Errors introduced by compensation

(Go back one page to 3-Color compensation: examples, or back to the introduction)

Unfortunately, the process of compensation introduces error into the measurement. It does not introduce a systematic error, but simply increases the cv of any measurement. This is because each compensated value is the convolution of several measurements; therefore, the error in each measurement contributes additively to the error in the compensated value.

A detailed discussion of the errors introduced by analog compensation (along with a depiction) is given in informal discussion; click here to go directly there (however, there is no direct way to navigate back to this page from there).

The remainder of this discussion is about digital compensation (for instance, in posthoc compensation analysis by software) and errors introduced in this process. Digital compensation introduces significantly greater errors than analog compensation, primarily because of the error introduced by "binning" the data.

Consider a cell which is negative for a PE reagent but brightly fluorescent for a FITC reagent. Assuming our (logarithmic) fluorescence scale ranges from 0.1 to 1,000 (4 decades), then the "true" fluorescences of this cell might be 0.5 for PE (i.e., negative except for some autofluorescence), and 100 for FITC. Because of the 15% spillover of FITC to PE, the measured PE fluorescence would be 15.5 (0.5 "true" + 0.15 x 100 "FITC spillover"). Note that if the measurement were made exact, then the true PE fluorescence could be determined. Using the first equation, PEtrue = 15.5 - 0.15 x 100 = 0.5. But what would happen if there were a one channel error in the measurement of fluorescence? In the PE channel (at this low level of fluorescence), this is not a whole lot; one channels corresponds to about 0.02 fluorescence units. But because of the logarithmic nature, one channel error at 100 units (the fluorescein measurement) translates into about 3.7 fluorescence units. If the machine were only one channels low (out of 256), then the FITC might be measured at 96.3 units. Now the "true" PE fluorescence is calculated as: 15.5 - 0.15 x 96.3 = 1.06. This is a shift of over 20 channels from the correct position: note how much error has been introduced into the "true" PE fluorescence value! A measurement that was ±1 channels is now ±20 channels. (Note, of course, that this is because of the logarithmic amplification: the error of the measurement is ±3.7 units; this results in an error after compensation of 15% of this, or ±0.56 units. But 0.56 units at the low end of the scale--negative cells--is much broader than 3.7 units at the positive population.)

Another source of error will be the logarithmic amplifiers. "Log amps" do not have a perfectly logarithmic response; they often vary from perfection by a few percent at different ranges of the scale. Since digital compensation assumes that the response of the log amps is perfect, a few percent error in the apparent measurement can be introduced. The magnitude of this effect can be as large (or larger) than the binning error discussed in the previous paragraph.

In multi-color experiments (> 4), where there is a large number of compensations to each channel being performed digitally, the effect can be significant. In general, what happens is that the populations are significantly "smeared," resulting in a lower ability to discriminate between populations of varying intensities.

Finish off.