Efficient computation of three-dimensional protein structures in solution from nuclear magnetic resonance data using the program DIANA and the supporting programs CALIBA, HABAS and GLOMSA.

More than 60 years after the analyses by Linderstrom-Lang and Kirkwood of their hypothetical 'protein' structures, we have now a plethora of experimental evidence and computational estimates of the electrostatic forces in proteins, with very many protein 3D structures at atomic resolution. In the mean time, there were in the beginning, many arguments and suggestions about the roles of electrostatics, mainly from empirical findings and tendencies. A few experimental results indicated that the electrostatic contribution is of the order of several kcal/mol, which was theoretically difficult to reproduce correctly, because a large opposing reaction field should be subtracted from a large, direct Coulombic field. Although the importance of the reaction field was recognized even 70 years ago, appropriate applications to protein molecules were made only in this decade, with the development of numerical computation. Now, an electrostatic molecular surface is one of the most popular pictures in journals of structural biology, indicating that the electrostatic force is one of the important components contributing to molecular recognition, which is a major focus of current biology and biochemistry. The development of NMR techniques has made it possible to observe the individual ionizations of ionizable groups in a protein, in addition to the determination of the 3D structure. Since it does not require any additional probe, each charge state can report the very local and heterogeneous electrostatic potentials working in the protein, without disturbing the original field. From the pKa values, the contributions of electrostatic interactions, ion pairs, charge-dipole interactions, and hydrogen bonds to protein stability have been correctly evaluated. Protein engineering also provides much more information than that obtainable from the native proteins, as the residues concerned can now be easily substituted with other amino acid residues having electrostatically different characteristics. Those experimental results have revealed smaller contributions than previously expected, probably because we underestimated the reaction field effects. Especially, a single ion pair stabilizes a protein only slightly, although a cooperative salt-bridge network can contribute significantly to protein stability. Marginal stabilities of proteins arise from small difference between many factors with driving and opposing forces. In spite of the small contribution of each single electrostatic interaction to the protein stability, the sum of their actions works to maintain the specific 3D structure of the protein. The 'negative' roles of electrostatics, which might destabilize protein conformation, should be pointed out. Unpaired buried charges are energetically too expensive to exit in the hydrophobic core. Isolated hydrogen bond donors and acceptors also exert negative effects, but they are not as expensive as the unpaired buried charges, with costs of a few kcal/mol. Therefore, statistical analyses of protein 3D structures reveal only rare instances of isolated hydrogen bond donors and acceptors. This must be the main reason why alpha-helices and beta-sheets are only observed in protein cores as the backbone structures. Such secondary structures do not leave any backbone hydrogen donors or acceptors unpaired, because of their intrinsically regular packing. Otherwise, it might be very difficult to construct a backbone structure, in which all the backbone amide and carbonyl groups had their own hydrogen bond partners in the protein core. There are two theoretical approaches to protein electrostatics, the macroscopic or continuum model, and the microscopic or molecular model. As described in this article, the macroscopic model has inherent problems because the protein-solvent system is very hetergeneous from the physical point of view...

Roles of electrostatic interaction in proteins.

Normal mode refinement : crystallographic refinement of protein dynamic structure. I. Theory and test by simulated diffraction data

A method is presented to describe the internal motions of proteins obtained from molecular dynamics or Monte Carlo simulations as motions of normal mode variables. This method calculates normal mode variables by projecting trajectories of these simulations onto the axes of normal modes and expresses the trajectories as a linear combination of normal mode variables. This method is applied to the result of the molecular dynamics and the Monte Carlo simulations of human lysozyme. The motion of the lowest frequency mode extracted from the simulations represents the hinge bending motion very faithfully. Analysis of the obtained motions of the normal mode variables provides an explanation of the anharmonic aspects of protein dynamics as due first to the anharmonicity of the actual potential energy surface near a minimum and second to trans-minimum conformational changes.

Projection of Monte Carlo and molecular dynamics trajectories onto the normal mode axes: human lysozyme.

The Metropolis Monte Carlo method has been added to the program FANTOM for energy refinement of polypeptides and proteins using a Newton–Raphson minimizer in torsion angle space. With this extension, different strategies for global minimization of the semiempirical energy function ECEPP/2 by various temperature schedules and restriction of conformational space were tested for locating local minimum conformations with low energy of the pentapeptide Met-enkephalin. In total, 1881 conformations below −10 kcal/mol were found. These conformations could be represented by 77 nonidentical conformations which were analysed for their pattern of hydrogen bonds, types of tight turn, pairwise root-mean-square-deviation (rmsd), Zimmermann codes and side chain conformations. All low energy conformations below −10.4 kcal/mol show strong similarity to the global minimum conformation in the backbone structure.

Efficient search for all low energy conformations of polypeptides by Monte Carlo methods

An improved algorithm is presented for rapid calculation of the hessian matrix for the conformational energy of a protein as a function of only dihedral angles. The speed of the calculation, which is about one order faster than by the previous method, is achieved by two considerations. First, the algorithm is designed to take advantage of the supercomputer pipeline architecture. Second, long-range, nonbonded interactions are cut off and long-range electrostatic interactions are approximated by dipole-dipole interactions in order to reduce the number of pairwise interactions that have to be computed. The results of benchmark tests of the program are given as applied for four globular proteins of different sizes.

Hiroshi Wako

Papers

Algorithm for rapid calculation of Hessian of conformational energy function of proteins by supercomputer