The purpose of the "standard" pipeline to which you refer is to decide if a gene is differentially expressed between two or more conditions. In this analysis, it is necessary to have replicates, because before we can say if a gene is different between two conditoins, one must first know how much it varies within one condition.

However, this is not the question that you are asking.

Firstly I'd like to say that I don't really believe in the distinction between "expressed" and "not-expressed". I believe that all genes are expressed to some extent in all cell types, its just a question of how rarely a transcript is made.

With that in mind, I think there are two ways you can proceed:

• You can look if a particular tissue is an "outlier" compared to other tissues. This would mean the calculation of robust Z score for each gene in each sample: z_ij = (TPM_ij - median(TPMi))/MAD(TPMi), were z_ij is the z score of the ith gene in the jth tissue, and median(TPMi) is the medium TPM for gene i and MAD(TPMi) is the median absolute deviation of the TPM of gene i. Ideally you'd want to think of some rotation or bootstrapping method for calculating an FDR on this.

• Look to see if a particular gene had a higher TPM than would be expected from backgournd genomic sequence. This would mean shifting your transcripts into non-expressed genomic space and quantifying these "not-transcripts" to produce a distribution of background TPMs, and then calculating the quantile position of each gene relative to that distribution. See my answers to a similar question on bioinformatics.stackexchange.com: https://bioinformatics.stackexchange.com/questions/687/what-methods-are-available-to-find-a-cutoff-value-for-non-expressed-genes-in-rna/712#712