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"          
##  [3] "CD3(Cd112)Di"           "CD235-61-7-15(In113)Di"
##  [5] "CD3(Cd114)Di"           "CD45(In115)Di"         
##  [7] "CD19(Nd142)Di"          "CD22(Nd143)Di"         
##  [9] "IgD(Nd145)Di"           "CD79b(Nd146)Di"        
## [11] "CD20(Sm147)Di"          "CD34(Nd148)Di"         
## [13] "CD179a(Sm149)Di"        "CD72(Eu151)Di"         
## [15] "IgM(Eu153)Di"           "Kappa(Sm154)Di"        
## [17] "CD10(Gd156)Di"          "Lambda(Gd157)Di"       
## [19] "CD24(Dy161)Di"          "TdT(Dy163)Di"          
## [21] "Rag1(Dy164)Di"          "PreBCR(Ho165)Di"       
## [23] "CD43(Er167)Di"          "CD38(Er168)Di"         
## [25] "CD40(Er170)Di"          "CD33(Yb173)Di"         
## [27] "HLA-DR(Yb174)Di"       
## 
## $functional
##  [1] "pCrkL(Lu175)Di"  "pCREB(Yb176)Di"  "pBTK(Yb171)Di"  
##  [4] "pS6(Yb172)Di"    "cPARP(La139)Di"  "pPLCg2(Pr141)Di"
##  [7] "pSrc(Nd144)Di"   "Ki67(Sm152)Di"   "pErk12(Gd155)Di"
## [10] "pSTAT3(Gd158)Di" "pAKT(Tb159)Di"   "pBLNK(Gd160)Di" 
## [13] "pP38(Tm169)Di"   "pSTAT5(Nd150)Di" "pSyk(Dy162)Di"  
## [16] "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] 76 932 198 574 324 429 360 138 796 274 ...
wand.nn[[1]][1:20, 1:10]
##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]   76  567  674  292  125  714  947  739  995   613
##  [2,]  932  592  418  315  172  290  291  500  743   624
##  [3,]  198  212  376   60  295  992  729   31  671   303
##  [4,]  574  548  766  435  166  944  997  798  506   488
##  [5,]  324  395  479  716  437  886  884  929  904   805
##  [6,]  429  358  316  586  348  173  715  846  976   335
##  [7,]  360  540  259  974  797  882  808  903  371    39
##  [8,]  138  810  682   29   96  322  830   27  887    37
##  [9,]  796  204  276  398  512   23  244  562  154   219
## [10,]  274  877  728  299  433  560  296  639  977   419
## [11,]  343  660  527  994  404  344  598   42  546   831
## [12,]  851  858   20  521  181   75  824  986  948   630
## [13,]   54  897  191  546  319  714  672  379  217   344
## [14,]  506  153  693  735  992  397  642  630  547   295
## [15,]  302   40  480  711  482   76  415  739   44   152
## [16,]  792  951  127    7  859  540  572  331  917   188
## [17,]  938  736  770  340  997  627  506  845  533   585
## [18,]   99  776  289  903  852  622  311  261   61   932
## [19,]  614  958  277   33  291  591  202  990  475   316
## [20,]  802  212    3  735  273  992  295  991  204   729
# Distance
str(wand.nn[[2]])
