Preprocessing with CATALYST

Helena L Crowell1,2*, Vito RT Zanotelli3, Stéphane Chevrier3, Bernd Bodenmiller3 and Mark D Robinson1,2

1Institute for Molecular Life Sciences, University of Zurich, Switzerland
2SIB Swiss Institute of Bioinformatics, University of Zurich, Switzerland
3Department of Quantitative Biomedicine, University of Zurich, Switzerland

*helena.crowell@uzh.ch

Abstract

By addressing the limit of measurable fluorescent parameters due to instrumentation and spectral overlap, mass cytometry (CyTOF) combines heavy metal spectrometry to allow examination of up to (theoretically) 100 parameters at the single cell level. While spectral overlap is significantly less pronounced in CyTOF than flow cytometry, spillover due to detection sensitivity, isotopic impurities, and oxide formation can impede data interpretability. We designed CATALYST (Cytometry dATa anALYSis Tools) to provide tools for (pre)processing and analysis of cytometry data, including compensation and in particular, an improved implementation of the single-cell deconvolution algorithm.

Package

CATALYST 1.18.1

Contents

---

Most of the pipeline and visualizations presented herein have been adapted from Chevrier et al. (2018)’s “Compensation of Signal Spillover in Suspension and Imaging Mass Cytometry” available here.

# load required packages
library(CATALYST)
library(cowplot)
library(flowCore)
library(ggplot2)
library(SingleCellExperiment)

1 Data examples

• Normalization:
  raw_data is a flowSet with 2 experiments, each containing 2’500 raw measurements with a variation of signal over time. Samples were mixed with DVS beads captured by mass channels 140, 151, 153, 165 and 175.
• Debarocoding:
  To demonstrate the debarcoding workflow with CATALYST, we provide sample_ff which follows a 6-choose-3 barcoding scheme where mass channels 102, 104, 105, 106, 108, and 110 were used for labeling such that each of the 20 individual barcodes are positive for exactly 3 out of the 6 barcode channels. Accompanying this, sample_key contains a binary code of length 6 for each sample, e.g. 111000, as its unique identifier.
• Compensation:
  Alongside the multiplexed-stained cell sample mp_cells, the package contains 36 single-antibody stained controls in ss_exp where beads were stained with antibodies captured by mass channels 139, 141 through 156, and 158 through 176, respectively, and pooled together. Note that, to decrease running time, we downsampled to a total of 10’000 events. Lastly, isotope_list contains a named list of isotopic compositions for all elements within 75 through 209 u corresponding to the CyTOF mass range at the time of writing (Coursey et al. 2015).

2 Data organization

Data used and returned throughout preprocessing are organized into an object of the SingleCellExperiment (SCE) class. A SCE can be constructed from a directory housing a single or set of FCS files, a character vector of the file(s), flowFrame(s) or a flowSet (from the flowCore package) using CATALYST’s prepData function.

prepData will automatically identify channels not corresponding to masses (e.g., event times), remove them from the output SCE’s assay data, and store them as internal event metadata (int_colData).

When multiple files or frames are supplied, prepData will concatenate the data into a single object, and argument by_time (default TRUE) specifies whether runs should be ordered by their acquisition time (keyword(x, "$BTIM"), where x is a flowFrame or flowSet). A "sample_id" column will be added to the output SCE’s colData to track which file/frame events originally source from.

Finally, when transform (default TRUE), an arcsinh-transformation with cofactor cofactor (defaults to 5) is applied to the input (count) data, and the resulting expression matrix is stored in the "exprs" assay slot of the output SCE.

data("raw_data")
(sce <- prepData(raw_data))

## class: SingleCellExperiment 
## dim: 61 5000 
## metadata(1): experiment_info
## assays(2): counts exprs
## rownames(61): BC1 Vol1 ... Pb208Di BC9
## rowData names(4): channel_name marker_name marker_class use_channel
## colnames: NULL
## colData names(1): sample_id
## reducedDimNames(0):
## mainExpName: NULL
## altExpNames(0):

# view number of events per sample
table(sce$sample_id)

## 
## raw_data_1.fcs raw_data_2.fcs 
##           2500           2500

# view non-mass channels
names(int_colData(sce))

## [1] "reducedDims"  "altExps"      "colPairs"     "Time"         "Event_length"
## [6] "Center"       "Offset"       "Width"        "Residual"

3 Normalization

CATALYST provides an implementation of bead-based normalization as described by Finck et al. (Finck et al. 2013). Here, identification of bead-singlets (used for normalization), as well as of bead-bead and cell-bead doublets (to be removed) is automated as follows:

1. beads are identified as events with their top signals in the bead channels
2. cell-bead doublets are remove by applying a separation cutoff to the distance between the lowest bead and highest non-bead signal
3. events passing all vertical gates defined by the lower bounds of bead signals are removed (these include bead-bead and bead-cell doublets)
4. bead-bead doublets are removed by applying a default \(median\;\pm5\;mad\) rule to events identified in step 2. The remaining bead events are used for normalization.

