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] 134 690 710 773 508 252 274 339 270 149 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  134  475  912  374  136  272  298  922  539   812
##  [2,]  690  175   18  177  767  396  410  979  985   693
##  [3,]  710  431  921  933  741  657  491  389   83   998
##  [4,]  773  632  449  630  777  859  570  295  247   901
##  [5,]  508  632  933  772  491  906  956  165  973   319
##  [6,]  252  361   51   31   49   10  664  149  391   825
##  [7,]  274   62  788  688  570  661  449  739  777   914
##  [8,]  339  875   93  843  394  776  437  794   46   478
##  [9,]  270  566  758  241  915  606  868  507  119   911
## [10,]  149  808  292  650    6  213  252   51  775    49
## [11,]  310  271  329  174  730  142   95  245   97   470
## [12,]  178  926  707  646  818  838  116  698  568   705
## [13,]  264  709  755  806  828  540  795  801   68   263
## [14,]  868  501  184  428  321  618  965  970   55   215
## [15,]   56  137  903  392  164  468  528  133  398   112
## [16,]  627  670  654   83  967  212  761  533  266   736
## [17,]  101  729  606  438  720  321  679  259  538   702
## [18,]  979  403  396  985  353  984  175   82   94   263
## [19,]  867   78  567   48  123  162  964  865  364   685
## [20,]  261  456  814  310  236  561  275  402  242   947
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 3.66 3.56 2.3 3.08 4.64 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 3.655312 3.710415 3.821441 3.843127 3.883353 3.896625 3.922677 3.963700
##  [2,] 3.564791 3.598313 3.605968 3.807738 3.898207 3.905923 4.008878 4.049655
##  [3,] 2.296113 2.740851 2.798149 2.882021 2.882089 2.973589 3.006233 3.012123
##  [4,] 3.075207 3.474140 3.850334 4.021719 4.173033 4.262167 4.418517 4.430607
##  [5,] 4.639681 5.078659 5.102001 5.177237 5.177547 5.242917 5.292503 5.345661
##  [6,] 3.388935 3.582441 3.738259 3.814607 4.137591 4.146279 4.150085 4.198159
##  [7,] 3.419766 3.670826 3.786256 3.893723 3.937955 4.004221 4.051921 4.090277
##  [8,] 3.902280 4.021114 4.170058 4.178921 4.200376 4.378969 4.463472 4.489206
##  [9,] 3.169344 3.307120 3.394217 3.465452 3.498359 3.585324 3.608535 3.609777
## [10,] 3.679249 3.904158 3.942074 3.943316 4.146279 4.253201 4.313055 4.395033
## [11,] 4.001273 4.186758 4.379717 4.423305 4.501913 4.516977 4.593997 4.635691
## [12,] 3.066991 3.112308 3.132371 3.197260 3.241773 3.445678 3.478168 3.478756
## [13,] 3.432329 3.463242 3.525090 3.672116 3.686215 3.692707 3.743823 3.750575
## [14,] 2.565037 2.573734 2.635397 2.650510 2.667544 2.752493 2.832915 2.862492
## [15,] 3.113533 3.567572 3.636588 3.712061 3.723023 3.757469 3.778574 3.811762
## [16,] 2.948288 3.380441 3.490019 3.748988 3.760997 3.778793 3.824310 3.846804
## [17,] 3.209440 3.298959 3.321523 3.346877 3.410238 3.440586 3.538967 3.612299
## [18,] 2.887469 3.174962 3.205037 3.206316 3.228291 3.232466 3.284541 3.305843
## [19,] 3.938531 3.960518 4.059438 4.075821 4.125478 4.247613 4.343641 4.346685
## [20,] 2.999142 3.674934 3.688778 3.719685 3.740716 3.797004 3.846122 3.855780
##           [,9]    [,10]
##  [1,] 3.975300 3.986317
##  [2,] 4.105608 4.135997
##  [3,] 3.012184 3.039439
##  [4,] 4.453382 4.465567
##  [5,] 5.372905 5.383269
##  [6,] 4.318640 4.337483
##  [7,] 4.155429 4.157550
##  [8,] 4.643685 4.650219
##  [9,] 3.689110 3.787543
## [10,] 4.469473 4.472910
## [11,] 4.678632 4.736042
## [12,] 3.595115 3.647111
## [13,] 3.760203 3.774978
## [14,] 2.964926 2.968273
## [15,] 3.818075 3.820665
## [16,] 3.904921 3.909770
## [17,] 3.632449 3.684777
## [18,] 3.314668 3.373050
## [19,] 4.351326 4.434867
## [20,] 3.892582 4.012733

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            0.891                1            0.994            0.979
##  2            0.997                1            0.691            0.905
##  3            0.567                1            0.781            1    
##  4            0.966                1            0.853            0.979
##  5            0.891                1            0.707            0.904
##  6            0.418                1            1                0.997
##  7            0.969                1            0.873            0.979
##  8            0.756                1            0.691            0.997
##  9            0.916                1            0.619            0.979
## 10            0.567                1            0.594            0.906
## # … 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        -0.121         -0.133        -0.0150            0.0321         0.292 
##  2        -0.241         -0.0568       -0.148            -0.0476        -0.0679
##  3         0.481          0.141        -0.490             0.263         -0.234 
##  4        -0.361         -0.272        -0.0987           -1.79          -0.0807
##  5        -0.0612        -0.199        -0.499            -0.615          0.132 
##  6        -0.429         -0.0598       -0.688             0.367          0.0952
##  7        -0.248         -0.698        -0.0275           -1.22          -0.946 
##  8        -0.0165        -0.0589       -0.00434          -1.10           0.978 
##  9        -0.100         -0.0925       -0.224            -0.475          0.596 
## 10        -0.280         -0.155        -0.494            -0.923         -0.347 
## # … 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] 0.239 0.236 0.323 0.22 0.184 ...