Molecular discreteness in reaction-diffusion systems yields steady states not seen in the continuum limit

We investigate the effects of the 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 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.