Anja B. Bohn^{*}, Bjarne K. Moller and Mikkel S. Petersen

*Correspondence: Anja B. Bohn anjsch@rm.dk

Department of Clinical Immunology, Aarhus University Hospital, Palle Juul-Jensens Boulevard 99, DK-8200, Aarhus, Denmark.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Flow cytometric analysis is a valuable technique for identification and characterization of cells. However, flow cytometric analysis of autofluorescent cells requires careful consideration. In particular, the outcome of fluorescence compensation in the presence of significant autofluorescence poses a challenge to the interpretation of multicolour flow cytometric data. In this paper, we explain the mathematical basis of fluorescence compensation and the effects of autofluorescence, both in theory and applied to mesenchymal stem cells, which are notoriously autofluorescent. We illustrate how failure to understand the consequences of compensation can easily lead to critical errors in data interpretation, particularly when autofluorescence is involved. In the process, the common pitfalls of flow cytometric analysis of mesenchymal stem cells are presented, as are the simple measures necessary to avoid them. Specifically, the counterintuitive concept of "negative fluorescence values" is explained and exemplified, and the phenomenon of "population broadening" is addressed. Researchers must be acutely aware of the effects of compensation on the positioning of cells. We recommend always displaying data in biexponential or logicle transformations and advice to include fluorescence-minus-one controls to establish thresholds of positivity.

**Keywords**: Mesenchymal stromal cells, flow cytometry, cultured cells, cellular structures

Autofluorescence occurs to some extent in all cell types and is part of the intrinsic "background" fluorescence signal in flow cytometry. In some cell types, such as mesenchymal stem cells, autofluorescence is especially high [1]. A high level of background fluorescence complicates flow cytometric analyses, which are often based on multiple, fluorochrome-labelled antibodies and weakly expressed antigens. Indeed, autofluorescence exposes effects of compensation that go unnoticed in "simple" flow cytometry of cells with little autofluorescence (such as lymphocytes) - effects that may catch a flow cytometrist unaccustomed to dealing with autofluorescence unawares.

In the following, we address two common pitfalls in flow cytometric analysis of autofluorescent cells - and describe the simple measures that can be taken to avoid them. As an example of highly autofluorescent cells, we here focus our attention on cultured mesenchymal stem cells, but the principles are universal, and should be considered regardless of cell type.

The most widely used model of spectral overlap compensation does not fully incorporate autofluorescence, which results in counterintuitive data positioning; indeed, highly autofluorescent populations can obtain negative fluorescence values after compensation. In addition, compensation results in broadening of populations, which necessitates the use of fluorescence-minus-one control staining.

**The consequence of autofluorescence in compensation**

Negative fluorescence values after compensation is a fairly
common occurrence in flow cytometric analysis of cell types
with high levels of autofluorescence (e.g., mesenchymal stem
cells). At first glance, the concept of negative fluorescence is
counterintuitive, and researchers may instinctively begin to
doubt the validity of the compensation, the flow cytometer,
or suspect a "bug" in the flow cytometric software. Worse, the
researcher may be sufficiently perplexed to conclude that flow
cytometry of such cells "doesn't work" and abandon flow cytometric
analyses altogether. However, negative fluorescence
values do make sense when one considers what compensation
does.

The classical approach to compensation involves recording the signals of single-stained compensation controls to determine the degree of spectral overlap between fluorochromes and detectors. Compensation is typically done by adjusting the values of the spectral overlap matrix elements (algorithmically by iteration or in rare cases manually by "visual inspection"), until the compensated median fluorescence intensity (MFI) of labelled cells (or beads) matches the compensated MFI of unlabelled cells in all detectors except the one assigned to the fluorochrome of the particular single-stained population.

Although mathematical models that incorporate autofluorescence exist [2], flow cytometry software algorithms for compensation typically rely on a simpler model, in which the signal on detector j can be described as:

where n is the number of fluorochromes/detectors, *M _{ij}* is the
spectral overlap matrix element representing the relative signal
of the

where S is the column vector of signals detected, *M* is the
spectral overlap matrix, and *F* is a vector representing the
amounts of fluorochromes. Correction for spectral overlap
then involves finding the inverse of matrix *M* (i.e., the compensation
matrix *M ^{-1}*), and applying it to the signal vector to
obtain the F-vector (which is used for data visualization), that is:

This operation is essentially a linear transformation affecting
the scale and relative angles of the axes of the coordinate
system *while leaving the origin unaffected*. As such, classical
compensation does not include translation of the coordinate
system. This fact can lead to surprises in data visualization when
autofluorescence is involved, as described in the following.

