  Common models of circadian rhythms are constructed as compartmental reactions
of well mixed biochemicals involving a negative-feedback loop containing
several intermediate reaction steps in order to enable oscillations. Spatial
transport of reactants is mimicked as an extra compartmental reaction step. In
this letter, we show that a single activation-repression biochemical reaction
pair is enough to produce sustained oscillations, if the sites of both
reactions are spatially separated and molecular transport is mediated by
diffusion. Our proposed scenario is the simplest possible one in terms of the
participating chemical reactions and provides a conceptual basis for
understanding biological oscillations and triggering in-vitro assays aimed at
constructing minimal clocks.
