Last updated: 2020-02-17

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First we load MLE estimates along with genotypes for top 235 genes and regression model outputs.

library(rlist)
Warning: package 'rlist' was built under R version 3.5.3
estimates<-list.load("C:/Users/Moonkin/Documents/GitHub/Thesis_single_RNA/analysis/estimates_for_235_genes.rds")
regression<-read.table("C:/Users/Moonkin/Documents/GitHub/Thesis_single_RNA/analysis/regression_for_235_genes.txt", header = T, sep = "\t")
mean_estimates=matrix(, nrow = 235, ncol = 3)
median_estimates=matrix(, nrow = 235, ncol = 3)

for (i in 1:235){
  current<-estimates[[i]][,1:3]
  mean_estimates[i,1]<-mean(as.numeric(current[,1]))
  mean_estimates[i,2]<-mean(as.numeric(current[,2]))
  mean_estimates[i,3]<-mean(as.numeric(current[,3]))
  median_estimates[i,1]<-median(as.numeric(current[,1]))
  median_estimates[i,2]<-median(as.numeric(current[,2]))
  median_estimates[i,3]<-median(as.numeric(current[,3]))
}
library(ggplot2)
Warning: package 'ggplot2' was built under R version 3.5.1
mean_estimates=data.frame(mean_estimates)
colnames(mean_estimates)<-c("kon","koff","kr")
ggplot(mean_estimates, aes(x=kon, y=koff))+geom_point()+labs(y = "k off",x="k on")

median_estimates=data.frame(median_estimates)
colnames(median_estimates)<-c("kon","koff","kr")
ggplot(median_estimates, aes(x=kon, y=koff))+geom_point()+labs(y = "k off",x="k on")

filtered_regression<-regression[which(median_estimates$koff<=10), ]
par(mfrow=c(1,3))
U=seq(0, 1, length.out = 112)
U=U[2:112]

plot(-log(U,base=10),-log(sort(filtered_regression$k_on_slope_p),base=10), main="k_on", xlab="Expected -log(p)", ylab="Observed  -log(p)")
lines(-log(U,base=10),-log(U,base=10))

plot(-log(U,base=10),-log(sort(filtered_regression$k_off_slope_p),base=10), main="k_off", xlab="Expected -log(p)", ylab="Observed  -log(p)")
lines(-log(U,base=10),-log(U,base=10))

plot(-log(U,base=10),-log(sort(filtered_regression$k_r_slope_p),base=10), main="k_r", xlab="Expected -log(p)", ylab="Observed  -log(p)")
lines(-log(U,base=10),-log(U,base=10))

filtered_regression[p.adjust(filtered_regression$k_on_slope_p, method = "BH" , n = length(filtered_regression$k_off_slope_p))<0.05,]
             gene k_on_int k_on_slope   k_on_int_p k_on_slope_p
2 ENSG00000197728 1.405574   2.012058 3.115331e-07  2.37079e-06
  k_on_int_se k_on_slope_se k_off_int k_off_slope k_off_int_p
2   0.2388814     0.3785599 -14.78051    193.1598   0.4750069
  k_off_slope_p k_off_int_se k_off_slope_se  k_r_int k_r_slope k_r_int_p
2   2.59334e-07     20.53759        32.5463 18.51257  120.4671 0.2022224
   k_r_slope_p k_r_int_se k_r_slope_se
2 2.457675e-06   14.32994     22.70893
filtered_regression[p.adjust(filtered_regression$k_off_slope_p, method = "BH" , n = length(filtered_regression$k_off_slope_p))<0.05,]
               gene k_on_int k_on_slope   k_on_int_p k_on_slope_p
2   ENSG00000197728 1.405574  2.0120582 3.115331e-07 2.370790e-06
147 ENSG00000151131 3.872758 -0.4931009 2.802306e-09 1.601740e-01
209 ENSG00000163811 5.073687 -1.0143604 1.708668e-13 2.073266e-03
    k_on_int_se k_on_slope_se k_off_int k_off_slope  k_off_int_p
2     0.2388814     0.3785599 -14.78051    193.1598 4.750069e-01
147   0.5391907     0.3459728 242.91804   -124.9144 3.696489e-05
209   0.5115814     0.3125421 409.08184   -179.6398 1.520882e-06
    k_off_slope_p k_off_int_se k_off_slope_se   k_r_int k_r_slope
2    2.593340e-07     20.53759       32.54630  18.51257  120.4671
147  6.714828e-04     53.73867       34.48152 533.49299 -270.0376
209  2.730323e-04     75.19260       45.93766 675.37453 -255.0446
       k_r_int_p  k_r_slope_p k_r_int_se k_r_slope_se
2   2.022224e-01 2.457675e-06   14.32994     22.70893
147 1.191089e-05 3.545150e-04  109.93939     70.54282
209 1.430224e-04 1.411996e-02  164.25906    100.35132
filtered_regression[p.adjust(filtered_regression$k_r_slope_p, method = "BH" , n = length(filtered_regression$k_off_slope_p))<0.05,]
               gene k_on_int k_on_slope   k_on_int_p k_on_slope_p
2   ENSG00000197728 1.405574  2.0120582 3.115331e-07  2.37079e-06
147 ENSG00000151131 3.872758 -0.4931009 2.802306e-09  1.60174e-01
    k_on_int_se k_on_slope_se k_off_int k_off_slope  k_off_int_p
2     0.2388814     0.3785599 -14.78051    193.1598 4.750069e-01
147   0.5391907     0.3459728 242.91804   -124.9144 3.696489e-05
    k_off_slope_p k_off_int_se k_off_slope_se   k_r_int k_r_slope
2    2.593340e-07     20.53759       32.54630  18.51257  120.4671
147  6.714828e-04     53.73867       34.48152 533.49299 -270.0376
       k_r_int_p  k_r_slope_p k_r_int_se k_r_slope_se
2   2.022224e-01 2.457675e-06   14.32994     22.70893
147 1.191089e-05 3.545150e-04  109.93939     70.54282
U=seq(0,30,by=0.01)
hist(filtered_regression$k_on_slope^2/filtered_regression$k_on_slope_se^2, breaks=100,freq = FALSE)
lines(U,dchisq(U,1))

