QM/MM Calculations on Solvated Molecules

The theoretical study of complex chemical systems
consisting of many hundreds or thousands of atoms
requires the use of various approximations for the interaction potential between atomic nuclei. These approximations are necessary because the exact, i.e. quantum mechanical (QM), solution rapidly becomes intractable as the number of atoms is increased. Consequently, the simpler molecular mechanics (MM) potentials are widely used in the simulation of large molecular aggregates and macromolecules to calculate thermodynamic properties or describe phenomena associated with the classical dynamics of the system. It only becomes necessary to use one of the QM methodologies in the calculations where, for example, chemical bond formation/breaking or electronic excitation processes are of interest, i.e. any process which involves a large change in the electronic structure. Since many of these processes are comparatively localised events, e.g. chemical bond formation, an obvious approach to the computational bottle-neck is to treat only a relatively small part of the system quantum mechanically. The remaining larger part of the system would be treated using molecular mechanics potentials.

In our approach to the combined QM and MM (QM/MM) methodology, we take advantage of the semiempirical QM approximation which is computationally more efficient than either the density functional or ab initio methods. This approach allows us to explore the possibility of generating ensemble averaged quantities using molecular dynamics simulation, thus facilitating the direct comparison of theory with experiment. The new QM/MM methods will be used to gain greater insight into the chemical processes occurring in solution and complex biomolecular systems.

Principal Investigator

Peter L. Cummins

Division of Biochemistry and Molecular Biology, John Curtin School of Medical Research

Co-Investigators

Jill E. Gready

Stephen Greatbanks

Division of Biochemistry and Molecular Biology, John Curtin School of Medical Research

Projects

u51 - PC, VPP

What are the results to date and the future of the work?

We have developed a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO and PM3 semiempirical molecular orbital methods and the TIP3P

- Appendix A

molecular mechanics model for liquid water. The model has been calibrated for each of the three molecular orbital methods (AM1, MNDO and PM3) using the experimental aqueous solvation free energies of a wide range of neutral organic molecules which are representative of side chains of the amino acids. This work has now been extended to ionized molecules in solution. Our initial parameterization studies of QM/MM potentials have yielded very encouraging results. The methodology should prove useful in a wide rang of ligand-binding and catalysis problems. We have used these QM/MM methods to study the hydride-ion transfer step between a novel substrate, 8-methylpterin, and cofactor molecule nicotinamide adenine dinucleotide phosphate (NADPH) in the enzyme dihydrofolate reductase (DHFR). Currently, we are investigating the relative affinities of the active (protonated) and inactive (neutral) forms of the substrate for DHFR. In the gas phase, i.e. in the absence of protein/solvent interactions, the neutral form is favoured. However, our results from QM/MM calculations show that this stability is reduced by protein-ligand interactions.

What computational techniques are used?

Free energies were computed using standard molecular dynamics (MD) simulation and thermodynamic integration (MD/TI) or free energy perturbation (MD/FEP) techniques using Molecular Orbital Programs for Simulations (MOPS). Generally, the MD/TI methods are used to calculate solvation and binding free energies, while the MD/FEP methods are used to calculate the free energy change along a reaction coordinate. An individual MD simulation is computationally intensive requiring tens of thousands of MD time-steps to minimise statistical error and compute sufficiently precise free energies. The QM/MM and MM/MM pair-wise interaction terms are readily vectorized, thus making this problem well suited to supercomputers. "State of the art" quantum chemical methods in Gaussian 98 are being used to compute gas-phase energetics.

Publications

Cummins, P.L., Gready, J.E., Coupled Semiempirical Quantum Mechanics and Molecular Mechanics (QM/MM) on the Aqueous Solution Free Energies of Ionized Molecules, Journal of Computational Chemistry, in press.

Cummins, P.L., Gready, J.E., Molecular Dynamics and Free Energy Perturbation (MD/FEP) Study of the Hydride-Ion Transfer Step in Dihydrofolate Reductase using a Combined Quantum and Molecular Mechanical (QM/MM) Model, Journal of Computational Chemistry, 19, 1998, 977-988.

Cummins, P.L., Gready, J.E., Investigating Enzyme Reaction Mechanisms with QM/MM+MD Calculations, in Hybrid Quantum Mechanical and Molecular Mechanical Methods, J. Gao and M.A. Thompson, eds, ACS Symposium series No. 712, American Chemical Society, Washington, Ch. 16.

Appendix A -