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Comparison of RPKM (reads per kilobase per million) and TPM (transcripts per million).
# RPKM versus TPM
#
# RPKM and TPM are both normalized for library size and gene length.
#
# RPKM is not comparable across different samples.
#
# For more details, see: http://blog.nextgenetics.net/?e=51
rpkm <- function(counts, lengths) {
rate <- counts / lengths
rate / sum(counts) * 1e6
}
tpm <- function(counts, lengths) {
rate <- counts / lengths
rate / sum(rate) * 1e6
}
genes <- data.frame(
Gene = c("A","B","C","D","E"),
Length = c(100, 50, 25, 5, 1)
)
counts <- data.frame(
S1 = c(80, 10, 6, 3, 1),
S2 = c(20, 20, 10, 50, 400)
)
rpkms <- apply(counts, 2, function(x) rpkm(x, genes$Length))
tpms <- apply(counts, 2, function(x) tpm(x, genes$Length))
genes
# Gene Length
# 1 A 100
# 2 B 50
# 3 C 25
# 4 D 5
# 5 E 1
counts
# S1 S2
# 1 80 20
# 2 10 20
# 3 6 10
# 4 3 50
# 5 1 400
rpkms
# S1 S2
# [1,] 8000 4e+02
# [2,] 2000 8e+02
# [3,] 2400 8e+02
# [4,] 6000 2e+04
# [5,] 10000 8e+05
tpms
# S1 S2
# [1,] 281690.14 486.618
# [2,] 70422.54 973.236
# [3,] 84507.04 973.236
# [4,] 211267.61 24330.900
# [5,] 352112.68 973236.010
# Sample means should be equal.
colSums(rpkms)
# S1 S2
# 28400 822000
colSums(tpms)
# S1 S2
# 1e+06 1e+06
colMeans(rpkms)
# S1 S2
# 5680 164400
colMeans(tpms)
# S1 S2
# 2e+05 2e+05
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