Applications of data science to flow cytometry

Flow cytometery for doctors

A bit of history

• In the year 1954, Wallace Coulter first proposed to devise an instrument, which can electronically measure cells in a conductive liquid. This form the basis of a flow cytometer.
• The first fluorescence-based flow cytometry device (ICP 11) was developed in 1968 by Wolfgang Göhde from the University of Münster, Germany.
• The original name - pulse cytophotometry - 1978 name changed to flow cytometry, at - (1971) from Bio/Physics Systems Inc. 
• PAS 8000 (1973) from Partec
• FACS instrument from Becton Dickinson (1974),
• ICP 22 (1975) from Partec/Phywe
• Epics from Coulter (1977/78)2.

Same principle -different outcomes

Fluoresence Spectrometer	Flow Cytometer
Molecules,Nanoparticles \(\le 500nm\)	Cells (\(\mu m\))
No statistical Information	Population behavior
Single molecule data unavailable	Single cell data

Block diagrams Fluoresence

Excitation of light leads to scattering and emission

Block Diagram Scattering

Two major scattering classes

Block Digram for a flow cytometer

The power of flow cytometry is illustrated in this diagram

The cytometric platform (cyto\(\equiv\) cell) is a combination of

• Instrument Design Fluidics,Optics,Electronics
• Synthesis of Fluorescent probes,Qdots
• Machine learning (supervised & som)
• Statistical techniques
  • t-SNE(T-stochastic neighbor embedding)
  • SPADE Spanning-tree progression analysis of density-normalized events)
  • PCA (Principal component analysis)
  • FLOCK (FLOw clustering without K).

Flow cytometry basic algorithmic issues

• Clean the data (using flowCore, flowQ, flowClean, flowStats, openCyto or flowDensity)
• Compensate
• Plot the scatter and marker values over time; filter out any regions with abnormal behaviour
• Compare samples to detect batch effects and normalize the data if necessary
• Correct for internal (for example, smoking status) or external confounding (for example, laboratory) effects
• Remove debris, dead cells and doublets
• Check boundary effects
• Consider pre-gating on a cell population of interest

Commercial software and Data

Flow cytometers can now measure dozens of parameters. Typically a given experiment of a flow cytometer will generate about 10000 rows of 8 to 24 columns (channels) of data. Software packages - FlowJo, - FCS Express

Flow cytometry as a treasure hunt for biological big data

Data repository

https://flowrepository.org/public_experiment_representations?top=10

https://www.cytobank.org/

Data mining in Flow Cytometry

• The data mining in flow cytometry is non trivial.
• Previously the data mining software was mainly properitary items of the flow cytometer manufacturing companies.
• R platform has been pionner in the computational flow cytometry
• Most accepted form of data format in a flow platform is a .FCS.
• In R the .FCS files are read as S4 objects Here is a simple R command to call a flow cytometric file

R command to call a FCS file

fname='./Compensation Controls/Patient_17_Unstained.fcs'
ff <- flowCore::read.FCS(fname)

The S4 Classes

• The object is not a simple atomic variable or an array or dataframe.

• The object that is returned above is of S4 type

• An S4 class definition is quite a bit different from a class definition in other programming languages such as C# and Python.

• An S4 class encapsulates data fields inside a setClass function, but doesn’t encapsulate class methods.

  Instead, S4 class methods are defined by pairs of special R functions named setMethod and setGeneric.

• https://advanced-r-solutions.rbind.io/s4.html

Converting an S4 object to a R data frame

library(flowCore)
fname='./Compensation Controls/Patient_17_Unstained.fcs'
ff <- flowCore::read.FCS(fname)
typeof(ff)

[1] "S4"

