K-nearest neighbors:

We read in input.scone.csv, which is our file modified (and renamed) from the get.marker.names() function. The K-nearest neighbor generation is derived from the Fast Nearest Neighbors (FNN) R package, within our function Fnn(), which takes as input the “input markers” to be used, along with the concatenated data previously generated, and the desired k. We advise the default selection to the total number of cells in the dataset divided by 100, as has been optimized on existing mass cytometry datasets. The output of this function is a matrix of each cell and the identity of its k-nearest neighbors, in terms of its row number in the dataset used here as input.

library(Sconify)
# Markers from the user-generated excel file
marker.file <- system.file('extdata', 'markers.csv', package = "Sconify")
markers <- ParseMarkers(marker.file)

# How to convert your excel sheet into vector of static and functional markers
markers
## $input
##  [1] "CD3(Cd110)Di"           "CD3(Cd111)Di"           "CD3(Cd112)Di"          
##  [4] "CD235-61-7-15(In113)Di" "CD3(Cd114)Di"           "CD45(In115)Di"         
##  [7] "CD19(Nd142)Di"          "CD22(Nd143)Di"          "IgD(Nd145)Di"          
## [10] "CD79b(Nd146)Di"         "CD20(Sm147)Di"          "CD34(Nd148)Di"         
## [13] "CD179a(Sm149)Di"        "CD72(Eu151)Di"          "IgM(Eu153)Di"          
## [16] "Kappa(Sm154)Di"         "CD10(Gd156)Di"          "Lambda(Gd157)Di"       
## [19] "CD24(Dy161)Di"          "TdT(Dy163)Di"           "Rag1(Dy164)Di"         
## [22] "PreBCR(Ho165)Di"        "CD43(Er167)Di"          "CD38(Er168)Di"         
## [25] "CD40(Er170)Di"          "CD33(Yb173)Di"          "HLA-DR(Yb174)Di"       
## 
## $functional
##  [1] "pCrkL(Lu175)Di"  "pCREB(Yb176)Di"  "pBTK(Yb171)Di"   "pS6(Yb172)Di"   
##  [5] "cPARP(La139)Di"  "pPLCg2(Pr141)Di" "pSrc(Nd144)Di"   "Ki67(Sm152)Di"  
##  [9] "pErk12(Gd155)Di" "pSTAT3(Gd158)Di" "pAKT(Tb159)Di"   "pBLNK(Gd160)Di" 
## [13] "pP38(Tm169)Di"   "pSTAT5(Nd150)Di" "pSyk(Dy162)Di"   "tIkBa(Er166)Di"
# Get the particular markers to be used as knn and knn statistics input
input.markers <- markers[[1]]
funct.markers <- markers[[2]]

# Selection of the k. See "Finding Ideal K" vignette
k <- 30

# The built-in scone functions
wand.nn <- Fnn(cell.df = wand.combined, input.markers = input.markers, k = k)
# Cell identity is in rows, k-nearest neighbors are columns
# List of 2 includes the cell identity of each nn, 
#   and the euclidean distance between
#   itself and the cell of interest

