Do these three terms in Score12.wts_patch and after have significant overlap?
How would one go ahead to explain a delta_delta_G upon a mutation that has contributon coming from these terms? In one protein case, three mutations T61N, H135Y and H257P, showed significant gain in half-life. The score terms show contribution from Rama, p_aa_pp and ref.
The rama and p_aa_pp terms are similar, in that they are both looking at the same basic data, but they're coming at it from a different direction.
The rama term is looking at the phi-psi angle preferences of a given amino acid. That is, for any particular amino acid, what is the probability that you'll see the current phi and psi backbone angles, and then use the Boltzmann relation to convert that into an energy. The p_aa_pp term comes at it from the opposite direction: given the current phi and psi angles, what's the probability that you'll see the current amino acid identity?
You'll sometimes see discussion about one term verus the other is more important for design/mutation versus folding, but the reality is that they're both important in both design contexts and folding contexts. Even though p_aa_pp invokes probability across multiple amino acid, it still influences folding because as you sample different phi/psi contexts the amino acid propensities change, and thus the energies change. Likewise with rama - change the amino acid and the phi/psi energy landscape changes, meaning a different score even with a fixed backbone.
The ref energy is something completely seperate. There's various interpretations of this term, but normally it's thought of as a compensation for the energy of the unfolded state, or as a normalization factor to compensate for the different levels of different amino acids (that is, it's an adjustable parameter so that every amino acid gets reasonable frequencies in design). The ref energy is only relevant in design/mutation contexts, as it's constant for any fixed-sequence sampling. It's also important to keep in mind that the size of the ref energy change is the same for any mutation of one given amino acid to another given amino acid, regardless of structural context. The importance of the ref term in mutations is not so much in itself, but how much it is countered (or not) by the other terms.
So in trying to explain your mutations, the contributions from rama and p_aa_pp may be pointing to an issue with backbone structure propensity. These mutations could be (de)stabilizing the secondary structure location where they are. I'd recommend taking a look at the standard explanation for secondary structure propensities, and if these sorts of mutations are typically invoked in those contexts. This is especially true given the contribution from the ref term. If you interpret this a representing the unfolded state, then the mutations can be (de)stabilizing the folded backbone structure with respect to the unfolded state.
But I'd be slightly wary about over interpreting Rosetta energy terms. Normally they can point you in a general direction (backbone vs. sidechain, particular hydrogen bonds), but because during energy optimization you're optimizing over all of them, you can get compensation between different factors. (This is a general feature of all modeling programs which split energy into terms - how the terms get split is somewhat arbitrary.) It's better to treat them as indications of avenues of further exploration, and then bolster your arguments with supporting evidence from other sources (e.g. the previously published amino acid structural propensities mentioned earlier).