(216f) Bistability and pH Oscillations in the Urea-Urease Reaction in a Flow Reactor

We present experimental evidence of pH oscillations and bistability in the urea-urease enzymatic reaction carried out in a continuous stirred tank reactor(CSTR)and compare these results with dynamics predicted by a model of urea-urease reaction. Unlike bistability, experimentally periodic oscillations have not been reported for this system yet.

The CSTR is open to the atmosphere with three inlet streams delivering solutions of urease, urea and sulphuric acid and one outlet stream. Sulphuric 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 inflowing reactants are taken as variable parameters as well as the flow rate k₀. As previously reported in Hu et al. [1], the system is bistable with coexisting acidic and weakly basic steady states implying hysteresis. We confirm these results and show experimental k₀-pH hysteresis curves, for a wide range of urease concentrations and various inlet concentrations of sulphuric acid. More importantly, we also report pH oscillatory behavior with amplitudes of ~1 pH units occurring in a region of parameters adjacent to the hysteresis region.

Simulation of the bistable mode is readily obtained by using a simple reaction mechanism based on the Michaelis-Menten kinetics extended by generic bell-shaped dependence of the reaction rate on pH [1]. This model has been slightly extended by including dynamical equilibration of non-enzymatic protonation-deprotonation processes [2]. However, such models do not predict oscillations under the CSTR conditions, i.e., when the transport coefficients for acid and urea coincide with the flow rate k₀, the models only show oscillations under differential transport conditions corresponding to a membrane reactor [2, 3]. In order to account for the observed experimental oscillations, the enzyme part of the mechanism needs to be expressed in terms of detailed kinetics. The enzyme urease catalyzes hydrolysis of urea forming carbon dioxide and ammonia. One consequence of the complexity of the detailed mechanism is that urease has double maxima bell shaped activity pH curve [4]. Starting from pH~3, where the activity of urease is nearly zero, the activity of urease is increased with increasing pH value up to the first maximum around pH~6.6, then the activity decreases with increasing pH but later increases again reaching another maximum at pH ~7.35. Then the activity drops and vanishes at pH~9.1.

Another aspect that is taken into account when formulating the detailed model is inhibition by ammonium ion [5]. When this part of the mechanism is included, the model predicts oscillations even under CSTR conditions. To understand this observation, we employ the concepts of reaction network theories, in particular, the stoichiometric network analysis. By using decomposition of the detailed network into subnetworks and analysing stability of these subnetworks, we identified the core mechanism that is responsible for observing CSTR oscillations and found the corresponding set of kinetic parameters.

The model accounting for our experimental findings consists of evolution equations considering the double hump pH sensitivity curve [1] and inhibition by the ammonia ion [5]. The core subnetwork providing the observed oscillatory behavior is identified by using the constrained stoichiometric network analysis [6], which also enables determining unknown kinetic parameters consistent with the experimentally observed oscillations. Subsequently, stability and bifurcation analysis is presented in terms of solution and bifurcation diagrams calculated by continuation method using program CONT [7]. Correspondence between model simulations and experimental oscillatory regimes are discussed.

[1] G. Hu, J. A. Pojman, S. K. Scott, M. M. Wrobel and A. F. Taylor, The Journal of Physical Chemistry B 114, 14059-14063, (2010).

[2] T. Bánsági Jr. and A. F. Taylor, J. Phys. Chem. B 118, 6092-6097, (2014).

[3] F. Muzika, M. Růžička, L. Schreiberová and I. Schreiber, Phys. Chem. Chem. Phys. 00 , 1-4, (2019). DOI: 10.1039/c9cp00630c

[4] B. Krajewska and S. Ciurli, Plant Physiology and Biochemistry 43, 651-658, (2005).

[5] J. P. Hoare and K. J. Laidler, J. Am. Chem. Soc. 72, 2487-2489, (1950).

[6] V. Radojković and I. Schreiber, Phys. Chem. Chem. Phys. 20, 9910-9921, (2018).

[7] M. Kubíček and M. Marek: Computational methods in bifurcation theory and dissipative structures. Springer Verlag, New York 1983; M. Kohout, I. Schreiber and M. Marek, Compt. and Chem. Eng. 26, 517-527, (2002).