# Indices
str(wand.nn[[1]])
##  int [1:1000, 1:30] 111 393 329 479 220 267 817 385 6 622 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  111  551  951   21  393  309  307  443  710   225
##  [2,]  393  632  377  163  767  631  904  660  762    76
##  [3,]  329  727  824   38  979  622  747  788  781   662
##  [4,]  479  568  761  309  624  616  140  832  964   951
##  [5,]  220  792  433  779  981  507  943  636   86   898
##  [6,]  267    9  305  224  279  347  552  464  646   742
##  [7,]  817  609  436  685  804   59  550  756  661   902
##  [8,]  385  347  552  530  224  464  516   46  702   742
##  [9,]    6  224  464  279  267  646  967  305  347   121
## [10,]  622  747  467  376  830  255  185  613   37   886
## [11,]  962  718  362  202  198  900  795  951  704   247
## [12,]  320  146  749  426  977  498  476   53  363   881
## [13,]  621  401  582  980  213  123  707  339  675    33
## [14,]  441  698  116  295  321  650  429  145  369   546
## [15,]  736  124  252  544  206   55  346  705  642   397
## [16,]  603  235   42   39  862  195  114   91  380   751
## [17,]  771   56  520  261  161  209  926  338  794   637
## [18,]  695  691  765  621  715  948  306  467  830   673
## [19,]  605  813  484  130  791  946  504  327  216   351
## [20,]  978  554  254  719  208  821  443  111  205   270
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 2.9 2.79 3.47 2.78 3.4 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 2.895198 3.002550 3.080490 3.184604 3.193548 3.258761 3.328288 3.338686
##  [2,] 2.787150 3.080818 3.280142 3.285030 3.311190 3.362343 3.379551 3.380944
##  [3,] 3.473465 3.756365 3.790943 3.816626 3.833741 3.869900 3.918043 3.946341
##  [4,] 2.781353 2.876176 2.976959 2.995162 3.071176 3.107513 3.231125 3.259912
##  [5,] 3.395116 3.549475 3.570003 3.585570 3.591775 3.640325 3.651202 3.739791
##  [6,] 3.388935 3.403529 3.482542 3.556980 4.220445 4.336553 4.457099 4.539583
##  [7,] 4.120911 4.415533 4.750902 4.865578 4.870006 4.933615 4.935016 4.955969
##  [8,] 2.317429 2.618296 3.597499 3.692919 3.988143 4.105591 4.119062 4.124570
##  [9,] 3.403529 4.166008 4.258111 4.278096 4.318640 4.400288 4.403793 4.664271
## [10,] 2.695392 2.961800 2.972418 3.073372 3.144543 3.176760 3.190561 3.286952
## [11,] 3.035757 3.153393 3.175229 3.299160 3.307555 3.413175 3.418544 3.516271
## [12,] 3.905281 4.209103 4.245753 4.451718 4.499129 4.723569 4.724508 4.758992
## [13,] 2.782354 3.510749 3.543710 3.559376 3.631369 3.915101 3.921525 4.011109
## [14,] 4.969233 5.021415 5.260817 5.330267 5.399785 5.469066 5.470642 5.500520
## [15,] 4.505724 4.671480 4.803985 4.938966 4.975562 4.994535 5.021473 5.044814
## [16,] 2.885774 3.358817 3.487800 3.678958 3.711000 3.712156 3.715603 3.740663
## [17,] 3.862779 4.235053 4.321065 4.509705 4.608804 4.728539 4.799891 4.805413
## [18,] 2.947010 3.361468 3.418536 3.601187 3.764586 3.818412 3.841144 3.964735
## [19,] 4.090966 4.126250 4.271325 4.335344 4.534095 4.626412 4.683479 4.691542
## [20,] 2.844415 3.067158 3.169344 3.175073 3.315478 3.401002 3.414808 3.433616
##           [,9]    [,10]
##  [1,] 3.364915 3.420631
##  [2,] 3.381849 3.382394
##  [3,] 3.972447 4.089640
##  [4,] 3.293423 3.318214
##  [5,] 3.821998 3.854713
##  [6,] 4.752419 4.804014
##  [7,] 4.959065 5.078920
##  [8,] 4.321430 4.348134
##  [9,] 4.874679 4.893000
## [10,] 3.300886 3.335064
## [11,] 3.519228 3.519340
## [12,] 4.775084 4.804957
## [13,] 4.039606 4.069782
## [14,] 5.504254 5.514457
## [15,] 5.053021 5.095593
## [16,] 3.750163 3.772547
## [17,] 4.824944 4.826902
## [18,] 4.055869 4.078780
## [19,] 4.758725 4.871558
## [20,] 3.477077 3.483039

Finding scone values:

This function iterates through each KNN, and performs a series of calculations. The first is fold change values for each maker per KNN, where the user chooses whether this will be based on medians or means. The second is a statistical test, where the user chooses t test or Mann-Whitney U test. I prefer the latter, because it does not assume any properties of the distributions. Of note, the p values are adjusted for false discovery rate, and therefore are called q values in the output of this function. The user also inputs a threshold parameter (default 0.05), where the fold change values will only be shown if the corresponding statistical test returns a q value below said threshold. Finally, the “multiple.donor.compare” option, if set to TRUE will perform a t test based on the mean per-marker values of each donor. This is to allow the user to make comparisons across replicates or multiple donors if that is relevant to the user’s biological questions. This function returns a matrix of cells by computed values (change and statistical test results, labeled either marker.change or marker.qvalue). This matrix is intermediate, as it gets concatenated with the original input matrix in the post-processing step (see the relevant vignette). We show the code and the output below. See the post-processing vignette, where we show how this gets combined with the input data, and additional analysis is performed.

