Publication in The Journal of Physical Chemistry Letters
The urease-catalysed hydrolysation of urea shows stochastic pH oscillations 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 behaviour.
News from Oct 05, 2021
The urea–urease clock reaction is a pH switch from acid to basic that can turn into a pH oscillator if it occurs inside a suitable open reactor. We numerically study the confinement of the reaction to lipid vesicles, which permit the exchange with an external reservoir by differential transport, enabling the recovery of the pH level and yielding a constant supply of urea molecules. For microscopically small vesicles, the discreteness of the number of molecules requires a stochastic treatment of the reaction dynamics. Our analysis shows that intrinsic noise induces a significant statistical variation of the oscillation period, which increases as the vesicles become smaller. The mean period, however, is found to be remarkably robust for vesicle sizes down to approximately 200 nm, but the periodicity of the rhythm is gradually destroyed for smaller vesicles. The observed oscillations are explained as a canard-like limit cycle that differs from the wide class of conventional feedback oscillators.
A. V. Straube, S. Winkelmann, Ch. Schütte, and F. Höfling,
Stochastic pH Oscillations in a Model of the Urea–Urease Reaction Confined to Lipid Vesicles,
J. Phys. Chem. Lett. 12, 9888 (2021).