Proton-Coupled Electron Transfer in Soybean Lipoxygenase:  Dynamical Behavior and Temperature Dependence of Kinetic Isotope Effects

Abstract

The dynamical behavior and the temperature dependence of the kinetic isotope effects (KIEs) are examined for the proton-coupled electron transfer reaction catalyzed by the enzyme soybean lipoxygenase. The calculations are based on a vibronically nonadiabatic formulation that includes the quantum mechanical effects of the active electrons and the transferring proton, as well as the motions of all atoms in the complete solvated enzyme system. The rate constant is represented by the time integral of a probability flux correlation function that depends on the vibronic coupling and on time correlation functions of the energy gap and the proton donor-acceptor mode, which can be calculated from classical molecular dynamics simulations of the entire system. The dynamical behavior of the probability flux correlation function is dominated by the equilibrium protein and solvent motions and is not significantly influenced by the proton donor-acceptor motion. The magnitude of the overall rate is strongly influenced by the proton donor-acceptor frequency, the vibronic coupling, and the protein/solvent reorganization energy. The calculations reproduce the experimentally observed magnitude and temperature dependence of the KIE for the soybean lipoxygenase reaction without fitting any parameters directly to the experimental kinetic data. The temperature dependence of the KIE is determined predominantly by the proton donor-acceptor frequency and the distance dependence of the vibronic couplings for hydrogen and deuterium. The ratio of the overlaps of the hydrogen and deuterium vibrational wavefunctions strongly impacts the magnitude of the KIE but does not significantly influence its temperature dependence. For this enzyme reaction, the large magnitude of the KIE arises mainly from the dominance of tunneling between the ground vibronic states and the relatively large ratio of the overlaps between the corresponding hydrogen and deuterium vibrational wavefunctions. The weak temperature dependence of the KIE is due in part to the dominance of the local component of the proton donor-acceptor motion.

Hydrogen Tunneling in an Enzyme Active Site: A Quantum Wavepacket Dynamical Perspective

“…From the timedependent evolution of the quantum wavepacket, we show that there is significant population of the higher-energy eigenstates. The significance of excited nuclear wave functions has also been observed by other investigators 12,79 through one-dimensional model potentials. Whereas p | -type states can be inferred from one-dimensional potentials, the contributions from p ⊥ -type states to the tunneling process cannot be envisioned through a onedimensional model.…”

“…19 Quantum mechanical tunneling is believed to be the fundamental reason behind this phenomenon. 7,12,16 (b) In some cases, a weak temperature dependence of the rate constant is seen in conjunction with large primary KIE. 20 (c) An elevated value for the Swain-Schaad exponent 21 [log(k H /k D )/log(k D /k T )] has also been noted.…”

“…The nonadiabatic rate expression 12 includes hydrogen and deuterium ground and excited nuclear wave functions, constructed on the basis of onedimensional Morse oscillator approximations, and the rate is computed through the product of an electronic coupling and a temperature-dependent term that attenuates the nuclear wavefunction overlap. 12 The full protein is explicitly treated through classical molecular dynamics simulations modified by empirical valence-bond [25][26][27][28] force-field corrections. Hammes-Schiffer and co-workers have also employed mixed quantum/classical dynamics to study hydrogen tunneling problems.…”

A chemical understanding for the enhanced hydrogen tunnelling in hydroperoxidation of linoleic acid catalysed by soybean lipoxygenase‐1

“…The supposed nonadiabaticity of this PCET motivated its treatment with radiationless transitions theories based on the golden rule of quantum mechanics. [3][4][5][6][7] In adiabatic reactions, the overlap of vibronic wavefunctions gives rise to nuclear tunnelling and is incorporated as a pre-exponential correction to the TST rate expression, Eq (7), while retaining the classical frequency of the nuclear motion along the reaction coordinate, n N % k B T/h.…”

“…The difficulties of TST stimulated the formulation of alternative theories. [2][3][4][5][6][7][8] Indeed, this KIE is much higher than that observed in other H-atom abstractions; for example, that of the H þ H 2 versus H þ D 2 hydrogen (deuterium) transfer is only 9.5 AE 1.4 at 30 8C. [9] The complexity of enzyme catalysis did not dissuade several groups of pursuing more sophisticated versions of TST in the treatment of these systems, to show that tunnelling and recrossing corrections may account for the extreme behaviours sometimes observed.…”