Title:

Novel QM/MM Investigations of Enzyme Catalysis

Enzymes facilitate specific chemical reactions by lowering the Gibbs free energy of activation (AG++),
thus increasing the rate of catalysis. It would be advantageous to understand exactly what within the
enzyme leads to this lowering ofthe activation energy. This work describes the development ofa
protocol for calculating the free energy barrier between two states of an enzyme, or other condensed
phase system using computer simulation. The natute of the calculation enables it to be decomposed to
reveal which vibrational modes observed in a molecular dynamics simulation are contributing to the
catalytic effects.
The energy gap fluctuations between the two states can be used to calculate a free energy function for
the reaction coordinate between two states. A probability distribution function can be generated using ,
these values and, given sufficient equilibrium sampling, the Central Limit Theorem may be invoked so
that the distribution can be represented by a Gaussian function. Using this distribution to represent the
equilibrium constant within Transition State Theory, the free energy difference is quadratic with
respect to the energy gap value. Assuming a linear response ofthe solvent bath (Marcus theory), the
free energy difference function is extrapolated to a zero energy gap value, thus giving the,
experimentally comparable, free energy of activation between those two states.
The thesis presents the progress made in developing this novel approach for obtaining the energy gap
between two states, and its initial application to the rate limiting hydride transfer step catalysed by the
extensively studied horse liver alcohol dehydrogenase (LADH) enzyme. Two, independent,
equilibrium trajectories ofthe states either side ofthis rate limiting step are propagated classically
using the AMBER force field. Time ordered snapshots ofthe simulation's coordinates are postprocessed
using a QMlMM method to obtain the ground state energy ofthe system; the active site is
treated quantum mechanically, with the polarising effects ofthe surrounding protein and water bath
incorporated as point charges in its one electron Hamiltonian. Development ofthe approach was
facilitated using the smaller test system ofMalachite Green.
This protocol offers a computationally cheaper alternative to the normal Empirical Valence Bond
(EVB) I Free Energy Perturbation (PEP) approach, since only two equilibrium trajectories of both
states are required instead of an ovedapping set of trajectories in the range between the states. The
additional complexity of a switching Hamiltonian is also avoided. The subtracted spectrum of
oscillators gives insight into which vibrational modes within the system are contributing to the
catalytic effect. '
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