The Influence of the Quantum Tunneling Phenomenon on Enzymatic Kinetics

Albert Jin and Brandon Walther

It is known within the scientific community that quantum tunneling plays a role in electron and proton transfer during enzymatic catalysis1-4, and certain mechanisms have been devised to describe these systems5,6.

The origins of this assumption arose from apparent disparities between measured and calculated rate constants within certain proteins that employ electron or proton transfer. Stemming from this correlation between electronic/hydrogenic transfer and increased rate constants, quantum tunneling was introduced into protein dynamics and catalysis to attempt to explain this phenomena. Experimental testing of the kinetic isotope effect (commonly used in chemical kinetics as well7,8) further solidified this hypothesis and tunneling was then considered an important factor in enzymatic catalysis.

This project seeks to develop a model that will mathematically mirror the tunneling phenomena's influence on the rate constants evident in nature.

The system was simplified to a one-dimensional, double-well harmonic oscillator which can be solved exactly to yield a transmission coefficient. This transmission coefficient, which relates the quantum rate constant to the classical rate constant, was then graphed to provide its dependence on the activation energy of the system (this value is analogous to to the height of the potential barrier in the wavefunction model of the system). It was found that many variable contribute to the degree of tunneling evident in protein catalysis such as temperature, internuclear distance, and, as stated earlier, the potential barrier.

In order to ascertain the accuracy of the model, the values that would be theoretically predicted using the model were applied to the kinetic isotope effect, which is a ratio of the rate of the light isotope to the heavy isotope that is often cited in literature7,8 to measure the degree of tunneling evident in a reaction mechanism. Heavier particles alter values within the quantum harmonic oscillator and lead to slower rates, which can be both calculated using our model and measured experimentally.