Let us consider a hypothetical staining experiment involving
only two fluorochromes *(F _{1}* and

Thus, assume that an unstained cell has a signal-vector
of [*S _{1},S_{2}*]=[50,0], so the entire signal actually represents autofluorescence
(i.e.,

Figure 1
:
**Two-dimensional data plots and the "basic model" of spectral overlap of
single stained and unstained (and autofluorescent) cell/populations.**

The X-axis is the signal on fluorescence detector 1, and the Y-axis is the signal on fluorescence detector 2. The slope of the red line is - by definition - the spectral overlap from fluorochrome 1 into detector 2, which in this case has a value of 1 (100%). Notice that the cells in this example are autofluorescent in detector 1 only. To the right in Figure 1A the "basic model" of spectral overlap is illustrated: The vector to the left of the equal sign represents the "raw" detector values; the vector to the right represents the compensated values; and the matrix represents the spectral overlap matrix. Within the spectral overlap matrix, each fluorochrome is represented as a single column, and each row represents the relative signal of the fluorochrome in each detector. Here, the spectral overlap matrix is set to "uncompensated" values (i.e., compensated data equal uncompensated data).

The classical approach to compensation of the spectral
overlap from fluorochrome *F _{1}* into the

Geometrically, this transformation can be thought of as vertical shearing of data; i.e., each data point is displaced on the Y-axis by an amount proportional to the position on the X-axis, to a degree that exactly counteracts the effect of spectral overlap.

The procedure is illustrated in Figure 1B (incomplete compensation) and 1C (proper compensation).

To the left in Figure 1B an insufficient compensation basis is illustrated graphically using the data points of Figure 1A. Notice that the slope of the F1-axis is only half the slope of the red line. The basic model of spectral overlap, with the spectral overlap matrix used in the plot on the left, is illustrated to the right (top) where the new X-axis basis is the vector (1,0.5), and the Y-axis basis vector is unchanged (0,1). To transform a set of coordinates from one basis to another, one must right-multiply with the inverse of the matrix composed of the new basis vectors expressed in the old coordinates. This inverse matrix of the spectral overlap matrix is called the "compensation matrix" and is illustrated to the right (middle).

The effect of applying the compensation matrix to singlestained cells and unstained cells is also illustrated to the right (bottom). Notice the different compensated Y-axis values of stained (dark blue arrow) and unstained (light blue arrow) populations.

The figure shows an "undercompensated" situation, in which
the spectral overlap from fluorochrome *F _{1}* into the

As can be seen, the position of the single-stained cell in
the new, compensated coordinate system is (100,0), whereas
the position of the unstained cell is (50, -25). Notice how the
transformation has reduced the Y-value of the single stained
cells by 50 to a value of 0, but also reduced the Y-value of the
unstained cells by 25 to a value of -25. In other words, the *Y-values
of stained and unstained cells are still not identical after
compensation*, so the compensation is insufficient.

This is a major pitfall in flow cytometry in general, and in mesenchymal stem cell analysis in particular. The remedy, fortunately, is simple: for proper compensation, stained and unstained cells/beads must have equal levels of auto-fluorescence.

It is perfectly possible to perform good compensation by staining cells with a high level of autofluorescence, as long as those same cells can still be identified in an unstained state. One should not, however, be tempted to base compensation on a population of positive, highly autofluorescent cells and another population of negative cells with low autofluorescence. The simplest way to isolate the contribution of the fluorochrome from the contribution of the autofluorescence is-obviously-to have the same baseline of autofluorescence in both positive and negative samples.

The use of compensation beads is generally recommended to ensure similar levels of autofluorescence, and comes with the extra benefits of a strong, positive signal, and a small staining variation within the positive population. But it is certainly possible to obtain a proper spectral overlap matrix with some fluorochromes on beads and others on cells, as long as the proper negative population is used in each case.

A proper compensation of our example is illustrated in Figure 1C. Notice to the left in the figure that the slope of the F1-axis now matches the slope of the red line. The basic model of spectral overlap with the spectral overlap matrix used in this plot is shown to the right (top) where the new X-axis basis is the vector (1,1), and the Y-axis basis vector (0,1) is unaffected by the transformation. The Compensation matrix, found by inversion of the spectral overlap matrix is shown in the middle to the right and the effect of applying the compensation matrix to single-stained cells and unstained cells is illustrated in the bottom (right). Notice the identical compensated Y-axis values of stained (dark blue arrow) and unstained (light blue arrow) populations.

In our particular example, the shear angle is 45 degrees
(corresponding to an overlap/slope/spillover-coefficient *M _{12}* of 1). In general, the angle is obtained simply as arctan (

Notice how this vertical shearing transformation has the
intended effect of rendering the compensated Y-axis values
of *F _{1}*-single-stained cells equal to the compensated Y-axis values of unstained cells-so rendering the compensated Yaxis
independent of

But the compensation also has the somewhat undesirable
side-effect of introducing negative "fluorescence"-values: the
unstained cell had an Y-axis of 0 before the compensation,
but ends with an Y-axis value of -50, as does the *F _{1}*-singlestained
cell.

