Last updated: 2023-01-25

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Rmd 1322230 DongyueXie 2023-01-25 wflow_publish(“analysis/gene_variance_expression.Rmd”)

Introduction

Here we study the gene specific variance and gene expression level.

Does a gene with high expression also have high variance?

\[\Lambda = l_0f_0^T\exp(LF^T)\] \[\lambda_{ij}=l_{0i}f_{0j}\exp(\sum_k l_{ik}f_{jk}) = \exp(\log(l_{0i})+\log(f_{0j})+\sum_k l_{ik}f_{jk})\] Interpretation of \(l_0,f_0\): from a data generating perspective, \(l_0\) can be thought of the size of samples, for example, the number of counts in a cell; \(f_0\) can be thought as the size of covariates, for example the gene expression level. So the \(i,j\)th entry is the gene \(j\) expression count in cell \(i\) then we can think it as: draw its baseline expression based on \(\exp(\sum_k l_{ik}f_{jk})\), then since it’s gene \(j\), it should multiple \(f_{0j}\) and since it’s in cell \(i\), it should multiple \(l_{0i}\).

pbmc

library(fastTopics)
library(Matrix)
data(pbmc_facs)
counts = pbmc_facs$counts
flash_pbmc3k = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k/flash_pbmc3k.rds')
plot(colSums(counts/c(rowSums(counts))),flash_pbmc3k$residuals.sd^2,xlab='gene expression',ylab='gene variance',main='pbmc3k, flash',pch='.',cex=2,col='grey40')

ebpmf_pbmc3k = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k/ebpmf_pbmc3k_vga3.rds')
plot(colSums(counts/c(rowSums(counts)))/colSums(counts)*sum(counts),ebpmf_pbmc3k$sigma2,xlab='gene expression/colsums(geneexpression)',ylab='gene variance',main='pbmc3k, ebpmf, l0 f0',pch='.',cex=2,col='grey40')

ebpmf_pbmc3k_multinom = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k/ebpmf_pbmc3k_multinom_vga3.rds')
plot(colSums(counts/c(rowSums(counts))),ebpmf_pbmc3k_multinom$sigma2,xlab='gene expression',ylab='gene variance',main='pbmc3k, ebpmf, l0',pch='.',cex=2,col='grey40')

glmpca_pbmc3k_poi = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k/glmpca_pbmc3k_poi.rds')
Warning: namespace 'glmpca' is not available and has been replaced
by .GlobalEnv when processing object ''

Look at one gene that has highest estimated variance.

l0 = rowMeans(counts)
which.max(ebpmf_pbmc3k_multinom$sigma2)
[1] 8589
gene_idx = which.max(ebpmf_pbmc3k_multinom$sigma2)
plot(ebpmf_pbmc3k_multinom$sigma2_trace[,gene_idx],type='l',xlab='iteration',ylab='sigma2 trace')

plot(counts[,gene_idx]/l0,ylab='after divided by cell size',xlab='cells',main='ebpmf latent')
lines(exp(ebpmf_pbmc3k_multinom$fit_flash$flash.fit$Y[,gene_idx]))

plot((fitted(ebpmf_pbmc3k_multinom$fit_flash)[,gene_idx]),main='ebpmf fitted latent')

So the m seems to represent the latent space ok, but it seems that the fitted \(LF^t\) are all negative and the sigma2 is large.

I don’t know exactly how to make sense of it right now. If we look at the factors corresponding to this gene:

plot(ebpmf_pbmc3k_multinom$fit_flash$F.pm[gene_idx,])

All of them are effectively 0…What is gene’s called?