wand.scone <- SconeValues(nn.matrix = wand.nn, 
                      cell.data = wand.combined, 
                      scone.markers = funct.markers, 
                      unstim = "basal")

wand.scone
## # A tibble: 1,000 x 34
##    `pCrkL(Lu175)Di… `pCREB(Yb176)Di… `pBTK(Yb171)Di.… `pS6(Yb172)Di.I…
##               <dbl>            <dbl>            <dbl>            <dbl>
##  1            1                    1            0.878            0.903
##  2            0.994                1            0.518            1    
##  3            0.994                1            0.587            0.987
##  4            0.994                1            0.940            1    
##  5            1                    1            0.834            0.977
##  6            0.994                1            0.906            1    
##  7            0.994                1            0.852            1    
##  8            0.994                1            0.944            1    
##  9            0.994                1            0.896            0.961
## 10            0.998                1            0.851            1    
## # … with 990 more rows, and 30 more variables:
## #   `cPARP(La139)Di.IL7.qvalue` <dbl>, `pPLCg2(Pr141)Di.IL7.qvalue` <dbl>,
## #   `pSrc(Nd144)Di.IL7.qvalue` <dbl>, `Ki67(Sm152)Di.IL7.qvalue` <dbl>,
## #   `pErk12(Gd155)Di.IL7.qvalue` <dbl>, `pSTAT3(Gd158)Di.IL7.qvalue` <dbl>,
## #   `pAKT(Tb159)Di.IL7.qvalue` <dbl>, `pBLNK(Gd160)Di.IL7.qvalue` <dbl>,
## #   `pP38(Tm169)Di.IL7.qvalue` <dbl>, `pSTAT5(Nd150)Di.IL7.qvalue` <dbl>,
## #   `pSyk(Dy162)Di.IL7.qvalue` <dbl>, `tIkBa(Er166)Di.IL7.qvalue` <dbl>,
## #   `pCrkL(Lu175)Di.IL7.change` <dbl>, `pCREB(Yb176)Di.IL7.change` <dbl>,
## #   `pBTK(Yb171)Di.IL7.change` <dbl>, `pS6(Yb172)Di.IL7.change` <dbl>,
## #   `cPARP(La139)Di.IL7.change` <dbl>, `pPLCg2(Pr141)Di.IL7.change` <dbl>,
## #   `pSrc(Nd144)Di.IL7.change` <dbl>, `Ki67(Sm152)Di.IL7.change` <dbl>,
## #   `pErk12(Gd155)Di.IL7.change` <dbl>, `pSTAT3(Gd158)Di.IL7.change` <dbl>,
## #   `pAKT(Tb159)Di.IL7.change` <dbl>, `pBLNK(Gd160)Di.IL7.change` <dbl>,
## #   `pP38(Tm169)Di.IL7.change` <dbl>, `pSTAT5(Nd150)Di.IL7.change` <dbl>,
## #   `pSyk(Dy162)Di.IL7.change` <dbl>, `tIkBa(Er166)Di.IL7.change` <dbl>,
## #   IL7.fraction.cond.2 <dbl>, density <dbl>

For programmers: performing additional per-KNN statistics

If one wants to export KNN data to perform other statistics not available in this package, then I provide a function that produces a list of each cell identity in the original input data matrix, and a matrix of all cells x features of its KNN.

I also provide a function to find the KNN density estimation independently of the rest of the “scone.values” analysis, to save time if density is all the user wants. With this density estimation, one can perform interesting analysis, ranging from understanding phenotypic density changes along a developmental progression (see post-processing vignette for an example), to trying out density-based binning methods (eg. X-shift). Of note, this density is specifically one divided by the aveage distance to k-nearest neighbors. This specific measure is related to the Shannon Entropy estimate of that point on the manifold (https://hal.archives-ouvertes.fr/hal-01068081/document).

I use this metric to avoid the unusual properties of the volume of a sphere as it increases in dimensions (https://en.wikipedia.org/wiki/Volume_of_an_n-ball). This being said, one can modify this vector to be such a density estimation (example http://www.cs.haifa.ac.il/~rita/ml_course/lectures_old/KNN.pdf), by treating the distance to knn as the radius of a n-dimensional sphere and incoroprating said volume accordingly.

