Department of Biology, University of Saskatchewan, Saskatoon, SK, Canada.
Methods Mol Biol. 2021;2180:129-172. doi: 10.1007/978-1-0716-0783-1_4.
Cryobiology is a multiscale and interdisciplinary field. The scope and scale of interactions limit the gains that can be made by one theory or experiment alone. Because of this, modeling has played a critical role in both explaining cryobiological phenomena and predicting improved protocols. Modeling facilitates understanding of the biophysical and some of the biochemical mechanisms of damage during all phases of cryopreservation including CPA equilibration and cooling and warming. Moreover, as a tool for optimization of cryopreservation protocols, modeling has yielded many successes. Modern cryobiological modeling includes very detailed descriptions of the physical phenomena that occur during freezing, including ice growth kinetics and spatial gradients that define heat and mass transport models. Here we reduce the complexity and approach only a small but classic subset of these problems. Namely, here we describe the process of building and using a mathematical model of a cell in suspension where spatial homogeneity is assumed for all quantities. We define the models that describe the critical cell quantities used to describe optimal and suboptimal protocols and then give an overview of classical methods of how to determine optimal protocols using these models. We include practical considerations of modeling in cryobiology, including fitting transport models to cell volume data, performing optimization with cell volume constraints, and a look at expanding cost functions to cooling regimes.
冷冻生物学是一个多尺度和跨学科的领域。相互作用的范围和规模限制了仅通过一种理论或实验可以取得的进展。因此，建模在解释冷冻生物学现象和预测改进的方案方面都发挥了关键作用。建模有助于理解在包括细胞内溶质平衡和冷却与升温在内的冷冻保存的所有阶段中损伤的生物物理和一些生化机制。此外，作为冷冻保存方案优化的工具，建模取得了许多成功。现代冷冻生物学建模包括对冷冻过程中发生的物理现象的非常详细的描述，包括冰生长动力学和定义热和质量传输模型的空间梯度。在这里，我们简化了复杂性，仅研究这些问题中的一小部分但很经典的问题。即，在这里我们描述了构建和使用悬浮细胞的数学模型的过程，其中假设所有数量都是空间均匀的。我们定义了描述最佳和次佳方案的关键细胞数量的模型，然后概述了如何使用这些模型确定最佳方案的经典方法。我们包括冷冻生物学中建模的实际考虑因素，包括将传输模型拟合到细胞体积数据，在细胞体积约束下进行优化，以及扩大成本函数以适应冷却模式。
