I think you are mixing two different concepts. Paired-end sequencing means that you obtain two reads from a given DNA fragment, one from each end, that may or not overlap depending of its size and the length of the reads. Directional sequencing means that, after sequencing, you know from which of both DNA strands a given RNA molecule is transcribed. This is done by adding two adaptors, different in sequence, to each 5' and 3' ends of every RNA molecule.
Bisulfite treatment of DNA and subsequent PCR amplification can give rise to four(bisulfite converted) strands for a given locus. Depending on the adapters used,BS-Seq libraries can be constructed in two different ways:
(a) If a library is directional, only reads which are (bisulfite converted) versions of the original top strand (OT)or the original bottom strand (OB) will be sequenced.Even though the strands complementary to OT (CTOT) and OB (CTOB) are generated in the BS-PCR step they will not be sequencedas they carry the wrong kind of adapter at their 5’-end.
(b) Alternatively, BS-Seq libraries can be constructed so that all four different strands generated in the BS-PCR can and will end up in the sequencing librarywith roughly the same likelihood.In this case all four strands (OT,CTOT, OB, CTOB) can produce valid alignmentsand the library is called non-directional.
To summarise this again: alignments to the original top strand or to the strand complementary to the original top strand (OT and CTOT) will both yield methylation information for cytosines on the top strand. Alignments to the original bottom strand or to the strand complementary to the original bottom strand (OB and CTOB) will both yield methylation information for cytosines on the bottom strand, i.e. they will appear to yield methylation information for G positions on the top strand of the reference genome.
@Ángel Zaballos, so it means directional sequencing for dna can not be performed because we dont know which read come from which strand and all reads cant be sequenced from any of the strand.
That's right, unless, as indicated above by Gaurauv Kadu, you are able to label by some means one of the strands specifically, for example by BS treatment.