News and Publications

Theoretical Studies of Molecular Electrostatics and Artificial Pore Transport

D. Bashford, E. Demchuk, V. Spassov, V. Dillet

We are developing and applying macroscopic dielectric models of the macromolecule-solvent system. The protein is treated as a low-dielectric medium immersed in a high-dielectric solvent, and the electric potential is determined by the Poisson-Boltzmann equation, which is solved numerically. The details of the atomic structure are incorporated into the placement of charges and dielectric boundaries. We call the model macroscopic electrostatics with atomic detail (MEAD).

Determination of pK_a values is a key test of methods of calculation and an important application. We recently completed a study of the pK_a values of the active-site residues of oxidized and reduced thioredoxin, including a cysteine residue with an unusually low pK_a that is crucial for the role of the residue as a nucleophile in the activity of the protein and an aspartic acid residue with an unusually high pK_a. We found that for calculations based on the x-ray crystallographic structure and for some, but not all, of the nuclear magnetic resonance structures, the calculated pK_a values were consistent with experimental values. The results help to settle some controversies in the assignment of active-site titrations and suggest that electrostatic calculations can be used to determine members of nuclear magnetic resonance ensembles that are more representative of the solution structure of the protein.

Cooperative ligand binding, the phenomenon in which the binding of 1 ligand to a protein with multiple ligand-binding sites increases the affinity for binding the same type of ligand at the other sites, is traditionally understood in terms of conformational changes that occur upon ligand binding. We showed that cooperativity in the binding of charged ligands can arise through an electrostatic mechanism that does not require conformational change. The binding of a charged ligand to 1 site alters the protonation states of pH-titratable sites in the protein in a way that makes the binding of a second ligand more favorable. This effect is pH dependent. In some cases, it only cancels a part of the anticooperative effect of ligand-ligand repulsion; in others, it leads to net cooperativity. Because of the large number of pH-titrating sites on protein surfaces, this mechanism most likely contributes to cooperativity in small globular proteins that have multiple binding sites for charged ligands.

The MEAD electrostatic model can be coupled with the techniques of quantum chemistry to provide a detailed model of protein active sites, or their analogs, in the protein or solvent environment. An inner region containing the active-site atoms is treated quantum mechanically while the surrounding region is treated as a classical electrostatic system that generates a reaction field, and possibly a field due to permanent atomic charges of the protein. This technique has been used to calculate the absolute and relative redox properties of iron-sulfur centers in ferredoxin and phthalate dioxygenase reductase, with results in reasonable agreement with experimental findings. We are also applying the method to active sites in superoxide dismutase. We recently completed a study of histidine pK_a values in bovine low molecular weight protein tyrosine phosphatase, and we are now applying the combined MEAD--quantum mechanics approach to the reaction profile of this enzyme. This work is being done in collaboration with L. Noodleman, Department of Molecular Biology.

We are continuing our studies of the diffusion of water and ions through peptide nanotubes of the type developed in the laboratory of M.R. Ghadiri, Department of Chemistry. Previous calculations showed that water in the nanotubes has a layered structure with deviations that allow water molecules to pass one another, in contrast to the single-file structure of water in the gramicidin pore, which has slower transport properties. Current work includes the development and application of "hopping models" of diffusion and molecular dynamics calculation of ion-transport.

PUBLICATIONS

Bashford, D. Macroscopic electrostatics: Calculation of solvated interactions and macromolecular titration. In: The Encyclopedia of Computational Chemistry. Schleyer, P.v.R., et al. (Eds.). Wiley, New York, in press.

Bashford, D. An object-oriented programming suite for electrostatic effects in biological molecules. In: Scientific Computing in Object-Oriented Parallel Environments. Ishikawa, Y., et al. (Eds.). Lecture Notes in Computer Science, Vol. 1343. Springer, New York, 1997, p. 233.

Demchuk, E., Bashford, D., Gippert, G.P., Case, D.A. Thermodynamics of a reverse turn motif: Solvent effects and side-chain packing. J. Mol. Biol. 270:305, 1997.

Dillet, V., Dyson, H.J., Bashford, D. Calculations of electrostatic interactions and pK_as in the active site of Escherichia coli thioredoxin. Biochemistry 37:10298, 1998.

Li, J., Nelson, M.R., Peng, C.-Y., Bashford, D., Noodleman, L. Incorporating protein environments in density functional theory: A self-consistent reaction field calculation of redox potentials of [2Fe2S] clusters in ferredoxin and phthalate dioxygenase reductase. J. Phys. Chem. A. 102:6311, 1998.

Spassov, V.Z., Bashford, D. Electrostatic coupling to pH-titrating sites as a source of cooperativity in protein-ligand binding. Protein Sci. 7:2012, 1998.

Tishmack, P.A., Bashford, D., Harms, E., VanEtten, R.L. Use of ¹H NMR spectroscopy and computer simulations to analyze histidine pK_a changes in a protein tyrosine phosphatase: Experimental and theoretical determination of electrostatic properties in a small protein. Biochemistry 36:11984, 1997.