3.1 Normalization workflow

3.1.1 normCytof: Normalization using bead standards

Since bead gating is automated here, normalization comes down to a single function that takes a SingleCellExperiment as input and only requires specification of the beads to be used for normalization. Valid options are:

• "dvs" for bead masses 140, 151, 153, 165, 175
• "beta" for bead masses 139, 141, 159, 169, 175
• or a custom numeric vector of bead masses

By default, we apply a \(median\;\pm5\;mad\) rule to remove low- and high-signal events from the bead population used for estimating normalization factors. The extent to which bead populations are trimmed can be adjusted via trim. The population will become increasingly narrow and bead-bead doublets will be exluded as the trim value decreases. Notably, slight over-trimming will not affect normalization. It is therefore recommended to choose a trim value that is small enough to assure removal of doublets at the cost of a small bead population to normalize to.

normCytof will return the following list of SCE(s)…

• data: Input dataset including normalized counts (and expressions, if transform = TRUE).
  • if remove_beads = FALSE, colData columns "is_bead" and "remove" indicate whether an event has been marker as a bead or for removal, respectively.
  • otherwise, bead and doublet events are excluded and the following additional data is returned:
    • beads: Subset of identified bead events.
    • removed: Subset of all cells that have been from the original dataset, including bead events as well as bead-bead and bead-cell doublets.

…and ggplot-objects:

• scatter: Scatter plot of bead vs. DNA intensities with indication of applied gates.
• lines: Running-median smoothed bead intensities vs. time before and after normalization.

Besides general normalized parameters (beads specifying the normalization beads, and running median windown width k), normCytof requires as input to assays corresponding to count- and expression-like data respectively. Here, correction factors are computed on the linear (count) scale, while automated bead-identification happens on the transformed (expression) scale.

By default, normCytof will overwrite the specified assays with the normalized data (overwrite = TRUE). In order to retain both unnormalized and normalized data, overwrite should be set to FALSE, in which case normalized counts (and expression, when transform = TRUE) will be written to separate assay normcounts/exprs, respectively.

# construct SCE
sce <- prepData(raw_data)
# apply normalization; keep raw data
res <- normCytof(sce, beads = "dvs", k = 50, 
  assays = c("counts", "exprs"), overwrite = FALSE)
# check number & percentage of bead / removed events
n <- ncol(sce); ns <- c(ncol(res$beads), ncol(res$removed))
data.frame(
    check.names = FALSE, 
    "#" = c(ns[1], ns[2]), 
    "%" = 100*c(ns[1]/n, ns[2]/n),
    row.names = c("beads", "removed"))

##           #    %
## beads   141 2.82
## removed 153 3.06

# extract data excluding beads & doublets,
# and including normalized intensitied
sce <- res$data
assayNames(sce)

## [1] "counts"     "exprs"      "normcounts" "normexprs"

# plot bead vs. dna scatters
res$scatter

# plot smoothed bead intensities
res$lines

4 Debarcoding

CATALYST provides an implementation of the single-cell deconvolution algorithm described by Zunder et al. (Zunder et al. 2015). The package contains three functions for debarcoding and three visualizations that guide selection of thresholds and give a sense of barcode assignment quality.

In summary, events are assigned to a sample when i) their positive and negative barcode populations are separated by a distance larger than a threshold value and ii) the combination of their positive barcode channels appears in the barcoding scheme. Depending on the supplied scheme, there are two possible ways of arriving at preliminary event assignments:

1. Doublet-filtering:
   Given a binary barcoding scheme with a coherent number \(k\) of positive channels for all IDs, the \(k\) highest channels are considered positive and \(n-k\) channels negative. Separation of positive and negative events equates to the difference between the \(k\)th highest and \((n-k)\)th lowest intensity value. If a numeric vector of masses is supplied, the barcoding scheme will be an identity matrix; the most intense channel is considered positive and its respective mass assigned as ID.
   
2. Non-constant number of 1’s:
   Given a non-uniform number of 1’s in the binary codes, the highest separation between consecutive barcodes is looked at. In both, the doublet-filtering and the latter case, each event is assigned a binary code that, if matched with a code in the barcoding scheme supplied, dictates which row name will be assigned as ID. Cells whose positive barcodes are still very low or whose binary pattern of positive and negative barcodes doesn’t occur in the barcoding scheme will be given ID 0 for “unassigned”.

All data required for debarcoding are held in objects of the SingleCellExperiment (SCE) class, allowing for the following easy-to-use workflow:

1. as the initial step of single-cell deconcolution, assignPrelim will return a SCE containing the input measurement data, barcoding scheme, and preliminary event assignments.
2. assignments will be made final by applyCutoffs. It is recommended to estimate, and possibly adjust, population-specific separation cutoffs by running estCutoffs prior to this.
3. plotYields, plotEvents and plotMahal aim to guide selection of devoncolution parameters and to give a sense of the resulting barcode assignment quality.

4.1 Debarcoding workflow

4.1.1 assignPrelim: Assignment of preliminary IDs

The debarcoding process commences by assigning each event a preliminary barcode ID. assignPrelim thereby takes either a binary barcoding scheme or a vector of numeric masses as input, and accordingly assigns each event the appropirate row name or mass as ID. FCS files are read into R with read.FCS of the flowCore package, and are represented as an object of class flowFrame:

data(sample_ff)
sample_ff

## flowFrame object 'anonymous'
## with 20000 cells and 6 observables:
##        name        desc     range  minRange  maxRange
## 1 (Pd102)Di       BC102   9745.80 -0.999912   9745.80
## 2 (Pd104)Di       BC104   9687.52 -0.999470   9687.52
## 3 (Pd105)Di       BC105   8924.64 -0.998927   8924.64
## 4 (Pd106)Di       BC106   8016.67 -0.999782   8016.67
## 5 (Pd108)Di       BC108   9043.87 -0.999997   9043.87
## 6 (Pd110)Di       BC110   8204.46 -0.999937   8204.46
## 0 keywords are stored in the 'description' slot

