Refinement of protein tertiary structure by using spin-spin coupling constants from nuclear magnetic resonance measurements

Modelling protein structure seems a challenging enterprise because the number of structure parameters required ordinarily exceeds the amount of independent data points available from experimental observations. Expressing the predominant conformation of a protein in terms of a geometry model, a polypeptide chain consisting of N atoms would command 3N – 6 Cartesian coordinates be fixed. Even for small proteins, this becomes a daunting number. Fortunately, so-called holonomic constraints limit the number of variables, leaving substantially fewer, truly relevant parameters for folding the polypeptide chain into its native tertiary structure. For example, adjusting bond lengths and the many angles between the covalent bonds connecting the atoms is of little concern and appropriate standard values can be inserted from tableworks (Pople & Gordon, 1967; Engh & Huber, 1991, 2006). Table 1 exemplifies for the 147-residue protein Desulfovibrio vulgaris flavodoxin how the number of truly independent internal rotational degrees of freedom amounts to less than one-tenth of the Cartesian coordinate set size..