(48f) Dynamics of the Urea-Urease Reaction in CSTR – Experiments and Detailed Model

We present experimental evidence of pH oscillations and bistability in the urea-urease enzyme reaction carried out in a continuous stirred tank reactor (CSTR) and compare these results with dynamics predicted by a detailed model of urea-urease reaction.

The CSTR is open to atmosphere with three inlet streams delivering solutions of urease, urea and sulphuric acid and one outlet stream. Sulfuric acid is used as a second substrate to form a feedback loop controlling production of ammonia making it possible to display nonlinear dynamical effects. The pH in the reaction mixture is measured via a pH electrode. Concentration of the inflow reactants are taken as variable parameters as well as the flow rate k₀. We show experimental k₀ - pH hysteresis curves for a wide range of urease concentrations and various inlet concentrations of sulfuric acid. More importantly, we also report pH oscillatory behavior with amplitudes of ~1 pH units occurring in a region of parameters adjacent to the region of hysteresis.

The model is based on a full scheme for protonation/deprotonation of the enzyme and its activated complex and, in addition, includes inhibition by the ammonium ions that are produced in weakly acidic conditions. A closer analysis based on the reaction network theory reveals that it is the inhibition that is responsible for the oscillatory behavior observed in the experiments. The model also shows an asymmetric double-bell-shaped curve of steady state reaction rate vs external pH in agreement with prior work. Near the higher peak there is a region of instability, where stable oscillations occur via Hopf bifurcation. Set of kinetic parameters for which the oscillatory behavior occurs was determined by the constrained stoichiometric network analysis, which uses linear optimization to select proper network parameters consistent with experimental observation of oscillations.