The debarcoding scheme should be a binary table with sample IDs as row and numeric barcode masses as column names:

data(sample_key)
head(sample_key)

##    102 104 105 106 108 110
## A1   1   1   1   0   0   0
## A2   1   1   0   1   0   0
## A3   1   1   0   0   1   0
## A4   1   1   0   0   0   1
## A5   1   0   1   1   0   0
## B1   1   0   1   0   1   0

Provided with a SingleCellExperiment and a compatible barcoding scheme (barcode masses must occur as parameters in the supplied SCE), assignPrelim will add the following data to the input SCE: - assay slot "scaled" containing normalized expression values where each population is scaled to the 95%-quantile of events assigend to the respective population. - colData columns "bc_id" and "delta" containing barcode IDs and separations between lowest positive and highest negative intensity (on the normalized scale) - rowData column is_bc specifying, for each channel, whether it has been specified as a barcode channel

sce <- prepData(sample_ff)
(sce <- assignPrelim(sce, sample_key))

## Debarcoding data...

##  o ordering

##  o classifying events

## Normalizing...

## Computing deltas...

## class: SingleCellExperiment 
## dim: 6 20000 
## metadata(2): experiment_info bc_key
## assays(3): counts exprs scaled
## rownames(6): BC102 BC104 ... BC108 BC110
## rowData names(5): channel_name marker_name marker_class use_channel
##   is_bc
## colnames: NULL
## colData names(3): sample_id bc_id delta
## reducedDimNames(0):
## mainExpName: NULL
## altExpNames(0):

# view barcode channels
rownames(sce)[rowData(sce)$is_bc]

## [1] "BC102" "BC104" "BC105" "BC106" "BC108" "BC110"

# view number of events assigned to each barcode population
table(sce$bc_id)

## 
##   A1   A2   A3   A4   A5   B1   B2   B3   B4   B5   C1   C2   C3   C4   C5   D1 
## 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 
##   D2   D3   D4   D5 
## 1000 1000 1000 1000

4.1.2 estCutoffs: Estimation of separation cutoffs

As opposed to a single global cutoff, estCutoffs will estimate a sample-specific cutoff to deal with barcode population cell yields that decline in an asynchronous fashion. Thus, the choice of thresholds for the distance between negative and positive barcode populations can be i) automated and ii) independent for each barcode. Nevertheless, reviewing the yield plots (see below), checking and possibly refining separation cutoffs is advisable.

For the estimation of cutoff parameters we consider yields upon debarcoding as a function of the applied cutoffs. Commonly, this function will be characterized by an initial weak decline, where doublets are excluded, and subsequent rapid decline in yields to zero. Inbetween, low numbers of counts with intermediate barcode separation give rise to a plateau. To facilitate robust estimation, we fit a linear and a three-parameter log-logistic function (Finney 1971) to the yields function with the LL.3 function of the drc R package (Ritz et al. 2015) (Figure 1). As an adequate cutoff estimate, we target a point that marks the end of the plateau regime and on-set of yield decline to appropriately balance confidence in barcode assignment and cell yield.

The goodness of the linear fit relative to the log-logistic fit is weighed as follow: \[w = \frac{\text{RSS}_{log-logistic}}{\text{RSS}_{log-logistic}+\text{RSS}_{linear}}\]

The cutoffs for both functions are defined as:

\[c_{linear} = -\frac{\beta_0}{2\beta_1}\] \[c_{log-logistic}=\underset{x}{\arg\min}\:\frac{\vert\:f'(x)\:\vert}{f(x)} > 0.1\]

The final cutoff estimate \(c\) is defined as the weighted mean between these estimates:

\[c=(1-w)\cdot c_{log-logistic}+w\cdot c_{linear}\]

Figure 1: Description of the automatic cutoff estimation for each individual population
The bar graphs indicate the distribution of cells relative to the barcode distance and the dotted line corresponds to the yield upon debarcoding as a function of the applied separation cutoff. This curve is fitted with a linear regression (blue line) and a three parameter log-logistic function (red line). The cutoff estimate is defined as the mean of estimates derived from both fits, weighted with the goodness of the respective fit.

# estimate separation cutoffs
sce <- estCutoffs(sce)
# view separation cutoff estimates
metadata(sce)$sep_cutoffs

##        A1        A2        A3        A4        A5        B1        B2        B3 
## 0.3811379 0.3262184 0.3225851 0.2879897 0.3423528 0.3583485 0.3113566 0.3242730 
##        B4        B5        C1        C2        C3        C4        C5        D1 
## 0.3200084 0.2955329 0.3909571 0.3462298 0.3288156 0.2532980 0.2397771 0.2469145 
##        D2        D3        D4        D5 
## 0.3221655 0.3319978 0.2804174 0.3311446

4.1.3 plotYields: Selecting barcode separation cutoffs

For each barcode, plotYields will show the distribution of barcode separations and yields upon debarcoding as a function of separation cutoffs. If available, the currently used separation cutoff as well as its resulting yield within the population is indicated in the plot’s main title.

