<p>I have some fastq files that contain a sequence length distribution that are not uniform. Most sequences are trimmed at 75bp with ~3/8ths at 74bp ~1/4th at 73bp and trailing off all the way to the 34bp length. This closely resembles an exponential curve. Anyway, I am curious if the varying lengths will cause problems when attempting to use TopHat2 to align to a reference genome.</p>

Tophat2 supports variable read-length. So using Tophat2 won't be an issue. Personally, I don't use reads with length less than 40 nt. I don't think reads with variable read lengths will cause any problem with the interpretation of results generated from Topaht2.