3 Publications

An efficient methodology, further referred to as ICM, for versatile modeling operations and global energy optimization on arbitrarily fixed multimolecular system is described. It is aimed at protein structure prediction, homology modeling, molecular docking, nuclear magnetic resonance (NMR) structure determination, and protein design. The method uses and further develops a previously introduced approach to model biomolecular structures in which bond lengths, bond angles, and torsion angles are considered as independent variables, any subset of them being fixed. Here we simplify and generalize the basic description of the system, introduce the variable dihedral phase angle, and allow arbitrary connections of the molecules and conventional definitions of the torsion angles. Algorithms for calculation of energy derivatives with respect to internal variables in the topological tree of the system and for rapid evaluation of accessible surface are presented. Multidimensional variable restraints are proposed to represent the statistical information about the torsion angle distributions in proteins. To incorporate complex energy terms as solvation energy and electrostatics into a structure prediction procedure, a "double-energy" Monte Carlo minimization procedure in which these terms are omitted diring the minimization stage of the random step and included for the comparison with the previous conformation in a Markov chain is proposed and justified. The ICM method is applied successfully to a molecular docking problem. The procedure finds the correct parallel arrangement of two rigid helices from a leucine zipper domain as the lowest-energy conformation (0.5 A root mean square, rms, deviation from the native structure) starting from completely random configuration. Structures with antiparallel helices or helices staggered by one helix turn had energies higher by about 7 or 9 kcal/mol, respectively. Soft docking was also attempted. A docking procedure allowing side-chain flexibility also converged to the parallel configuration starting from the helices optimize individually. To justify an internal coordinate approach to the structure prediction as opposed to a Cartesian one, energy hypersurfaces around the native structure of the squash seeds trypsin inhibitor were studied. Torsion angle minimization from the optimal conformation randomly distorted up to the rms deviation of 2.2 A or angular rms deviation of 10 degrees restored the native conformation in most cases. In contrast, Cartesian coordinate minimization did not reach the minimum from deviations as small as 0.3 A or 2 degrees. We conclude that the most promising detailed approach to the protein folding problem would consist of some coarse global sampling strategy combined with the local energy minimization in the torsion coordinate space.