Mathematical Modeling and Optimization of Cryopreservation in Single Cells.

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.