Intrinsic nature of the three-dimensional structure of proteins as determined by distance geometry with good sampling properties

A protocol for distance geometry calculation is shown to have excellent sampling properties in the determination of three-dimensional structures of proteins from nuclear magnetic resonance (NMR) data. This protocol uses a simulated annealing optimization employing mass-weighted molecular dynamics in four-dimensional space (Havel, T.F. (1991) Prog. Biophys. Mol. Biol., 56, 43-78). It attains an extremely large radius of convergence, allowing a random coil conformation to be used as the initial estimate for the succeeding optimization process. Computations are performed with four systems of simulated distance data as tests of the protocol, using an unconstrained L-alanine 30mer and three different types of proteins, bovine pancreatic trypsin inhibitor, the alpha-amylase inhibitor Tendamistat, and the N-terminal domain of the 434-repressor. The test of the unconstrained polypeptide confirms that the sampled conformational space is that of the statistical random coil. In the larger and more complicated systems of the three proteins, the protocol gives complete convergence of the optimization without any trace of initial structure dependence. As a result of an exhaustive conformational sampling by the protocol, the intrinsic nature of the structures generated with distance restraints derived from NMR data has been revealed. When the sampled structures are compared with the corresponding X-ray structures, we find that the averages of the sampled structures always show a certain pattern of discrepancy from the X-ray structure. This discrepancy is due to the short distance nature of the distance restraints, and correlates with the characteristic shape of the protein molecule.