Modeling of coupled enzyme membrane oscillators—Effects of an electric field

Abstract

Effects of an external electric field on dynamical patterns in a model of two coupled reaction units, each comprising a reservoir–reactor system are studied using numerical bifurcation analysis. A pH-sensitive enzyme reaction involving ionic species is assumed to take place in the stirred reactors mutually coupled by a permeable passively conducting membrane. Reactants are fed to reactors through the same type of membrane from adjacent reservoirs. An external electric voltage is applied to this system. An intra-membrane electric field caused by the applied voltage generates electrophoretic fluxes of each charged reaction component. Dynamical regimes including multiple steady states, oscillations and excitability occur in the absence of electric fields due to a combination of autocatalytic reaction and diffusive transport. We focus on dynamical patterns occurring as a consequence of electric current, either constant or periodically varying, that passes through the system. In the static case we find that the field suppresses oscillatory dynamics and promotes multiplicity of steady states including occurrence of reaction–ionic migration patterns analogous to Turing patterns. Sinusoidal variations of the current cause a rich variety of dynamical responses, ranging from periodic phase-locked patterns to quasiperiodicity to chaos.