Hello all,

I understand the differences between RPKM, which normalizes for read depth and then gene length; FPKM, the same thing as RPKM but does not count reads twice if both came from the same fragment; and TPM which normalizes for gene length, then read length - allowing comparison of read count proportion between samples.

However, I have not come across any literature on whether the same principle of not counting reads twice from the same fragment (FPKM) has been applied to the TPM method. I don't doubt that this is done, I would just like to know how.

Thanks
Yes, the TPM measure accounts for fragments.  In a single-end library, each fragment is represented by a sequencing read, while in a paired-end library, each fragment is represented by a read pair.  If `r_i` is the number of fragments mapping to transcript `t_i` then we can define 

`TPM_i = 1,000,000 * [(r_i / l_i) /  (Σ_j (r_j / l_j))]`

where `l_i` is the *effective length* of transcript `i`.  The denominator normalizes for the length scaled abundance of all transcripts in this sample.  In a single-end library `r_i` represents the number of reads mapping to transcript `t_i`, while in a paired-end library, it represents the number of read pairs (ignoring, for simplicity, that an orphaned read is representative of the entire pair for this purpose).