4 Critical Rules For Spectral Unmixing

Spectral unmixing is the mathematical process by which a spectrum is broken down into the abundances of the different fluorochromes that make up the observed spectrum. This was described in the paper by Novo et al., (2013), which presented a generalized model for spectral unmixing of flow cytometry data. Of course, like compensation in traditional fluorescent flow cytometry, there are important rules to observe regarding the controls that are used to unmix the sample. If you need a refresher on the rules for TFF compensation, you can read about them here.   

This blog will discuss the generalized process of spectral unmixing and highlight some important rules to consider.

First, let’s look at the process of unmixing a spectrum. Figure 1 shows the resulting spectra from a cell with various levels of three different fluorochromes on a system with 12 detectors. 

Figure 1: Simulated Spectrum on a cell with three fluorochromes. 

To extract the relative abundance of each of the fluorochromes in question, we will need a set of single color controls, just like TFF. 

Figure 2: Simulated spectra of the three reagents

Figure 2 shows the spectra of the three reagents. These single color controls will be used to determine the abundance of each of these fluorochromes on the cell of interest. To do that, we need to turn to the data.  That is the relative intensity of each individual fluorochrome in each detector as well as the intensity of the signal on the cell of interest. 

On the left side, we have the relative intensity of each fluorochrome in each detector. We will call this the mixing matrix or M. On the right we have the Observed or measured spectra, which we will call r.

What we need to determine is how much of each fluorochrome is on the cell to give the observed spectra based on M. We will call this value the abundance, or a. 

Figure 3: The data necessary for determining the abundance of each fluorochrome. 

Another way to describe this is Ma = r. In this case we have three matrices, and if we want to determine a, we are going to need to multiply both sides by M-1 which results in the following equation

a = rM-1

If this looks familiar, you would be right. It is similar to how we calculate compensation. Now if we do the math correctly, as shown in figure 4, the sum of the abundances of each fluorochrome times the fluorochrome intensity in a given channel yields the observed spectra. 

Figure 4: Demonstration that the sum of the abundance of each fluorochrome results in the observed spectra. 

Now let’s turn our attention to the rules that our single color controls must adhere to. 

Rule 1: The control must be at least as bright as the experimental sample. This is the same as the first rule of compensation, so no differences here. 

Rule 2: There must be good separation between the positive and negative. While this is not explicitly stated in the rules of compensation, is it good practice. 

Rule 3: The negative and positive must have the same autofluorescence. Again this is just like the second rule of compensation.

Rule 4:The fluorescence spectrum needs to be identical to the experimental sample. Sounds like the third rule of compensation. But there is more to this as we talk about below. 

Bonus Rule 5: Collect sufficient events. 

So overall, the rules are pretty similar to compensation, but there is more to rule 4 than meets the eye. In TFF, we can either use the cells or antibody capture beads for our controls.

Generally antibody capture beads are preferred as they allow us to save cells for the experiment, capture all the antibodies and give a good separation between the negative and positive. However, It turns out that when we measure the full spectrum of a fluorochrome attached to a bead versus a cell, there may be differences.

Figure 5: Fluorescence spectra of fluorochrome A on either cells (Ac) or beads (Ab) 

As shown in figure 5, there is a significant difference in the spectra of fluorochrome A depending on what carrier it is bound to. Since we know the actual abundance of A in this experiment, look what happens when we plot this data like in figure 4.

Figure 6: Impact of the incorrect spectrum on the data. 

Clearly the fact that the spectrum from the bead control is different from the cell control results in a completely different outcome. In fact, this would result in the wrong abundances from being determined by the algorithm. 

It is recommended to run both bead and cell single color controls when setting up your initial experiment  so that if there are differences in the spectra between the beads and the cells, you will have the correct control for unmixing.

Often these libraries of spectra can be saved from run to run, and only have to be evaluated when you start using a different lot of reagents, especially if it is a tandem dye – and if in doubt, go check out the fluorochrome of interest on a spectral viewer. 

Concluding Remarks

At the end of the day, a good spectral unmixing requires good controls that adhere to a certain set of rules. These rules are familiar to the flow cytometrist from the days of traditional fluorescent flow work. There are some twists that those new working with spectral cytometry need to consider, one of the most important is that there can be spectral mismatches based on the carrier, so labeling both beads and cells to look for these mismatches will guide you in the proper selection of the control. 

The ultimate output from the spectral cytometer is an FCS file with the abundances (intensities) of each fluorochrome on each cell, allowing you to analyze the data as you traditionally would, using your favorite tools. 

To learn more about important control measures for your flow cytometry lab, and to get access to all of our advanced materials including 20 training videos, presentations, workbooks, and private group membership, get on the Flow Cytometry Mastery Class wait list.

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Tim Bushnell, PhD
Tim Bushnell, PhD

Tim Bushnell holds a PhD in Biology from the Rensselaer Polytechnic Institute. He is a co-founder of—and didactic mind behind—ExCyte, the world’s leading flow cytometry training company, which organization boasts a veritable library of in-the-lab resources on sequencing, microscopy, and related topics in the life sciences.

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