11institutetext: Raytheon BBN, 10 Moulton Street, Cambridge, MA, USA, 11email:
<EMAIL_ADDRESS>
# Flow Cytometry Quantification of Transient Transfections in Mammalian Cells

Jacob Beal

###### Abstract

Flow cytometry is a powerful quantitative assay supporting high-throughput
collection of single-cell data with a high dynamic range. For flow cytometry
to yield reproducible data with a quantitative relationship to the underlying
biology, however, requires that 1) appropriate process controls are collected
along with experimental samples, 2) these process controls are used for unit
calibration and quality control, and 3) data is analyzed using appropriate
statistics. To this end, this article describes methods for quantitative flow
cytometry through addition of process controls and analyses, thereby enabling
better development, modeling, and debugging of engineered biological
organisms. The methods described here have specifically been developed in the
context of transient transfections in mammalian cells, but may in many cases
be adaptable to other categories of transfection and other types of cells.

##  1 Introduction

Flow cytometry is a long-established method for assaying the optical
properties of large numbers of single cells, in use for more than half a
century fulwyler1965electronic ; kamentsky1973cytology . Much of the
development and use of flow cytometry has been in clinical applications
focused on categorization of cells into classes, such as immunoassays and
diagnosis of blood diseases. In recent years, however, flow cytometers have
also been used to great effect in synthetic biology for measuring the
properties of individual cells, e.g., measuring the expression level of a gene
by estimating the number of molecules of a proxy fluorescent reporter.

In a typical flow cytometer, a stream of cells are passed in front of one or
more lasers, with an arrangement of optical filters and detectors collecting
information on the light scattering and fluorescence properties of each cell-
like particle as it passes. Flow cytometer optical detectors often have high
sensitivity and range, with signals distinguishable on the order of a $10^{3}$
to $10^{6}$ ratio between the highest and lowest distinguishable values. Data
is typically collected from on the order of $10^{3}$ to $10^{5}$ particles per
sample over the time span from seconds to minutes, and automated samplers
allow high-throughput processing of dozens to hundreds of samples from
microplates.

Figure 1: Flow cytometry provides high-dynamic range data from large numbers
of single cells at a single time point, complementary to the properties of
other common fluorescence-based assays.

Flow cytometers can thus be prodigious sources of single-cell data with a high
dynamic range, and form an important part of the synthetic biology engineering
toolkit. Compared to other broadly accessible fluorescence assays (Figure 1),
flow cytometry shines in number of cells assayed and sensitivity (i.e.,
dynamic range). Because cells must be suspended in sheath fluid and passed
through the instrument, however, the assay is typically disruptive to cell
state and thus generally not suitable for collecting time series data. Plate
readers provide a useful complementary capability for flow cytometry, since
they are effective at collecting time series data and can be calibrated to
equivalent units beal2021comparative ; beal2020robust . Likewise, microscopy
provides the complementary capabilities of subcellular resolution and time
series data. Indeed, imaging flow cytometry can fuse microscopy and flow
cytometry by adding a microscopy stage to a flow cytometer
barteneva2012imaging , though it is still disruptive to cell states.

The relationship between the properties of a cell and the optical signal
measured in a channel of a flow cytometer, however, is highly sensitive to
specifics of the instrument’s configuration, current settings, and level of
optical wear, as well as to choice of fluorescent reporter, cell state, and
interference from other measurement channels Roederer2001 ; Roederer2002 ;
gaigalas2005quantitating . As a consequence, interpreting flow cytometry data
to produce precise, reproducible, and biologically relevant estimates of
molecule counts requires careful use of process controls linked to appropriate
quality control and analytical methods beal2022meeting . When appropriate
process control, calibration, and analysis protocols are applied, however,
flow cytometry can produce reliably produce reproducible measurements with a
quantitative relationship to the underlying biology.

This article aims to increase the accessibility of quantitative flow cytometry
by summarizing methods for:

  1. 1.

enhancing a flow cytometry study by adding process controls to support
calibration and quantification,

  2. 2.

using data from these process controls for unit calibration and quality
control, and

  3. 3.

analysis of the resulting calibrated data using appropriate statistics.

More specifically, this article focuses on methods that were developed in the
context of transient transfections in mammalian cells over the course of a
number of studies that used these methods to develop, model, refine, and
predict the behavior of a variety of genetic devices beal2012method ;
DavidsohnBeal14 ; kiani2014crispr ; kiani2015cas9 ; beal2015model ;
wagner2018small ; siciliano2018engineering ; weinberg2019high ;
kiwimagi2021quantitative . Note that these methods are modular with respect to
most aspects of cell type, transfection, and culturing, so the actual
preparation of the experimental samples will be largely abstracted, while the
methods focus on the process controls necessary for effective calibration, and
the analysis used to make use of those process controls. Likewise, many
aspects of the methods should be adaptable to non-transient transfections and
to non-mammalian cells, and to this end the methods will explicitly identify
the points where enabling assumptions are made based on mammalian transient
transfection in order to better understand limits and enable adaptation to
other contexts.

