Browsing by Author "Kästner, Johannes (Jun.-Prof.)"

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Improvements to the instanton method : tunneling rates in the enzyme glutamate mutase
(2012) Rommel, Judith Barbara; Kästner, Johannes (Jun.-Prof.)
Atom tunneling occurs in many chemical reactions involving hydrogen transfers. Tunneling increases the reaction rate compared to the classical over-the-barrier model especially at low temperature. In many enzymes tunneling of hydrogen atoms influences the reaction rate even at room temperature which can experimentally be observed by unusually high kinetic isotope effects (KIEs). A high KIE shows that tunneling accelerates the rate limiting step. Computer simulations can directly quantify the effect of tunneling in a reaction by switching it on and off. The enzyme glutamate mutase catalyzes the radical conversion mechanism of (S)-glutamate to (2S,3S)-3-methylaspartate including two hydrogen transfer steps. The protium/deuterium KIEs measured in glutamate mutase range from 4.1 to 35 at 10°C. Thus, it is unclear whether tunneling is involved or important for the catalytic process. Glutamate mutase is studied by a multiscale approach combining quantum mechanics with molecular mechanics (QM/MM), with quantum mechanical (QM) calculations used for the atoms directly involved in bond rearrangements and force field calculations (MM) for the environment. The QM part is investigated with density functional theory and coupled cluster theory. The results of the QM/MM simulations show new details of the catalyzed reaction and lead to an improved understanding of the catalysis by glutamate mutase: the conversion of (S)-glutamate to (2S,3S)-3-methylaspartate is found to proceed via a fragmentation-recombination mechanism. The involved hydrogen atom transfer steps exhibit the highest barrier, 101 kJ/mol (M06 functional). The barriers of the hydrogen transfers match for density functional theory (M06 functional) and coupled cluster (LUCCSD(T)) calculations. It turned out that the influence of the enzyme is mainly electrostatical and to a lesser degree sterical. The calculations shed light on the atomistic details of the reaction mechanism. The well-known arginine claw (Arg 66, Arg 100, and Arg 149) and Glu 171 are found to have the strongest influence on the reaction. The arginine claw keeps the intermediate fragments in place, and is important for the recombination process. However, significant catalytic roles of amino acids close to the active center, e.g., Glu 214, Lys 322, Gln 147, Glu 330, Lys 326, and Met 294 are found as well. These results predict new promising experimental targets. The role of tunneling in the enzyme glutamate mutase is investigated by QM/MM simulations based on instanton theory with up to 78 atoms allowed to tunnel. Primary protium/deuterium KIEs of hydrogen transfers are in good agreement with experiment. The secondary tritium KIEs hint that coupled motions on a ribose ring of the cofactor are part of the tunneling motions. The enzyme uses both classical and tunneling motions for a successful catalysis. The instanton method (also called imaginary free energy method) is based on Feynman's path integral formalism. The instanton is the most-likely tunneling path. The instanton is also a first-order saddle point of the Euclidean action. The problem of finding an instanton is addressed as a saddle-point search problem. Four algorithms implemented to locate instantons are compared: a modified Newton-Raphson method, the partitioned rational function optimization algorithm, the dimer method, and a newly proposed mode-following algorithm. These algorithms are tested on three chemical systems. Overall, the Newton-Raphson turns out to be the most promising method, consistently efficient and stable, with the newly proposed mode-following method being the fall-back option. Two bottlenecks are challenging in instanton rate calculations: (1) Hessian calculations subsequent to the instanton optimization are expensive for large systems like enzymes. (2) At lower temperature more and more discretization points (images) on the equidistantly discretized path tend to accumulate at the ends of the instanton path. Thus, methods that allow to use fewer discretization points for the same quality in the rates are required. The development of a quadratically convergent optimizer significantly increases the efficiency of instanton optimizations. In combination with a new, flexible, and variable discretization of the integration along the instanton, the computational costs are reduced by one or two orders of magnitude.