The glmpca latent is also plotted here for comparison:

plot(counts[,8589]/l0,ylab='after divided by cell size',xlab='cells',main='glmpca latent')
lines(exp(tcrossprod(as.matrix(glmpca_pbmc3k_poi$loadings),as.matrix(glmpca_pbmc3k_poi$factors))[,8589]))

How about fit flash on the latent representation learned by glmpca? Then what’s the relationship between gene expression and the variance?

flash_glmpca = readRDS('/project2/mstephens/dongyue/poisson_mf/pbmc3k/flash_glmpca.rds')
plot(colSums(counts/rowSums(counts)),flash_glmpca$residuals.sd^2,xlab='gene expression',ylab='gene variance',main='pbmc3k, flash fit on glmpca',pch='.',cex=2,col='grey40')

droplet

load('/project2/mstephens/pcarbo/git/fastTopics-experiments/data/droplet.RData')
flash_droplet = readRDS('/project2/mstephens/dongyue/poisson_mf/droplet/flash_droplet.rds')
plot(colSums(counts/c(rowSums(counts))),flash_droplet$residuals.sd^2,xlab='gene expression',ylab='gene variance',main='droplet, flash',pch='.',cex=2,col='grey40')

ebpmf_droplet = readRDS('/project2/mstephens/dongyue/poisson_mf/droplet/ebpmf_droplet_vga3.rds')
f0 = colSums(counts)
plot(colSums(counts/rowSums(counts))/f0*sum(counts),ebpmf_droplet$sigma2,xlab='gene expression/colsums(geneexpression)',ylab='gene variance',main='droplet, ebpmf, l0 f0',pch='.',cex=2,col='grey40')

plot(colSums(counts/rowSums(counts)),ebpmf_droplet$sigma2,xlab='gene expression',ylab='gene variance',main='droplet, ebpmf, l0 f0',pch='.',cex=3,col='grey40')


sessionInfo()
R version 3.6.1 (2019-07-05)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: CentOS Linux 7 (Core)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] Matrix_1.5-3       fastTopics_0.6-100 workflowr_1.6.2   

loaded via a namespace (and not attached):
 [1] httr_1.4.1         tidyr_1.1.0        splines_3.6.1     
 [4] jsonlite_1.6       viridisLite_0.3.0  RcppParallel_4.4.3
 [7] assertthat_0.2.1   horseshoe_0.2.0    mixsqp_0.3-17     
[10] deconvolveR_1.2-1  yaml_2.2.0         progress_1.2.2    
[13] ggrepel_0.9.1      ebnm_1.0-9         pillar_1.4.2      
[16] lattice_0.20-38    quantreg_5.41      glue_1.3.1        
[19] quadprog_1.5-7     digest_0.6.20      promises_1.0.1    
[22] colorspace_1.4-1   cowplot_1.1.1      htmltools_0.3.6   
[25] httpuv_1.5.1       pkgconfig_2.0.2    invgamma_1.1      
[28] SparseM_1.77       purrr_0.3.4        scales_1.1.0      
[31] whisker_0.3-2      later_0.8.0        Rtsne_0.15        
[34] MatrixModels_0.4-1 git2r_0.26.1       tibble_2.1.3      
[37] ggplot2_3.3.5      ashr_2.2-50        pbapply_1.4-0     
[40] lazyeval_0.2.2     magrittr_1.5       crayon_1.3.4      
[43] mcmc_0.9-6         evaluate_0.14      fs_1.3.1          
[46] MASS_7.3-51.4      truncnorm_1.0-8    tools_3.6.1       
[49] data.table_1.14.2  prettyunits_1.0.2  softImpute_1.4    
[52] hms_0.5.3          lifecycle_0.1.0    stringr_1.4.0     
[55] MCMCpack_1.4-5     plotly_4.9.0       trust_0.1-7       
[58] munsell_0.5.0      flashier_0.2.32    irlba_2.3.3       
[61] compiler_3.6.1     rlang_0.4.10       grid_3.6.1        
[64] htmlwidgets_1.3    rmarkdown_1.13     gtable_0.3.0      
[67] R6_2.4.0           knitr_1.23         dplyr_0.8.3       
[70] uwot_0.1.11        rprojroot_2.0.2    stringi_1.4.3     
[73] parallel_3.6.1     SQUAREM_2017.10-1  Rcpp_1.0.5        
[76] vctrs_0.3.1        tidyselect_1.1.0   xfun_0.8          
[79] coda_0.19-3