  Enzyme-enriched condensates can organize the spatial distribution of their
substrates by catalyzing non-equilibrium reactions. Conversely, an
inhomogeneous substrate distribution induces enzyme fluxes through
substrate-enzyme interactions. We find that condensates move towards the center
of a confining domain when this feedback is weak. Above a feedback threshold,
they exhibit self-propulsion, leading to oscillatory dynamics. Moreover,
catalysis-driven enzyme fluxes can lead to interrupted coarsening, resulting in
equidistant condensate positioning, and to condensate division.
