ABSTRACT: 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 canardlike
limit cycle that differs from the wide class of conventional feedback oscillators