# Converting S4 to dataframe 
df=data.frame(ff@exprs[,1:6])
# typical structure of the data frame 
summary(df)

     FSC.A            FSC.H            FSC.W       
 Min.   :  2909   Min.   :  5009   Min.   : 36588  
 1st Qu.: 21116   1st Qu.: 19694   1st Qu.: 66662  
 Median : 46014   Median : 43265   Median : 71521  
 Mean   : 72403   Mean   : 64801   Mean   : 72133  
 3rd Qu.:128617   3rd Qu.:117858   3rd Qu.: 76619  
 Max.   :262143   Max.   :257923   Max.   :180780  
     SSC.A              SSC.H            SSC.W       
 Min.   :   569.5   Min.   :   600   Min.   : 42355  
 1st Qu.:  7990.4   1st Qu.:  7897   1st Qu.: 65152  
 Median : 19952.3   Median : 19438   Median : 66967  
 Mean   : 40328.2   Mean   : 37823   Mean   : 67712  
 3rd Qu.: 52786.3   3rd Qu.: 50038   3rd Qu.: 69002  
 Max.   :262143.0   Max.   :257327   Max.   :198544  

attach(df)
plot(FSC.H,SSC.H,pch=16,cex=0.2)

Flow Cytometry of PBMC

Targets in Flow analysis

Target Applications - Cell Cycle Analysis - Immunophenotyping - Cell counting and sorting - Biomarker detection In the above vase we have used unstained samples from PBMC

A typical unlabelled flow cytometric phase space - FSC.H-FSC.H

plot(FSC.H,SSC.H,pch=16,cex=0.2)

Cluster = Function_of(CellType)

The above scatter plot shows a typical scattering cluster for unlabelled (no fluoresence label) PBMC suspension.A major computational challenge is to identify the cell types and associate them with a flow cytometric cluster.

Automated gating Flow Clust

# Using the flowClust code to remove outliers
library(flowClust)
fname='./Compensation Controls/Patient_17_Unstained.fcs'
ff <- flowCore::read.FCS(fname)
df=data.frame(ff@exprs[,1:6])
res1 <- flowClust(df,
varNames=c("FSC.H", "SSC.H"), K=1) 
df2=Subset(df,res1)
res2<-flowClust(df2, varNames=c("FSC.H", "SSC.H"), K=1:6, B=100)
criterion(res2,"BIC")

[1] -1392214 -1378289 -1361787 -1354436 -1353362 -1350507

# There will be 6 clusters 
# 6 clusters 
plot(res2[[6]], data=df2, level=0.8, z.cutoff=0)

Rule of identifying outliers: 80% quantile

# Now suppose we want to identify a particular cluster
# Let us identify the clusters 
ik1=which(res2[[6]]@label==1)
ik2=which(res2[[6]]@label==2)
ik3=which(res2[[6]]@label==3)
ik4=which(res2[[6]]@label==4)
ik5=which(res2[[6]]@label==5)
ik6=which(res2[[6]]@label==6)
attach(df2)

Gating out a single cluster out

Now suppose we want to gate one and see the other 5 clusters

plot(FSC.H,SSC.H,pch=16,cex=0.3,col="red")

points(FSC.H[ik4],SSC.H[ik4],pch=16,cex=0.3)

Gating the cell debris out

plot(FSC.H[-ik4],SSC.H[-ik4],pch=16,cex=0.3)

Flow peaks

FlowPeaks is a fast unsupervised clustering for flow cytometry data via K-means and density peak finding, 2012, Bioinformatics 8(15):2052-8

library(flowPeaks)
fp<-flowPeaks(asinh(ff@exprs[,c(1,2)]))
plot(fp) #an alternative of using summary(fp) 

The prescribed manual clustering

Origin of Doublets

• A doublet is a single event that actually consists of 2 independent particles.

• The cytometer classified these particles as a single event because they passed through the interrogation point very close to one another.

• In other words, the particles were so close together when they passed through this laser spot, that the instrument was incapable of distinguishing them as individual events or particles.

A non-rocket-science approach

What has been seen in case of the elimination of doublets the conventional clustering method for gating fails , as gating in this case has something to do with whether the cells are present in singlets or doublets. The common sense knowledge that is used in this case is that points with higher area-height ratio are more likely to be doublets. This is true for both the forward and side scattering.