An individual with basic programming skills can iterate through these elements to perform the statistics of one’s choosing. Examples would include per-KNN regression and classification, or feature imputation. The additional functionality is shown below, with the example knn.list in the package being the first ten instances:

# Constructs KNN list, computes KNN density estimation
wand.knn.list <- MakeKnnList(cell.data = wand.combined, nn.matrix = wand.nn)
wand.knn.list[[8]]
## # A tibble: 30 x 51
##    `CD3(Cd110)Di` `CD3(Cd111)Di` `CD3(Cd112)Di` `CD235-61-7-15(… `CD3(Cd114)Di`
##             <dbl>          <dbl>          <dbl>            <dbl>          <dbl>
##  1        -0.0230        -0.197         -0.110           -0.901          0.0434
##  2        -0.0638        -0.235         -0.265           -0.240         -0.159 
##  3        -0.114         -0.0571        -0.215           -0.887         -0.226 
##  4        -0.116         -0.170         -0.402           -0.816         -0.441 
##  5        -0.0337        -0.117         -0.583            0.0137        -0.0686
##  6        -0.0458        -0.195         -0.180           -0.708          0.329 
##  7        -0.0744         0.170          0.0230          -0.481          0.694 
##  8        -0.0698        -0.164         -0.0780          -0.688          0.894 
##  9        -0.370         -0.470         -0.638           -0.102          1.96  
## 10         0.200          0.333          0.227            0.779          0.358 
## # … with 20 more rows, and 46 more variables: `CD45(In115)Di` <dbl>,
## #   `CD19(Nd142)Di` <dbl>, `CD22(Nd143)Di` <dbl>, `IgD(Nd145)Di` <dbl>,
## #   `CD79b(Nd146)Di` <dbl>, `CD20(Sm147)Di` <dbl>, `CD34(Nd148)Di` <dbl>,
## #   `CD179a(Sm149)Di` <dbl>, `CD72(Eu151)Di` <dbl>, `IgM(Eu153)Di` <dbl>,
## #   `Kappa(Sm154)Di` <dbl>, `CD10(Gd156)Di` <dbl>, `Lambda(Gd157)Di` <dbl>,
## #   `CD24(Dy161)Di` <dbl>, `TdT(Dy163)Di` <dbl>, `Rag1(Dy164)Di` <dbl>,
## #   `PreBCR(Ho165)Di` <dbl>, `CD43(Er167)Di` <dbl>, `CD38(Er168)Di` <dbl>,
## #   `CD40(Er170)Di` <dbl>, `CD33(Yb173)Di` <dbl>, `HLA-DR(Yb174)Di` <dbl>,
## #   Time <dbl>, Cell_length <dbl>, `cPARP(La139)Di` <dbl>,
## #   `pPLCg2(Pr141)Di` <dbl>, `pSrc(Nd144)Di` <dbl>, `pSTAT5(Nd150)Di` <dbl>,
## #   `Ki67(Sm152)Di` <dbl>, `pErk12(Gd155)Di` <dbl>, `pSTAT3(Gd158)Di` <dbl>,
## #   `pAKT(Tb159)Di` <dbl>, `pBLNK(Gd160)Di` <dbl>, `pSyk(Dy162)Di` <dbl>,
## #   `tIkBa(Er166)Di` <dbl>, `pP38(Tm169)Di` <dbl>, `pBTK(Yb171)Di` <dbl>,
## #   `pS6(Yb172)Di` <dbl>, `pCrkL(Lu175)Di` <dbl>, `pCREB(Yb176)Di` <dbl>,
## #   `DNA1(Ir191)Di` <dbl>, `DNA2(Ir193)Di` <dbl>, `Viability1(Pt195)Di` <dbl>,
## #   `Viability2(Pt196)Di` <dbl>, wanderlust <dbl>, condition <chr>
# Finds the KNN density estimation for each cell, ordered by column, in the 
# original data matrix
wand.knn.density <- GetKnnDe(nn.matrix = wand.nn)
str(wand.knn.density)
##  num [1:1000] 0.288 0.288 0.243 0.295 0.256 ...