Imagine a system with 2 energetic basins A and B separated by a high barrier. We cannot sample that barrier for whatever reason (ie. because the lowest energy path is very "long" with lots of frames and therefore out of scope). However, initial configurations for both minima are present, so we can use umbrella sampling to explore their surroundings.

When we unbias the data with WHAM, there are two possible ways to do that:

1) treat the data separately to get 2 PMFs for the surrounding of A and B with unknown relationship between them

2) unbias the whole data together even though there is no connection between A and B.

I now wonder if method 2) is a valid approach. Is it correct to assume that the delta G between the two spots A and B derived by method 2) is correct even if there is no sampled path between them in the biased data? Or is the whole resulting PMF wrong? In this case we would have to look at the data as two separate PMFs.