##  2 Materials

For calibration and quality control on a flow cytometry study, two classes of
calibrants are needed: calibrant reagents and cellular calibrants.

Calibrant reagents are materials with known optical properties that are used
to compute a unit conversion factor between the arbitrary unit values output
by a flow cytometer and the physical properties of size and molecule count.
Failures in calibrant reagents are typically uncorrelated with failures in the
preparation of the experimental samples to be assayed, so these calibrants
serve as a process control testing for correct operation of the flow
cytometer.

Cellular calibrants, on the other hand, are positive and negative controls
that establish the expected dynamic range of cellular behaviors in each
fluorescent channel and the relationships between measurements in different
channels. Failures in cellular calibrants are typically correlated with
failures in the preparation of experimental samples, so these calibrants serve
as a process control testing for correct execution of the preparation of
experimental samples.

###  2.1 Calibrant Reagents

  * •

SpheroTech Ultra Rainbow Quantitative Particle Kit (URQP-38-6K)

    * –

This kit provides beads with six different intensities of fluorescence and
NIST-certified Equivalent Reference Fluorophore (ERF) value that map each
intensity to an equivalent number of fluorescent molecules on four channels:
fluorescein, Nile Red, APC and Coumarin 30. Calibrant should be stored,
handled, and dispensed according to the manufacturer directions. One kit
provides sufficient materials for many assays.

    * –

These beads are used to compute a linear unit conversion factor that maps
fluorescence channel values to molecules of equivalent fluorophore. The
specific units depend on the channel, e.g., Molecules of Equivalent
FLuorescein (MEFL).

    * –

Alternate beads may be substituted, but must have multiple separable
intensities and certified ERF values, one set of which must be for
fluorescein.

  * •

SpheroTech Polystyrene Particle Size Standard Kit (PPS-6K)

    * –

This kit provides beads with six different diameters. Calibrant should be
stored, handled, and dispensed according to the manufacturer directions. One
kit provides sufficient materials for many assays.

    * –

These beads are used to compute a non-linear unit conversion function that
maps forward scatter area (FSC-A) values to estimated diameter in units of
equivalent micron particle diameter (E$\mu$m).

    * –

Alternate beads may be substituted, but must be monodisperse and must have
multiple separable sizes.

    * –

Certified size beads are not currently available, but should be preferred if
they become available in the future.

###  2.2 Cellular Calibrants

Figure 2: Example genetic constructs for cellular controls, for an experiment
with red and green fluorescence, adding blue fluorescence as a transfection
marker, plus the optional null transfection control (see Section 4.1).

  * •

Wild Type Negative Control

    * –

For each strain of cell used, at least one replicate with a sample of wild-
type cells, i.e., not transformed with any construct. For example, if CHO and
HEK293 cells are included in the experiment, there should be at least one
sample of wild-type CHO and at least one sample of wild-type HEK293.

    * –

The wild type control is used to estimate autofluorescence and to assess
strain response to culturing and/or other sample preparation activities.

    * –

The wild type control should be cultured and/or otherwise prepared alongside
the experimental samples, but not given any other experimental treatment.

  * •

Single Color Controls

    * –

For each fluorescent reporter used, at least one replicate transiently
transfected with a construct for strong constitutive expression of the
fluorescent reporter (and no other genetic function in its design).

    * –

Transient transfection is preferable to integration, as it is both faster and
produces a wider range of expression levels, including some that are much
stronger.

    * –

The single color controls are used estimate spectral overlap between channels
and to assess strain response to culturing.

    * –

Fluorescent reporters should be selected such that no pair of channels have
more than a 10% spectral overlap. This typically allows three fluorescent
reporters (red/green/blue), or four if deep red / infrared fluorescence is
used.

    * –

The single color controls should be cultured and/or otherwise prepared
alongside the experimental samples, but not given any other experimental
treatment.

  * •

Multi-Color Control

    * –

At least one replicate transiently co-transfected with equal doses of single
color control constructs for all of the fluorescent reporters used, where the
constructs differ only in their fluorescent reporter (i.e., the vector and
regulatory regions are identical) and have identical dosages in the co-
transfection.

    * –

The multi-color control is used to estimate unit conversions from fluorescent
channels, such that the expression levels of different fluorescent reporters
can be directly compared in the same molecular units. If only reference
fluorophores are used, then ERF values can be compared directly, but reference
fluorophores are typically small-molecule dyes rather than biologically-
expressed reporter constructs. With biologically expressed reporters, ERF
values for different channels are generally incommensurate due to the
differences in relationship between fluorescent reporter and reference
fluorophore. For example, the relationship between fluorescein and GFPmut3 in
the FITC-A channel is expected to be different than the relationship between
Coumarin 30 and EBFP2 in the Pacific Blue-A channel.

    * –

The recommended unit to convert to is Molecules of Equivalent FLuorescein
(MEFL), as fluorescein channels are common and often have similar spectral
properties, and as fluorescein has similar spectral properties to those of
many green fluorescent reporters.

