FCS Express allows users of both conventional flow cytometers and spectral cytometers to access, define, and adjust compensation and unmixing matrices.

 

In conventional flow cytometry

•Mirrors and filters are used to select specific bands of the optical spectrum.

•The number of bands usually matches the number of labels (i.e. fluorochromes), with each band being a priori dedicated to mainly collect the signal of a specific label.

 

In spectral cytometry

•Prisms or gratings, and arrays of detectors are used to collect a continuous, high resolution, optical spectrum.

•The number of detectors in the array is larger than the number of labels, and no particular detector is a priori dedicated to the measurement of any particular label.

 

Data generated by both instrument types, has to be processed to account for spillover which is the overlap of signals coming from different dyes into the same band/detectors.

 

For conventional cytometers, the process is named Compensation, while for spectral cytometers it is named Spectral Unmixing.

Although  the above-mentioned processes share the same conceptual goal (i.e. estimating the abundance of each label), they are based on different mathematical calculations.

 

FCS Express 7 allows user to perform both Compensation and Spectral Unmixing through an easy to use wizard via the Compensation and Unmixing window.

 

 

Compensation

 

Ideally, when one uses a dye in an experiment, its emission spectrum will be narrow enough that fluorescence from that dye is only detected by a single detector in the instrument. In practice, because of the broad emission spectra of available fluorochromes, the dye you are using will likely emit significant amounts of fluorescence in several different detectors. In other words, the light reaching a given detector consists of the signals from multiple fluorochromes.

 

Compensation is the process of transforming the data such that the values from a single detector come from an individual dye. In order to do this, a percentage of the overlapping emission is subtracted from the target emission. Traditionally, this compensation was performed by the instrument during acquisition. However, modern instruments are capable of storing the data in uncompensated form and compensation can be applied by the analysis software.

 

Example of the calculation: Compensated Parameter 2 Fluorescence = Observed Parameter 2 Fluorescence minus 5% of Observed Parameter 1 Fluorescence.

 

Compensation involves creating two matrices. The spillover matrix represents the percentage of the signal from a given channel that spills into adjacent channels. The compensation matrix, used to correct for the spillover, is the inverse of the spillover matrix.

 

FCS Express uses the following terminology when dealing with compensation. The target parameter is the parameter that is detecting signal (potentially from multiple sources). The source parameter is the primary parameter that you want the signal to be in, but that dye is also bleeding (potentially) into multiple targets. In other words, we are subtracting the percentage of the source that is “bleeding” into the target.

 

In the example given above, Parameter 2 is the target and Parameter 1 is the source. A family of sources and targets is called a compensation definition. A compensation definition describes all the ways that fluorescence from different channels affect each other under a given set of conditions and is equivalent to a single compensation matrix. Typically, the instrument user will set the gains for all the channels at the beginning of the experiment and use these settings for the duration of the experiment. Thus, the compensation definition would apply for the entire experiment.

 

FCS Express can store multiple compensation definitions in a single layout which is useful when one wants to analyze data acquired on different days in the same layout. It is likely that the gains will be different on different days and will require a different compensation definition for each day. Each overlay on a plot can use a different compensation definition.

 

In addition, the compensation definition can be assigned to a data file. This means that when the .fcs file is loaded into a plot, it will automatically use the proper compensation. By assigning a compensation to a data file, you do not have to remember the appropriate compensation definition for each of your data files.

 

Software Compensation Caveats

Software compensation is not a panacea for all compensation problems. Software compensation works best on high-resolution (> 1024 channel) linear data. Compensation must be performed on linear data. Therefore, data that is stored in logarithmic format (as is sometimes the case with FCS 2.0 data files) must be converted to linear prior to compensation. This conversion from logarithmic to linear can introduce rounding errors. In addition, older data that is stored as less than 1024 channels is rarely compensated accurately with software. However, the majority of data stored as 1024 channels or greater can be software compensated.

 

Additionally, certain file formats supported by FCS Express do not support storing compensation matrices separately from the data file and the these data sets will only display and utilize the raw data values, compensated values, from the time of acquisition. Examples include .csv files and .MQD (MacsQuant) files.

 

For a detailed description of how software compensation is implemented in FCS Express, please see our Frequently Asked Questions at https://denovosoftware.com/faq/kb-what-is-compensation/.

 

 

Spectral Unmixing

 

With spectral cytometry instruments, a continuous, high resolution, optical spectrum is collected for each event in the sample. The spectrum is the sum of the spectra derived from all the dyes present on the event of interest. Spectral Unmixing is the process of transforming the data to determine the contribution of each dye to the total signal.

 

Several mathematical models can be used to perform the spectral unmixing calculation. However, the most widely used calculation is the Ordinary Least Square method. The Ordinary Least Square method assumes a linear contribution of unchanging reference spectra to the mixture spectra of an unknown sample. In turn, the calculation allows us to estimate the contribution of each spectrum (i.e. each dye).

 

Ordinary Least Square uses a linear decomposition algorithm to solve the equation:

 

Y = A x C + E

 

For the sake of simplicity we can put aside the term "E" , which is the random measurement error, and focus on the remaining terms:

 

•Y is the measured spectrum matrix (i.e. a 1-column matrix containing the spectrum of the event of interest).

•A is the reference spectra matrix (i.e. a n-columns matrix containing the spectrum of each reference dye)

•C is the concentration matrix (i.e. a 1-row matrix containing the contribution values of each dye to the total measured spectrum)

 

Provided a series of reference spectra (A), and a measured spectrum (Y), this method allows to estimate the term C, an thus the contribution of each dye to the total signal intensity of the event of interest.