  The anchor of most integral membrane proteins consists of one or several
helices spanning the lipid bilayer. The WALP peptide, GWW(LA)$_n$(L)WWA, is a
common model helix to study the fundamentals of protein insertion and folding,
as well as helix-helix association in the membrane. Its structural properties
have been illuminated in a large number of experimental and simulation studies.
In this combined coarse-grained and atomistic simulation study, we probe the
thermodynamics of a single WALP peptide, focusing on both the insertion across
the water-membrane interface, as well as folding in both water and a membrane.
The potential of mean force characterizing the peptide's insertion into the
membrane shows qualitatively similar behavior across peptides and three force
fields. However, the Martini force field exhibits a pronounced secondary
minimum for an adsorbed interfacial state, which may even become the global
minimum---in contrast to both atomistic simulations and the alternative PLUM
force field. Even though the two coarse-grained models reproduce the free
energy of insertion of individual amino acids side chains, they both
underestimate its corresponding value for the full peptide (as compared with
atomistic simulations), hinting at cooperative physics beyond the residue
level. Folding of WALP in the two environments indicates the helix as the most
stable structure, though with different relative stabilities and chain-length
dependence.
