Evaluation of individual particle capillary electrophoresis experiments via quantile analysis

Abstract

The number of particles in a sample heavily influences the shape of a distribution corresponding to the individual particle measurements. Selecting an adequate number of particles that prevents biases due to sample size is particularly difficult for complex biological systems in which statistical distributions are not normal. Quantile analysis is a powerful statistical technique that can rapidly compare differences between multiple distributions of individual particles. This report utilizes quantile analysis to show that the number of events detected affects the mobility distributions for rat liver and mouse liver mitochondria, sample individual particles, when analyzed via capillary electrophoresis with laser-induced fluorescence. When the mitochondrial sample is small (e.g. <78), there are not enough events to obtain statistically relevant mobility data. Adsorption to the capillary surface also significantly affects the mobility distribution at a small number of events in uncoated and dynamically coated capillaries. These adsorption effects can be overcome when the mitochondrial load on the capillary is sufficiently large (i.e. >609 and >1426 events for mouse liver on uncoated capillaries and rat liver on dynamically coated capillaries, respectively). It is anticipated that quantile analysis can be used to study other distributions of individual particles, such as nanoparticles, organelles, and biomolecules, and that distributions of these particles will also be dependent on sample size.

Figure 1

Quantile-Quantile plots of mitochondrial populations. Every 0.05 quantile from 0.05 to 0.95 (left to right) for each sample population (y-axis data) is plotted versus the quantiles of the population with the largest number of events (x-axis data). The solid line is a reference that represents a perfect match between the two data sets. A) mouse liver on uncoated capillaries, B) mouse liver on AAP capillaries, C) rat Liver on AAP capillaries, and D) rat liver with PVA coated capillaries. Legends for the symbols are presented in supporting information (Table S-1).

Figure 2

Electrophoretic mobility quartiles from distributions of individual mitochondrial events. (A) mouse liver mitochondria on uncoated capillaries, (B) mouse liver mitochondria on AAP capillaries, (C) rat liver mitochondria on PVA capillaries, and (D) rat liver mitochondria on AAP capillaries. Open symbols represent data pooled from undersampled populations (<269 for rat liver mitochondria on PVA capillaries, <78 for all other samples). Graphs are presented in log scale along the x-axis to more easily perceive all the data. Legend: ■ first quartile, ◆ median, and ▲ third quartile.

Figure 3

Mobility histograms of mouse liver mitochondria separated on an uncoated capillary with varying number of events. A) 45 events, B) 351 events, and C) 1196 events, D) compiled from undersampled distributions, and E) compiled from undersampled distributions of rat liver mitochondria data on PVA dynamically coated capillaries.

Figure 4

Quantile-Quantile plots of the distributions of mitochondria undergoing adsorption to the capillary surface. The x-axis is the average of the quantiles from the three largest distributions and the y-axis is the quantiles from individual distributions. The thin line represents the reference line and the heavy line represents 1.5 SD from the reference line. A) Mouse liver mitochondria separated on uncoated capillaries. B) Rat liver mitochondria separated on PVA coated capillaries.