This raises another important point when compensating autofluorescent cells: if these compensated data are represented on a simple log scale, negative events will be invisible (or piled up in the lowest channel, depending on the software). In an extreme situation, this could lead to misinterpretation of data. The simple remedy is to always use biexponential or logicle [3] representation of compensated data to ensure that all data are visible, even when values are highly negative.

It is important to emphasise that negative values after
compensation *per* se do not imply over-compensation, as
is sometimes erroneously surmised. Rather, they arise as a
natural consequence of the mathematical transformation.
Differences in compensated values are still proportional to
differences in the amount of fluorochrome bound to the
cell-but the absolute value is, of course, largely arbitrary, and
depends (among other factors) on the level of autofluorescence
in the cell.

To avoid excessively negative values, one could theoretically move the coordinate system origin to the centre of the unstained cell population before applying the compensation matrix (or adjust voltage/gain settings to fix the centre of the unstained, autofluorescent cells at the coordinate system origin before recording compensation controls-never after recording, since adjusting voltage/gain will change the compensation needed.). This would leave the position of the unstained cells unaffected by compensation. In actual practice, however, flow cytometry acquisition software rarely permits such data translation, or is fixed in a log-display mode.

An entirely different approach is to devote a fluorescence detector to measure autofluorescence directly on a cell-bycell basis, and "compensate" away the autofluorescence in other channels [4]. Although occasionally useful, the method requires careful selection of the "autofluorescence" detector and may severely limit the number and type of fluorochromes available for staining.

**Compensation of autofluorescent mesenchymal stem cells**

To illustrate the points raised, consider the following data from
staining of fourth-passage mesenchymal stem cells (MSC).

Figure 2A shows data of unstained (left) and single-stained (middle) MSC that have been stained with an anti-CD90 antibody conjugated with a PerCP-Cy5.5 fluorochrome (events have been gated on FSC/SSC to exclude debris and non-MSC remnants). On the particular flow cytometer used, the best detector available for PerCP-Cy5.5 emissions is the PerCP detector (X-axis), but a strong spectral overlap is evident in the PE-Cy7 detector (Y-axis) as illustrated in the middle and right part of Figure 2A. Furthermore, MSC have strong autofluorescence in the PerCP-channel, but only moderate/low autofluorescence in the PE-Cy7 channel. Such combinations set the stage for "negative fluorescence": we need to correct for a major spectral overlap from a channel with high autofluorescence into a channel with relatively low autofluorescence.

Figure 2
:
**Flow cytometric data of mesenchymal stem cells unstained or stained with anti-CD90 PerCP-Cy5.5.**

And so, after applying a compensation matrix (typically obtained from staining of compensation beads), we arrive at the situation depicted in Figure 2B.

At first glance, all is in reasonably good order - although one might be tempted to conclude that the spillover coefficient has been slightly underestimated (it is approximately 16%), inasmuch as the stained population still seems to have a slightly higher median Y-axis position than the unstained cells - but surely nothing terribly amiss. A careless flow cytometrist might even make slight, manual adjustments to the compensation matrix to "set matters straight" based on these plots.

But a closer look reveals that something is very wrong. When a gate is placed around the visible population of cells after compensation, only slightly more than 50% of the total stained cells are included. The reason is simple: compensation has introduced negative fluorescence values on the Y-axis, and such values cannot be displayed on a logarithmic scale, leading to "loss" of roughly half the events. Fortunately, switching to biexponential scaling saves the day (illustrated in Figure 2C).

The biexponential scale reveals that the compensation is indeed correct: the median Y-axis value of single-stained MSC after compensation is equal to the median Y-axis value of unstained MSC after compensation (that value is -32, incidentally).

The biexponential axis also exposes another consequence of compensation-population broadening-which is discussed in the following.

**The importance of fluorescence-minus-one controls**

In a perfect flow cytometer, there would be no error in
fluorescence measurements, and one could safely assume
that the measurements were "true" indications of the actual
fluorescences on each cell. The "width" (or spread, or variation)
of a population of cells on any given parameter would then
reflect the actual, physical variation of that parameter within
the population, and nothing else. In this case, compensation
would not affect the "width" or shape of the population (other
than the purely visual changes introduced by redefining the
basis of the coordinate system by shearing transformation) -
and the "width" of the stained cell population would closely
resemble that of the unstained cells, both before and after
compensation (insofar as a "perfect" compensation truly
eliminates the contribution of irrelevant fluorochromes on
each individual cell, leaving only the natural variation of the
background/autofluorescence).

In reality, measurements are always less-than-perfect, and there is some uncertainty associated with each fluorescence measurement - at the very least, there is always the intrinsic "photon count"/Poisson uncertainty. This is true of the measurements used to determine spectral overlap (so the compensation matrix itself is not "perfect"), and of the measurements of each cell on each parameter.

