Recent Research Developments

November 24, 2004

New methods for treatment of long-range electrostatic interactions in quantum simulations of biochemical reactions

The study of biochemical reactions using combined quantum mechanical/molecular mechanical (QM/MM) methods has gained tremendous attention.  Biological reactions occur in a complex solvated macromolecular environment where electrostatic effects play are often attributed as being a main source of catalytic activity.  The challenge in theoretical studies of biochemical mechanisms is to move accurate quantum electronic structure calculations from the gas phase into complex biological environments.  A key step toward this end involves the accurate and efficient modeling of electrostatic interactions for these very large systems.

Recently, the research group of Prof. Darrin York of the Department of Chemistry has made several advances in the design of new methods to treat long range electrostatic interactions in QM/MM simulations of biochemical reactions.  Prof. Darrin York, along with graduate student Brent Gregersen have recently introduced a new method for treatment of long-ranged electrostatic interactions in QM/MM stochastic boundary molecular dynamics (SBMD) simulations.  The method allows the electrostatic environment due to a tremendously large system to be accurately modeled in an enzyme's active site for a fraction of the computational cost of direct methods (Figure 1).  The first publication on the Variational Electrostatic Projection (VEP) method is currently in press in the Journal of Physical Chemistry B.

Figure 1.  Average relative error (RELE) vs. fraction of evaluated pairwise interactions.  Black line shows the errors for a residue-based cut-off with switching.

In some instances, it is important to apply more rigorous full periodic boundary simulations with explicit solvent.  Although for molecular mechanical force field models, linear-scaling electrostatic methods for periodic systems exist, these methods have been sluggish in being generalized to combined QM/MM potentials due to the added complexity of the quantum mechanical electron density.  Recently, Professor York, along with graduate student Kwangho Nam and Prof. Jiali Gao have developed a linear-scaling Ewald method for combined QM/MM simulations.  Application of the linear-scaling QM/MM-Ewald method (Figure 2) demonstrates the importance of rigorous treatment of electrostatic interactions of reactions, especially those that involve ionic transition states or intermediates.  The  linear-scaling QM/MM-Ewald method is in press and is scheduled to appear in the first issue of the new ACS journal, Journal of Chemical Theory and Computation, in January, 2005.

Figure 2.  Comparison of potential of mean force (PMF) profiles for the ionic separation of ammonium metaphosphate in water. Profiles were constructed from MD simulations with periodic boundary conditions using the combined QM/MM-Ewald sum (solid blue line) and periodic boundary MD simulations with 11.5 angstrom cut-off (dashed blue line), and with full-electrostatic SBMD (solid red line) and SMBD with 11.5 angstrom cut-off (dashed red line).  The QM/MM-Ewald method and SBMD method with full electrostatics have correct exponential decay of the free energy as a function of ion separation.  The cut-off simulations, on the other hand, exhibit artificial linear drift in the free energy that result in severe errors.