  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 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. The observed oscillations are explained as a canard-like
limit cycle that differs from the wide class of conventional feedback
oscillators.