##  num [1:1000, 1:30] 2.9 4.09 2.52 3.65 4.11 ...
wand.nn[[2]][1:20, 1:10]
##           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]
##  [1,] 2.903163 3.190725 3.346728 3.543066 3.587619 3.602325 3.607594
##  [2,] 4.093142 4.241363 4.253033 4.277992 4.306909 4.333221 4.372952
##  [3,] 2.523659 2.867231 3.178829 3.318162 3.390046 3.518837 3.568717
##  [4,] 3.648497 4.285868 4.428155 4.560822 4.664446 4.706743 4.804098
##  [5,] 4.114331 4.144629 4.400274 4.450696 4.570147 4.620270 4.705938
##  [6,] 3.018432 3.206609 3.290427 3.443968 3.447538 3.463247 3.481977
##  [7,] 2.595939 2.748842 2.869548 2.871399 2.879931 2.881293 2.972628
##  [8,] 3.420631 3.756897 3.773349 3.806209 3.859219 3.859671 3.870613
##  [9,] 4.535107 4.842285 4.933615 5.094219 5.145122 5.301940 5.307418
## [10,] 4.291241 4.429173 4.509749 4.796773 5.065862 5.317487 5.687485
## [11,] 4.508172 4.516729 4.548852 4.597105 4.679682 4.775977 4.813346
## [12,] 4.916860 4.982559 5.136715 5.143827 5.191339 5.206551 5.291771
## [13,] 3.238647 3.248423 3.793809 3.939331 4.059348 4.061989 4.116736
## [14,] 3.096696 3.842865 3.904964 4.031992 4.142554 4.318562 4.352212
## [15,] 3.897873 3.912981 3.954685 4.008490 4.072789 4.135402 4.205364
## [16,] 3.832822 4.127802 4.208518 4.216739 4.227662 4.264990 4.294982
## [17,] 5.096301 5.203686 5.312953 5.346273 5.455912 5.604068 5.623401
## [18,] 3.101829 3.102051 3.208460 3.274835 3.282958 3.340364 3.380470
## [19,] 4.109448 4.163996 4.278298 4.292908 4.325495 4.392679 4.426677
## [20,] 3.703559 3.898640 3.950076 4.023790 4.078480 4.188525 4.241100
##           [,8]     [,9]    [,10]
##  [1,] 3.704443 3.732782 3.734646
##  [2,] 4.382291 4.459908 4.546279
##  [3,] 3.697669 3.710303 3.729892
##  [4,] 4.844865 4.856048 4.930607
##  [5,] 4.753374 4.924406 5.008210
##  [6,] 3.491684 3.578993 3.609493
##  [7,] 2.993510 3.022016 3.144814
##  [8,] 3.912247 3.935354 3.958678
##  [9,] 5.322587 5.334413 5.459404
## [10,] 5.750151 5.927361 5.935412
## [11,] 4.886832 4.983323 5.205886
## [12,] 5.392086 5.445631 5.451377
## [13,] 4.129074 4.185224 4.185250
## [14,] 4.445199 4.529453 4.536179
## [15,] 4.214673 4.218315 4.223790
## [16,] 4.304390 4.317096 4.372530
## [17,] 5.651117 5.684103 5.825025
## [18,] 3.432843 3.443903 3.474294
## [19,] 4.449122 4.478456 4.487642
## [20,] 4.290163 4.364901 4.390428

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            0.997            0.889            0.665            0.994
##  2            0.978            0.932            0.975            0.994
##  3            0.978            0.751            0.957            1    
##  4            0.978            0.974            1                0.994
##  5            0.978            0.936            0.945            0.955
##  6            0.978            0.761            0.808            0.974
##  7            0.978            0.811            0.612            0.974
##  8            0.978            0.896            0.830            1    
##  9            0.978            0.856            0.709            0.994
## 10            0.978            0.936            0.886            0.929
## # ... 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(~
##             <dbl>          <dbl>          <dbl>            <dbl>
##  1        -0.203      -0.105          -0.347              -0.137
##  2        -0.0851     -0.0979         -0.178              -0.258
##  3        -0.0785     -0.00929        -0.00777            -0.802
##  4        -0.0363     -0.184          -0.0884              0.733
##  5        -0.358      -0.252          -0.000680            0.181
##  6        -0.0855     -0.406          -0.487              -0.833
##  7        -0.262      -0.335           0.212              -0.866
##  8        -0.0575     -0.166          -0.232               0.201
##  9        -0.0398     -0.0000977      -0.615              -0.474
## 10        -0.125      -0.0787         -0.174              -1.12 
## # ... with 20 more rows, and 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>, `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] 0.267 0.217 0.256 0.198 0.201 ...