Generalized unmixing model for multispectral flow cytometry utilizing nonsquare compensation matrices

Abstract

Multispectral and hyperspectral flow cytometry (FC) instruments allow measurement of fluorescence or Raman spectra from single cells in flow. As with conventional FC, spectral overlap results in the measured signal in any given detector being a mixture of signals from multiple labels present in the analyzed cells. In contrast to traditional polychromatic FC, these devices utilize a number of detectors (or channels in multispectral detector arrays) that is larger than the number of labels, and no particular detector is a priori dedicated to the measurement of any particular label. This data-acquisition modality requires a rigorous study and understanding of signal formation as well as unmixing procedures that are employed to estimate labels abundance. The simplest extension of the traditional compensation procedure to multispectral data sets is equivalent to an ordinary least-square (LS) solution for estimating abundance of labels in individual cells. This process is identical to the technique employed for unmixing spectral data in various imaging fields. The present study shows that multispectral FC data violate key assumptions of the LS process, and use of the LS method may lead to unmixing artifacts, such as population distortion (spreading) and the presence of negative values in biomarker abundances. Various alternative unmixing techniques were investigated, including relative-error minimization and variance-stabilization transformations. The most promising results were obtained by performing unmixing using Poisson regression with an identity-link function within a generalized linear model framework. This formulation accounts for the presence of Poisson noise in the model of signal formation and subsequently leads to superior unmixing results, particularly for dim fluorescent populations. The proposed Poisson unmixing technique is demonstrated using simulated 8-channel, 2-fluorochrome data and real 32-channel, 6-fluorochrome data. The quality of unmixing is assessed by computing absolute and relative errors, as well as by calculating the symmetrized Kullback–Leibler divergence between known and approximated populations. These results are applicable to any flow-based system with more detectors than labels where Poisson noise is the dominant contributor to the overall system noise and highlight the fact that explicit incorporation of appropriate noise models is the key to accurately estimating the true label abundance on the cells.

Assessing FRET using spectral techniques

“…Another alternative may be to employ spectral phasor analysis, which could significantly speed up the spectral analysis process, albeit at a loss of some spectral and/or intensity information (35). Furthermore, in limited signal-to-noise systems, an unmixing algorithm that accounts for the noise characteristics of the detector may be preferable (36). Despite this, linear unmixing will likely provide satisfactory results for a range of FRET applications that are not prohibitively noise-limited or complex, as is the case in many fluorescence microscopy and flow cytometry assays.…”

Flow Cytometry Instrumentation – An Overview

“…Mathematically, if a linear model for spectral unmixing is applied, both approaches are essentially identical (Bagwell & Adams, ). However, researchers have investigated other approaches for spectral unmixing under different conditions (Novo, Grégori, & Rajwa, ; Schmutz, Valente, Cumano, & Novault, ). Nevertheless, the main difference in operation is that “traditional” spectrally optimized flow cytometers are superior in sensitivity, when used with matching dye‐combinations and especially so when almost all available channels are used.…”

“…Mathematically, if a linear model for spectral unmixing is applied, both approaches are essentially identical (Bagwell & Adams, 1993). However, researchers have investigated other approaches for spectral unmixing under different conditions (Novo, Grégori, & Rajwa, 2014;Schmutz, Valente, Cumano, & Novault, 2016). Nevertheless, the main difference in operation is that…”

Classifying Immunophenotypes With Templates From Flow Cytometry

“…This data needs to be pre-processed by spectral unmixing, gating to identify cell populations of interest (e.g., lymphocytes), and a variance-stabilizing transformation (commonly a generalized logarithm). Unmixing recovers the correct abundances of a protein marker by removing the contributions of other markers at the observed frequency of the fluorescence [18]. Stabilizing the variances of the cell populations, i.e., making the variance independent of the value of the mean, is a step needed for correct statistical analysis using ANOVA methods, but this will be discussed in another publication [4].…”