hist(filtered_regression$k_off_slope^2/filtered_regression$k_off_slope_se^2, breaks=100,freq = FALSE)
lines(U,dchisq(U,1))

hist(filtered_regression$k_r_slope^2/filtered_regression$k_r_slope_se^2, breaks=100,freq = FALSE)
lines(U,dchisq(U,1))

ks.test(filtered_regression$k_on_slope^2/filtered_regression$k_on_slope_se^2,dchisq(U,1))

    Two-sample Kolmogorov-Smirnov test

data:  filtered_regression$k_on_slope^2/filtered_regression$k_on_slope_se^2 and dchisq(U, 1)
D = 0.80329, p-value < 2.2e-16
alternative hypothesis: two-sided
ks.test(filtered_regression$k_off_slope^2/filtered_regression$k_off_slope_se^2,dchisq(U,1))

    Two-sample Kolmogorov-Smirnov test

data:  filtered_regression$k_off_slope^2/filtered_regression$k_off_slope_se^2 and dchisq(U, 1)
D = 0.76561, p-value < 2.2e-16
alternative hypothesis: two-sided
ks.test(filtered_regression$k_r_slope^2/filtered_regression$k_r_slope_se^2,dchisq(U,1))

    Two-sample Kolmogorov-Smirnov test

data:  filtered_regression$k_r_slope^2/filtered_regression$k_r_slope_se^2 and dchisq(U, 1)
D = 0.77121, p-value < 2.2e-16
alternative hypothesis: two-sided

Here the scatterplot of estimates vs genotype for ENSG00000197728 gene, the only one that with all slopes coefficients being significant at 0.05 level after BH adjustment.

ENSG00000197728=estimates[[2]]
ENSG00000151131=estimates[[147]]
ENSG00000163811=estimates[[209]]

par(mfrow=c(1,3))
model1<- lm(k_on~genotype, data=ENSG00000197728)
model2<- lm(k_off~genotype, data=ENSG00000197728)
model3<- lm(k_r~genotype, data=ENSG00000197728)

plot(ENSG00000197728$genotype,ENSG00000197728$k_on, xlab="genotype", ylab="k_on estimate", main= "k_on scatterplot by genotype")
abline(model1, col="red")

plot(ENSG00000197728$genotype,ENSG00000197728$k_off, xlab="genotype", ylab="k_off estimate", main= "k_off scatterplot by genotype")
abline(model2, col="red")

plot(ENSG00000197728$genotype,ENSG00000197728$k_r, xlab="genotype", ylab="k_r estimate", main= "k_r scatterplot by genotype")
abline(model3, col="red")

print(summary(lm(k_on~genotype, data=ENSG00000197728)))

Call:
lm(formula = k_on ~ genotype, data = ENSG00000197728)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.2954 -0.4779 -0.2745  0.2301  6.7212 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   1.4056     0.2389   5.884 3.12e-07 ***
genotype      2.0121     0.3786   5.315 2.37e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.546 on 51 degrees of freedom
Multiple R-squared:  0.3565,    Adjusted R-squared:  0.3438 
F-statistic: 28.25 on 1 and 51 DF,  p-value: 2.371e-06
print(summary(lm(k_off~genotype, data=ENSG00000197728)))

