Dynamic patterning of specific proteins is essential for the spatio-temporal regulation of many important intracellular processes in prokaryotes, eukaryotes 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 Escherichia coli, Cdc42 polarization in Saccharomyces cerevisiae and the bipolar PAR protein patterns found in Caenorhabditis elegans. By analysing 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.This article is part of the theme issue ‘Self-organization in cell biology’.

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Arp2/3 complex-mediated actin assembly at cell membranes drives the formation of protrusions or endocytic vesicles. To identify the mechanism by which different membrane deformations can be achieved, we reconstitute the basic membrane deformation modes of inward and outward bending in a confined geometry by encapsulating a minimal set of cytoskeletal proteins into giant unilamellar vesicles. Formation of membrane protrusions is favoured at low capping protein (CP) concentrations, whereas the formation of negatively bent domains is promoted at high CP concentrations. Addition of non-muscle myosin II results in full fission events in the vesicle system. The different deformation modes are rationalized by simulations of the underlying transient nature of the reaction kinetics. The relevance of the regulatory mechanism is supported by CP overexpression in mouse melanoma B16-F1 cells and therefore demonstrates the importance of the quantitative understanding of microscopic kinetic balances to address the diverse functionality of the cytoskeleton.

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