    * –

It is preferable that the multicolor control have at least three colors, as
this will allow better segmentation into subpopulations for analysis.

    * –

The multi-color control should be cultured and/or otherwise prepared alongside
the experimental samples, but not given any other experimental treatment.

    * –

This control may be omitted if the only experimental fluorescent reporter is
measured in the fluorescein channel (e.g., GFP, YFP). If there is no
experimental reporter measured in the fluorescein channel, then a strong
constitutive expression construct for such a reporter should be added to the
multi-color control and also as an additional single color control.

    * –

This control depends on the relatively low sensitivity of mammalian promoter
transcription rates to the contents of the coding sequences being transcribed,
such that the transcriptional activity of each co-transfected construct can be
expected to be equivalent. This control also depends on co-transfection
introducing a large number of plasmids to each cell (typical of many protocols
for mammalian transient transfection, e.g., lipofection), which means that
strongly transfected cells should have a ratio between plasmids tightly
distributed around 1:1. These assumptions often do not hold for other types of
cells or transformations.

###  2.3 Experimental Samples

  * •

Experimental samples should be prepared according to the experimenter’s study
design.

  * •

The single color control for a non-conflicting fluorescent reporter should be
co-transfected along with the experimental construct or constructs. During
analysis, this fluorescence channel will be used as a transfection marker,
enabling parametric analysis of behavior with respect to transfection copy
count.

  * •

Experimental samples should be cultured along with the cellular calibrants and
should be measured at the same time as both the calibrant reagents and
cellular calibrants, in order to maximize the likelihood that issues with the
protocol or instrument can be detected. Note that single-color and multi-color
controls may simultaneously server as experimental samples, if appropriate for
the experiment design.

##  3 Methods

The analytical methods below are described with sufficient detail to allow
them to be understood and implemented by the reader. Note, however, that
application of these analysis methods can be simplified by using the TASBE
Flow Analytics Matlab software package beal2019tasbe , an existing
implementation of methods and workflows to automate all of the steps described
in this section, as well as to support the debugging steps listed below in
Section 4. Many of these steps are also automatable using existing Python
implementations in FlowCal castillo2016flowcal  or CytoFlow teague2022cytoflow
.

###  3.1 Data Collection

Figure 3: Examples of data collection gating with size thresholds that are too
permissive (left), appropriate (center), and too restrictive (right), adapted
from protocol in beal2022meetingBioRxiv

  * •

Set a conservative forward scatter (particle size) trigger, such that the
number of small non-cell particle events is minimized while not removing
smaller cells (Figure 3).

    * –

The minimum size threshold trigger is needed because flow cytometers typically
have limits in the rate at which events can be recorded, and if the
instrument’s recording capability is saturated then many cell measurements
will be lost.

    * –

Other instrument gating should not be used, as it is generally better to use
post-facto filtering to ignore unneeded events, rather than to discard cell
data that may later prove valuable.

  * •

Record all forward scatter (FSC) and side scatter (SSC) channels, and the area
channel for each fluorescent reporter.

    * –

Forward scatter and size scatter will be used to gate out non-cell particles
and multi-cell clumps, and thus the height and width channels, if available,
are useful in addition to the area channels.

    * –

In fluorescent channels only area is needed, as that is the channel that will
be used to estimate equivalent molecule counts.

    * –

Ensure that the instrument is putting laser and filter information in FCS
files, and that the values for these are correct. This is valuable for
ensuring that instrument settings are kept consistent between samples.

  * •

Gather between 50,000 and 100,000 events per sample.

    * –

In a transient transfection, cells generally receive a widely varied number of
copies of the plasmid or co-transfected set of plasmids. Collecting a larger
number of events allows parametric analysis in which events are divided into
subpopulations by transfection marker (see Section 3.2).

    * –

If subpopulation analysis is not needed needed (e.g., for integrated
constructs), the number of events can be reduced to 10,000 to 30,000.

###  3.2 Log-Scale Statistical Analyses

Figure 4: Cell behavior often shows distributions that are better suited to
geometric statistics on the log scale, rather than arithmetic statistics on
the linear scale. In many cases, fits with bi-modal or multimodal log-normal
distributions are appropriate. Figure adapted from beal2017lognormal .

All of the subsequent stages of this protocol are analytical, and most depend
on log-scale statistical analyses of data, so here we will discuss the reasons
for these analysis and provide their formulations for those who may be
unfamiliar.

Log-scale analysis is motivated by the fact that strong gene expression
typically has a log-normal distribution beal2017lognormal . Transient
transfections in mammalian cells typically deliver many copies of a genetic
construct to each cell, and fluorescent reporter signals are typically
engineered to be as strong as an experimenter can obtain, both of which mean
that strong overall expression is the typical case. For this reason, cell
behavior often shows distributions that are better suited to geometric
statistics on the log scale, rather than arithmetic statistics on the linear
scale, as illustrated in the example in Figure 4 (other statistical
alternatives are discussed in Section 4.3).

