Multiple cryoprotectant toxicity model for vitrification solution optimization

Abstract

Vitrification is a promising cryopreservation technique for complex specimens such as tissues and organs. However, it is challenging to identify mixtures of cryoprotectants (CPAs) that prevent ice formation without exerting excessive toxicity. In this work, we developed a multi-CPA toxicity model that predicts the toxicity kinetics of mixtures containing five of the most common CPAs used in the field (glycerol, dimethyl sulfoxide (DMSO), propylene glycol, ethylene glycol, and formamide). The model accounts for specific toxicity, non-specific toxicity, and interactions between CPAs. The proposed model shows reasonable agreement with training data for single and binary CPA solutions, as well as ternary CPA solution validation data. Sloppy model analysis was used to examine the model parameters that were most important for predictions, providing clues about mechanisms of toxicity. This analysis revealed that the model terms for non-specific toxicity were particularly important, especially the non-specific toxicity of propylene glycol, as well as model terms for specific toxicity of formamide and interactions between formamide and glycerol. To demonstrate the potential for model-based design of vitrification methods, we paired the multi-CPA toxicity model with a published vitrification/devitrification model to identify vitrifiable CPA mixtures that are predicted to have minimal toxicity. The resulting optimized vitrification solution composition was a mixture of 7.4 molal glycerol, 1.4 molal DMSO, and 2.4 molal formamide. This demonstrates the potential for mathematical optimization of vitrification solution composition and sets the stage for future studies to optimize the complete vitrification process, including CPA mixture composition and CPA addition and removal methods.

Keywords: Cryopreservation; Cryoprotectants; Optimization; Sloppy models; Toxicity; Vitrification.

Figure 1.

The toxicity rates of the five single CPAs tested from our previous work [38], with the error bars representing the 95% confidence intervals of the experimental toxicity rates. The curves represent fits to Equation 2.

Figure 2.

The toxicity rates of three binary CPA mixtures obtained in our previous work [38] plotted alongside the predicted toxicity rates using Equation 3. (A) CPA mixture with the best agreement between the data and the toxicity rate prediction. (B) CPA mixture exhibiting a gross overestimate of the toxicity rate. (C) CPA mixture exhibiting a gross underestimate of the toxicity rate. The error bars represent the 95% confidence intervals of the experimental toxicity rates.

Figure 3.

The toxicity rates of three CPA mixture types obtained in our previous work [38] plotted alongside the predicted toxicity rates using Equation 4. (A) CPA mixture with the best agreement between the data and the toxicity rate prediction. (B) CPA mixture with a gross overestimate of the toxicity rate. (C) CPA mixture with a gross underestimate of the toxicity rate. The error bars represent the 95% confidence intervals of the experimental toxicity rates.

Figure 4.

Toxicity rate fits for all single and binary CPA cases. Predictions are shown for the full toxicity model (Eqs. 6–9) using the best-fit model parameters (solid lines), as well as for a reduced version of the model that omits some terms (dashed lines). See text for details on the reduced model. For each individual CPA case, the unweighted R² is given. CPAs are abbreviated as follows: glycerol (Gly), propylene glycol (PG), ethylene glycol (EG), and formamide (FA). Error bars represent the 95% confidence intervals of the experimental toxicity rates.

Figure 5.

Parameters for the full toxicity model (Eqs. 6–9), showing ensemble means with 95% confidence intervals as well as best-fit parameter values. Panels A and B show specific toxicity parameters, panel C shows non-specific toxicity parameters, and panel D shows the equilibrium constants for CPA complex formation. The non-specific toxicity exponent α_n is not shown; it has an ensemble mean of 9.28 (+1.36 for the upper bound and −1.14 for the lower bound) and a best-fit value of 9.66. Note that several upper bounds of the 95% confidence intervals are out of the range of the graphs. Two parameter values are also out of range (β_ij for Gly + PG and PG + FA). For a comprehensive list of the parameters and 95% confidence intervals see Tables S1 and S2. CPAs are abbreviated as follows: glycerol (Gly), propylene glycol (PG), ethylene glycol (EG), and formamide (FA).

Figure 6.

Toxicity rate data for 7 molal (total concentration) equi-molal ternary CPA mixtures compared against both full and reduced toxicity model predictions using the best-fit parameters. CPAs are abbreviated as follows: glycerol (Gly), propylene glycol (PG), ethylene glycol (EG), and formamide (FA). Error bars represent the 95% confidence intervals of the experimental toxicity rates.

Figure 7.

The least toxic vitrification solution compositions predicted using three vitrification/devitrification constraints presented by Weiss et al [39]: 50% probability of vitrification (Vit), 50% probability of complete devitrification (Devit 1), and 50% probability of no devitrification (Devit 4). Panels A and B include formamide as a potential solution constituent, while Panels C and D do not. Panels A and C use the full toxicity model with the best-fit parameters, and Panels B and D use the reduced toxicity model with the best-fit parameters. The predicted toxicity rate (dotted line) of each solution is also shown on the secondary vertical axis. CPAs are abbreviated as follows: glycerol (Gly), propylene glycol (PG), ethylene glycol (EG), and formamide (FA).