FCS Express: Compensation Implementation

The emission spectrum (the wavelengths of light at which a given fluorophore emits) generally overlaps several detection channels of a typical commercial flow cytometer. Although most of the fluorescence signal will be recorded in a single primary channel, it is common that signal from the same fluorophore can be detected in two (or sometimes more) secondary channels. Compensation is the process of removing the unwanted fluorophore signal from secondary channels. A classic example is that although the fluorescence from fluorescein is primarily measured in the “green” channel (~530 nm), a significant amount of fluorescein fluorescence can also be detected in the “yellow” channel (~570 nm). Thus, if you are trying to detect another fluorochrome in the “yellow” channel (i.e. PE), the signal you observe in the “yellow” channel will comprise fluorescence from both PE and FITC.

More information on compensation can be found at:

Flow Cytometry A Basic Introduction: Chapter 5.2 - Compensation

Introduction to Compensation and Spectral Overlap

In many flow cytometers, compensation is built directly into electronics of the flow cytometer. This is typically called hardware compensation or analog compensation. There would be dials or buttons that would allow the user to change the compensation parameters before acquiring the data.

The dial would typically be labeled something like:. FL2-%FL1, Where FL2 is the total amount of fluorescence observed or measured in the FL2 channel and the %FL1 is the percentage of fluorescence measured in the FL2 channel that is from the FL1 fluorochrome. By changing the dial, the user is changing the amount of fluorescence from the FL1 fluorochrome to subtract from the total fluorescence measured in the FL2 channel. For example, if the FL2-%FL1 value was 20, this means that the true FL2 value is the observed FL2 value minus 20% of the observed FL1 value.

Manual (hardware) Compensation

FCS Express can mimic analog compensation through the use of sliders. This is called manual compensation.

In the example below, we are going to manually apply compensation to a sample that is already stained with both FITC and PE. This is only to illustrate manual compensation in FCS Express. For an experiment, the most accurate way of applying manual compensation is using single stained controls or antibody capture beads stained with your antibody-fluorochrome combination.

The plot below shows a data file that is in obvious need of compensation. The FITC fluorescence, detected primarily in FL1-H, is spilling into the FL2-H channel. In addition, the PE fluorescence, detected primarily in the FL2-H channel, is spilling into the FL1-H channel.

If you right click on the plot you can create a new compensation setting:

After giving the new compensation setting a name, a set of sliders will appear, as shown below.

The sliders that appear pertain to the axes that are currently displayed on the plot. Beneath each slider is the classic, albeit slightly confusing, formula describing what that slider is doing. To the left of the slider is a picture showing how the data will move if you increase the compensation value. Moving the slider to the left or right decreases or increases the compensation value, respectively.

The following pictures show the effects of increasing the FL2-H - % of FL1-H slider.

15% Compensation
20% Compensation
25% Compensation

 

In FCS Express you set the manual compensation identically to the way you would set it in hardware. i.e. iteratively adjust the compensation value to until you like the picture that you get.

Automatic (software) Compensation

As an alternative to manual compensation in FCS Express or in acquisition hardware, the data can be acquired uncompensated and then automatically compensated in FCS Express. For FCS 2.0 data files in which hardware compensation is written into the data irreversibly, automatic compensaton may be a better choice in that you never have to worry that the data was under- or overcompensated. Automatic compensation is also useful for FCS 3.0/3.1 data files, as it can save valuable time on the cytometer by eliminating time spend compensating. It also provides for objective post-acquisition adjustment of hardware compensation settings (which are saved with modern .fcs files as metadata rather than intrinsically).

To use the automatic compensation feature of FCS Express it is necessary to have data from single-stained positive control cells or from antibody capture beads for each parameter that requires compensation

Software compensation works by solving the system of equations described below, where:

Then for a 2-color system,

Solving for the real values,

Note again that the real values are calculated only from the observed values, not as a percentage of the real values.

In matrix notation, equations 1.1 and 1.2 can be written as

Equation 1.5 can be written more succinctly as:

Thus, in order to find the real values for a given parameter, we have to use the inverse matrix. The inverse matrix is a set of coefficients that are multiplied by the observed signals. This is equivalent to FCS Express determining the value of the dials in manual compensation..

When you do automatic compensation in FCS Express. You see the inverted matrix K-1 (often called the compensation matrix) in the compensation screen . The non-inverted matrix K is often called the spillover matrix. Right now, FCS Express does not display the spillover matrix, which will be added in the future. The spillover matrix is calculated internally from the means or medians of your single stained controls.

However, to reiterate, there is no difference between how the compensation matrix values are applied, and how manual values would be applied. That is why you can still adjust "automatic" compensation values using the sliders. It just gets very difficult to compensate more than a few parameters "by eye". Also, automatic compensation guarantees that the correct matrix coefficients are calculated based on your single stained controls.

That being said, there is an important difference between how compensation is usually implemented in hardware and the matrix method. In hardware compensation there is usually no way to change the coefficient from a single channel into itself.

from rearranging equation (1.3) you can see that

if either k21 or k12 is small, the first term will be negligible. However, if both k21 and k12 are large, this first term becomes important. That is why, in FCS Express, after you perform automatic compensation, you often find that kxx is not exactly 1.

In FCS Express you can look at the crossover matrix from the compensation screen. It displays the matrix as source and target values. Source is where the fluorescence is coming from, target is where the fluorescence is appearing. The kxx value appears where there source and target are the same. If you do not see a value where the source and target are the same, FCS Express is assuming that the crossover value for kxx is 100%.

Please be aware that you are not compensating properly if you change the values that FCS Express calculates for the compensation matrix, assuming the correct single stained and negative control data were used.

For a more practical discussion on how to set up automatic compensation, please see our compensation tutorial.