Option which = 0 will render a summary plot of all barcodes. All yield functions should behave as described above: decline, stagnation, decline. Convergence to 0 yield at low cutoffs is a strong indicator that staining in this channel did not work, and excluding the channel entirely is sensible in this case. It is thus recommended to always view the all-barcodes yield plot to eliminate uninformative populations, since small populations may cause difficulties when computing spill estimates.

plotYields(sce, which = c(0, "C1"))

4.1.4 applyCutoffs: Applying deconvolution parameters

Once preliminary assignments have been made, applyCutoffs will apply the deconvolution parameters: Outliers are filtered by a Mahalanobis distance threshold, which takes into account each population’s covariance, and doublets are removed by excluding events from a population if the separation between their positive and negative signals fall below a separation cutoff. Current thresholds are held in the sep_cutoffs and mhl_cutoff slots of the SCE’s metadata. By default, applyCutoffs will try to access the metadata "sep_cutoffs" slopt of the input SCE, requiring having run estCutoffs prior to this, or manually specifying a vector or separation cutoffs. Alternatively, a numeric vector of cutoff values or a single, global value may be supplied In either case, it is highly recommended to thoroughly review the yields plot (see above), as the choice of separation cutoffs will determine debarcoding quality and cell yield.

# use global / population-specific separation cutoff(s)
sce2 <- applyCutoffs(sce)
sce3 <- applyCutoffs(sce, sep_cutoffs = 0.35)

# compare yields before and after applying 
# global / population-specific cutoffs
c(specific = mean(sce2$bc_id != 0),
    global = mean(sce3$bc_id != 0))

## specific   global 
##  0.68035  0.66970

# proceed with population-specific filtering
sce <- sce2

4.1.5 plotEvents: Normalized intensities

Normalized intensities for a barcode can be viewed with plotEvents. Here, each event corresponds to the intensities plotted on a vertical line at a given point along the x-axis. Option which = 0 will display unassigned events, and the number of events shown for a given sample may be varied via argument n. If which = "all", the function will render an event plot for all IDs (including 0) with events assigned.

# event plots for unassigned events
# & barcode population D1
plotEvents(sce, which = c(0, "D1"), n = 25)

4.1.6 plotMahal: All barcode biaxial plot

Function plotMahal will plot all inter-barcode interactions for the population specified with argument which. Events are colored by their Mahalanobis distance. NOTE: For more than 7 barcodes (up to 128 samples) the function will render an error, as this visualization is infeasible and hardly informative. Using the default Mahalanobis cutoff value of 30 is recommended in such cases.

plotMahal(sce, which = "B3")

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

## Warning: `guides(<scale> = FALSE)` is deprecated. Please use `guides(<scale> =
## "none")` instead.

5 Compensation

CATALYST performs compensation via a two-step approach comprising:

1. identification of single positive populations via single-cell debarcoding (SCD) of single-stained beads (or cells)
2. estimation of a spillover matrix (SM) from the populations identified, followed by compensation via multiplication of measurement intensities by its inverse, the compensation matrix (CM).

Retrieval of real signal. As in conventional flow cytometry, we can model spillover linearly, with the channel stained for as predictor, and spill-effected channels as response. Thus, the intensity observed in a given channel \(j\) are a linear combination of its real signal and contributions of other channels that spill into it. Let \(s_{ij}\) denote the proportion of channel \(j\) signal that is due to channel \(i\), and \(w_j\) the set of channels that spill into channel \(j\). Then

\[I_{j, observed}\; = I_{j, real} + \sum_{i\in w_j}{s_{ij}}\]

In matrix notation, measurement intensities may be viewed as the convolution of real intensities and a spillover matrix with dimensions number of events times number of measurement parameters:

\[I_{observed}\; = I_{real} \cdot SM\]

Therefore, we can estimate the real signal, \(I_{real}\;\), as:

\[I_{real} = I_{observed}\; \cdot {SM}^{-1} = I_{observed}\; \cdot CM\] where \(\text{SM}^{-1}\) is termed compensation matrix (\(\text{CM}\)). This approach is implemented in compCytof(..., method = "flow") and makes use of flowCore’s compensate function.

While mathematically exact, the solution to this equation will yield negative values, and does not account for the fact that real signal would be strictly non-negative counts. A computationally efficient way to adress this is the use of non-negative linear least squares (NNLS):

\[\min \: \{ \: ( I_{observed} - SM \cdot I_{real} ) ^ T \cdot ( I_{observed} - SM \cdot I_{real} ) \: \} \quad \text{s.t.} \: I_{real} ≥ 0\]

This approach will solve for \(I_{real}\) such that the least squares criterion is optimized under the constraint of non-negativity. To arrive at such a solution we apply the Lawson-Hanson algorithm (Lawson and Hanson 1974, 1995) for NNLS implemented in the nnls R package (method="nnls").

Estimation of SM. Because any signal not in a single stain experiment’s primary channel \(j\) results from channel crosstalk, each spill entry \(s_{ij}\) can be approximated by the slope of a linear regression with channel \(j\) signal as the response, and channel \(i\) signals as the predictors, where \(i\in w_j\). computeSpillmat() offers two alternative ways for spillover estimation, summarized in Figure 2.

