So they're interested in measuring how Dnmt3a binding and formation of the fibers affects the rate of dissociation of Dnmt3a from the DNA. Condition 1 tests this by incubating first with biotinylated DNA and then with non-biotinylated DNA. If fiber formation results in a slow off rate of Dnmt3a from DNA, then the biotinylated DNA will get methylated and the non-biotinylated DNA will not because the all the Dnmt3a will be bound by the biotinylated DNA and if the off rate is slow, the subsequent incubation with non-biotinylated DNA won't do anything - the Dnmt3a will remain bound to the biotinylated DNA and this is what will get methylated.
But say you do this experiment and find that your scintillation counter gives you 100 counts/s. What does that mean? It means nothing. It's just a number. You need something to compare that number to. So you do controls and baselines. Condition 2 is one of those. In condition 2, you incubate first with non-biotinylated DNA and then with biotinylated DNA. So applying the same logic, it's going to be the non-biotinylated DNA that gets methylated if the off rate is slow. Since non-biotinylated DNA won't bind to avidin, it's going to get washed off the column and when you pass your scintillation counter over it, you should get no reading. But let's say you get 2 counts/s because the off-rate is slow but not zero and so you get some exchange of non-biotinylated DNA with biotinylated DNA bound to Dnmt3a. Now you have something to compare to. You have two numbers.
But what if for some reason your Dnmt3a has different binding constants for biotinylated DNA and non-biotinylated DNA? That would confound your results because now, you can't assume that it'll bind both with equal selectivity. So let's control for that by incubating with both biotinylated and non-biotinylated DNA at the same time. That provides a reference point with which to compare everything else.
