In a biochemistry course I'm taking, the lecturer emphasised that there are 10 possible base pair steps; I've included a screenshot of a slide stating this. This confuses me, because I cannot work out why it's not 16; why are the 6 greyed out in the image not allowed (for example, CG stacked on CG counts, but GC stacked on GC doesn't)? TA|AT is listed as distinct from AT|TA, so it's not that the greyed ones are redundant. I've found a couple of papers mentioning that there are 10 base steps, but not why. (I can't get hold of the lecturer.)
2$\begingroup$ CG stacked on CG and GC stacked on GC are the same step with the chain turned by $180^\circ$, so there is no need to count it (and other similar steps) twice. $\endgroup$– Roger VadimDec 22, 2020 at 11:09
1$\begingroup$ @Vadim, would you mind expanding your comment as an answer? $\endgroup$– acvillDec 22, 2020 at 14:49
Unlike RNA, where the sense of the molecule is unique, DNA is double stranded, with the two strands having the opposite sense. In the sense of chemical stability it odesn't matter, which sense is considered positive, and which is negative.
Thus, if we consider a base pair step WX|YZ, we have Y folowing W on the positive sense strand (W->Y), and X following Z in the negative sense (antisense) strand (Z -> X). This means that, if we labeled the strands differently, we would have Z->X on the positive strand and W->Y on the negative one, i.e., we would have base pair step ZY|XW. I.e., the general symmetry rule is $$ WX|YZ \rightarrow ZY|XW $$
In particular, this means that CG|CG is identical with GC|GC, whereas TA|AT is identical with itself, rather than with AT|TA.
Visually, this symmetries are obtained by rotating the image of the base pair step by 180 degrees, as can be readily seen in the image provided in the question.
4$\begingroup$ Maybe worth pointing out that OPs own image demonstrates why there is 10. It shows the 16 'possibilities' and grays out those that are duplicate via rotation. With the picture in hand you can just... count. $\endgroup$– Bryan Krause ♦Dec 23, 2020 at 14:54