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.

Join Expert Cytometry's Mastery Class
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.

Similar Articles

How To Buy A Flow Cytometer - What You Need To Evaluate From A To Z

How To Buy A Flow Cytometer - What You Need To Evaluate From A To Z

By: Tim Bushnell, PhD

So you have the money to buy a flow cytometer. Is it a sorter? Or perhaps a spectral analyzer? No wait, maybe an imaging mass cytometer?  Big or small?  What to choose?  How to choose?  More importantly, once you sign the contract to purchase the instrument, you don’t want to be struck with buyers remorse.  It is indeed a big decision and we have the best advice for you to consider before making the purchase. Let’s discuss some of the steps you should take to prevent buyers remorse and ensure you are getting the best instrument for your needs.  Do…

How small can you go? Flow cytometry of bacteria and viruses

How small can you go? Flow cytometry of bacteria and viruses

By: Tim Bushnell, PhD

Flow cytometers are traditionally designed for measuring particles, like beads and cells. These tend to fall in the small micron size range. Looking at the relative size of different targets of biological interest, it is clear the most common targets for flow cytometry (cells) are comparatively large (figure 1). Figure 1:  Relative size of different biological targets of interest. Image modified from Bioninja.    In the visible spectrum, where most of the excitation light sources reside, it is clear the cells are larger than the light. This is important as one of the characteristics that we typically measure is the amount…

What Is Spectral Unmixing And Why It's Important In Flow Cytometry

What Is Spectral Unmixing And Why It's Important In Flow Cytometry

By: Tim Bushnell, PhD

As the labeled cell passes through the interrogation point, it is illuminated by the excitation lasers. The fluorochromes, fluoresce; emitting photons of a higher wavelength than the excitation source. This is typically modeled using spectral viewers such as in the figure below, which shows the excitation (dashed lines) and emission (filled curves) for Brilliant Violet 421TM (purple) and Alexa Fluor 488Ⓡ (green).  Figure 1: Excitation and emission profiles of BV421TM and AF488Ⓡ  In traditional fluorescent flow cytometry (TFF), the instrument measures each fluorochrome off an individual detector. Since the detectors we use — photomultiplier tubes (PMT) and avalanche photodiodes (APD)…

How To Extract Cells From Tissues Using Laser Capture Microscopy

How To Extract Cells From Tissues Using Laser Capture Microscopy

By: Tim Bushnell, PhD

Extracting specific cells still remains an important aspect of several emerging genomic techniques. Prior knowledge about the input cells helps to put the downstream results in context. The most common isolation technique is cell sorting, but it requires a single cell suspension and eliminates any spatial information about the microenvironment. Spatial transcriptomics is an emerging technique that can address some of these issues, but that is a topic for another blog.  So what does a researcher who needs to isolate a specific type of cell do? The answer lies in the technique of laser capture microdissection (LCM). Developed at the National…

The Importance Of Quality Control And Quality Assurance In Flow Cytometry (Part 4 Of 6)

The Importance Of Quality Control And Quality Assurance In Flow Cytometry (Part 4 Of 6)

By: Tim Bushnell, PhD

Incorporating quality control as a part of the optimization process in  your flow cytometry protocol is important. Take a step back and consider how to build quality control tracking into the experimental protocol.  When researchers hear about quality control, they immediately shift their attention to those operating and maintaining the instrument, as if the whole weight of QC should fall on their shoulders.   It is true that core facilities work hard to provide high-quality instruments and monitor performance over time so that the researchers can enjoy uniformity in their experiments. That, however, is just one level of QC.  As the experimental…

How To Optimize Instrument Voltage For Flow Cytometry Experiments  (Part 3 Of 6)

How To Optimize Instrument Voltage For Flow Cytometry Experiments (Part 3 Of 6)

By: Tim Bushnell, PhD

As we continue to explore the steps involved in optimizing a flow cytometry experiment, we turn our attention to the detectors and optimizing sensitivity: instrument voltage optimization.  This is important as we want to ensure that we can make as sensitive a measurement as possible.  This requires us to know the optimal sensitivity of our instrument, and how our stained cells are resolved based on that voltage.  Let’s start by asking the question what makes a good voltage?  Joe Trotter, from the BD Biosciences Advanced Technology Group, once suggested the following:  Electronic noise effects resolution sensitivity   A good minimal PMT…

Optimizing Flow Cytometry Experiments - Part 2         How To Block Samples (Sample Blocking)

Optimizing Flow Cytometry Experiments - Part 2 How To Block Samples (Sample Blocking)

By: Tim Bushnell, PhD

In my previous blog on  experimental optimization, we discussed the idea of identifying the best antibody concentration for staining the cells. We did this through a process called titration, which  focuses on finding the best signal-to-noise ratio at the lowest antibody concentration. In this blog we will deal with sample blocking As a reminder, there are two other major binding concerns with antibodies. The first is the specific binding of the Fc fragment of the antibody to the Fc Receptor expressed on some cells. This protein is critical for the process of destroying microbes or other cells that have been…

How To Determine The Optimal Antibody Concentration For Your Flow Cytometry Experiment (Part 1 of 6)

How To Determine The Optimal Antibody Concentration For Your Flow Cytometry Experiment (Part 1 of 6)

By: Tim Bushnell, PhD

Over the next series of blog posts, we will explore the different aspects of optimizing a polychromatic flow cytometry panel. These steps range from figuring out the best voltage to use, which controls are critical for data interpretation, what quality control tools can be integrated into the assay; how to block cells, and more. This blog will focus on determining the optimal antibody concentration.  As a reminder about the antibody structure, a schematic of an antibody is shown below.  Figure 1: Schematic of an antibody. Figure from Wikipedia. The antibody is composed of two heavy chains and two light chains that…

2020 - A Year Turned Upside Down

2020 - A Year Turned Upside Down

By: Tim Bushnell, PhD

What an incredible year 2020 has been. It started off like any other year and bam SARS-CoV-2 (aka COVID 19) entered the equation, bringing chaos and havoc to the world. Things kept changing overnight as new rules and regulations popped up. Masking, quarantine, and flatten the curve became common words in the news. How we met, how we interacted changed almost overnight. Throughout all of this, as we look to 2021, there is hope and optimism. Multiple vaccines have been developed, building on years of research into the SARS-CoV virus, with some approved for human use, and others on the horizon.…

Top Technical Training eBooks

Get the Advanced Microscopy eBook

Get the Advanced Microscopy eBook

Heather Brown-Harding, PhD

Learn the best practices and advanced techniques across the diverse fields of microscopy, including instrumentation, experimental setup, image analysis, figure preparation, and more.

Get The Free Modern Flow Cytometry eBook

Get The Free Modern Flow Cytometry eBook

Tim Bushnell, PhD

Learn the best practices of flow cytometry experimentation, data analysis, figure preparation, antibody panel design, instrumentation and more.

Get The Free 4-10 Compensation eBook

Get The Free 4-10 Compensation eBook

Tim Bushnell, PhD

Advanced 4-10 Color Compensation, Learn strategies for designing advanced antibody compensation panels and how to use your compensation matrix to analyze your experimental data.