Learning about protein hydrogen bonding by minimizing contrastive divergence

Defining the strength and geometry of hydrogen bonds in protein structures has been a challenging task since early days of structural biology. In this article, we apply a novel statistical machine learning technique, known as contrastive divergence, to efficiently estimate both the hydrogen bond strength and the geometric characteristics of strong interpeptide backbone hydrogen bonds, from a dataset of structures representing a variety of different protein folds. Despite the simplifying assumptions of the interatomic energy terms used, we determine the strength of these hydrogen bonds to be between 1.1 and 1.5 kcal/mol, in good agreement with earlier experimental estimates. The geometry of these strong backbone hydrogen bonds features an almost linear arrangement of all four atoms involved in hydrogen bond formation. We estimate that about a quarter of all hydrogen bond donors and acceptors participate in these strong interpeptide hydrogen bonds.