Geometric mean and geometric standard deviation may be computed by computing
the aithmetic mean and standard deviation of a variable that has been
transformed onto the log scale:

  * •

Geometric mean of variable $X$:

$\mu_{g}(X)=10^{\mu(log_{10}(X))}$

  * •

Geometric standard deviation of variable $X$:

$\sigma_{g}(X)=10^{\sigma(log_{10}(X))}$

Comparison of these statistics should also be discussed with respect to
geometric (fold) differences. For example, a decrease from 4000 MEFL to 1000
MEFL or 250 MEFL should be interpreted as a 4-fold or 16-fold decrease,
respectively, and not 75% or 94%.

Histograms should likewise generally be computed on the log scale. For
purposes of the analyses discussed here, histograms should be computed using a
granularity of 10 bins per decade: for example, in the range between 100 and
1000, there is a bin for values from 100 to 125.9, from 125.9 to 158.5, etc.,
until the last bin hold values from 794.3 to 1000. This may be computed by
taking a histogram of data transformed onto the log scale. This granularity
matches well with typical flow cytometer precision and the number of data
points recommended for capture in Section 3.1. If bin-to-bin variability is
too high, however, the granularity may be reduced, e.g., from 10 bins per
decade to 5 bins per decade.

Parametric analysis combines histograms on the log scale with geometric
statistics. Parametric analysis is computed by grouping flow cytometry events
into log-scale bins with respect to a selected fluorescent channel, at a
granularity of 10 bins per decade. Then, for each bin, the geometric mean and
standard deviation of other fluorescent channels are calculated over all of
the events in the bin. Bins with less than a minimum count of 10 events are
excluded from the parametric results, due to the uncertainty of values
computed from small numbers of data points. The result is a function capturing
the relationship between the selected channel and the other fluorescence
channels. Examples of its use are measuring the spillover fluorescence in a
spectrally overlapping channel as a function of fluorescence in the intended
channel (Section 3.6), or the value of an experimental variable as a function
of transfection marker expression (Section 3.8).

###  3.3 Bead-based Fluorescence Channel Calibration

(a) MEFL bead peaks

(b) MEFL bead fit

Figure 5: Example of color bead analysis, showing (a) peak identification for
the fluorescein channel against an alternate calibration bead, SpheroTech
RCP-30-5A. This is an 8-peak calibrant, and in this case only the top 6 peaks
are being used. Note the small doublet peaks slightly above each identified
peak. (b) Scaling fit for unit conversion function mapping FITC area channel
arbitrary units to Molecules of Equivalent FLuorescein (MEFL). Figure adapted
from tasbe_tutorial .

For each channel for a fluorescent reporter, compute the unit scaling between
arbitrary units on the fluorescence channel and units of Equivalent Reference
Fluorophore (ERF) for that channel:

  * •

Compute a log-scale histogram of the channel values for the rainbow bead
sample.

  * •

Identify the peaks in the channel and compute the geometric mean for each peak
region, as shown in the example in Figure 5(a).

    * –

Channel range (e.g., voltage) should be set based on the cells to be measured,
not the beads. It is acceptable for some beads to be saturated high, lost to
low noise, or otherwise not have usable peaks. For purposes of fit quality,
however, it is preferable to have at least three usable peaks.

    * –

Low-valued peaks, typically below around $10^{2}$ arbitrary units, will often
be blurred due to instrument noise or other issues. It is better to exclude
these peaks and use only the better-defined peaks at higher values.

    * –

Bead doublets will often form a small peak with a value twice that of the
primary peak for each expected bead intensity. Sometimes, a third triplet peak
with a three-times value will also be distinguishable. Data from these doublet
and triplet peaks should be excluded from peak calculations.

  * •

Perform a constrained linear fit (slope=1) on the log scale between peak
values and manufacturer supplied peak ERF values, as shown in the example in
Figure 5(b).

    * –

Mean fit error should be under 10%. Higher error typically indicates that
peaks have not been correctly identified: see Section 4.4 for likely issues.

Remember that the ERF values are not actually number of molecules of the
fluorescent reporter, but the amount of fluorescence that would be produced by
that number of molecules of the reference fluorophore. With good spectral
matching between the fluorescent reporter, reference fluorophore, and
measurement channel, however, the impact of this difference is likely to be
less than the magnitude of error from other sources beal2022meeting .
Fluorescent reporter molecules also may not properly mature to give full
fluorescence due to biological issues such as incomplete folding, lack of
oxygen, pH range, etc.

When channel conversion is used (Section 3.7), only the Molecules of
Equivalent FLuorescein (MEFL) scaling factor will actually be used.
Nevertheless, unit scaling should be computed for all fluorescence channels,
as the ability to compute a reliable unit scaling all channels is a process
control indicating correct instrument operation.

