  We investigate the effects of spatial discreteness of molecules in
reaction-diffusion systems. It is found that discreteness within the so called
Kuramoto length can lead to a localization of molecules, resulting in novel
steady states that do not exist in the continuous case. These novel states are
analyzed theoretically as the fixed points of accelerated localized reactions,
an approach that was verified to be in good agreement with stochastic particle
simulations. The relevance of this discreteness-induced state to biological
intracellular processes is discussed.
