Determination of three-dimensional structures of proteins by simulated annealing with interproton distance restraints. Application to crambin, potato carboxypeptidase inhibitor and barley serine proteinase inhibitor 2

Abstract

An automated method, based on the principle of simulated annealing, is presented for determining the three-dimensional structures of proteins on the basis of short (less than 5 A) interproton distance data derived from nuclear Overhauser enhancement (NOE) measurements. The method makes use of Newton's equations of motion to increase temporarily the temperature of the system in order to search for the global minimum region of a target function comprising purely geometric restraints. These consist of interproton distances supplemented by bond lengths, bond angles, planes and soft van der Waals repulsion terms. The latter replace the dihedral, van der Waals, electrostatic and hydrogen-bonding potentials of the empirical energy function used in molecular dynamics simulations. The method presented involves the implementation of a number of innovations over our previous restrained molecular dynamics approach [Clore, G.M., Brünger, A.T., Karplus, M. and Gronenborn, A.M. (1986) J. Mol. Biol., 191, 523-551]. These include the development of a new effective potential for the interproton distance restraints whose functional form is dependent on the magnitude of the difference between calculated and target values, and the design and implementation of robust and fully automatic protocol. The method is tested on three systems: the model system crambin (46 residues) using X-ray structure derived interproton distance restraints, and potato carboxypeptidase inhibitor (CPI; 39 residues) and barley serine proteinase inhibitor 2 (BSPI-2; 64 residues) using experimentally derived interproton distance restraints. Calculations were carried out starting from the extended strands which had atomic r.m.s. differences of 57, 38 and 33 A with respect to the crystal structures of BSPI-2, crambin and CPI respectively. Unbiased sampling of the conformational space consistent with the restraints was achieved by varying the random number seed used to assign the initial velocities. This ensures that the different trajectories diverge during the early stages of the simulations and only converge later as more and more interproton distance restraints are satisfied. The average backbone atomic r.m.s. difference between the converged structures is 2.2 +/- 0.3 A for crambin (nine structures), 2.4 +/- 0.3 A for CPI (eight structures) and 2.5 +/- 0.2 A for BSPI-2 (five structures). The backbone atomic r.m.s. difference between the mean structures derived by averaging the coordinates of the converged structures and the corresponding X-ray structures is 1.2 A for crambin, 1.6 A for CPI and 1.7 A for BSPI-2.