Analysis of Hydrogen Tunneling in an Enzyme Active Site using von Neumann Measurements

We build on our earlier quantum wavepacket study of hydrogen transfer in the biological enzyme, soybean lipoxygenase-1, by using von Neumann quantum measurement theory to gain qualitative insights into the transfer event. We treat the enzyme active site as a measurement device which acts on the tunneling hydrogen nucleus via the potential it exerts at each configuration. A series of changing active site geometries during the tunneling process effects a sequential projection of the initial, reactant state onto the final, product state. We study this process using several different kinds of von Neumann measurements and show how a discrete sequence of such measurements not only progressively increases the projection of the hydrogen nuclear wavepacket onto the product side but also favors proton over deuteron transfer. Several qualitative features of the hydrogen tunneling problem found in wavepacket dynamics studies are also recovered here. These include the shift in the "transition state" towards the reactant as a result of nuclear quantization, greater participation of excited states in the case of deuterium, and presence of critical points along the reaction coordinate that facilitate hydrogen and deuterium transfer and coincide with surface crossings. To further "tailor" the dynamics, we construct a perturbation to the sequence of measurements, that is a perturbation to the dynamical sequence of active site geometry evolution, which leads us to insight on the existence of sensitive regions of the reaction profile where subtle changes to the dynamics of the active site can have an effect on the hydrogen and deuterium transfer process.