simulateSC {noise}

Simulate single-cell expression levels of two reporters

Description

This function simulates expression levels of two reporters across single cells, mimicking the two-reporter assay. The hierarchical model described in Fu and Pachter (2016) is used for simulation. We further make the simplifying assumption that intrinsic noise is the same across cells.

Usage

simulateSC(n = 1000, intrinsic = 0.7, extrinsic = 0.8, mean = 1)

Arguments

n

Number of single cells (sample size).

intrinsic

Scalar. The (unscaled) intrinsic noise (or within-cell variability), denoted by \sigma^2 (equation 8) in Fu and Pachter (2016).

extrinsic

Scalar. The (unscaled) extrinsic noise (or between-cell variability), denoted by \sigma^2_\mu (equation 9) in Fu and Pachter (2016).

mean

Scalar. The overall mean of expression level, denoted by \mu (equation 6) in Fu and Pachter (2016).

Value

A data frame of two columns and n rows. Each column contains the expression levels of a reporter. Each row is a single cell.

Author(s)

Audrey Q. Fu

References

Fu, A. Q. and Pachter, L. (2016). Estimating intrinsic and extrinsic noise from single-cell gene expression measurements. arXiv:1601.03334.

See Also

computeIntrinsicNoise, computeExtrinsicNoise.

Examples

# simulation #1

# simulate 500 data sets
n.simu <- 500

# true intrinsic and extrinsic noise
int.true <- 0.7
ext.true <- 0.8

# create matrices to hold estimated intrinsic and extrinsic noise
# using different estimators
int.simu.mtx <- matrix (0, nrow=n.simu, ncol=8)
ext.simu.mtx <- matrix (0, nrow=n.simu, ncol=4)

for (i in 1:n.simu) {
    n <- 1000
    simu <- simulateSC (n=n, intrinsic=int.true, extrinsic=ext.true, mean=1)
    
    int.simu.mtx[i,] <- c(unlist (computeIntrinsicNoise (simu[,1], simu[,2])), 
        cor (simu[,1], simu[,2]))
    ext.simu.mtx[i,] <- unlist (computeExtrinsicNoise (simu[,1], simu[,2]))
    
}

# add column names to simulation estimates
colnames (int.simu.mtx) <- c("ELSS", "unbiasedGeneral", "unbiasedEqualMean", 
    "minMSEGeneral", "minMSEEqualMean", "asymptoticGeneral", 
    "asymptoticEqualMean", "cor")
colnames (ext.simu.mtx) <- c("ELSS", "unbiased", "minMSE", "asymptotic")


# simulation #2

# simulate 500 data sets
n.simu <- 500

# true intrinsic and extrinsic noise
int.true <- 0.7
ext.true <- 0.8

# use true correlation for the min-MSE estimates of extrinsic noise
true.cor <- ext.true / (ext.true + int.true)

# create matrices to hold estimated intrinsic and extrinsic noise
# using different estimators
int.simu.mtx <- matrix (0, nrow=n.simu, ncol=8)
ext.simu.mtx <- matrix (0, nrow=n.simu, ncol=4)
ext.simu.mtx.2 <- matrix (0, nrow=n.simu, ncol=4)

for (i in 1:n.simu) {
    n <- 50
    simu <- simulateSC (n=n, intrinsic=int.true, extrinsic=ext.true, mean=1)
    
    int.simu.mtx[i,] <- c(unlist (computeIntrinsicNoise (simu[,1], simu[,2])), 
      cor (simu[,1], simu[,2]))
    ext.simu.mtx[i,] <- unlist (computeExtrinsicNoise (simu[,1], simu[,2]))
    ext.simu.mtx.2[i,] <- c(unlist (computeExtrinsicNoiseKnownCor (simu[,1], 
      simu[,2], true.cor)))
}

# add column names to simulation estimates
colnames (int.simu.mtx) <- c("ELSS", "unbiasedGeneral", "unbiasedEqualMean", 
    "minMSEGeneral", "minMSEEqualMean", "asymptoticGeneral", 
    "asymptoticEqualMean", "cor")
colnames (ext.simu.mtx) <- c("ELSS", "unbiased", "minMSE", "asymptotic")
colnames (ext.simu.mtx.2) <- c("ELSS", "unbiased", "minMSE", "asymptotic")

# compute the MSE of estimates
computeMSE <- function (a, t) {return (mean((a-t)^2))}
apply (int.simu.mtx[,1:7], 2, computeMSE, t=int.true)
apply (ext.simu.mtx, 2, computeMSE, t=ext.true)
apply (ext.simu.mtx.2, 2, computeMSE, t=ext.true)