As I understand, the Gibbs free energy not only depends on the structure but also depends on the surrounding solution conditions. That is why under certain conditions (e.g. pH, temperature, ionic strength), the protein tends to unfold or remain native structure. So I wonder if there is a theoretical assumption to set the scoring background? For example, is it under pH 7, 25 degree C, or vacuum state? Thank you.
"Physiological (probably)" is likely the best answer to that question.
Rosetta doesn't really have expelicitly defined solution conditions in its modeling. Instead, the solution conditions are implicitly rolled into the various statistical parameters for sampling/scoring, and the various benchmark sets that Rosetta has been tuned against.
The Rosetta energy function has a number of statistical potentials. These are derived from high quality structures in the PDB, so the solution conditions they reflect are the solution conditions averaged across all those structures. Likewise with sampling (backbone fragments, sidechain rotamers, etc.). These are derived from the PDB, and thus represent the conditions at which those structures were determined.
There's also been a number of fitting and tuning of the sampling and scoring of Rosetta. Some of these are based off of structures (so same argument as above), and others are tuned against experimental results (mutational data, binding energies, etc.). There's been a number of such experimental data that's been rolled into Rosetta over the years, each with their own particular conditions. Thus the results reflect the sum/average across all such experiments.
So, generally speaking, the conditions under which Rosetta models proteins is a representative approximation of the typical conditions under which the majority of structural biologists examine their proteins. All this is tempered by the fact that Rosetta modeling is approximate, and not laser-focused precise. There's system-to-system variability and within system inaccuracy in the result - typically, these are greater than the changes you see with changes in temperature, pH, ionic strength, etc. (Ignoring systems which exhibit major pH/temperature/etc. triggered changes.)
What I can say is that Rosetta by default models everything in implicit solvent, histidine in the singly-protonated state, and cysteine as protonated. (Though see Kilambi et al.'s work for attempts to look at pH dependence.) Off the top of my head I can't recally anyone explicitly looking at temperature or ionic strength dependent properties. Could this account for some of the current inaccuracies in the ddg_monomer results? Quite possibly.
Thank you very much! I think it explains in a great detail!
I have done experiments meant to mimic high-salt conditions (by just turning fa_pair off, this was back in score12). It worked more or less as expected - in the wet experiment, a highly charged interface was weaker, and in Rosetta modeling, the expected interface was harder to sample / weaker. These were sketchy/back of the envelope and we never bothered publishing it.