where can I download a file indicating the distance of each Fantom5 enhancer to its associated TSS?
Have you seen this file? There is also sets of enhancer and TSS-enhancer association data available for download. The latter was based on the An atlas of active enhancers across human cell types and tissues paper. Ensembl has also got the TSS and enhancers from Fantom5 as other Regulatory data. The Fantom5 TSSs can be used in combination with the Ensembl Regulation build to find out how far the TSS is from an enhancer predicted from the ENCODE, Blueprint and Roadmap project (human and mouse only though). This is what you can see in their browser view as an example.
Unfortunatly I dont think you can - mostly because the "association" to an enhancer is not something that is clear how to best do.
So you will have to first deside which enhancers and TSSs you define as associated and then the rest should be easy using fx GenomicRanges in R with the distance() function.
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