###  3.4 Bead-based Particle Size Calibration

(a) Size bead peaks

(b) Size bead fit

Figure 6: Example of size bead analysis, showing (a) peak identification, and
(b) log-log fit for unit conversion function mapping forward scatter area
(FCS-A) channel arbitrary units to equivalent micro-meter (E$\mu$m) diameter.
Note that the fit function does not a have a 1:1 slope in the log scale,
meaning that it is a not a linear scaling relationship. Figure adapted from
tasbe_tutorial .

  * •

Compute a log-scale histogram of the forward scatter area (FSC-A) channel
values for the size bead sample.

  * •

Identify the peaks in the channel and compute the geometric mean for each peak
region, as shown in the example in Figure 6(a).

    * –

Channel range (e.g., voltage) should be set based on the cells to be measured,
not the beads. Due to the smaller range of typical cell sizes, however, it is
typically possible to set FSC-A range to be appropriate for cell measurement
and also to keep all beads in a range where peaks can be clearly
distinguished.

    * –

If the channel cannot be adjusted to make all bead peaks distinguishable, it
is acceptable for some beads to be saturated high, lost to low noise, or
otherwise not have usable peaks. For purposes of fit quality, however, it is
preferable to have at least three usable peaks.

    * –

Likewise, if there are low-valued peaks, typically below around $10^{2}$
arbitrary units, that are blurred due to instrument noise or other issues. It
is better to exclude these peaks and use only the better-defined peaks at
higher values.

    * –

Note that at present there is generally a higher degree of variability in size
beads than rainbow beads due to differences in the available calibrant
materials. Doublet and triplet peaks are typically less of an issue with size
beads, however, due to the lower amount of separation between peaks.

  * •

Compute the unit scaling factor from FSC-A arbitrary units to equivalent
micro-meter (E$\mu$m) diameter by performing a linear fit on the log scale
between peak values and manufacturer supplied peak diameter values, as shown
in the example in Figure 6(b).

    * –

Unlike with color beads, this conversion should not have a unit slope, as
there is a non-linear relationship between diameter and forward scatter
koch96FSC ; chandler11FSC . Unit transformation will thus be a non-linear
function.

    * –

Mean fit error should be under 10%. Higher error typically indicates that
peaks have not been correctly identified: see Section 4.4 for likely issues.

###  3.5 Cell Gating

Figure 7: Example of gate to select cell events via a Gaussian mixture model
(GMM), in this case a two-component GMM built against forward and side scatter
area. The smaller, bright red, component selects events likely to be from
cells. Figure adapted from tasbe_tutorial .

  * •

Load events from the negative control (or null transfection, if one was used
per Section 4.1)

  * •

Compute a two-component n-dimentional Gaussian mixture model (GMM) fit jointly
on all the forward and side scatter channels.

    * –

Forward scatter area (FSC-A) and side scatter area (SSC-A) channels are often
sufficient for this purpose.

    * –

Including height and width channels can help further refine cell selection,
particularly with respect to excluding doublet events.

  * •

To gate for cells, select all events that are within two standard deviations
of the mean of the GMM component with the smallest standard deviation, and
also not closer to the mean of any other component. These are candidate cell
events.

  * •

Plot a two-dimensional density map of all events, with a convex hull around
the selected events.

    * –

Optionally, also plot the convex hulls of the events that would be selected
for each other component.

    * –

Figure 7 shows an example of selecting the cell component for a two-component
GMM.

    * –

Compare selected component with size beads to determine is estimated diameter
of cell-like events is consistent with experimental expectations.

    * –

If the distribution of events is such that cell-like events are not well-
identified by two standard deviations from the smaller standard deviation
component of a two-component GMM, then select a different component, adjust
the number of components, and/or adjust the number of standard deviations
until an reasonable selection is achieved. Adjust components before adjusting
number of standard deviations, increasing number incrementally until the best
fit is identified.

###  3.6 Fluorescence Compensation

In order to quantify the fluorescence due to the presence of a fluorescent
reporter, two other source of fluorescence must be removed from its channel:
cell autofluorescence (estimated from the negative control or null control),
and spill-over fluorescence from other fluorescent reporters due to spectral
overlap (estimated from single-color controls). Together, this removal process
is known as compensation, and is handled via linear transformations. Here we
present a minimal protocol for compensation for this context; a more general
presentation of compensation and the principles behind it may be found in
Roederer2001 ; Roederer2002 .

Figure 8: Example of autofluorescence model computed from a negative control
(solid red line shows mean, dotted red lines show $\pm 2$ std.dev.), plotted
against a linear-scale histogram of events from the sample. Note the use of a
linear scale and arithmetic statistics rather than logarithmic in this case.
Figure adapted from tasbe_tutorial .

For each channel for a fluorescent reporter, compute an autofluorescence model
for that channel:

  * •

Load events from the negative control (or null transfection, if one was used
per Section 4.1)

  * •

Gate events to retain only cell events, using the gate computed in Section
3.5.

  * •

Compute the arithmetic mean and standard deviation for all cell events in the
sample.

