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The Nextera mate pair libraries involve circularising large (up to 12kb with a median of ~4kb) DNA fragments with the junction adapter:

    CTGTCTCTTATACACATCT+AGATGTGTATAAGAGACAG

this circularised DNA is then fragmented again into smaller typical PE sized chunks (several hundred bp). The chunks containing this adapter are then sequenced. DNA on either side of the adapter sequence will be in Reverse-Forward orientation with a mate-pair insert size. The can adapter occur (roughly) uniformly across the shorter fragment. We now enumerate the possible outcomes of the adapter location, note we use arbitrarily short read lengths for readability, in practice 2 x 151bp (or larger) lengths can be expected.

For example we will commonly observe read-pairs containing the partial or whole adapter sequence (we use X to denote true DNA from the left of the adapter and Y for the right):

R1--------------------------------------------------->
  XXXXXXXXXXXXXXXXXXXXXXXXCTGTCTCTTATACACATCTAGATGTGTATAAGAGACAGYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
                                                                                                  <---------------------------------------------------R2

There are cases where the adapter is not observed either because

 1. the reads were not long enough to reach the adapter:

R1--------------------------------------------------->
  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXCTGTCTCTTATACACATCTAGATGTGTATAAGAGACAGYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
                                                                                                  <---------------------------------------------------R2

 2. the read is a PE contaminant and had no adapter:

R1--------------------------------------------------->
  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
                                                                                                  <---------------------------------------------------R2

the first case is far more frequent, but there can be a small amount of contamination from PE reads.

Another thing to consider is that the adapter may occur very early in one of the reads, meaning the preceding DNA (if any) is far to short to be of use for assembly:

R1--------------------------------------------------->
  XXCTGTCTCTTATACACATCTAGATGTGTATAAGAGACAGYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
                                                                                                  <---------------------------------------------------R2

Clearly the artificial DNA sequence in the adapter needs to be removed before any analysis. We now describe our adapter trimming routine, which attempts to maximise the amount of genomic DNA retained. We achieve this by creating four "virtual" libraries:

1. MP: Known mate-pair (long insert, RF orientation)
2. UNKNOWN: Unknown (but likely mate-pair with long insert RF orientation)
3. PE: Paired-end (short insert, FR orientation)
4. SE: Single read (read has no mate)