Application of Linear Scaling Semiempirical Quantum Chemical Methods to the Study of Enzyme Reaction Mechanisms
Jill E. Gready
John Curtin School of Medical Research
Stephen J. Titmuss
John Curtin School of Medical Research
Alistair P. Rendell
ANU Supercomputer Facility
x11 - VPP, PC
|The quantum mechanical (QM) methods required for the modelling of chemical
reactions rapidly become computationally intractable as the system size
increases. Even the more efficient QM techniques, such as semiempirical
calculations, have an O(N3) computationtime dependence on the
number of atoms. While QM treatment of small chemical systems (up to 100
atoms) is routine, enzyme reaction mechanisms have traditionally required
the protein environment to be modelled using faster molecular mechanical
(MM) techniques, with only the small crucial portions of the substrate and
active site treated quantum mechanically. MOZYME is one of several
recently developed linear scaling QM methods that may offer an alternative
to these hybrid QM/MM methods. By treating molecular orbitals as being highly
localised in space the O(N3) bottleneck can be eliminated, allowing
systems of several thousand atoms to be modelled quantum mechanically.
We aim to evaluate and optimise the potential of the MOZYME methodology as a tool for the study of enzyme reaction mechanisms, specifically determining the effects on accuracy and performance of the localised molecular orbital (LMO) approximations and the relative benefits of applying a complete QM treatment to the entire enzymesubstrate system compared with the more complex partitioned QM/MM schemes.
What are the results to date and the future of the work?
Initial studies were directed towards defining an optimal set of parameters to balance accuracy, precision and computational performance for the future study of biological systems by QM methods. These parameters can be determined by comparison of MOZYME calculations, using a range of cutoffs for the size of the LMOs and representing longerrange electrostatic interactions, with conventional semiempirical calculations. The small protein systems studied during this stage approach the practical limit of the conventional methods (e.g.a 573 atom system requires 2 hours of PC time for a single point energy evaluation), while being well within the potential of the new method (8 minutes for the same calculation). These calculations have shown that the default LMO approximations introduce approximately only 0.1kcal/mol error into the calculated heat of formation of systems containing up to 1000 atoms, and the cutoffs can be relaxed even further to improve computational performance without significantly increasing the error.
Appendix A -
Full QM geometry optimisation on a 573 atom protein was performed using the PM3 hamiltonian and BFGS method. This was characterised by an initial rapid reduction in heat of formation associated with bond length optimisation, followed by very slow convergence over 1000 cycles. Performance of the geometry optimisation algorithm and the molecule specification needs to be improved to make the method more suitable for the large systems to be studied.
Calculations are currently being performed on a 3000 atom enzyme system (dihydrofolate reductase) using both MOZYME and a hybrid QM/MM package, with the aim of comparing the two methods.
What computational techniques are used?
The MOPAC2000 semiempirical molecular orbital package (Fujitsu Limited, J.J.P.Stewart) is used for single point and QM geometry optimisation calculations. This program incorporates both the conventional O(N3) algorithm of previous versions of MOPAC as well as the new linear scaling MOZYME functionality. These calculations make heavy demands on memory (>500MB), particularly for conventional MOPAC calculations and MOZYME geometry optimisations, although recent implementation of a direct SCF approach (A.Bliznyuk) has reduced MOZYME memory requirements by more than half, with an insignificant increase in computation time. The hybrid QM/MM package MOPS (P.L.Cummins) is also being used for comparison of the MOZYME methodology to more established techniques.
- Appendix A