Landau theory for cellular patterns driven by lateral inhibition interaction.

The phenomenology of Landau theory with spatial coupling through diffusion has been widely used in the study of phase transitions and patterning. Here we follow this theory and apply it to study theoretically and numerically continuous and discontinuous transitions to periodic spatial cellular patterns driven by lateral inhibition coupling. As opposed to diffusion, lateral inhibition coupling drives differences between adjacent cells. We analyze the appearance of errors in these patterns (disordered metastable states) and propose mechanisms to prevent them. These mechanisms are based on a temporal-dependent lateral inhibition coupling strength, which can be mediated, among others, by gradients of diffusing molecules. The simplicity and generality of the framework used herein is expected to facilitate future analyses of additional phenomena taking place through lateral inhibition interactions in more complex scenarios.