Imagine, for example, that the uncertainty associated with the actual fluorescence measurements of each cell is on the order of one "pixel" in the plot (that is, each dot in the plot could be "off" by plus or minus one pixel). Because of the logarithmic nature of the axes, this "one-pixel error" could easily mean an absolute uncertainty of several thousand (arbitrary) fluorescence units in brightly stained populations (i.e., populations far from the origin). When such populations are "brought down" towards background levels by compensation, the transformation does not reduce the uncertainty of the original measurements. Indeed, an uncertainty of one pixel in the uncompensated sample is "magnified" by displaying the population further down on a logarithmic (or biexponential) scale, where a given absolute range takes up more and more space.

As a result, populations are "widened" by compensation. It is important to understand that this effect does not reflect a deficiency of compensation as such. Rather, it is the unavoidable consequence of the fact that each compensated event relies on several measurements: (at least) two measurements of fluorescence, each with its own, independent error; in addition to a systematic error that may or may not arise from a slightly incorrect compensation matrix. These errors are additive, and nothing can be done about it (short of constructing ever more "perfect" fluorescence detectors).

The consequences of population broadening are clearly visible in our example with mesenchymal stem cells in Figure 2C. Notice (in the overlay-plot) how the compensated, singlestained population extends both above and below the more "compact" population formed by the unstained population, even though compensation is "perfect" (in the sense that the median fluorescences of the Y-axis are equal).

Importantly, the unstained sample does not tell us at what level we should consider a cell "positive" on the Y-axis after compensation.

Looking at the unstained cells of Figure 2C, we might be tempted to surmise that anything with a PE-Cy7 signal above, say 500 fluorescence units, should be considered positive. After all, all unstained cells lie below 500, so the claim does not seem unreasonable at first glance. However, if we were to apply this threshold to the single-stained population, a sizable fraction of the cells would be PE-Cy7 positive, simply because of population broadening.

The answer is to base such thresholds on so-called "fluorescenceminus-
one" (FMO) controls [5]. These controls are simply cells
stained with all antibodies except one-so in a sense, they are
"reverse" compensation controls (i.e., omitting one antibody
at a time, rather than including one antibody at a time). If we
want to determine the threshold at which a cell should be
considered truly PE-Cy7 positive, we would stain the cells with
all antibodies except PE-Cy7, apply the compensation matrix
(and thus introduce the population broadening arising from
the combined spectral overlap of all fluorochromes), and *then* consider the position of these compensated cells on the PE-Cy7
axis. This approach not only addresses autofluorescence, but
also the added uncertainties that arise from compensation
of all other fluorochromes in the sample.

In a two-colour experiment such as that presented, the single-stained control also conveniently serves as an FMO control-but more complicated situations obviously require separate single-stained compensation controls and FMO controls.

What FMOs do not accomplish, however, is to settle doubts of unspecific antibody binding. For this purpose, isotype controls are sometimes useful. The chief limitation of isotype controls is the difficulty of finding an isotype control antibody preparation that is truly comparable to the "real" antibody in terms of antibody concentration, isotype, conjugation efficiency, and fluorochrome composition.

Autofluorescent cells, including mesenchymal stem cells, are indeed amenable to flow cytometric analyses, in spite of high levels of autofluorescence. However, researchers must be acutely aware of the effects of compensation on the positioning of cells (and thus always display data in biexponential or logicle transformations). Compensation controls can be based on beads (recommended) or cells, or a combination thereof, with no theoretical implications for the compensation matrix, insofar as the matrix is solely based on slopes. Compensations must, however, compare stained and unstained populations with identical autofluorescences. Finally, researchers are advised to include fluorescence-minus-one controls to establish thresholds of positivity.

The authors declare that they have no competing interests.

Authors' contributions |
ABB |
BKM |
MSP |

Research concept and design | √ | √ | √ |

Collection and/or assembly of data | √ | -- | -- |

Data analysis and interpretation | √ | -- | √ |

Writing the article | √ | -- | √ |

Critical revision of the article | -- | √ | √ |

Final approval of article | -- | -- | √ |

Statistical analysis | -- | -- | -- |

Financial support for this study was provided by Karen Elise Jensens Foundation.

EIC: Prasad S. Koka, Haffkine Institute for Training, Research & Testing,
India.

Received: 21-Oct-2015 Final Revised: 23-Nov-2015

Accepted: 30-Nov-2015 Published: 11-Dec-2015

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Volume 2

Bohn AB, Moller BK and Petersen MS. **Flow cytometry and compensation of highly autofluorescent cells: the example of mesenchymal stem cells**. *Stem Cell Biol Res*. 2015; **2**:4. http://dx.doi.org/10.7243/2054-717X-2-4

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