Simulating protein pixel intensities in fibre sections with freezing artefacts

freeze.R

# A possible problem with freezing artefacts and correlations
# Need MASS library to sample from multivariate normal distribution (correlated datasets)
library(MASS)

R_good = matrix(c(0.55, 0.5,
              0.5, 0.55), 
            nrow = 2, ncol = 2, byrow = TRUE)

R_bad = matrix(c(1, 0.5,
              0.5, 1), 
            nrow = 2, ncol = 2, byrow = TRUE)

R_hole = matrix(c(0.1, 0.05,
              0.05, 0.1), 
            nrow = 2, ncol = 2, byrow = TRUE)

# Simulate fibre where proteins are well correlated
dat_good = MASS::mvrnorm(1000, mu = c(X = 10, Y = 10), Sigma = R_good)
# Simulate fibre where proteins are poorly correlated
dat_bad = MASS::mvrnorm(1000, mu = c(X = 10, Y = 10), Sigma = R_bad)
# Simulate poor correlation between proteins within the "missing" pixels of a fibre with a hole caused by freezing artefact
dat_hole = MASS::mvrnorm(1000, mu = c(X = 2, Y = 2), Sigma = R_hole)

# Simulate a fibre with a mixture of some normal pixels (where protein correlation is poor) 
# and some pixels with freezing artefacts
dat_mix = rbind(dat_bad[1:500,],dat_hole[1:500,])

op = par(mfrow=c(2,2))
 plot(dat_good[,1],dat_good[,2],xlab="log(VDAC1)",ylab="log(NDUFB8)",main=paste("Good correlation:",formatC(cor(dat_good[,1],dat_good[,2]),3)),xlim=c(0,15),ylim=c(0,15),pch=16,col=rgb(0,0,0,0.1))
 plot(dat_bad[,1],dat_bad[,2],xlab="log(VDAC1)",ylab="log(NDUFB8)",main=paste("Bad correlation:",formatC(cor(dat_bad[,1],dat_bad[,2]),3)),xlim=c(0,15),ylim=c(0,15),pch=16,col=rgb(0,0,0,0.1))
 plot(dat_hole[,1],dat_hole[,2],xlab="log(VDAC1)",ylab="log(NDUFB8)",main=paste("Hole correlation:",formatC(cor(dat_hole[,1],dat_hole[,2]),3)),xlim=c(0,15),ylim=c(0,15),pch=16,col=rgb(0,0,0,0.1))
 plot(dat_mix[,1],dat_mix[,2],xlab="log(VDAC1)",ylab="log(NDUFB8)",main=paste("Mix correlation:",formatC(cor(dat_mix[,1],dat_mix[,2]),3)),xlim=c(0,15),ylim=c(0,15),pch=16,col=rgb(0,0,0,0.1))
par(op)