Our laboratory is working on a “gel-enzyme” oscillator intended to deliver rhythmic hormone replacement therapy. Gonadotropin releasing hormone (GnRH), the primary hormone of interest, regulates sexual function with pulses released every 1-2 hours. Hypogonadotropic hypogonadism (HH) is a clinical condition of dysfunctional GnRH secretion that leads to symptoms such as sexual immaturity or sterility. Currently, neither oral delivery nor controlled release technologies provide the “round the clock” rhythmic timing required for effective GnRH replacement therapy.

The gel-enzyme oscillator combines enzymatic feedback with nonlinear hydrogel membrane permeability to achieve rhythmic hormone release. The hydrogel membrane is a weakly acidic hydrophobic gel, poly(N-isopropyl acrylamide-co-methacrylic acid), which exhibits bistability in its solute permeability when exposed to a dynamic pH gradient. Enzymatic conversion of glucose to gluconic acid provides a destabilizing feedback on the gel membrane, leading to oscillatory switching between permeability states. These nonlinear system dynamics have been modeled previously, but with a homogeneous representation of the gel membrane. In reality, the gel membrane itself contains dynamically changing pH gradients, leading to potentially complex spatiotemporal behaviors, such as dynamically shifting coexistent phases. A miniaturized version of the device has been proposed using microelectromechanical (MEMS) fabrication techniques. Such a substantial reduction in size could have significant impact on device behavior. However, predicting the behavior of new designs is limited by an incomplete understanding of nonlinear permeability mechanisms.

In this dissertation, the gel-enzyme oscillator is modeled using a distributed representation of the gel membrane to study nonlinear permeability and its role in oscillations. First, the nonlinear pH-dependence of the hydrogel membrane’s permeability is studied theoretically and experimentally. A model developed to account for the membrane’s behavior under “open loop” conditions is then coupled to a simple model of enzymatic feedback to model the behavior of the gel-enzyme oscillator. Based on insights from this model, a layered membrane is proposed to enable oscillations in a physiological environment.