The limits of log-ratios

Abstract

Background: DNA microarray assays typically compare two biological samples and present the results of those comparisons gene-by-gene as the logarithm base two of the ratio of the measured expression levels for the two samples.

Results: Because of the fixed dynamic range of fluorescence and other detection systems, there is a limit to the range of comparisons that can be made using any array technology, and this must be taken into account when interpreting the results of any such analysis.

Conclusions: The dynamic range of microarray data collection systems results in limits in the comparative analyses that can be derived from such measurements and suggests that optimal results can be obtained by making measurements that avoid the boundaries of that dynamic range.

Figure 1

R-I plots for microarray expression data exhibit the limits of log-ratio measurements obtained on arrays. As the measured intensity on the arrays approaches its upper and lower limits, the dynamic range for accurately estimating fold-change measurements is also limited. Shown here are R-I plots for three different data sets showing the entire range (A,C,E) and a close-up of the upper end of the end of the effective range for array measurements (respectively B,D,F). The diamond-shape delimits the range of measurements obtainable on microarrays.

Figure 2

The limitation on the dynamic range of log-ratio measurements, (A) shown here in the diamond-shaped gray-shaded box between the colored lines on an R-I plot, reflects the limited range of values that can be obtained from existing microarray technology which typically employ 16-bit array scanners that allow each channel on the arrays to produce measurements ranging in log₂ values from 0 through 16. (B) The diamond area represents a rotation of the original axes, x = log₂(G) and y = log₂(R) to new axes and , followed by a simple rescaling to x" = [log₂(R) + log₂(G)]/2 and y" = [log₂(R) - log₂(G)].

Figure 3

A common practice for low-intensity elements on the array is to set a "floor" representing a minimum intensity that is reported. This eliminates "undefined" log-ratio values that come from reported zeros, but produces "whiskers" in the R-I plot.