Helmholtz free energies of atom pair interactions in proteins.
BACKGROUND: Proteins fold to unique three-dimensional structures, but how they achieve this transition and how they maintain their native folds is controversial. Information on the functional form of molecular interactions is required to address these issues. The basic building blocks are the free energies of atom pair interactions in dense protein solvent systems. In a dense medium, entropic effects often dominate over internal energies but free energy estimates are notoriously difficult to obtain. A prominent example is the peptide hydrogen bond (H-bond). It is still unclear to what extent H-bonds contribute to protein folding and stability of native structures. RESULTS: Radial distribution functions of atom pair interactions are compiled from a database of known protein folds. The functions are transformed to Helmholtz free energies using a recipe from the statistical mechanics of dense interacting systems. In particular we concentrate on the features of the free energy functions of peptide H-bonds. Differences in Helmholtz free energies correspond to the reversible work required or gained when the distance between two particles is changed. Consequently, the functions directly display the energetic features of the respective thermodynamic process, such as H-bond formation or disruption. CONCLUSIONS: In the H-bond potential, a high barrier isolates a deep narrow minimum at H-bond contact from large distances, but the free energy difference between H-bond contact and large distances is close to zero. The energy barrier plays an intriguing role in H-bond formation and disruption: both processes require activation energy in the order of 2kT. H-bond formation opposes folding to compact states, but once formed, H-bonds act as molecular locks and a network of such bonds keeps polypeptide chains in a precise spatial configuration. On the other hand, peptide H-bonds do not contribute to the thermodynamic stability of native folds, because the energy balance of H-bond formation is close to zero.