suspensions were further cooled at 5, 10, and 15 °C min−1 for samples without incubation, and 10, 15, and 20 °C min−1 for samples with incubation. Although cooling rates should be as slow as possible to clearly study the subzero water transport process of the cells, 5 °C min−1 was not utilized for cell suspensions with incubation since we found these cells were severely squeezed when they stuck in the gap of the extracellular ice at the lower temperatures. In this case, the contours of the cell became quite long and narrow, making it difficult to assume the projected area of the cells being circular anymore since the projected area would be transformed to cell volume based on the assumption that the cell is spherical. This unusual phenomenon may be associated with the incubation condition, possibly because the interactions of HA nanoparticles and cells at that high temperature (37 °C) made the cell membrane more fragile. However, it is worth noting that the circular and spherical approximations could cause errors more or less in the prediction of cell volume no matter which cooling rate is used, because the cells are inevitably under the mechanical stress from surrounding ice crystals during freezing.

###### Water Transport Model.

The water transport process at various cooling rates was modeled using the following equations [6,23]:Display Formula

(1)$dVcdT=-LpARTBvw·[ΔHfR(1TR-1T)-InVc-Vb-Vs(Vc-Vb-Vs)+φsnsvw]$
Display Formula
(2)$Lp=Lpgexp[-ELpR(1T-1TR)]$

where VC is the cell volume, A is the surface area of the cell, B is the cooling rates, R is the universal gas constant (8.314 J mol−1 K−1), ΔHf is the molar heat of fusion of water (6016.52 J mol−1), ϕs is the dissociation constant for salt (two for NaCl), ns is the molar amount of intracellular salt (ns = (V0 − Vb) × cs, cs is the molarity of salt in saline (0.142 M)), Vb is the osmotic inactive volume of the cell, Vs is the salt volume of the cell based on the assumption that only one water molecule is in the hydration shell associated with one NaCl molecule [24] (Vs = ns × (νs + νw), νs and νw are specific volumes of NaCl (26.99 ml mol−1) and water (18 ml mol−1), respectively, TR is the reference temperature (273.15 K), Lp is the water permeability of cell plasma membrane, Lpg is the hydraulic conductivity of cell plasma membrane at TR, Elp is the activation energy for transmembrane water transport of cells. Among these parameters, Lpg, Elp, and Vb are to be determined by fitting the model to experimental data.

###### Individual Curve Fitting Methods.

Individual curve fitting was achieved by fitting the transient volumes of a single cell during freezing with the water transport model given above. For the five cell suspensions, there were five groups of transmembrane transport parameters (Lpg and Elp) to be obtained by individual curve fitting.

###### Combined Curve Fitting Methods.

Actually, when obtaining a single cell volume, the cell heterogeneity is greatly enlarged by extracellular ice and image processing error. One possible and effective approach to avoid the aberrant error is to analyze a group of cells all together. Therefore, aside from individual curve fitting, we also used combined curve fitting [25] to obtain the transmembrane transport parameters (Lpg and Elp) of HeLa cells.

For each cell suspension, we averaged the cell volume data during freezing at each cooling rate first. We then pooled the averaged data sequences at three cooling rates together and achieved the simultaneous fitting using the water transport model. Therefore, we got one pair of Lpg and Elp for each cell suspensions. The combined curve fitting methods eliminate the effect of cooling rate on determining the water transport parameters, which is beneficial for further prediction of the water transport behavior of cells when using the water transport model. Besides, the effect of cell heterogeneity on the two parameters is also reduced by combined curve fitting.

###### SEM Analysis.

Cells were immersed in 3% glutaraldehyde first. After a few days, the cell suspensions were washed in 0.1 M PBS and the extracellular solutions were replaced with 1% osmium tetroxide. After approximately 90 min, the cell suspensions were washed again in 0.1 M PBS. Cells were then dehydrated in a graded ethyl alcohol and washed with acetone by following the standard procedure. Next, we transferred the cells to a critical point drier (K850, Quorum, UK). After coated with palladium–gold, the dried cells were examined using a field emission scanning electron microscope (S-4800, Hitachi, Japan).

###### Statistical Analysis.

Student t-test was performed to compare the water transport parameters of cells in 1 × PBS and those of cells in 1 × PBS containing 0.05% or 0.1% HA with or without incubation for individual curve fitting results. A p value of less than 0.05 was taken to be statistically significant. All water transport parameters obtained from individual curve fitting are presented as mean ± standard deviation (SD).

