In addition to hardware compensation, the data can also be acquired uncompensated and then compensated in software. The advantage of this is that since you never compensate the raw data, you never have to worry that you acquired the data with the wrong compensation settings.

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:

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 will 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. The Compensation and the Spillover Matrix can be viewed in FCS Express. 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 resources.

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 fluorescein 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.

Below is a plot of a data file that is in obvious need of compensation. The fluorescein fluorescence, detected primarily in the FITC-A parameter, is spilling into the PE-A parameter. In addition, the PE fluorescence, detected primarily in the PE-A parameter, is spilling into the FITC-A parameter.

If you right click on the plot you can create a new compensation setting, as seen below:

After giving the new compensation setting a name, a set of sliders will appear, as seen in Figure 3.

The sliders that appear pertain to the axes that are currently displayed on the plot. Beneath each slider is the classic 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. Increasing the compensation value is accomplished by moving the slider to the right, and decreasing the compensation value is achieved by moving the slider to the left.

The following pictures show the effects of increasing the PE-A - % of FITC-A slider.

15% Compensation	20% Compensation	25% Compensation

In FCS Express you set the manual compensation identically to the way you would set it on your instrument. In other words, you iteratively adjust the compensation value until you like the picture that you get.