Finding the Combined Linear Range with Empiria Studio

Currently, identification of the combined linear range of detection is a manual and inherently subjective process. Empiria Studio takes an entirely new approach to this process. When Empiria Studio software is used to analyze a blot with serial dilutions of sample, it automatically plots the data and provides a combined graph that displays the target and ILC results together. A color bar above the graph indicates the regions of linearity and proportionality identified by the algorithm.

Analysis of linearity typically uses a regression to fit the entire data set to the equation of a straight line, y = mx + b, where b indicates the y-intercept on the graph. Linearity occurs in the range where the relationship between signal input and output can be represented by a straight line – but it does not imply or guarantee proportionality. For this reason, the R² value may provide little useful information for QWB analysis. R², the coefficient of determination, describes the variation and indicates how well that regression line represents the actual data. If the data fit the regression line perfectly, R² = 1. However, if the line does not pass through the origin, R² may be equal to 1 for a data set that does not display a proportional signal response.

Accurate QWB analysis requires both linearity and proportionality. A proportional relationship is defined by the equation y = mx, representing a straight line that passes through the origin with b (the y-intercept) equal to zero. When you fit an entire data set to a straight line, the fitted line may or may not indicate a linear and proportional relationship. The line may have a non-zero intercept (b ≠ 0). However, even if the full data set cannot be fit to a line passing through the origin with b = 0, some regions of the data may be proportional.

For these reasons, Empiria Studio does not use a linear regression or R² value to determine the linear range. Rather than fitting a single function to define the line, multiple functions are derived in a piecewise manner to examine segments of the data set and identify regions of linearity and proportionality. In these regions, the y-intercept approaches zero. Signal intensity is proportional to the abundance of target protein or ILC and quantitative analysis can be performed.

On the View Linear Range and Combined Linear Range graphs in Empiria Studio, these regions of proportionality are indicated by green areas (excellent linearity) and yellow areas (good linearity) of the color bar. This guidance indicates appropriate ranges of sample loading in the linear range of detection. The upper color bar shows regions of proportionality for the ILC and the lower bar displays information for the target protein. Overlapping areas of green or yellow on the color bars indicate the available range of sample loading for accurate detection of the target and ILC in the combined linear range. The middle of this range is suggested as a starting point for sample loading.