# Simulate single-cell expression levels of two reporters 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. ```r 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). ## Returns A data frame of two columns and $n$ rows. Each column contains the expression levels of a reporter. Each row is a single cell. ## References Fu, A. Q. and Pachter, L. (2016). Estimating intrinsic and extrinsic noise from single-cell gene expression measurements. arXiv:1601.03334. ## Author(s) Audrey Q. Fu ## See Also `computeIntrinsicNoise`, `computeExtrinsicNoise`. ## Examples ```r # 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) ```

simulateSC function