## Results

###### Volumetric Response of HeLa Cells During Freezing.

Figure 3 shows the volumetric responses of HeLa cells during freezing. Note that the extracellular ice did not completely melt at −0.5 °C after 3 min of equilibrium and the size of the extracellular ice was comparable to that of the cells. The HA nanoparticles were noticeable in the 500 × microscopic field and at higher HA contents, HA nanoparticles were more visible. The areas inside the cell contour were considered as projected area, which were further transformed to cell volume based on the assumption that the cell was spherical.

###### Individual Curve Fitting Results.

Five representative normalized cell volume data and the corresponding fitting curves are shown in Fig. 4(a). It can be seen that with the decrease of temperature, the cell shrinks as a result of dehydration. The obtained Lpg and Elp for each group of cell suspensions are shown in Fig. 4(b) and Table 1. Here V0 is determined to be (2.1 ± 0.5) × 10−15 m3 (n = 302).

We tried to regard incubation and HA concentration as separate factors. For example, to find the influence of incubation, we performed student t-test for the groups at the same HA concentration; to find the influence of HA concentration, we performed student t-test for the groups either with incubation or without incubation. However, as shown in Fig. 4(b), the influence of incubation on water transport is significant only for conditions with 0.1% HA. Besides, for the influence of HA concentration on water transport, only Lpg of cells in 0.05% HA nanoparticle suspensions without incubation is significantly different from that of cells in 0.1% HA nanoparticle suspensions without incubation. Therefore, the effects of incubation or HA concentration on the two parameters seem to be quite complicated and is difficult to draw a definitive conclusion. However, Lpg and Elp of cells in 1 × PBS with 0.05% HA and incubation is significantly different from those of cells in 1 × PBS.

###### Combined Curve Fitting Results.

The averaged cell volumes at three cooling rates for each kind of cell suspension (symbols in Fig. 5(a)) were pooled together to achieve combined fitting. The obtained water transport parameters (Lpg and Elp) are given in Table 1 and Fig. 5(b). The data indicate that with and without incubation, the Lpg was almost constant with the exception of the value for the condition of 0.05% HA and incubation, while Elp kept constant at each HA concentration. The Arrhenius plot from −45 °C to 0 °C is shown in Fig. 5(c). The slopes of the curves indicate the water permeability of HeLa cell membrane (Lp) is not sensitive to the presence of nanoparticles.

###### Predictions of Dehydration of HeLa Cells.

To better illustrate the effect of HA nanoparticles on water transport of HeLa cells, we predicted the subzero water transport processes of HeLa cells at various cooling rates using the Lpg and Elp obtained from the combined curve fitting, which not only eliminates the effect of cooling rates but also reduces the effect of cell heterogeneity on the two parameters. As indicated in Fig. 6, the differences of dehydration response of HeLa cells among the five conditions are minor at lower cooling rates. However, with the increase of the cooling rates, the curves diverge more from each other, and the final entrapped intracellular water is obviously different. Be consistent with the statistical analysis, cells in 1 × PBS with 0.05% HA and incubation dehydrate the most compared to cells in the other four groups at the same temperature.

The incubation condition seems to have impact on water transport for the condition of 0.05% HA cell suspensions since the normalized cell volume curves at 0.05% HA with and without incubation differ a lot from each other, whereas the curves at 0.1% HA with and without incubation are mostly overlapped with each other.

###### Morphological Results.

Figure 7 shows the microscopic topography of the cell membrane under the five conditions studied. Compared to cells in 1 × PBS (Fig. 7(a)), a few of HA nanoparticles are found to aggregate on cell membranes in the other four groups (arrows in Figs. 7(b)7(e)). Cells incubated with HA nanoparticles at higher concentrations appeared to adsorb larger-sized HA nanoparticle clusters (Figs. 7(b) and 7(c) versus Figs. 7(d) and 7(e)).

## Discussion

Although the values of the transmembrane water transport parameters (Lpg and Elp) obtained from both individual and combined curve fittings are on the same order of magnitude (Table 1), the parameters obtained from combined curve fitting are possibly more reliable since the combined curve fitting minimizes the effect of cell heterogeneity and eliminates the effect of cooling rate on prediction of cell volumes.

