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] 753 475 520 847 992 398 463 586 374 494 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  753  494  289  485  326  549  200  300   27   826
##  [2,]  475  263  656  833  670  231  294  100  761    78
##  [3,]  520  561  806  907  304  748  791  681  177   154
##  [4,]  847  203  249  408  543  778  496  888  695   763
##  [5,]  992  975  832  183  642  512  213  999  756   721
##  [6,]  398  244  174  372  406  673  810  315  989   351
##  [7,]  463  309  759   35  826  663  900  348  517   281
##  [8,]  586   63   92  991  789  835  764  509  309   458
##  [9,]  374  912   51  672  104  667  922  630  773   965
## [10,]  494  702  247   68  880  652  253   94  149   633
## [11,]   59   46  845  252  507   81  459   68  427   826
## [12,]  939  692  845  826  427  252  486  925  658   378
## [13,]   43  176  273  268  348  571  566  764  735   619
## [14,]  795  912  579  380  691  627  155  773   29    51
## [15,]   57  105  165  566   45  222  422  400   87   285
## [16,]  294  340    4  847  491  859  122  952  511   284
## [17,]  595  773  224  476  643  231  244  136  624    18
## [18,]  874   44  374  263  376  761  595  670  773    51
## [19,]  466  100  152  936  347  848  890  867  198   937
## [20,]  561  553  951  806  879  520  830  278  748   324
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 2.73 3.98 3.24 3.61 5.1 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 2.731706 2.754043 2.776866 2.779366 2.961980 2.977156 2.990896 3.027949
##  [2,] 3.984278 3.996332 4.328697 4.392967 4.439480 4.538187 4.585490 4.596258
##  [3,] 3.244238 3.659957 3.815576 3.850592 3.939764 3.974999 4.003249 4.082309
##  [4,] 3.606343 3.742459 4.011622 4.037374 4.095586 4.141763 4.222709 4.252544
##  [5,] 5.096301 5.203686 5.312953 5.346273 5.387677 5.455912 5.481237 5.561407
##  [6,] 3.555676 4.064845 4.213306 4.304861 4.374337 4.378823 4.412804 4.419537
##  [7,] 3.475064 3.599945 3.635163 3.674064 3.728996 3.732867 3.784510 3.817044
##  [8,] 3.172684 3.211234 3.292320 3.303263 3.333152 3.351309 3.528282 3.554566
##  [9,] 2.903163 3.105208 3.493578 3.602325 3.604967 3.607594 3.644417 3.649726
## [10,] 3.617761 3.623503 3.665716 3.697564 3.754726 3.827799 3.840619 3.892174
## [11,] 3.242709 3.349494 3.408268 3.464100 3.548138 3.574754 3.583722 3.612292
## [12,] 3.561527 3.656104 3.720733 3.738319 3.822681 3.835872 3.872963 3.875122
## [13,] 2.614302 2.663104 2.670281 3.004736 3.172732 3.201109 3.265436 3.365401
## [14,] 3.288704 3.308502 3.411552 3.464850 3.592468 3.598036 3.683985 3.684131
## [15,] 3.340251 3.412893 3.457041 3.497966 3.574911 3.632760 3.680311 3.884876
## [16,] 4.133291 4.519412 4.521023 4.581570 4.679746 4.715303 4.747115 4.772071
## [17,] 3.179104 3.188749 3.239590 3.322334 3.524686 3.561743 3.598864 3.615391
## [18,] 2.474032 2.908386 2.956495 2.969394 3.008786 3.025276 3.165508 3.252539
## [19,] 4.989852 5.204365 5.494584 5.524886 5.551937 5.621657 5.629288 5.649932
## [20,] 3.846971 4.149865 4.152537 4.465981 4.664139 4.759512 4.787987 4.839777
##           [,9]    [,10]
##  [1,] 3.040271 3.198957
##  [2,] 4.612405 4.649337
##  [3,] 4.109970 4.204069
##  [4,] 4.260511 4.307663
##  [5,] 5.689126 5.701672
##  [6,] 4.438153 4.441986
##  [7,] 3.951036 3.971680
##  [8,] 3.565380 3.604993
##  [9,] 3.654425 3.694518
## [10,] 3.902825 4.045153
## [11,] 3.649849 3.669487
## [12,] 3.912308 3.940771
## [13,] 3.399457 3.408421
## [14,] 3.694385 3.699110
## [15,] 3.902945 3.914471
## [16,] 4.832044 4.841647
## [17,] 3.674816 3.683914
## [18,] 3.257129 3.326228
## [19,] 5.727689 5.765416
## [20,] 4.855429 4.979139

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 × 34
##    `pCrkL(Lu175)Di.IL7.qvalue` pCREB(Yb176)Di.IL7.qvalu…¹ pBTK(Yb171)Di.IL7.qv…²
##                          <dbl>                      <dbl>                  <dbl>
##  1                       0.891                          1                  0.924
##  2                       0.988                          1                  0.977
##  3                       0.976                          1                  1    
##  4                       0.984                          1                  0.924
##  5                       0.986                          1                  0.977
##  6                       0.977                          1                  0.983
##  7                       0.913                          1                  0.880
##  8                       0.891                          1                  0.924
##  9                       0.977                          1                  0.977
## 10                       0.927                          1                  0.983
## # ℹ 990 more rows
## # ℹ abbreviated names: ¹​`pCREB(Yb176)Di.IL7.qvalue`,
## #   ²​`pBTK(Yb171)Di.IL7.qvalue`
## # ℹ 31 more variables: `pS6(Yb172)Di.IL7.qvalue` <dbl>,
## #   `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>, …

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 × 51
##    `CD3(Cd110)Di` `CD3(Cd111)Di` `CD3(Cd112)Di` `CD235-61-7-15(In113)Di`
##             <dbl>          <dbl>          <dbl>                    <dbl>
##  1         0.846         -0.313         -0.262                   -0.207 
##  2         0.0970         0.530         -0.0602                   0.280 
##  3        -0.151         -0.252         -0.123                   -0.168 
##  4        -0.438         -0.0758        -0.118                   -0.678 
##  5        -0.136         -0.242          0.532                    0.0579
##  6         0.186          0.432          0.564                    0.557 
##  7        -0.0498         0.201          0.573                   -0.355 
##  8        -0.465         -0.459          0.787                   -0.299 
##  9        -0.452         -0.117         -0.127                    0.540 
## 10         0.432          0.694          0.801                   -0.453 
## # ℹ 20 more rows
## # ℹ 47 more variables: `CD3(Cd114)Di` <dbl>, `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>, …
# 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] 0.312 0.21 0.235 0.228 0.167 ...