Small proteins (one to two alpha helices) can now be routinely folded (that is, starting form a fully unfolded state, to getting stick in the minimum around the final structure) using ab initio simulations that last several multiples of the folding time.
Larger proteins (a few alpha helices and beta sheets), the folding process can be studied if you start with structures near the native state.
None of this means to say that we can routinely take any protein and fold it from unfolded state using simulations and expect any sort of accuracy for the final structure.
When I say ab initio I mean "classical newtonian force field with approximate classical terms derived from QM", AKA something like https://ambermd.org/AmberModels.php
Other people use ab initio very differently (for example, since you said "level of theory" I think you mean basis set). I don't think something like QM levels of theory provide a great deal of value on top of classical (and at a significant computational cost), but I do like 6-31g* as a simple set.
Other people use ab initio very differently. For example, CASP, the protein structure prediction, uses ab initio very loosely to me: "some level of classicial force field, not using any explicit constraints derived from homology or fragment similarity" which typically involves a really simplified or parameterized function (ROSETTA).
Personally I don't think atomistic simulations of cells really provide a lot of extra value for the detail. I would isntead treat cell objects as centroids with mass and "agent properties" ("sticks to this other type of protein for ~1 microsecond"). A single ribosome is a single entity, even if in reality it's made up of 100 proteins and RNAs, and the cell membrane is modelled as a stretchy sheet enclosing an incompressible liquid.
Level of theory as it relates to an-initio QM calculations usually indicates Hartee Fock, MP2 and so on, then the basis set gets specified after.
I also agree that QM doesn't provide much for the cost at this scale, I just wish the term ab initio would be left to QM folks, as everything else is largely just the parameterization you mentioned.
The systemn I work with, AMBER, explains how individual classical terms are derived: https://ambermd.org/tutorials/advanced/tutorial1/section1.ht... which appears te be MP2/6-31g* (sorry, I never delved deeply into the QM parts). Once those terms are derived, along with various approximated charges (classical fields usually just treat any charge as point-centered on the nucleus, which isn't great for stuff like polarizable bonds), everything is purely classical springs and dihedrals and interatomic potentials based on distance.
I am more than happy to use "ab initio" purely for QM, but unfortunately the term is used widely in protein folding and structure prediction. I've talked exdtensively with David Baker and John Moulton to get them to stop, but they won't.
Sure. But in the protein structure prediction field, "ab initio" is used to mean "structure was predicted with no homology or other similarity information" even though the force fields incorporate an enormous amount of protein structural knowledge.
Larger proteins (a few alpha helices and beta sheets), the folding process can be studied if you start with structures near the native state.
None of this means to say that we can routinely take any protein and fold it from unfolded state using simulations and expect any sort of accuracy for the final structure.