Title: Protein Pattern Formation,
Abstract: Protein pattern formation is essential for the spatial organization of many
intracellular processes like cell division, flagellum positioning, and
chemotaxis. A prominent example of intracellular patterns are the oscillatory
pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological
function is to ensure precise cell division. Cell polarization, a prerequisite
for processes such as stem cell differentiation and cell polarity in yeast, is
also mediated by a diffusion-reaction process. More generally, these functional
modules of cells serve as model systems for self-organization, one of the core
principles of life. Under which conditions spatio-temporal patterns emerge, and
how these patterns are regulated by biochemical and geometrical factors are
major aspects of current research. Here we review recent theoretical and
experimental advances in the field of intracellular pattern formation, focusing
on general design principles and fundamental physical mechanisms.