    * –

The mean will be used for compensation, subtracted from each event to convert
total fluorescence to net fluorescence.

    * –

The standard deviation will be used to determine where values cannot be
distinguished from autofluorescence. Any value less than 2 std.dev. net
fluorescence should be considered equivalent to autofluorescence. Truncating
such values (e.g., to a minimum net fluorescence of 1) will also remove non-
positive net fluorescence values, which are problematic for log-scale
statistics.

    * –

Linear statistics are used because instrument measurement noise is typically
expected to dominate the variability of autofluorescence measurements. If this
is not the case, it may be necessary to use a null transfections and/or to
switch to geometric statistics.

(a) Single Color Control analysis

(b) Compensated Single Color Control

Figure 9: (a) Example of calculating spectral overlap, in this case from the
PE-Tx-Red-YG channel (driven) into the FITC-A channel (passive), finding a
spillover rate of a little under 1%. Black dots are the parametric means of
significant bins, and the red line is the constrained linear fit for spectral
overlap. (b) Example of compensation verification plot using the compensated
values for the same sample and channels. Black dots are means of selected
bins, and black lines are visualizing bin levels. Figure adapted from
tasbe_tutorial .

For each channel for a fluorescent reporter, compute the spectral overlap
model from that channel into other channels:

  * •

Load events from the single color control for the channel.

  * •

Gate events to retain only cell events, using the gate computed in Section 3.5
and subtract autofluorescence means to convert to net fluorescence.

  * •

Compute a parametric analysis of all other fluorescence channels (passive
channels) with respect to the expressed fluorescent reporter (driven channel).

    * –

The parametric function for each channel should either be consistently near
zero (no significant overlap) or a “dog-leg” that is near zero for low values
but then switches to a tight linear relation with unit slope at the point
where spectral overlap begins to exceed autofluorescence.

  * •

For each passive channel, select the significant bins by selecting only those
where the passive channel mean net value is above 2 std.dev. of channel
autofluorescence.

  * •

If there is at least one significant bin, the spectral overlap is computed as
a constrained linear fit (slope=1) for passive versus driven values for the
significant bins. Otherwise, spectral overlap is zero.

    * –

For good resolution on low values, spectral overlap should be less than 10%.

    * –

An example of computing spectral overlap is shown in Figure 9(a).

    * –

Compensation for spectral overlap is computed by dividing a vector of net
fluorescence values by the spectral overlap matrix.

    * –

Correct compensation can be verified by a log-linear plot of compensated event
values for each single color control with respect to each driven channel,
which should produce a balanced distribution centered on zero. An example is
shown in Figure 9(b).

Given the autofluorescence and spectral overlap model, compensated
fluorescence values are produced by first subtracting autofluorescence mean
from each channel, then dividing by the spectral overlap matrix.

###  3.7 Fluorescent Channel Conversion

Figure 10: Example of multicolor control being used to build a channel unit
conversion model. Colors show density of data; black marks show parametric
geometric mean of blue (Pacific Blue-A) and yellow (FITC-A) fluorescence with
respect to red fluorescence (parametric axis not shown) for significant bins
at 10 bins per decade. The red line shows the mean scaling factor for blue
arbitrary units to yellow arbitrary units. Figure adapted from tasbe_tutorial
.

  * •

Load events from the multi-color control.

  * •

Gate events to retain only cell events, using the gate computed in Section 3.5
and compensate to net fluorescence using the compensation model computed in
Section 3.6.

  * •

For each fluorescent channel $C$ other than the Molecules of Equivalent
FLuorescein (MEFL) channel, compute a parametric analysis of channel $C$ and
the MEFL channel with respect to a third channel.

    * –

If there are only two channels, compute a parametric analysis of the second
channel against the MEFL channel.

    * –

If there is no MEFL channel, another ERF-calibrated channel can be
substituted, but this is not desirable because it will make it more difficult
to compare data with data produced by experiments using MEFL.

  * •

Select the significant bins by selecting only those where channel mean net
value for both the $C$ and MEFL channels is above 2 std.dev. of channel
autofluorescence.

  * •

The unit conversion factor from $C$ to MEFL is computed as a constrained
linear fit (slope=1) for $C$ mean net values versus MEFL mean net values for
the significant bins.

    * –

Figure 10 shows an example of computing a color translation model from the
Pacific Blue channel to FITC channel, parameterized by values on a Texas Red
channel.

    * –

If there are no significant bins or the mean fit error is more than 10%, this
indicates a problem with the multi-color control. See Section 4.6 for likely
issues.

###  3.8 Experimental Sample Analysis

(a) Raw FCS data distribution (b) Calibrated cell data distribution

Figure 11: Example of data from a flow cytometry file transformed by the full
gating and calibration model (gating, compensation color translation, ERF
units). Colors show density of data; black marks show parametric geometric
mean of yellow fluorescence with respect to red fluorescence at 10 bins per
decade. Note that the transformed data has an enriched relative density of
strongly transfected cells, that these cells have a more balanced
distribution, and that the two axes have the same MEFL units. Figure adapted
from tasbe_tutorial .

