  Dynamic patterning of specific proteins is essential for the spatiotemporal
regulation of many important intracellular processes in procaryotes,
eucaryotes, and multicellular organisms. The emergence of patterns generated by
interactions of diffusing proteins is a paradigmatic example for
self-organization. In this article we review quantitative models for
intracellular Min protein patterns in E. coli, Cdc42 polarization in S.
cerevisiae, and the bipolar PAR protein patterns found in C. elegans. By
analyzing the molecular processes driving these systems we derive a theoretical
perspective on general principles underlying self-organized pattern formation.
We argue that intracellular pattern formation is not captured by concepts such
as "activators"', "inhibitors", or "substrate-depletion". Instead,
intracellular pattern formation is based on the redistribution of proteins by
cytosolic diffusion, and the cycling of proteins between distinct
conformational states. Therefore, mass-conserving reaction-diffusion equations
provide the most appropriate framework to study intracellular pattern
formation. We conclude that directed transport, e.g. cytosolic diffusion along
an actively maintained cytosolic gradient, is the key process underlying
pattern formation. Thus the basic principle of self-organization is the
establishment and maintenance of directed transport by intracellular protein
dynamics.
