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October 5, 2021

The pH oscillations in the urea–urease reaction confined to a vesicle show a stochastic rhythm

Background & motivation: Oscillations are important for a variety of technological and intracellular processes involving enzyme-catalyzed reactions. Enzymatic activity is strongly dependent on the acidity of the medium or, simply, the pH level. Such a dependence can give rise to pronounced periodic pH variations, the key driving factor for pH oscillators. Their theoretical studies have mostly been limited to deterministic models operating concentrations and relying on well-mixed conditions. However, the reaction kinetics is typically confined to small vesicles, i.e. permeable membrane-based micro- to nano-sized compartments. Such small reactors typically host only very limited copy numbers of molecules, necessitating a discrete stochastic treatment of the reaction dynamics. Motivated by experimental implementations and direct relevance to applications, we have considered an urea-urease-based pH oscillator confined to a lipid vesicle and studied the impact of intrinsic noise caused by such molecular discreteness.

Figure: The urease-catalyzed hydrolyzation of urea (bottom) shows stochastic pH oscillations (left: lines for deterministic and dots for stochastic trajectories) upon confinement to a lipid vesicle. The limit cycle of this slow-fast dynamics results from the interplay of an unstable focus point and a canard-like behavior (right: schematic).

Findings: We have drawn a threefold conclusion inaccessible within the deterministic models: i) intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller; ii) the mean period depends on the vesicle size and remains remarkably robust for vesicle sizes down to approximately 200 nm; iii) for smaller vesicles, intrinsic noise becomes so strong that the periodicity of the rhythm is gradually destroyed. More generally, the explanation of the observed oscillations as a general canard-like limit cycle suggests that similar trends may take place for other chemical oscillators.

A.V. Straube, S. Winkelmann, Ch. Schütte, F. Höfling,
Stochastic pH oscillations in a model of the urea–urease reaction confined to lipid vesicles,
J. Phys. Chem. Lett. 12, 9888 (2021) [arXiv:2110.03465]