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. 2015 Jun 25:3:e1039.
doi: 10.7717/peerj.1039. eCollection 2015.

A Bayesian approach to optimizing cryopreservation protocols

Affiliations

A Bayesian approach to optimizing cryopreservation protocols

Sammy Sambu. PeerJ. .

Abstract

Cryopreservation is beset with the challenge of protocol alignment across a wide range of cell types and process variables. By taking a cross-sectional assessment of previously published cryopreservation data (sample means and standard errors) as preliminary meta-data, a decision tree learning analysis (DTLA) was performed to develop an understanding of target survival using optimized pruning methods based on different approaches. Briefly, a clear direction on the decision process for selection of methods was developed with key choices being the cooling rate, plunge temperature on the one hand and biomaterial choice, use of composites (sugars and proteins as additional constituents), loading procedure and cell location in 3D scaffolding on the other. Secondly, using machine learning and generalized approaches via the Naïve Bayes Classification (NBC) method, these metadata were used to develop posterior probabilities for combinatorial approaches that were implicitly recorded in the metadata. These latter results showed that newer protocol choices developed using probability elicitation techniques can unearth improved protocols consistent with multiple unidimensionally-optimized physical protocols. In conclusion, this article proposes the use of DTLA models and subsequently NBC for the improvement of modern cryopreservation techniques through an integrative approach.

Keywords: 3D cryopreservation; CPA loading; Cell attachment; Decision-tree learning (DTL); Encapsulation; Meta-data; Modified alginates; Mouse embryonic stem cells; Naïve Bayes Classifier (NBC); Sugars.

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Conflict of interest statement

The author declares there is no competing interests.

Figures

Figure 1
Figure 1. The decision tree learning model.
A recursive partitioning in detail showing the hot-spots at “Integrins,” “Sucrose” and “controlled seeding.” The validation scores were 77% (match) and 23% (failed) for the DTL model.
Figure 2
Figure 2. Tracking the coefficient of determination as the DTL model is built.
A line plot of the R-squared for each branch added at each step in the generation of the decision tree learning model. The prediction is the cell survival (a continuous variable) after cryopreservation.
Figure 3
Figure 3. A Decision Tree Learning Analysis of cryopreservation data with branch-validation tracker underneath.
(A) A metadata analysis of cryopreservation data showing that the right-side analysis is conserved across methods—Temperatures are in °C and Cooling rates in °C/min; (B) plot showing coefficient of determination during model validation; the corresponding classification scores for test data are at 84% correct match and 16% misclassification.
Figure 4
Figure 4. A summary scatter-plot analysis of key values for meta-data on main decision factors.
A scatter plot matrix capturing the summary statistics for the meta-data collected from previous analyses used to develop a heuristic for predicting the posterior survival probabilities for cells for a given set of process decisions (Sambu et al., 2011; Heng, Yu & Ng, 2004; Kashuba Benson, Benson & Critser, 2008; Miszta-Lane et al., 2007). Key decision variable combinations with 100% “live” cells are framed in purple. The numbers on each axis represent the categories identified within a decision variable. Red dots represent short-living cells while green dots represent long-living cells.
Figure 5
Figure 5. A 2D plot zooming in on a classification boundary for the plunge temperature.
(A) A change in survival against the plunge temperature set point against which the prediction changes the ‘leaf’ value. (B) A 2D plot of the survival rate against plunge temperature was drawn from a DTL analysis. The cooling rate is used to lower the temperature from CPA loading temperature (temperature when cells are exposed to CPA for equilibration) to the plunge temperature—this rate is a separate decision factor (see methods section).
Figure 6
Figure 6. A nested summary table of the NBC model.
Prediction of survival using the Naïve Bayes Classifier on the following factors: dimensionality, location, biomaterial, sugars, step-loading & integrins. The training set has a 79% accuracy while the smaller test set has an 89% accuracy showing that the Naïve Bayes Classifier is a demonstrably accurate predictor even when reduced to a smaller test set where the samples are all cryopreserved in 3D natural RGD-containing biomaterials using controlled slow-cooling with sucrose for lyoprotection, in a two-step loading process. (Similar to the optimal leaves from the recursive partitioning trees developed earlier.) Cross-validations are 10-fold (i.e., k = 0.1 for the NBC model construct).

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