Electric Field Effects on an Enzyme Membrane Oscillator

Abstract

A simple two compartment model system composed of a reservoir and a reactor is studied by means of numerical bifurcation analysis. An enzyme reaction involving ionic species is assumed to take place in the reactor connected to the reservoir via a semi-permeable electrically inert membrane. An external electric voltage is applied to this system via electrodes connected to each of the two compartments. An intra-membrane electric field caused by the applied voltage generates electrophoretic fluxes of each charged reaction component. We study the effects of a static and a periodically varying electric field on the dynamical regimes in the reactor. In the static case we find that a negative field supports the oscillatory dynamics while a positive field promotes multiplicity. Sinusoidal variations of the field cause a rich variety of dynamical responses, ranging from various periodic firing patterns to quasiperiodicity and chaos. These dynamical modes are associated with characteristic bifurcation structures in a forcing period -forcing amplitude bifurcation diagram which can be used for their classification.