The default method approximates this slope with the following single-cell derived estimate: Let \(i^+\) denote the set of cells that are possitive in channel \(i\), and \(s_{ij}^c\) be the channel \(i\) to \(j\) spill computed for a cell \(c\) that has been assigned to this population. We approximate \(s_{ij}^c\) as the ratio between the signal in unstained spillover receiving and stained spillover emitting channel, \(I_j\) and \(I_i\), respectively. The expected background in these channels, \(m_j^-\) and \(m_i^-\), is computed as the median signal of events that are i) negative in the channels for which spill is estimated (\(i\) and \(j\)); ii) not assigned to potentionally interacting channels; and, iii) not unassigned, and subtracted from all measurements:

\[s_{ij}^c = \frac{I_j - m_j^{i-}}{I_i - m_i^{i-}}\]

Each entry \(s_{ij}\) in \(\text{SM}\) is then computed as the median spillover across all cells \(c\in i^+\):

\[s_{ij} = \text{med}(s_{ij}^c\:|\:c\in i^+)\]

In a population-based fashion, as done in conventional flow cytometry, method = "classic" calculates \(s_{ij}\) as the slope of a line through the medians (or trimmed means) of stained and unstained populations, \(m_j^+\) and \(m_i^+\), respectively. Background signal is computed as above and substracted, according to:

\[s_{ij} = \frac{m_j^+-m_j^-}{m_i^+-m_i^-}\]

Figure 2: Population versus single-cell based spillover estimation.

On the basis of their additive nature, spill values are estimated independently for every pair of interacting channels. interactions = "default" thereby exclusively takes into account interactions that are sensible from a chemical and physical point of view:

• \(M\pm1\) channels (abundance sensitivity)
• the \(M+16\) channel (oxide formation)
• channels measuring isotopes (isotopic impurities)

See Table 1 for the list of mass channels considered to potentionally contain isotopic contaminatons, along with a heatmap representation of all interactions considered by the default method in Figure 3.

Table 1: List of isotopes available for each metal used in CyTOF
In addition to \(M\pm1\) and \(M+16\) channels, these mass channels are considered during estimation of spill to capture channel crosstalk that is due to isotopic contanimations (Coursey et al. 2015).

Metal	Isotope masses
La	138, 139
Pr	141
Nd	142, 143, 144, 145, 146, 148, 150
Sm	144, 147, 148, 149, 150, 152, 154
Eu	151, 153
Gd	152, 154, 155, 156, 157, 158, 160
Dy	156, 158, 160, 161, 162, 163, 164
Er	162, 164, 166, 167, 168, 170
Tb	159
Ho	165
Yb	168, 170, 171, 172, 173, 174, 176
Tm	169
Lu	175, 176

Figure 3: Heatmap of spill expected interactions
These are considered by the default method of computeSpillmat.

Alternatively, interactions = "all" will compute a spill estimate for all \(n\cdot(n-1)\) possible interactions, where \(n\) denotes the number of measurement parameters. Estimates falling below the threshold specified by th will be set to zero. Lastly, note that diagonal entries \(s_{ii} = 1\) for all \(i\in 1, ..., n\), so that spill is relative to the total signal measured in a given channel.

5.1 Compensation workflow

5.1.1 computeSpillmat: Estimation of the spillover matrix

Given a SCE of single-stained beads (or cells) and a numeric vector specifying the masses stained for, computeSpillmat estimates the spillover matrix (SM) as described above; the estimated SM will be stored in the SCE’s metadata under "spillover_matrix".

Spill values are affected my the method chosen for their estimation, that is "median" or "mean", and, in the latter case, the specified trim percentage. The process of adjusting these options and reviewing the compensated data may iterative until compensation is satisfactory.

# get single-stained control samples
data(ss_exp)

# specify mass channels stained for & debarcode
bc_ms <- c(139, 141:156, 158:176)
sce <- prepData(ss_exp)
sce <- assignPrelim(sce, bc_ms, verbose = FALSE)
sce <- applyCutoffs(estCutoffs(sce))

# compute & extract spillover matrix
sce <- computeSpillmat(sce)
sm <- metadata(sce)$spillover_matrix

# do some sanity checks
chs <- channels(sce)
ss_chs <- chs[rowData(sce)$is_bc]
all(diag(sm[ss_chs, ss_chs]) == 1)

## [1] TRUE

all(sm >= 0 & sm <= 1)

## [1] TRUE

5.1.2 plotSpillmat: Spillover matrix heatmap

plotSpillmat provides a visualization of estimated spill percentages as a heatmap. Channels without a single-antibody stained control are annotated in grey, and colours are ramped to the highest spillover value present. Option annotate = TRUE (the default) will display spill values inside each bin, and the total amount of spill caused and received by each channel on the top and to the right, respectively.

plotSpillmat will try and access the SM stored in the input SCE’s "spillover_matrix" metadata slot, requiring having run computeSpillmat or manually specifying a matrix of appropriate format.

plotSpillmat(sce) 

## Warning in sprintf("%2.2f", colSums(sm) * 100 - 100, "%"): one argument not used
## by format '%2.2f'

## Warning: It is deprecated to specify `guide = FALSE` to remove a guide. Please
## use `guide = "none"` instead.

5.1.3 compCytof: Compensation of mass cytometry data

Assuming a linear spillover, compCytof compensates mass cytometry based experiments using a provided spillover matrix. If the spillover matrix (SM) does not contain the same set of columns as the input experiment, it will be adapted according to the following rules:

1. columns present in the SM but not in the input data will be removed from it
2. non-metal columns present in the input but not in the SM will be added such that they do neither receive nor cause spill
3. metal columns that have the same mass as a channel present in the SM will receive (but not emit) spillover according to that channel
4. if an added channel could potentially receive spillover (as it has +/-1M or +16M of, or is of the same metal type as another channel measured), a warning will be issued as there could be spillover interactions that have been missed and may lead to faulty compensation

To omit the need to respecify the cofactor(s) for transformation, transform = TRUE will auto-transform the compensated data. compCytof will thereby try to reuse the cofactor(s) stored under int_metadata(sce)$cofactor from the previously applied transformation; otherwise, the cofactor argument should be specified.

