single cell library size distribution
DongyueXie
2022-12-08
Last updated: 2022-12-08
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Introduction
I look at the distribution of single cell library size on two datasets. The main purpose is to learn a distribution of library size and generate data from it.
So to make it scale with the number of genes, the library size in the following is divided by the number of genes.
The pbmc dataset.
library(fastTopics)
library(Matrix)
data("pbmc_facs")
s = rowSums(pbmc_facs$counts)/ncol(pbmc_facs$counts)
hist(s,breaks = 100,main='pbmc data library size',probability = T)
| Version | Author | Date |
|---|---|---|
| 9259fc2 | DongyueXie | 2022-12-08 |
Fit a gamma distribution on \(s\), using method of moment.
rate = mean(s)/var(s)
shape = mean(s)*rate
rate[1] 16.16446shape[1] 1.913245hist(rgamma(1e5,shape=shape,rate=rate),breaks = 100,main='simulated library size',probability = T)
| Version | Author | Date |
|---|---|---|
| 9259fc2 | DongyueXie | 2022-12-08 |
Fit a inverse gamma distribution on \(s\), using method of moment.
library(invgamma)
shape = 2 + mean(s)^2/var(s)
rate = (shape-1)*mean(s)
shape[1] 3.913245rate[1] 0.3448151dd = rinvgamma(1e5,shape=shape,rate=rate)
hist(dd,breaks = 100,main='simulated library size',probability = T)
| Version | Author | Date |
|---|---|---|
| 9259fc2 | DongyueXie | 2022-12-08 |
hist(dd[dd<max(s)],breaks = 100,main='simulated library size',probability = T)
droplet data
load('data/real_data_singlecell/droplet.RData')s = rowSums(counts)/ncol(counts)
hist(s,breaks = 100,main='droplet data library size',probability = T)
| Version | Author | Date |
|---|---|---|
| 9259fc2 | DongyueXie | 2022-12-08 |
Fit a gamma distribution on \(s\), using method of moment.
rate = mean(s)/var(s)
shape = mean(s)*rate
rate[1] 6.503457shape[1] 2.258288hist(rgamma(1e5,shape=shape,rate=rate),breaks = 100,main='simulated library size',probability = T)
| Version | Author | Date |
|---|---|---|
| 9259fc2 | DongyueXie | 2022-12-08 |
Fit a inverse gamma distribution on \(s\), using method of moment.
library(invgamma)
shape = 2 + mean(s)^2/var(s)
rate = (shape-1)*mean(s)
shape[1] 4.258288rate[1] 1.131422dd = rinvgamma(1e5,shape=shape,rate=rate)
hist(rinvgamma(1e5,shape=shape,rate=rate),breaks = 100,main='simulated library size',probability = T)
| Version | Author | Date |
|---|---|---|
| 9259fc2 | DongyueXie | 2022-12-08 |
hist(dd[dd<max(s)],breaks = 100,main='simulated library size',probability = T)
| Version | Author | Date |
|---|---|---|
| 9259fc2 | DongyueXie | 2022-12-08 |
Conclusion
Gamma distribution seems not able to capture the peak of library size distribution. Inverse-gamma has heavier tails. I’ll use inverse-Gamma, but set a maximum library size(truncate it).
sessionInfo()R version 4.2.1 (2022-06-23)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.5 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.9.0
LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.9.0
locale:
[1] LC_CTYPE=C.UTF-8 LC_NUMERIC=C LC_TIME=C.UTF-8
[4] LC_COLLATE=C.UTF-8 LC_MONETARY=C.UTF-8 LC_MESSAGES=C.UTF-8
[7] LC_PAPER=C.UTF-8 LC_NAME=C LC_ADDRESS=C
[10] LC_TELEPHONE=C LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] invgamma_1.1 Matrix_1.5-1 fastTopics_0.6-142 workflowr_1.7.0
loaded via a namespace (and not attached):
[1] mcmc_0.9-7 fs_1.5.2 progress_1.2.2 httr_1.4.4
[5] rprojroot_2.0.3 tools_4.2.1 bslib_0.4.0 utf8_1.2.2
[9] R6_2.5.1 irlba_2.3.5.1 uwot_0.1.14 DBI_1.1.3
[13] lazyeval_0.2.2 colorspace_2.0-3 tidyselect_1.2.0 prettyunits_1.1.1
[17] processx_3.7.0 compiler_4.2.1 git2r_0.30.1 cli_3.4.1
[21] quantreg_5.94 SparseM_1.81 plotly_4.10.1 sass_0.4.2
[25] scales_1.2.1 SQUAREM_2021.1 quadprog_1.5-8 callr_3.7.2
[29] pbapply_1.6-0 mixsqp_0.3-48 stringr_1.4.1 digest_0.6.29
[33] rmarkdown_2.17 MCMCpack_1.6-3 pkgconfig_2.0.3 htmltools_0.5.3
[37] highr_0.9 fastmap_1.1.0 htmlwidgets_1.5.4 rlang_1.0.6
[41] rstudioapi_0.14 jquerylib_0.1.4 generics_0.1.3 jsonlite_1.8.2
[45] dplyr_1.0.10 magrittr_2.0.3 Rcpp_1.0.9 munsell_0.5.0
[49] fansi_1.0.3 lifecycle_1.0.3 stringi_1.7.8 whisker_0.4
[53] yaml_2.3.5 MASS_7.3-58 Rtsne_0.16 grid_4.2.1
[57] parallel_4.2.1 promises_1.2.0.1 ggrepel_0.9.2 crayon_1.5.2
[61] lattice_0.20-45 cowplot_1.1.1 splines_4.2.1 hms_1.1.2
[65] knitr_1.40 ps_1.7.1 pillar_1.8.1 glue_1.6.2
[69] evaluate_0.17 getPass_0.2-2 data.table_1.14.6 RcppParallel_5.1.5
[73] vctrs_0.4.2 httpuv_1.6.6 MatrixModels_0.5-1 gtable_0.3.1
[77] purrr_0.3.5 tidyr_1.2.1 assertthat_0.2.1 ashr_2.2-54
[81] cachem_1.0.6 ggplot2_3.3.6 xfun_0.33 coda_0.19-4
[85] later_1.3.0 survival_3.4-0 viridisLite_0.4.1 truncnorm_1.0-8
[89] tibble_3.1.8 ellipsis_0.3.2