A simple combined algo

• X=log(FSC.A) and Y=log(FSC.H)
• X1=log(SSC.A) and Y1=log(SSC.H)
• Find slopes & intercepts (m,c) and (m1,c1) of Y~X and Y1~X1
• Find ik for which (Y>mX+c) & (Y1>m1X1+C) are simultaneously satisfied.

Effect of doublet filtering on the FSC-SSC clusters

Histogram gating (from easyGgpplot2)

library(easyGgplot2)
# Let us construct data using three patients 
fname='./Compensation Controls/Patient_17_Unstained.fcs'
ff1 <- flowCore::read.FCS(fname)
df=data.frame(ff1@exprs[,1:6])
attach(df) 
ggplot2.histogram(FSC.H,xlab="Forward Scattering",fill="white", color="black",addDensityCurve=TRUE,addMeanLine=TRUE, densityFill='#FF6666')

Compensation

• All fluorochromes have excitation and emission spectra. The excitation spectrum is a range of light wavelengths that add energy to a fluorochrome, causing it to emit light in another range of wavelengths, the emission spectrum.
• Within a flow cytometer, the appropriate ranges of excitation and emission wavelengths are selected by bandpass filters.
• However, when emission spectra overlap, fluorescence from more than one fluorochrome may be detected.
• To correct for this spectral overlap, a process of fluorescence compensation is used. This ensures that the fluorescence detected in a particular detector derives from the fluorochrome that is being measured.
• In the example below, following excitation with 488 nm light, PE emission is largely detected in the detector specific for PE but the emission tail lies within the range of the bandpass filter used for detection of PE-Cy5.
• This will be seen as “false positive” signals in the PE-Cy5 channel and fluorescence compensation is needed to correct for this overlap.

An example

In this hypothetical experiment, cells were stained with FITC CD3 and with a PE isotype control, and collected at different compensation values to correct for the FITC spillover into the PE channel (panel 1 is uncompensated; 2-5 are for increasing compensation values). ## The questions - Which panel represents proper compensation? - On what basis did you make this determination?

Twocolor compensation

http://www.drmr.com/compensation/ Let’s consider an experiment where we stain human peripheral blood lymphocytes with - FITC CD3 \(\rightarrow ^{Stains}\) CD4 and CD8 T cells) - PE CD8 \(\rightarrow ^{Stains}\) CD8 T cells and, less brightly, NK cells.

Four populations

• We should have four major populations of cells: -B cells, which will be unstained -CD4 T cells, which will have only fluorescein (CD3) fluorescence
  • CD8 T cells, which will have both fluorescein and PE fluorescence
  • NK cells, which will only have PE fluorescence (they do not express CD3).

Qunatitative Measures

• Assume CD3 fluorescence (FITC) on T cells gives 100 units of true fluorescence (i.e., the amount of fluorescence in FL1 when no compensation is set and no PE had been included in the stain);
• CD8 fluorescence on CD8 T cells is 400 units.
• CD8 on NK is 50 units.

Measured fluorescence for each cell

• Let us assume that the spillover constants have been measured at 15% and 1% (from the compensation samples)?

• For B cells, it will be zero in both FL1 and FL2 (remember, we are ignoring autofluorescence for the time being).

• CD4 T cells will have 100 in FL1, and 15 in FL2 (i.e., 15% of the 100 units of fluorescein signal will appear in FL2).

• NK cells will have 50 units in FL2, and 0.5 units in FL1 (i.e., 1% of the 10 units of PE signal).

• CD8 T cells will have 104 units in FL1 (100 units of fluorescein CD3 signal plus 1% of the 400 units of PE CD8 signal), and 415 units FL2 (400 units of PE signal plus 15% of the 100 units of fluorescein signal).