Call:
lm(formula = k_off ~ genotype, data = ENSG00000197728)

Residuals:
    Min      1Q  Median      3Q     Max 
-370.79   15.02   15.71   16.62  628.46 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   -14.78      20.54  -0.720    0.475    
genotype      193.16      32.55   5.935 2.59e-07 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 132.9 on 51 degrees of freedom
Multiple R-squared:  0.4085,    Adjusted R-squared:  0.3969 
F-statistic: 35.22 on 1 and 51 DF,  p-value: 2.593e-07
print(summary(lm(k_r~genotype, data=ENSG00000197728)))

Call:
lm(formula = k_r ~ genotype, data = ENSG00000197728)

Residuals:
    Min      1Q  Median      3Q     Max 
-253.97   -0.49    5.03   11.63  464.30 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)    18.51      14.33   1.292    0.202    
genotype      120.47      22.71   5.305 2.46e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 92.73 on 51 degrees of freedom
Multiple R-squared:  0.3556,    Adjusted R-squared:  0.3429 
F-statistic: 28.14 on 1 and 51 DF,  p-value: 2.458e-06
print(summary(lm(k_off~genotype, data=ENSG00000151131)))

Call:
lm(formula = k_off ~ genotype, data = ENSG00000151131)

Residuals:
    Min      1Q  Median      3Q     Max 
-224.66 -111.19    8.66   13.75  757.08 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   242.92      53.74   4.520  3.7e-05 ***
genotype     -124.91      34.48  -3.623 0.000671 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 153.3 on 51 degrees of freedom
Multiple R-squared:  0.2047,    Adjusted R-squared:  0.1891 
F-statistic: 13.12 on 1 and 51 DF,  p-value: 0.0006715
print(summary(lm(k_r~genotype, data=ENSG00000151131)))

Call:
lm(formula = k_r ~ genotype, data = ENSG00000151131)

Residuals:
    Min      1Q  Median      3Q     Max 
-473.08 -228.95   27.97   40.47 1660.48 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   533.49     109.94   4.853 1.19e-05 ***
genotype     -270.04      70.54  -3.828 0.000355 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 313.7 on 51 degrees of freedom
Multiple R-squared:  0.2232,    Adjusted R-squared:  0.208 
F-statistic: 14.65 on 1 and 51 DF,  p-value: 0.0003545
print(summary(lm(k_off~genotype, data=ENSG00000163811)))

Call:
lm(formula = k_off ~ genotype, data = ENSG00000163811)

Residuals:
    Min      1Q  Median      3Q     Max 
-228.49  -74.45  -44.73   49.12  714.02 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   409.08      75.19   5.440 1.52e-06 ***
genotype     -179.64      45.94  -3.911 0.000273 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 211.7 on 51 degrees of freedom
Multiple R-squared:  0.2307,    Adjusted R-squared:  0.2156 
F-statistic: 15.29 on 1 and 51 DF,  p-value: 0.000273

sessionInfo()
R version 3.5.0 (2018-04-23)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 17763)

Matrix products: default

locale:
[1] LC_COLLATE=English_United States.1252 
[2] LC_CTYPE=English_United States.1252   
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.1252    

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

other attached packages:
[1] ggplot2_3.1.0 rlist_0.4.6.1

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.2        compiler_3.5.0    pillar_1.4.2     
 [4] later_0.8.0       git2r_0.26.1      highr_0.7        
 [7] plyr_1.8.4        workflowr_1.5.0   tools_3.5.0      
[10] digest_0.6.17     evaluate_0.11     tibble_2.1.3     
[13] gtable_0.2.0      pkgconfig_2.0.2   rlang_0.4.2      
[16] yaml_2.2.0        withr_2.1.2       stringr_1.3.1    
[19] dplyr_0.8.3       knitr_1.20        fs_1.3.1         
[22] rprojroot_1.3-2   grid_3.5.0        tidyselect_0.2.5 
[25] glue_1.3.0        data.table_1.11.8 R6_2.3.0         
[28] rmarkdown_1.10    purrr_0.2.5       magrittr_1.5     
[31] backports_1.1.2   scales_1.0.0      promises_1.0.1   
[34] htmltools_0.3.6   assertthat_0.2.0  colorspace_1.3-2 
[37] httpuv_1.5.1      labeling_0.3      stringi_1.1.7    
[40] lazyeval_0.2.1    munsell_0.5.0     crayon_1.3.4