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Select random sequences matched by distance to TSS and width

Hello, I have a set of genomic regions (a bed file) and I would like to get random sequences with the following characteristics:

1) same width as the original sequences 2) similar distance to a TSS (transcription start site) 3) Random sequences should not overlap with the original sequences 4) Random sequences must be located in the same chromosome as the original sequences

For aims 1,3 and 4 I have been using the function shuffle from bedtools but I need a tool that allows me also to match the sequences by distance to TSS. I was thinking of making bins of the distance to TSS of the original sequences but I don't know how to select the random sequences.

Any suggestion would be appreciated, thanks.

tss sequences random

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