Mathematical formulea for 2 color compensation

\[ FL1_{measured}=FITC_{true}+0.01\cdot PE_{true}\\ FL2_{measured}=0.15\cdot FITC_{true} +PE_{true} \] ## Finding the true value of fluoresence Let’s apply these equations to our measured values for CD8 T cells (FL1 = 104, FL2 = 415). We may find PE true and FITC true from:

   1*x1 + 0.15*x2  =  104 
0.01*x1    + 1*x2  =  415 

          [,1]
[1,]  41.81272
[2,] 414.58187

Multicolor compensation

Multi-color compensation is a simple extension of two-color compensation:

M(1) = A(11) x F(1) + A(21) x F(2) + … A(n1) x F(n) M(2) = A(12) x F(1) + A(22) x F(2) + … A(n2) x F(n) … M(n) = A(1n) x F(1) + A(2n) x F(2) + … A(nn) x F(n)

where M(i) is the measured fluorescence in channel i; F(i) is the amount of fluorescent molecule (i) present on the cell of interest, and A(ij) is the ratio of the fluorescence of molecule (i) in channel (i) to the fluorescence of molecule (i) in channel (j).

–> # Immuno Phenotyping A good link to start with https://www.abcam.com/protocols/flow-cytometry-immunophenotyping

Basic Idea

• Antibodies are used to identify cells by detecting specific antigens (markers) expressed by these cells
• These markers are usually functional membrane proteins involved in cell communication, adhesion, or metabolism.
• Immunophenotyping using flow cytometry has become the method of choice in identifying and sorting cells within complex populations, for example the analysis of immune cells in a blood sample.

FLOW CYTOMETRIC ANALYSIS OF LEUKEMIA - A case study

The flow cytometric charecterization is more qunatitative than the microscopic detection.

• Blast window ?
• Monocyte detection?
• Solution

The minimal approach

# Immunophenotyping the leukomia cells Blood cells are immunophenotypically coated with fluorescent antibodies at the time of the sample preparation, and then the sample tube is placed in the flow cytometry device.

Blast cells

• Gate out the singlets only

• Construct SSC-H vs CD45 to gate the blast population.

• Next CD19 (CD19 is a B cell–specific antigen expressed on chronic lymphocytic leukemia (CLL) cells)vs CD10 (The human CD10 antigen is present in common acute lymphoblastic leukemia as a cancer specific antigen ) scatterplot.

• The propensity and type of leukomia and efficacy of chemotherapy with time can be determined.

The classic BLMG gates

Leukomia File CMC

      Time            FSC.A            FSC.H       
 Min.   :  53.6   Min.   : 10144   Min.   : 10024  
 1st Qu.: 565.5   1st Qu.: 60168   1st Qu.: 43537  
 Median :1085.2   Median : 79984   Median : 57508  
 Mean   :1083.5   Mean   : 93186   Mean   : 61014  
 3rd Qu.:1595.3   3rd Qu.:109668   3rd Qu.: 73634  
 Max.   :2111.9   Max.   :262143   Max.   :258709  
     SSC.A              SSC.H            FITC.A         
 Min.   :   155.4   Min.   :   156   Min.   :   -51.45  
 1st Qu.:  1407.0   1st Qu.:  1101   1st Qu.:   138.60  
 Median :  1939.3   Median :  1443   Median :   213.15  
 Mean   :  3243.5   Mean   :  1914   Mean   :   722.33  
 3rd Qu.:  2998.8   3rd Qu.:  1943   3rd Qu.:   348.60  
 Max.   :262143.0   Max.   :224332   Max.   :262143.00  
      PE.A          PerCP.Cy5.5.A         PE.Cy7.A       
 Min.   :   -81.9   Min.   :  -105.0   Min.   :   -90.3  
 1st Qu.:   444.1   1st Qu.:   536.5   1st Qu.:  1098.3  
 Median :   828.5   Median :  1029.0   Median :  2794.6  
 Mean   :  1237.3   Mean   :  1814.5   Mean   :  4506.2  
 3rd Qu.:  1395.5   3rd Qu.:  1857.5   3rd Qu.:  6019.6  
 Max.   :239286.6   Max.   :262143.0   Max.   :262143.0  
     APC.A              APC.H7.A            V450.A        
 Min.   :   -89.28   Min.   :  -224.1   Min.   :  -439.3  
 1st Qu.:    70.68   1st Qu.:   306.0   1st Qu.:   213.9  
 Median :   169.26   Median :   580.3   Median :   378.4  
 Mean   :  1781.22   Mean   :  1516.5   Mean   :  1291.5  
 3rd Qu.:   778.41   3rd Qu.:  1208.1   3rd Qu.:   670.5  
 Max.   :262143.00   Max.   :262143.0   Max.   :262143.0  
    V500c.A        
 Min.   :  -284.1  
 1st Qu.:   159.8  
 Median :   316.2  
 Mean   :  1187.2  
 3rd Qu.:   621.0  
 Max.   :262143.0  