If overwrite = TRUE (the default), compCytof will overwrite the specified counts assay (and exprs, when transform = TRUE) with the compensated data. Otherwise, compensated count (and expression) data will be stored in separate assays compcounts/exprs, respectively.

# construct SCE of multiplexed cells
data(mp_cells)
sce <- prepData(mp_cells)
# compensate using NNLS-method; keep uncompensated data
sce <- compCytof(sce, sm, method = "nnls", overwrite = FALSE)
# visualize data before & after compensation
chs <- c("Er167Di", "Er168Di")
as <- c("exprs", "compexprs")
ps <- lapply(as, function(a) 
    plotScatter(sce, chs, assay = a))
plot_grid(plotlist = ps, nrow = 1)

6 Scatter plot visualization

plotScatter provides a flexible way of visualizing expression data as biscatters, and supports automated facetting (should more than 2 channels be visualized). Cells may be colored by density (default color_by = NULL) or other (non-)continous variables. When coloring by density, plotScatter will use geom_hex to bin cells into the number of specified bins; otherwise cells will be plotted as points. The following code chunks shall illustrate these different functionalities:

6.1 Example 1: Coloring by cell density

# biscatter of DNA channels colored by cell density
sce <- prepData(raw_data)
chs <- c("DNA1", "DNA2")
plotScatter(sce, chs)

# biscatters for selected CD-channels
sce <- prepData(mp_cells)
chs <- grep("^CD", rownames(sce), value = TRUE)
chs <- sample(chs, 7)
p <- plotScatter(sce, chs)
p$facet$params$ncol <- 3; p

6.2 Example 2: Coloring by variables

sce <- prepData(sample_ff)
sce <- assignPrelim(sce, sample_key)
# downsample channels & barcode populations
chs <- sample(rownames(sce), 4)
ids <- sample(rownames(sample_key), 3)
sce <- sce[chs, sce$bc_id %in% ids]

# color by factor variable
plotScatter(sce, chs, color_by = "bc_id")

# color by continuous variable
plotScatter(sce, chs, color_by = "delta")

6.3 Example 3: Facetting by variables

# sample some random group labels
sce$group_id <- sample(c("groupA", "groupB"), ncol(sce), TRUE)

# selected pair of channels; split by barcode & group ID
plotScatter(sce, sample(chs, 2), 
  color_by = "bc_id",
  facet_by = c("bc_id", "group_id"))

# selected CD-channels; split by sample
plotScatter(sce, chs, bins = 50, facet_by = "bc_id")

7 Conversion to other data structures

While the SingleCellExperiment class provides many advantages in terms of compactness, interactability and robustness, it can be desirous to write out intermediate files at each preprocessing stage, or to use other packages currently build around flowCore infrastructure (flowFrame and flowSet classes), or classes derived thereof (e.g., flowWorkspace’s GatingSet). This section demonstrates how to safely convert between these data structures.

7.1 Writing FCS files

Conversion from SCE to flowFrames/flowSet, which in turn can be writting to FCS files using flowCore’s write.FCS function, is not straightforward. It is not recommended to directly write FCS via write.FCS(flowFrame(t(assay(sce)))), as this can lead to invalid FCS files or the data being shown on an inappropriate scale in e.g. Cytobank. Instead, CATALYST provides the sce2fcs function to facilitate correct back-conversion.

sce2fcs allows specification of a variable to split the SCE by (argument split_by), e.g., to split the data by sample after debarcoding; whether to keep or drop any cell metadata (argument keep_cd) and dimension reductions (argument keep_dr) available within the object; and which assay data to use (argument assay)111 Only count-like data should be written to FCS files and is guaranteed to show with approporiate scale in Cytobank!:

# run debarcoding
sce <- prepData(sample_ff)
sce <- assignPrelim(sce, sample_key)
sce <- applyCutoffs(estCutoffs(sce))
# exclude unassigned events
sce <- sce[, sce$bc_id != 0]
# convert to 'flowSet' with one frame per sample
(fs <- sce2fcs(sce, split_by = "bc_id"))

## A flowSet with 20 experiments.
## 
## column names(6): (Pd102)Di (Pd104)Di ... (Pd108)Di (Pd110)Di

# split check: number of cells per barcode ID
# equals number of cells in each 'flowFrame'
all(c(fsApply(fs, nrow)) == table(sce$bc_id))

## [1] TRUE

Having converted out SCE to a flowSet, we can write out each of its flowFrames to an FCS file with a meaningul filename that retains the sample of origin:

# get sample identifiers
ids <- fsApply(fs, identifier)
for (id in ids) {
    ff <- fs[[id]]                     # subset 'flowFrame'
    fn <- sprintf("sample_%s.fcs", id) # specify output name that includes ID
    fn <- file.path("...", fn)         # construct output path
    write.FCS(ff, fn)                  # write frame to FCS
}

