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] 763 459 711 95 310 834 421 189 506 504 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]  763  951  663    6  402  878  492  243  949    67
##  [2,]  459  272  506  575  786  140  399  943  569   886
##  [3,]  711  652  506  194    9  488  101   87  855   980
##  [4,]   95  506  391  684  386   74  284  571    9   106
##  [5,]  310  441  970   85  943  458  448  529  459   703
##  [6,]  834  402  939  436  306  916   67    1  950   608
##  [7,]  421   48    5  131  183  390  448   84  617   388
##  [8,]  189  973  424  928  809  768  367  360   74   906
##  [9,]  506  652  291  894  803  474  265  505   85   922
## [10,]  504  156  405  844  893  561  367  514  946   400
## [11,]  856  386  798  905  571  803  689  135  209   738
## [12,]  341  446  703  695  994  447  529  670  176   587
## [13,]  635  845  971  181  694  750  645  680   51   986
## [14,]  240  988  511  107  748  618  500  431  546   933
## [15,]  974  984  591  119  958  263  874  715  769   998
## [16,]  500  860   64   67  950  878  816  788  328   978
## [17,]  857  611  200  591  614  195  609  153  728   661
## [18,]  950  492  590  939  369  878  978  402   30   490
## [19,]  859  958  339  759  254  263  345  769  111   998
## [20,]  161  402  816  511  500  763  565  328  988   752
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 3.73 2.31 3.01 2.67 3.56 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
##  [1,] 3.732467 3.943752 3.969009 4.332826 4.336712 4.393850 4.422141 4.514198
##  [2,] 2.310442 2.740851 2.815045 2.828404 2.973589 2.983170 3.006233 3.039439
##  [3,] 3.011302 3.101360 3.196670 3.284251 3.323518 3.405819 3.464398 3.587676
##  [4,] 2.668782 2.959003 3.399978 3.450353 3.495232 3.506941 3.535020 3.536589
##  [5,] 3.560172 3.569068 3.610449 3.661371 3.680563 3.763411 3.793470 3.817142
##  [6,] 3.817037 4.018558 4.067644 4.130807 4.154497 4.220931 4.285856 4.332826
##  [7,] 3.632760 3.845536 3.951215 3.991113 4.059086 4.157371 4.174669 4.235983
##  [8,] 2.961004 3.127436 3.182050 3.186410 3.200009 3.212491 3.258179 3.258794
##  [9,] 2.457702 2.733413 3.118784 3.193276 3.198298 3.218097 3.237597 3.248938
## [10,] 3.217416 3.351930 3.694704 3.756897 3.773349 3.800538 3.806209 3.820494
## [11,] 2.572952 2.594500 2.955330 3.228989 3.245368 3.247383 3.260248 3.331167
## [12,] 4.327196 4.371005 4.375177 4.464914 4.510921 4.552659 4.587073 4.597608
## [13,] 3.033480 3.747357 4.188512 4.317661 4.367062 4.459449 4.502357 4.845573
## [14,] 4.032526 4.420810 4.576001 4.816199 4.862952 4.996553 5.006532 5.098635
## [15,] 2.469631 2.722951 2.749710 2.874365 2.874492 2.963328 2.967493 2.989109
## [16,] 2.867231 3.077660 3.178829 3.390046 3.418372 3.518837 3.584649 3.644989
## [17,] 2.603127 2.961742 3.137996 3.154311 3.159903 3.368900 3.465246 3.560424
## [18,] 3.746514 4.233413 4.459076 4.489870 4.493819 4.517013 4.536105 4.671120
## [19,] 2.864099 3.357628 3.713032 3.830255 3.918866 3.964005 4.026742 4.102203
## [20,] 3.284390 3.849542 3.872867 4.078992 4.211292 4.352254 4.359839 4.386872
##           [,9]    [,10]
##  [1,] 4.561329 4.610233
##  [2,] 3.072468 3.080809
##  [3,] 3.597270 3.616170
##  [4,] 3.538380 3.539819
##  [5,] 3.833874 3.836570
##  [6,] 4.378235 4.425686
##  [7,] 4.321731 4.342622
##  [8,] 3.271165 3.280457
##  [9,] 3.269940 3.270958
## [10,] 3.847745 3.859671
## [11,] 3.348188 3.393072
## [12,] 4.760918 4.802921
## [13,] 4.977026 5.003251
## [14,] 5.129706 5.150931
## [15,] 2.992920 3.013243
## [16,] 3.697669 3.710303
## [17,] 3.570024 3.602934
## [18,] 4.720122 4.720609
## [19,] 4.126963 4.134691
## [20,] 4.398015 4.409507

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               0.963               0.847              0.971              1    
##  2               0.813               0.897              0.794              1    
##  3               0.853               0.867              0.912              0.930
##  4               0.945               0.897              0.895              0.906
##  5               0.923               0.847              0.903              0.997
##  6               0.991               0.750              1                  0.985
##  7               0.887               0.897              0.965              0.894
##  8               0.923               0.918              0.870              0.985
##  9               1                   0.897              0.583              1    
## 10               0.844               0.897              0.965              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(I~ `CD3(Cd114)Di`
##             <dbl>          <dbl>          <dbl>             <dbl>          <dbl>
##  1       -0.0657         -0.243         -0.0264            -0.319        -0.187 
##  2        0.332          -0.438         -0.294             -0.210        -0.329 
##  3        0.00357        -0.0435        -0.777             -0.183        -0.448 
##  4       -0.234          -0.0953        -0.451             -0.721        -0.393 
##  5       -0.0695         -0.197         -0.213              0.774        -0.304 
##  6       -0.446          -0.204         -0.0761            -0.996        -0.288 
##  7       -0.0363         -0.184         -0.0884             0.733        -0.0411
##  8       -0.255           0.179         -0.241             -1.58         -0.159 
##  9       -0.0645         -0.488         -0.289             -0.325         0.186 
## 10       -0.0882          1.04           0.385             -0.361        -0.492 
## # ... 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] 0.213 0.318 0.272 0.28 0.253 ...