A Nonparametric Method for Estimating Rates of Intracellular Ice Formation Due to Independent Competing Mechanisms

Abstract

The probability of intracellular ice formation (IIF) has conventionally been analyzed by counting the cumulative number of IIF events observed in a cell population, and normalizing to the total cell count to estimate the cumulative IIF probability. However, this method is invalid when attempting to distinguish among multiple, independent IIF mechanisms, because of confounding effects due to competition for a finite pool of unfrozen cells. Therefore, an alternative approach for analyzing IIF data is proposed, based on treating IIF as a marked point process, in which the points represent IIF events and the marks represent different mechanisms of IIF. Using the new method, it is possible to quantify the kinetics associated with any IIF mechanism for which corresponding events can be marked (i.e., experimentally distinguished from competing IIF mechanisms). The proposed approach is nonparametric, making possible characterization of IIF mechanisms that have not yet been fully elucidated. The new analytical approach was compared to the conventional method of IIF analysis using data from a simulated experiment, demonstrating that the new method yielded superior estimates of the cumulative distribution function of IIF times when two competing mechanisms of IIF were active. The proposed algorithm was also applied to cryomicroscopic IIF observations in adherent endothelial cells, yielding rate estimates for two concurrent IIF processes. Furthermore, a proof is presented to demonstrate that when the proposed data analysis algorithm is applied to IIF data from a single mechanism of IIF, the results are equivalent to those obtained by the conventional method of analysis.