7.2 Gating & visualization

Besides writing out FCS files, conversion to flowFrames/flowSet also enables leveraging the existing infrastructure for these classes such as ggcyto for visualization and openCyto for gating:

# load required packages
library(ggcyto)      
library(openCyto)     
library(flowWorkspace) 

# construct 'GatingSet'
sce <- prepData(raw_data) 
ff <- sce2fcs(sce, assay = "exprs")   
gs <- GatingSet(flowSet(ff))

# specify DNA channels
dna_chs <- c("Ir191Di", "Ir193Di")

# apply elliptical gate
gs_add_gating_method(
    gs, alias = "cells", 
    pop = "+", parent = "root",
    dims = paste(dna_chs, collapse = ","),
    gating_method = "flowClust.2d", 
    gating_args = "K=1,q=0.9")

# plot scatter of DNA channels including elliptical gate
ggcyto(gs, 
    aes_string(dna_chs[1], dna_chs[2])) + 
    geom_hex(bins = 128) + 
    geom_gate(data = "cells") +
    facet_null() + ggtitle(NULL) +
    theme(aspect.ratio = 1, 
        panel.grid.minor = element_blank())

8 Session information

sessionInfo()

## R version 4.1.2 (2021-11-01)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 20.04.3 LTS
## 
## Matrix products: default
## BLAS:   /home/biocbuild/bbs-3.14-bioc/R/lib/libRblas.so
## LAPACK: /home/biocbuild/bbs-3.14-bioc/R/lib/libRlapack.so
## 
## locale:
##  [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
##  [3] LC_TIME=en_GB              LC_COLLATE=C              
##  [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
##  [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
##  [9] LC_ADDRESS=C               LC_TELEPHONE=C            
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       
## 
## attached base packages:
## [1] stats4    stats     graphics  grDevices utils     datasets  methods  
## [8] base     
## 
## other attached packages:
##  [1] openCyto_2.6.0              ggcyto_1.22.0              
##  [3] flowWorkspace_4.6.0         ncdfFlow_2.40.0            
##  [5] BH_1.78.0-0                 RcppArmadillo_0.10.7.5.0   
##  [7] scater_1.22.0               ggplot2_3.3.5              
##  [9] scuttle_1.4.0               diffcyt_1.14.0             
## [11] flowCore_2.6.0              cowplot_1.1.1              
## [13] CATALYST_1.18.1             SingleCellExperiment_1.16.0
## [15] SummarizedExperiment_1.24.0 Biobase_2.54.0             
## [17] GenomicRanges_1.46.1        GenomeInfoDb_1.30.0        
## [19] IRanges_2.28.0              S4Vectors_0.32.3           
## [21] BiocGenerics_0.40.0         MatrixGenerics_1.6.0       
## [23] matrixStats_0.61.0          BiocStyle_2.22.0           
## 
## loaded via a namespace (and not attached):
##   [1] scattermore_0.7             R.methodsS3_1.8.1          
##   [3] tidyr_1.1.4                 knitr_1.37                 
##   [5] irlba_2.3.5                 multcomp_1.4-18            
##   [7] DelayedArray_0.20.0         R.utils_2.11.0             
##   [9] data.table_1.14.2           RCurl_1.98-1.5             
##  [11] doParallel_1.0.16           generics_0.1.1             
##  [13] ScaledMatrix_1.2.0          TH.data_1.1-0              
##  [15] ggpointdensity_0.1.0        xml2_1.3.3                 
##  [17] assertthat_0.2.1            viridis_0.6.2              
##  [19] xfun_0.29                   jquerylib_0.1.4            
##  [21] evaluate_0.14               DEoptimR_1.0-10            
##  [23] fansi_1.0.2                 Rgraphviz_2.38.0           
##  [25] igraph_1.2.11               DBI_1.1.2                  
##  [27] tmvnsim_1.0-2               purrr_0.3.4                
##  [29] ellipsis_0.3.2              RSpectra_0.16-0            
##  [31] ks_1.13.3                   dplyr_1.0.7                
##  [33] ggnewscale_0.4.5            ggpubr_0.4.0               
##  [35] backports_1.4.1             cytolib_2.6.1              
##  [37] bookdown_0.24               RcppParallel_5.1.5         
##  [39] sparseMatrixStats_1.6.0     vctrs_0.3.8                
##  [41] abind_1.4-5                 withr_2.4.3                
##  [43] ggforce_0.3.3               aws.signature_0.6.0        
##  [45] robustbase_0.93-9           mclust_5.4.9               
##  [47] mnormt_2.0.2                cluster_2.1.2              
##  [49] crayon_1.4.2                drc_3.0-1                  
##  [51] ellipse_0.4.2               edgeR_3.36.0               
##  [53] pkgconfig_2.0.3             labeling_0.4.2             
##  [55] tweenr_1.0.2                nlme_3.1-155               
##  [57] vipor_0.4.5                 rlang_0.4.12               
##  [59] lifecycle_1.0.1             sandwich_3.0-1             
##  [61] rsvd_1.0.5                  polyclip_1.10-0            
##  [63] graph_1.72.0                flowClust_3.32.0           
##  [65] Matrix_1.4-0                carData_3.0-5              
##  [67] boot_1.3-28                 zoo_1.8-9                  
##  [69] base64enc_0.1-3             beeswarm_0.4.0             
##  [71] ggridges_0.5.3              GlobalOptions_0.1.2        
##  [73] pheatmap_1.0.12             png_0.1-7                  
##  [75] viridisLite_0.4.0           rjson_0.2.21               
##  [77] bitops_1.0-7                R.oo_1.24.0                
##  [79] ConsensusClusterPlus_1.58.0 KernSmooth_2.23-20         
##  [81] DelayedMatrixStats_1.16.0   shape_1.4.6                
##  [83] stringr_1.4.0               jpeg_0.1-9                 
##  [85] rstatix_0.7.0               ggsignif_0.6.3             
##  [87] aws.s3_0.3.21               beachmat_2.10.0            
##  [89] scales_1.1.1                magrittr_2.0.1             
##  [91] plyr_1.8.6                  hexbin_1.28.2              
##  [93] zlibbioc_1.40.0             hdrcde_3.4                 
##  [95] compiler_4.1.2              RColorBrewer_1.1-2         
##  [97] plotrix_3.8-2               clue_0.3-60                
##  [99] lme4_1.1-27.1               rrcov_1.6-0                
## [101] cli_3.1.0                   XVector_0.34.0             
## [103] FlowSOM_2.2.0               MASS_7.3-55                
## [105] tidyselect_1.1.1            stringi_1.7.6              
## [107] RProtoBufLib_2.6.0          highr_0.9                  
## [109] yaml_2.2.1                  BiocSingular_1.10.0        
## [111] locfit_1.5-9.4              latticeExtra_0.6-29        
## [113] ggrepel_0.9.1               grid_4.1.2                 
## [115] sass_0.4.0                  tools_4.1.2                
## [117] parallel_4.1.2              CytoML_2.6.0               
## [119] circlize_0.4.13             foreach_1.5.1              
## [121] gridExtra_2.3               farver_2.1.0               
## [123] Rtsne_0.15                  digest_0.6.29              
## [125] BiocManager_1.30.16         pracma_2.3.6               
## [127] FNN_1.1.3                   Rcpp_1.0.8                 
## [129] car_3.0-12                  broom_0.7.11               
## [131] fda_5.5.1                   httr_1.4.2                 
## [133] IDPmisc_1.1.20              ComplexHeatmap_2.10.0      
## [135] flowStats_4.6.0             colorspace_2.0-2           
## [137] rainbow_3.6                 XML_3.99-0.8               
## [139] splines_4.1.2               uwot_0.1.11                
## [141] RBGL_1.70.0                 fds_1.8                    
## [143] jsonlite_1.7.2              nloptr_1.2.2.3             
## [145] corpcor_1.6.10              R6_2.5.1                   
## [147] pillar_1.6.4                htmltools_0.5.2            
## [149] nnls_1.4                    glue_1.6.0                 
## [151] fastmap_1.1.0               minqa_1.2.4                
## [153] BiocParallel_1.28.3         deSolve_1.30               
## [155] BiocNeighbors_1.12.0        codetools_0.2-18           
## [157] pcaPP_1.9-74                mvtnorm_1.1-3              
## [159] utf8_1.2.2                  lattice_0.20-45            
## [161] bslib_0.3.1                 tibble_3.1.6               
## [163] flowViz_1.58.0              curl_4.3.2                 
## [165] ggbeeswarm_0.6.0            colorRamps_2.3             
## [167] gtools_3.9.2                magick_2.7.3               
## [169] survival_3.2-13             limma_3.50.0               
## [171] rmarkdown_2.11              munsell_0.5.0              
## [173] GetoptLong_1.0.5            GenomeInfoDbData_1.2.7     
## [175] iterators_1.0.13            reshape2_1.4.4             
## [177] gtable_0.3.0

