Fig 1.
Cell yield after 15 min exposure to hypotonic (A) or hypertonic conditions (B).
Hypertonic solutions were prepared using either sucrose or NaCl, as indicated. Lines show best-fit logistic models (Eq 2). Arrows indicate the osmotic tolerance limits used in our mathematical optimization algorithm.
Fig 2.
Cytotoxicity of glycerol solutions at 21°C and 37°C.
Lines show best-fit exponential decay models.
Fig 3.
Effect of concentration and temperature on the toxicity rate constant k.
Lines represent predictions of the concentration- and temperature-dependent toxicity rate model (Eq 9), and the shaded bands represent 95% confidence intervals. Best-fit model parameters are shown on the plot.
Table 1.
Mathematically optimized procedures for addition and removal of 17 molal glycerol at 37°C.
Fig 4.
Predicted cell volume excursions for the mathematically optimized procedure in Table 1.
Temperature was fixed at 37°C in the optimization algorithm. Horizontal dashed lines show the osmotic tolerance limits.
Fig 5.
Cell yield for the mathematically optimized procedure in Table 1.
For comparison, the results for single step and conventional multistep procedures are also shown. All experiments were carried out at 37°C. Bars marked with distinct letters are significantly different (p < 0.05).
Table 2.
Mathematically optimized procedures for addition and removal of 17 molal glycerol with temperature constrained between 4°C and 37°C.
Fig 6.
Effect of temperature and cell swelling on cell yield.
The bar labelled “optimal” refers to the procedure in Table 1, with the first CPA addition step carried out at 37°C and the second at 4°C. The procedure labeled “no swell” was identical, except that an isotonic concentration of nonpermeating solutes was used in the first loading step, instead of the hypotonic concentration shown in Table 1. Bars marked with distinct letters are significantly different (p < 0.05).
Fig 7.
Vitrification of cultured endothelial cells.
Time-lapse images during cooling and warming show clear evidence of intra- and extracellular ice formation for cells in isotonic buffer (Top), but no evidence of ice formation for cells in vitrification solution (Bottom).
Fig 8.
Effects of the CPA cytotoxicity model parameter α (see Eq 9) on mathematically optimized procedures for addition of 17 molal glycerol.
While the second CPA addition step was essentially identical for all α-values, the conditions in the first step can be divided into low α and high α regimes. In the low α regime, the cells are exposed to a relatively high CPA concentration for a relatively short duration (bottom panel), resulting in shrinkage to the minimum volume limit (top left panel). In contrast, the high α regime involves exposure to a relatively low CPA concentration for a relatively long duration, which results in swelling to the maximum volume limit (top right panel).
Fig 9.
Effects of the activation energy for CPA cytotoxicity (Ea, see Eq 9) on mathematically optimized procedures for addition of 17 molal glycerol.
While the temperature in the second CPA addition step was 4°C for all Ea values, the temperature in the first step can be divided into low Ea and high Ea regimes. The transition between these regimes occurs at 89 kJ/mol (vertical dashed line); this value matches the activation energy for glycerol transport [32].