Mathematical modeling of molecular recognition by an ion-gating membrane oscillator

A mathematical model to explain the mechanism of molecular recognition by an ion-gating membrane oscillator has been proposed, in which the hydrostatic pressure-driven flow (pore-open state) and osmotic flow (pore-closed state) are switched alternatively in response to a specific ion signal. The model was based on transport equations derived from nonequilibrium thermodynamics, where the dependency of the reflection coefficient and the solvent hydrostatic permeability on the signal ion concentration were assumed to follow the Hill equation, based on experimental data. A time-delay effect was also introduced into the permeation parameters by first derivation. As a result, the model reproduced the characteristic parameters of the oscillator, such as the period and amplitude. It also clarified that an autocatalytic process, the key for nonlinear oscillation, was generated for an osmotic period by a slow response of the reflection coefficient and a fast response of the solvent hydrostatic permeability, i.e., the osmotic flow removes the signal ions out of the membrane to the ion-fed side, which increases the osmotic flow, and then more ions are removed from the membrane on opening the pores from the solvent side of the membrane.