References

Chevrier, Stéphane, Helena L Crowell, Vito R T Zanotelli, Stefanie Engler, Mark D Robinson, and Bernd Bodenmiller. 2018. “Compensation of Signal Spillover in Suspension and Imaging Mass Cytometry.” Cell Systems 6 (5): 612–620.e5.

Coursey, J S, D J Schwab, J J Tsai, and R A Dragoset. 2015. “Atomic Weights and Isotopic Compositions with Relative Atomic Masses.” NIST Physical Measurement Laboratory.

Finck, Rachel, Erin F Simonds, Astraea Jager, Smita Krishnaswamy, Karen Sachs, Wendy Fantl, Dana Pe’er, Garry P Nolan, and Sean C Bendall. 2013. “Normalization of Mass Cytometry Data with Bead Standards.” Cytometry A 83 (5): 483–94.

Finney, D J. 1971. “Probit Analysis.” Journal of Pharmaceutical Sciences 60 (9): 1432.

Lawson, Charles L, and Richard J Hanson. 1995. Solving Least Squares Problems. Philadelphia, PA: SIAM.

Lawson, Charles L, and R J Hanson. 1974. Solving Least Squares Problems Prentice-Hall. Englewood Cliffs, NJ: Prentice Hall.

Ritz, Christian, Florent Baty, Jens C Streibig, and Daniel Gerhard. 2015. “Dose-Response Analysis Using R.” PLoS One 10 (12): e0146021.

Zunder, Eli R, Rachel Finck, Gregory K Behbehani, El-Ad D Amir, Smita Krishnaswamy, Veronica D Gonzalez, Cynthia G Lorang, et al. 2015. “Palladium-Based Mass Tag Cell Barcoding with a Doublet-Filtering Scheme and Single-Cell Deconvolution Algorithm.” Nature Protocols 10 (2): 316–33.