By using the two water transport parameters obtained from combined curve fitting, we predicted the subzero water transport of HeLa cells at 10, 30, 60, and 100 °C min−1 to elucidate the effect of HA nanoparticles on subzero water transport of HeLa cells. Predicted curves suggest that the existence of HA nanoparticles facilitates the subzero water transport of HeLa cells. And this influence is more apparent at higher cooling rates (Fig. 6). Being consistent with the statistical analysis, the predicted dehydration curves of cells in 0.05% HA nanoparticles with incubation is apparently different from that of cells in 1 × PBS.

Generally, transmembrane water transport is closely associated with the lethal IIF. For example, if cells contain excessive water at a certain subzero temperature, the water can be catalyzed to form ice, which may induce mechanical and nonmechanical injury to cells [2]. For years, researchers try to find the optimal combination of cooling rates and concentration of CPAs in slow freezing to minimize cell injury due to both cell dehydration and IIF [26]. Therefore, by modulating the water transport of the cells, it is possible to design a specific protocol for a given type of cells to reduce the toxicity of the CPAs as well as increase the cell viability through the incorporation of nanoparticles. According to the findings in this study that the nanoparticles can facilitate the water transport of HeLa cells, especially at high cooling rates, HA nanoparticles may offer new means in developing optimum cryopreservation protocols for cells to modulate their transmembrane water transport during freezing.

The microscopic topography of the cell membrane surface indicates that the HA nanoparticles may attach on the cell membrane as clusters and the phenomenon is more obvious for cells with incubation, which can be attributed to the good affinity of the HA nanoparticles to cell membrane [18]. Also, it should be noticed that as impurities, the HA clusters on the cell membrane are capable of facilitating IIF via the surface catalyzed nucleation mechanisms in HeLa cells according to the heterogeneous nucleation theory [7], which could be beneficial for cryotherapy applications to destroy unwanted cells.

On the other hand, the HA nanoparticles also facilitate the water transport across HeLa cells although more studies are needed to identify the mechanisms. One might suspect that the mechanism may be attributed to the change in osmolality of extracellular solutions because theoretically, HA nanoparticles are capable of changing the osmolality of the solutions since it is reported that HA nanoparticles (polar particles) can adsorb water molecules in solution, forming a hydration layer on its surface [15] which may reduce free water in solution. However, the osmolality measurements (all measured to be 290 mOsm) indicate that the HA concentration may not be enough to change the osmolality of the solution. During freezing, however, the nanoparticles could be rejected into the unfrozen solution at the ice–solution interface and increase the concentration of solutes in the unfrozen solution.

Another hypothesis is the uptake of nanoparticles via endocytosis may facilitate the water transport simultaneously. Since endocytosis is dependent on temperature [27], the incubation condition (37 °C) may be used to test such hypothesis. However, the observation that the incubation condition affects the subzero water transport behavior of cells incubated with 0.05% more than 0.1% HA nanoparticles (Fig. 6) suggests endocytosis may be more active in cells incubated with 0.05% HA nanoparticle. This is possible because the smaller aggregates (Figs. 7(b) and 7(c) versus Figs. 7(d) and 7(e)) associated with the 0.05% HA nanoparticles could be more easily taken up the cells.

Nevertheless, because endocytosis is suppressed at lower temperature [27], the endocytosis hypothesis might be weak to explain the influence of HA nanoparticles here. Therefore, we suspect some proteins on the cell membrane may participate in transferring HA nanoparticles, which facilitate the water transport at the same time. However, this hypothesis remains to be further investigated.

## Conclusion

In this study, the influence of HA nanoparticles on subzero water transport of HeLa cells was studied. The membrane permeability parameters were obtained by fitting the volumetric data of HeLa cells during freezing with a water transport model. Based on these parameters, we predicted the subzero water transport process of HeLa cells at various cooling rates. The results reveal that HA nanoparticles facilitate the subzero water transport of HeLa cells. Since modulation of subzero biotransport of living cells plays a crucial role in determining cell injury, the findings in this study is valuable for developing new strategies using nanoparticles to optimize typical cryopreservation or cryotherapy protocols. The specific mechanism with regard to the influence of HA nanoparticles on the water transport across cells remains to be further investigated.

## Acknowledgements

This work was supported by National Natural Science Foundation of China (Nos. 51476160 and 51276179), and the Fundamental Research Funds for the Central Universities (WK 2100230009). We thank Xiaoli Liu, Chenlin Xu and Xia Li for their helpful technical assistance.