CD45(V500c.A) CD 19(PE.Cy7.A) and CD 10 (APC.A)

[1] -988502.2 -986779.2 -986474.7 -986135.8

Rule of identifying outliers: 50% quantile

[1] -1141117 -1123068 -1119284 -1117204

Rule of identifying outliers: 50% quantile

      Time            FSC.A            FSC.H       
 Min.   :  53.6   Min.   : 10144   Min.   : 10024  
 1st Qu.: 565.5   1st Qu.: 60168   1st Qu.: 43537  
 Median :1085.2   Median : 79984   Median : 57508  
 Mean   :1083.5   Mean   : 93186   Mean   : 61014  
 3rd Qu.:1595.3   3rd Qu.:109668   3rd Qu.: 73634  
 Max.   :2111.9   Max.   :262143   Max.   :258709  
     SSC.A              SSC.H            FITC.A         
 Min.   :   155.4   Min.   :   156   Min.   :   -51.45  
 1st Qu.:  1407.0   1st Qu.:  1101   1st Qu.:   138.60  
 Median :  1939.3   Median :  1443   Median :   213.15  
 Mean   :  3243.5   Mean   :  1914   Mean   :   722.33  
 3rd Qu.:  2998.8   3rd Qu.:  1943   3rd Qu.:   348.60  
 Max.   :262143.0   Max.   :224332   Max.   :262143.00  
      PE.A          PerCP.Cy5.5.A         PE.Cy7.A       
 Min.   :   -81.9   Min.   :  -105.0   Min.   :   -90.3  
 1st Qu.:   444.1   1st Qu.:   536.5   1st Qu.:  1098.3  
 Median :   828.5   Median :  1029.0   Median :  2794.6  
 Mean   :  1237.3   Mean   :  1814.5   Mean   :  4506.2  
 3rd Qu.:  1395.5   3rd Qu.:  1857.5   3rd Qu.:  6019.6  
 Max.   :239286.6   Max.   :262143.0   Max.   :262143.0  
     APC.A              APC.H7.A            V450.A        
 Min.   :   -89.28   Min.   :  -224.1   Min.   :  -439.3  
 1st Qu.:    70.68   1st Qu.:   306.0   1st Qu.:   213.9  
 Median :   169.26   Median :   580.3   Median :   378.4  
 Mean   :  1781.22   Mean   :  1516.5   Mean   :  1291.5  
 3rd Qu.:   778.41   3rd Qu.:  1208.1   3rd Qu.:   670.5  
 Max.   :262143.00   Max.   :262143.0   Max.   :262143.0  
    V500c.A        
 Min.   :  -284.1  
 1st Qu.:   159.8  
 Median :   316.2  
 Mean   :  1187.2  
 3rd Qu.:   621.0  
 Max.   :262143.0  

Flow peaks

FlowPeaks is a fast unsupervised clustering for flow cytometry data via K-means and density peak finding, 2012, Bioinformatics 8(15):2052-8

        step 0, set the intial seeds, tot.wss=1040.56
        step 1, do the rough EM, tot.wss=712.991 at 0.281295 sec
        step 2, do the fine transfer of Hartigan-Wong Algorithm
                 tot.wss=703.557 at 0.495917 sec

** The Beauty of SOM**

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