Model for magnetic field effects on radical pair recombination in enzyme kinetics

A prototypical model for describing magnetic field effects on the reaction kinetics of enzymes that exhibit radical pair recombination steps in their reaction cycle is presented. The model is an extended Michaelis-Menten reaction scheme including an intermediate enzyme-substrate complex where a spin-correlated radical pair state exists. The simple structure of the scheme makes it possible to calculate the enzyme reaction rate explicitly by combining chemical kinetics with magnetic field-dependent spin kinetics (radical pair mechanism). Recombination probability is determined by using the exponential model. Simulations show that the size of the magnetic field effect depends on relations between different rate constants, such as 1) the ratio between radical pair-lifetime and the magnetic field-sensitive intersystem crossing induced by the hyperfine interaction and the delta g mechanisms and 2) the chemical rate constants of the enzyme reaction cycle. An amplification factor that is derived from the specific relations between the rate constants is defined. It accounts for the fact that although the magnetic field-induced change in radical pair recombination probability is very small, the effect on the enzyme reaction rate is considerably larger, for example, by a factor of 1 to 100. Model simulations enable a qualitative comparison with recent experimental studies reporting magnetic field effects on coenzyme B12-dependent ethanolamine ammonia lyase in vitro activity that revealed a reduction in Vmax/KM at low flux densities and a return to the zero-field rate or an increase at high flux densities.