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## References

Mazur, P., 1984, “Freezing of Living Cells—Mechanisms and Implications,” Am. J. Physiol., 247(3), pp. C125–C142. [PubMed]
Karlsson, J. O. M., and Toner, M., 1996, “Long-Term Storage of Tissues by Cryopreservation: Critical Issues,” Biomaterials, 17(3), pp. 243–256. [PubMed]
He, X., 2011, “Thermostability of Biological Systems: Fundamentals, Challenges, and Quantification,” Open Biomed. Eng. J., 5, pp. 47–73. [PubMed]
Yan, J. F., and Liu, J., 2008, “Nanocryosurgery and Its Mechanisms for Enhancing Freezing Efficiency of Tumor Tissues,” Nanomed.-Nanotechnol. Biol. Med., 4(1), pp. 79–87.
Jing, L., and Zhong-Shan, D., 2009, “Nano-Cryosurgery: Advances and Challenges,” J. Nanosci. Nanotechnol., 9(8), pp. 4521–4542. [PubMed]
Yang, G., Veres, M., Szalai, G., Zhang, A. L., Xu, L. X., and He, X. M., 2011, “Biotransport Phenomena in Freezing Mammalian Oocytes,” Ann. Biomed. Eng., 39(1), pp. 580–591. [PubMed]
Toner, M., 1993, “Nucleation of Ice Crystals Inside Biological Cells,” Advances in Low-Temperature Biology, JAI Press Ltd., London, UK.
Zhang, W. J., Gilstrap, K., Wu, L. Y., Bahadur, K. C. R., Moss, M. A., Wang, Q. A., Lu, X. B., and He, X. M., 2010, “Synthesis and Characterization of Thermally Responsive Pluronic F127-Chitosan Nanocapsules for Controlled Release and Intracellular Delivery of Small Molecules,” ACS Nano, 4(11), pp. 6747–6759. [PubMed]
Rao, W., Zhang, W. J., Poventud-Fuentes, I., Wang, Y. C., Lei, Y. F., Agarwal, P., Weekes, B., Li, C. L., Lu, X. B., Yu, J. H., and He, X. M., 2014, “Thermally Responsive Nanoparticle-Encapsulated Curcumin and Its Combination With Mild Hyperthermia for Enhanced Cancer Cell Destruction,” Acta Biomater., 10(2), pp. 831–842. [PubMed]
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## Figures

Fig. 1

The radius of particles with regard to the weight ratio of Na6(PO3)6 to HA. Each value was automatically averaged (n  > 10) and calculated by the machine software according to the preset property of the solution (1 × PBS) and particles (assumed to be circular).

Fig. 2

Sedimentation of nanoparticle suspensions at different time points. Arrows indicate the aggregation of the HA nanoparticles. 0 h, 0.5 h, 1 h, 1.5 h, and 2 h.

Fig. 3

Volumetric responses of HeLa cells at various temperatures during freezing at 15 °C min−1. (a) Cells in 1 × PBS, (b) cells in 1 × PBS with 0.05% HA nanoparticle suspensions without incubation, and (c) cells in 0.1% HA nanoparticles solutions without incubation.

Fig. 4

Results obtained from individual curve fitting. (a) Representative normalized cell volume data (circles) with their individual fitting curves (solid lines) and (b) transmembrane water permeability parameters obtained from individual curve fitting and related statistical analysis results. Error bar: SD.

Fig. 5

Results obtained from combined curve fitting. (a) Normalized cell volume at different HA concentrations with and without incubation (symbols). Solid lines show the combined fitting curves. Error bar indicates the standard error of mean. (b) Transmembrane water permeability parameters. (c) Arrhenius plot of water permeability of HeLa cells membrane (Lp) at different HA concentrations with and without incubation.

Fig. 6

Predicted subzero water transport of HeLa cells cooled at 10, 30, 60, and 100 °C min−1. Here Vb is set as 0.35 V0.

Fig. 7

SEM images of HeLa cells in 1 × PBS with 0–0.1% HA nanoparticles either with or without incubation at 37 °C. Arrows indicate the HA nanoparticles clusters on the cell membrane. (a) 1 × PBS, (b) 1 × PBS/0.05% HA, (c) 1 × PBS/0.1% HA, (d) 1 × PBS/0.05% HA/incubation, and (e) 1 × PBS/0.1% HA/incubation.

## Tables

Table 1 Transmembrane water transport parameters obtained from individual curve fitting (means ± SD) and combined curve fitting
aDenotes the averaged data at three cooling rates.

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