Examining the meaning of the peptide transfer free energy obtained from blocked (Gly)_n and cyclic-diglycine model compounds

In experiments, the free energy of transferring the peptide group from water to an osmolyte solution is obtained using the transfer free energy of (Gly)_n with the added assumption that a constant incremental change in free energy with n implies that each additional unit makes an independent contribution to the free energy. Here we test this assumption and uncover its limitations. Together with results for cyclic-diglycine, we show that, in principle, it is not possible to obtain a peptide group transfer free energy that is independent of the model system. We calculate the hydration free energy of acetyl-(Gly)_n-methyl amide (n=1..7) peptides modeled in the extended conformation in water and osmolyte solutions and find that the hydration free energy is linear in n, suggestive of independent, additive group-contributions. To probe the observed linearity further, we study the hydration of the solute bereft of water molecules in the first hydration shell. This conditioned solute arises naturally in the theoretical formulation and helps us focus on hydration effects uncluttered by the complexities of short-range solute-water interactions. We subdivide the conditioned solute into n+1 peptide groups and a methyl end group. The binding energy of each of these groups with the solvent is Gaussian distributed, but the near neighbor binding energies are themselves correlated: the (i,i+1) correlation is the strongest and tends to lower the free energy over the independent group case. We show that the observed linearity can be explained by the similarity of near neighbor correlations. Implications for group additive transfer free energy models are indicated.