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] 897 855 72 957 937 438 194 338 369 320 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  897  281  248  611  754  962  134  894  983   233
##  [2,]  855  278  716  235  392  904   72  812  873   917
##  [3,]   72   57  516   61  830  291  856  993  166   768
##  [4,]  957  234  443  237   59  990   27  841  566   224
##  [5,]  937  354  543  560  566  491  639  176  109   286
##  [6,]  438  295  542  795  311   86  569  483  684   280
##  [7,]  194  422  362  638  440  576  807  538  527   774
##  [8,]  338  329  590  533   23  520  598  641  571   239
##  [9,]  369  684  907   87  918  463   54  986   69   910
## [10,]  320  326  698  236  416  396  157  131  820   308
## [11,]  881  615  281  834  414   71  593  691  106   178
## [12,]  410  283  388  687  538  197  236  467   48   242
## [13,]   96  262  800  506  936  122  908  213  131    32
## [14,]  630  804  985   59  968  117  330    4  841   957
## [15,]  446  947  162  738  848  918  910  279  566   241
## [16,]  881   91  637  471  922  958   53  834  281   997
## [17,]  273  565  296  755  884  398  955  131  654   320
## [18,]  834  691  212  809  123  881  744  922  888   851
## [19,]  358  839  122  547  816  515  257  406  640   604
## [20,]  293  743  290  724  657  250  759  188  313   882
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 2.55 3.92 3.36 2.47 2.21 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 2.551057 2.877558 3.149285 3.359316 3.636517 3.670123 3.673624 3.676229
##  [2,] 3.924930 4.020163 4.329155 4.502649 4.511740 4.601139 4.612490 4.701388
##  [3,] 3.363588 3.453381 3.554492 3.636421 3.657169 3.700616 3.761648 3.798015
##  [4,] 2.474032 2.908386 2.956495 2.960426 2.969394 3.055646 3.252302 3.252539
##  [5,] 2.206203 2.756434 2.829583 3.034378 3.093143 3.129549 3.197459 3.241631
##  [6,] 3.905281 4.209103 4.245753 4.711475 4.723569 4.775084 4.775266 4.778753
##  [7,] 2.548095 2.671363 2.843630 2.922730 3.015991 3.061599 3.179717 3.208087
##  [8,] 3.911108 4.140878 4.229922 4.398263 4.408850 4.423437 4.455586 4.468671
##  [9,] 3.097720 4.202864 4.206411 4.207700 4.414333 4.515455 4.621298 4.661396
## [10,] 2.668344 2.735375 3.030267 3.053310 3.090663 3.109112 3.114050 3.122590
## [11,] 3.028344 3.747673 3.958279 4.011496 4.038856 4.106526 4.110042 4.214606
## [12,] 2.857515 2.896975 2.945146 2.978146 3.126776 3.200580 3.217015 3.264566
## [13,] 4.841182 4.928045 4.951130 4.993592 5.019089 5.032813 5.084089 5.150506
## [14,] 3.849132 3.890322 4.520806 4.597226 4.742255 4.766004 4.890565 4.899291
## [15,] 2.832967 2.966594 2.978875 3.035715 3.064958 3.259878 3.317191 3.339832
## [16,] 4.520879 4.658434 4.907575 5.006399 5.102403 5.159696 5.375401 5.404872
## [17,] 3.351930 3.756897 3.768833 3.782414 3.800538 3.806209 3.820494 3.859219
## [18,] 4.067747 4.321824 4.353073 4.419587 4.529473 4.646032 4.739847 4.745397
## [19,] 3.486064 3.505017 3.516958 3.559220 3.628879 3.649255 3.656602 3.678844
## [20,] 3.603838 3.720459 3.761407 3.850478 3.875571 3.898668 4.049438 4.258111
##           [,9]    [,10]
##  [1,] 3.748873 3.794629
##  [2,] 4.713851 4.731090
##  [3,] 3.800711 3.856201
##  [4,] 3.257129 3.308979
##  [5,] 3.252635 3.266114
##  [6,] 4.804957 4.851907
##  [7,] 3.234322 3.287074
##  [8,] 4.496290 4.547326
##  [9,] 4.671356 4.826079
## [10,] 3.146573 3.172517
## [11,] 4.353556 4.391577
## [12,] 3.305846 3.316546
## [13,] 5.160283 5.165224
## [14,] 5.004431 5.025780
## [15,] 3.405926 3.435292
## [16,] 5.459774 5.524838
## [17,] 3.870613 3.958678
## [18,] 4.752040 4.858189
## [19,] 3.689623 3.770356
## [20,] 4.401926 4.443299

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.IL… `pCREB(Yb176)Di.IL… `pBTK(Yb171)Di.IL… `pS6(Yb172)Di.IL7…
##                  <dbl>               <dbl>              <dbl>              <dbl>
##  1                   1               1                  0.714              0.868
##  2                   1               1                  0.837              0.878
##  3                   1               1                  0.968              0.775
##  4                   1               1                  0.884              0.955
##  5                   1               1                  0.929              0.985
##  6                   1               1                  0.763              0.985
##  7                   1               1                  0.944              0.894
##  8                   1               0.387              0.954              0.912
##  9                   1               1                  0.973              0.899
## 10                   1               0.903              0.751              0.899
## # … 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(I… `CD3(Cd114)Di`
##             <dbl>          <dbl>          <dbl>             <dbl>          <dbl>
##  1        -0.212         -0.0522        0.302              0.479           0.346
##  2         0.771         -0.0114       -0.226              0.760          -0.360
##  3        -0.218         -0.0773        0.369             -0.167          -0.384
##  4        -0.0854        -0.247         0.780             -0.302          -0.581
##  5        -0.236         -0.109         0.00696           -1.02            0.734
##  6        -0.234         -0.273        -1.18              -1.08           -0.873
##  7         0.782          0.779         0.143              0.0405          0.115
##  8        -1.38          -1.14         -1.33               0.799          -1.03 
##  9        -0.452         -0.231        -0.304             -0.543          -0.370
## 10        -0.204         -0.0512       -0.240             -1.90           -0.375
## # … 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] 0.261 0.209 0.252 0.297 0.3 ...