Role of differential transport in an oscillatory enzyme reaction

As a result of the bell-shaped pH-rate characteristic of enzymatic processes, feedback may arise in enzyme reactions having non-neutral products. This special type of product activation has been shown to lead to self-sustained pH oscillations in an enzyme-loaded membrane. We investigate the possibility of oscillations in a model of the urea-urease reaction, prompted by the recent experimental discovery of feedback in this reaction. An open system is considered in which acid and urea are transported to a cell containing the enzyme. Using linear stability analysis we determine the range of transport coefficients limit cycles may exist for and show that differential transport is required for oscillations in a class of compartmentalized enzyme processes similar to the urea-urease system. We demonstrate that although the transport rate of acid (k_H) must be greater than that of urea (k_S) for oscillations in a urease-loaded membrane, bistability is possible for k _S≥ k_H.