  Free-energy landscapes for short peptides -- specifically for variants of the
pH Low Insertion Peptide (pHLIP) -- in the heterogeneous environment of a lipid
bilayer or cell membrane are constructed, taking into account a set of dominant
interactions and the conformational preferences of the peptide backbone. Our
methodology interprets broken internal H-bonds along the backbone of a
polypeptide as statistically interacting quasiparticles, activated from the
helix reference state. The favored conformation depends on the local
environment (ranging from polar to nonpolar), specifically on the availability
of external H-bonds (with $\mathrm{H_2O}$ molecules or lipid headgroups) to
replace internal H-bonds. The dominant side-chain contribution is accounted for
by residue-specific transfer free energies between polar and nonpolar
environments. The free-energy landscape is sensitive to the level of pH in the
aqueous environment surrounding the membrane. For high pH, we identify pathways
of descending free energy that suggest a coexistence of membrane-adsorbed
peptides with peptides in solution. A drop in pH raises the degree of
protonation of negatively charged residues and thus increases the
hydrophobicity of peptide segments near the C terminus. For low pH, we identify
insertion pathways between the membrane-adsorbed state and a stable
trans-membrane state with the C terminus having crossed the membrane.
