An Improved Model for Nucleation-Limited Ice Formation in Living Cells during Freezing

Abstract

Ice formation in living cells is a lethal event during freezing and its characterization is important to the development of optimal protocols for not only cryopreservation but also cryotherapy applications. Although the model for probability of ice formation (PIF) in cells developed by Toner et al. has been widely used to predict nucleation-limited intracellular ice formation (IIF), our data of freezing Hela cells suggest that this model could give misleading prediction of PIF when the maximum PIF in cells during freezing is less than 1 (PIF ranges from 0 to 1). We introduce a new model to overcome this problem by incorporating a critical cell volume to modify the Toner's original model. We further reveal that this critical cell volume is dependent on the mechanisms of ice nucleation in cells during freezing, i.e., surface-catalyzed nucleation (SCN) and volume-catalyzed nucleation (VCN). Taken together, the improved PIF model may be valuable for better understanding of the mechanisms of ice nucleation in cells during freezing and more accurate prediction of PIF for cryopreservation and cryotherapy applications.

The role of structural order in heterogeneous ice nucleation

“…[95][96][97] In addition, the formation of ice in biological matter, which is key in the context of cryopreservation, does involve the formation of ice on/through the lipid bilayers which form the building blocks of cells. [98][99][100][101] Control of ice nucleation very oen improves the outcomes of cryopreservation procedures 76,102 and, critically, the origin of ice formation inside cells remains very poorly understood. 103 Improved understanding of the mechanism of heterogeneous ice nucleation by biological substances has the potential to both facilitate synthesis of new and effective biocompatible ice nucleators and shed light on the start of damaging intracellular ice formation.…”

Modeling and experimental studies of enhanced cooling by medical gauze for cell cryopreservation by vitrification

“…To evaluate the efficiency of vitrification cryopreservation, we considered the probability of IIF (PIF) as an approximate evaluation of the final cell survival rate after cryopreservation. PIF can be estimated using the model as follows [23–25]: $$P_{\mathit{IIF}}=P_{\mathit{IIF}}^{\mathit{SCN}}+\left(1-P_{\mathit{IIF}}^{\mathit{SCN}}\right)P_{\mathit{IIF}}^{\mathit{VCN}}$$ $$P_{\mathit{IIF}}^{\mathit{SCN}}=1-\exp \left[-true{\int }_0^t{A}_c{I}_{\mathrm{italicSCN}}dt\right]$$ $$P_{\mathit{IIF}}^{\mathit{VCN}}=1-\exp \left[-true{\int }_0^t{V}_c{I}_{\mathrm{italicVCN}}dt\right]$$ where t is time, A c and V c are cell surface area and volume, respectively, and I is nucleation rate of that can be computed as follows: $$I^{\mathit{XCN}}={\mathrm{\Omega }}_0^{\mathit{XCN}}\frac{N^{\mathrm{italicXCN}}}{N_0^{\mathrm{italicXCN}}}\frac{{\eta }_0}{\eta }{\left(\frac{T}{T_{f,0}}\right)}^{0.5}\exp \left[\frac{-{\kappa }_0^{\mathrm{italicXCN}}{\left(T_f/T_{f,0}\right)}^4}{{\left(T-T_f\right)}^2{T}^3}\right]$$ where XCN represents either SCN or VCN , ‘ 0 ’ refers to isotonic condition, Ω and κ are thermodynamic and kinetic parameters for nucleation, N is number of water molecules in contact with the substrate, and η and T f are viscosity and equilibrium freezing temperature of the cytoplasm, respectively.…”

Principles and advances of cell cryopreservation

“…Zhao等人 [73] 通过在Mazur方程中引入细胞 内冰晶体积项, 实现了细胞内水的两种竞争发展机制 (渗透到细胞外、在细胞内结冰)的理论描述(实质上就 是Mazur的两因素假说的理论描述), 进而将Karlsson模 型的适用范围拓宽至不受低温保护剂浓度限制, 使用 新模型成功预测了慢速冷冻保存和玻璃化保存的低温 保护剂和降温速率耦合区间 [74] (图4A), 以及细胞内溶 液的非理想性对相关预测结果的影响 [75] . 针对该模型 所需参数, 本团队进一步建立了基于活动轮廓的细胞 追踪和分割方法, 实现了细胞脱水过程的动态分析 [76] (图4B); 验证了差示扫描量热法测定冻结过程细胞膜 渗透性参数的可行性 [77] ; 使用低温显微成像方法系统 地研究了多种细胞冻结过程的水输运和胞内冰成核现 象 [78~80] ; 拓宽了Toner的细胞内冰晶成核理论, 使之可 适用于最终胞内冰概率小于100%的情况 [81] (图4B).…”