  * •

Load events for each experimental sample.

    * –

Note that some of the process controls above are likely to also be used as
experimental controls.

  * •

Gate events to retain only cell events, using the gate computed in Section
3.5.

  * •

Compensate to net fluorescence using the compensation model computed in
Section 3.6.

  * •

Translate all fluorescence channels to the MEFL channel using the conversion
factor computed in Section 3.7.

  * •

Convert to units of MEFL (fluorescence channels) and E$\mu$m (FSC-A) using the
conversion factors calculated in Section 3.3 and 3.4, respectively.

    * –

Figure 11 shows an example of a sample’s raw event distribution converted to a
calibrated cell event distribution.

(a) Histogram Analysis

(b) Parametric Analysis

Figure 12: Examples of log-scale statistical analysis, as applied to transient
transfection samples: (a) Log-scale histogram analysis of transfection marker
expression, showing a bimodal distribution of transfection levels. (b)
Parametric analysis of two test conditions of a repressor under high or low
induction, comparing input fluorescence protein (IFP) expression levels versus
output fluorescence protein (OFP) expression levels, binned with respect to
the strongly transfected range of a constitutive fluorescent protein. Figure
adapted from tasbe_tutorial .

Once data has been gated and converted to MEFL and E$\mu$m, the further
analyses that will be of value will depend on the specifics of the experiment.
The same histogram and parametric analyses as have been used above, however,
are also typically useful for analyzing some common experimental properties of
interest.

  * •

Distribution of transfection levels can be analyzed by fitting a Gaussian
mixture model (GMM) to a log-scale histogram analysis of a constitutive
fluorescent reporter.

    * –

Figure 12(a) shows a typical transient transfection distribution from
lipofection.

    * –

There are typically two major components: strongly transfected cells and
transfection failures. A strong lipofection should typically have more than
50% of the cells in the strongly transfected component.

    * –

If less than 30% are in the strongly transfected component, this usually
indicates a failure of the transfection protocol.

    * –

Biologically, it is not clear whether transfection failure means no
transfection or just few copies. The transfection failure component should
typically be excluded from experimental analysis in any case, as the behavior
of cells in the transfection failure component are generally qualitatively
different from those in the strongly transfected component.

    * –

In some cases, the fit is better when a third component is included in the
middle, though it is unclear whether this represents a true third population
or if the better fit is due to a distribution asymmetry, e.g., due to cellular
resource limitations.

    * –

A significant drop in the strongly transfected component from run to run or
from sample to sample is often an indication of problems in protocol execution
that will render the data from the less-well-transfected samples unreliable.

  * •

The behavior of transfected constructs can be analyzed by a parametric
analysis of the experimental fluorescent reporters with respect to a
constitutive fluorescent reporter.

    * –

With transient transfection, parametric analysis generally provides more
insight than bulk statistical analysis because of the high variability in
transfection level.

    * –

The parametric range should be limited to only strongly transfected cells.

    * –

Figure 12(b) shows an example of comparing test conditions using parametric
analysis with respect to a constitutive fluorescent reporter.

##  4 Notes

This section presents common issues that can occur in quantifying transient
transfections in mammalian cells with flow cytometry and adjustments to the
method that can be used to resolve these issues.

###  4.1 Null Transfection Control

Some strains of cell respond to some transfection protocols or some vector
backbones with large increases in autofluorescence. This is most often in red
channels, and often indicates that cell viability is degraded. If this is
suspected to be the case, then a null transfection control should be added, in
which cells are transfected with a vector that contains none of the constructs
under study. This construct will then be used for estimating autofluorescence
instead of the wild-type, but wild-type will still be used for assessing
strain response to culturing.

###  4.2 Small fraction of cell-like particles

If the number of cell-like particles making it through gating is small (under
50%), this may indicate problems with data collection. This may be diagnosed
with a plot of forward versus side scatter for the wild type negative control.

  * •

If the distribution of cell-like particles is truncated against a low
threshold, the instrument’s forward scatter trigger for event capture likely
needs to be lowered.

  * •

If there are more smaller particles than cell-like particles, the instrument’s
forward scatter trigger for event capture likely needs to be raised.

  * •

If shifting triggers does not correct the problem, then the flow rate may need
to be lowered in order to decrease the rate at which events occurs.

###  4.3 Alternative Statistics Analyses

Many flow cytometry analyses recommend the use of median or mode values
instead of geometric means. The median often gives values that are very
similar to the geometric mean, but it does not have a biological distribution
theory supporting its use. As a result, although other percentiles can provide
some notion of deviation, there is no principled equivalent of geometric
standard deviation of multi-modal log-normal fits to guide the interpretation
of median-based analyses.

