Aleks,

I used Epicentre ScriptSeq strand-specific library construction protocol, which I assume, produces a second-strand library.

This an assumption probably worth verifying before going further. The Tophat documentation may be helpful as well: http://tophat.cbcb.umd.edu/manual.html

When I set FR option to "second strand" and run TopHat and Cufflinks it results in confusing transcript orientation. Cufflinks-assembled transcript with multiple exons are oriented as expected. However, transcripts that entirely reside in one exon/intron or intergenic region are labeled in an opposite way. If TopHat accepted hits track contains negative-strand reads (colored red), transcript is labeled as "positive" and vice versa. An example is shown in the attached screenshot. Both transcripts TCONS_00000014 and TCONS_00000015 were mapped to "+" strand, though reads that represent them had been mapped to "-" strand.

Is there a way to solve this issue?

I haven't heard of or encountered this problem before. Your best bet is probably to email the Tophat/Cufflinks authors and see if they can shed light on your issues: tophat.cufflinks@gmail.com Good luck, J.