Do they exactly represent a given spacial configuration ?
I've the impression that these names are random, because different visual display can have the same rotamer name (or a given name can show different visual configuration).
It's a short heuristic based on the angles of each of the dihedrals in the rotamer. "m" for -120 to 0 degrees, "p" for 0 to 120 and "t" for 120 through 180 to -120. I believe these are mnemonics for "gauche minus", "gauche positive" and "trans". (Read more from the Dunbrack lab). Each of the sidechain dihedral angles are represented as a letter, starting from closest to the backbone going out.
While this works for rough binning most rotamers, it can be that there's multiple rotamers with the same designation, as these are somewhat coarse bins (Particularly for the "semirotameric" residues like Asp,Glu,Gln & Asn, where the last dihedral isn't really binned.). Also, the rotamer library we use is backbone dependent, so small movements in the backbone can change which exact rotamers are available. (So where a mtpp rotamer places things will be roughly the same, but will have slight variations based on what the backbone is like.)
Thank you. Shall I conclude the following from the Dunbrack lab paper:
The integer number of available rotamers is an approximation (just like the shake positions ?). Further wiggling might move the sidechains slightly arround the provided discrete positions set by rotamer.SetRotamer function (or the keyboard arrows). In reality, there is an infinity of positions. Correct ?
Theoretically, there are an infinite number of positions a sidechain can adopt. However, when we look at experimental structures of protein, there's clear trends. There's variation, but they tend to center around particular dihedral angles. Rotamers are a discretization of the continuous sidechain conformational space. That's what the Dunbrack lab has done with their rotamer library work – they've looked at the trends in sidechain conformations, and figured out what the "typical" value of these angles are, and what sort of spread is encountered.
When you work with rotamers, you're explicitly working with those discretized values. The "on rotamer" structure would be the most likely angles from that particular bin (a peak of the probability distribution). We do allow sidechains to go off-rotamer during wiggle and certain other processes, but anything which is based on rotameric sampling (shake, the rotamer picker, set rotamer, etc.) will be picking sidechains from the discretized rotamer space. While the discretization is an approximation of the continuous rotamer space, for any given rotamer library, there's a pre-defined set of on-rotamer conformations for any given amino acid/backbone conformation.
(Note that the rotamer information is also used in scoring, even for off-rotamer structures. Part of the standard Rosetta score is looking at how close a particular off-rotamer conformation is to the on-rotamer value, and even how probable that closest rotamer is. The higher the probability, the better the score. This keeps wiggle and other optimizations from going too far off-rotamer.)
Interesting to observe that in our best scoring solutions (all scoring together), some strategic rotamers (like Hbinding ones) can be in low probability states. I suppose that in the "ideal world", all types of subscores would be on their maximum. We are in practice far from this (only our bonus are at their optimum, but this could be due to our strategy to first try to maximize the bonus if they are high enough).
It actually has been observed in native proteins that functional residues (e.g. residues in the active site of enzymes and residues in protein/protein binding interfaces) do tend to be less "ideal" than residues elsewhere.
I think you're correct that ideally you'd maximize the score of the structure, but often times you're trying to do a multi-objective optimization - you don't just want a solid rock of a protein, but instead you need particular functional characteristics in the key active locations. It's likely that you just can't satisfy all constraints at the same time, so you have to trade off stability for functionality. It's been theorized that this might be why proteins often seem to be larger than strictly necessary. All the rest of the protein is there to help stabilize the (intrinsically less stable) active bits in the structure they need to be in, which isn't necessarily the structure they'd otherwise want to be in.