Mode-based analysis is typically presented as finding a peak or maximum in a
histogram. While this works well in some cases, biological variability and the
inherent quantization associated with binning to produce a histogram means
that there is often significant uncertainty in the location of the mode, and
the value can be strongly affected by the details of how a histogram is
computed. The same qualitative goals can thus often be better satisfied by use
of multi-modal geometric statistics.

Finally, it is useful to note that log-scale statistics are ill-defined for
non-positive numbers and thus do not provide correct results for small values,
where error tends to be dominated by arithmetic contributions from instrument
noise or fluorescence compensation. This is often addressed in visualization
by using a bi-exponential or “logicle” remapping tung2007modern , which
provides a clean visual transition between regions of geometric and arithmetic
error dominance, but which involves an arbitrary cutoff and does not shed
light on the underlying question of biological activity. Better methods for
incorporation of low and negative flow cytometry values into analysis remains
an open question.

###  4.4 Bead Peak Problems

In addition to the notes already presented in Section 3.3 and 3.4, other
common issues in identifying bead peaks are small counts, high background,
blurred peaks, and offset peaks.

  * •

If the number of events per peak is small, on the order of 200 or less per
peak, then the precision of unit conversion is likely to be poor. This issue
also typically indicates problems with the FSC threshold for event capture.

    * –

If the total number of events in the bead file is low, this typically
indicates that the event capture threshold is too high.

    * –

If the total number of events is as expected, but most are low values not
forming clean peaks, this typically indicates that the event capture threshold
is too low.

  * •

High levels of background events between peaks can make peaks difficult to
identify or separate. If this occurs for values higher than around the
$10^{2}$ arbitrary units, this typically indicates an instrument that is dirty
or has other service issues that are creating the high rates of background
events.

  * •

If there are peaks, but they do not generally have a single highly distinct
maximum (e.g., wide peaks or doubled peaks), then this generally indicates an
instrument hardware issue that requires service, such as lasers having come
out of alignment.

  * •

If there are clear peaks, but they do not produce a good linear fit, this
typically indicates that the peak identities have been offset from their true
identities, e.g., peaks 4-6 have been mis-labelled as peaks 2-4.

###  4.5 Compensation Problems

  * •

If spectral overlap is more than 10%, the level of effective overlap can be
reduced by adjusting choice of fluorescent reporter and/or channel voltage.

  * •

Expression of the single color control is too weak if it could not be used to
identify at least a 1% spectral overlap. Typically this means that there
should be significant numbers of events through at least the $10^{4}$ to
$10^{5}$ arbitrary unit range. Weak expression can be caused by a number of
issues:

    * –

The selected channel may not be a close enough match for the excitation and
emission properties of the fluorescent reporter, such that only a small
fraction of the potential fluorescent energy is being measured, in which case
either the channel or the reporter should be changed.

    * –

The fluorescent reporter may have poor brightness or there may be stronger
than usual autofluorescence in the selected channel, in which case the
reporter should be changed.

    * –

The fluorescent reporter may be a poor choice for the protocol (e.g.,
mismatched chemical properties), in which case the reporter should be changed.

    * –

If none of these is the case, then it is an indicator that there are problems
with the reporter construct (e.g., poor promoter strength, interference
between promoter and reporter) and/or the experimental protocol.

  * •

If compensation verification shows a failure, i.e., the center of the
distribution does not stay roughly centered on zero, this is typically caused
by problems with one or more of the single color controls or their analysis.

    * –

Weak expression can cause compensation failures, and should be addressed as
discussed above.

    * –

If the control has a “messy” distribution instead of the expected pattern of
autofluorescence followed by a tight linear unit slope, then it typically
indicates problems in either the reporter construct, experimental protocol, or
cell gating.

    * –

Instrument problems can also cause compensation failures, but it is highly
unlikely for this to be the case without the problem already being identified
during peak identification for the color beads.

###  4.6 Channel Conversion Problems

  * •

If there are no significant bins or there is a poor fit (more than 10% error),
first check the single color controls to see if their expression is weak or
“messy,” per Section 4.5.

  * •

If all of the single color controls are strong and have clean distributions,
then it is likely that there is a problem with the co-transfection protocol or
the specifics of the multi-color control.

###  4.7 Transfection Problems

(a) Problematic Samples

(b) Problematic Experiment

Figure 13: Example of distribution expectations allowing identification of
individual bad samples (a) and a full batch of samples gone wrong from a badly
executed protocol (b).

Figure 13 shows examples of experimental samples failing quality control due
to differences between expected and observed transfection distributions. In
Figure 13(a), the lowest three samples have significantly lower strongly
transfected components than the rest, which are tightly bunched. Those three
samples were thus considered to be likely protocol failures and excluded, even
though they have more than 50% of their events in the strongly transfected
component. In Figure 13(b), the entire collection of samples is showing a
strongly transfected component containing less than 30% of the cell events,
and thus the entire experimental run was considered likely to have been
affected by a protocol failure and was re-run.

###### Acknowledgements.

This document does not contain technology or technical data controlled under
either the U.S. International Traffic in Arms Regulations or the U.S. Export
Administration Regulations.

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