Size matters for nonlinear (protein) wave patterns

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Bergmann, Fabian ; Rapp, Lisa ; Zimmermann, Walter:
Size matters for nonlinear (protein) wave patterns.
In: New Journal of Physics. Bd. 20 (2018) . - 072001.
ISSN 1367-2630
DOI: https://doi.org/10.1088/1367-2630/aad457

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Abstract

Pattern formation and selection are fundamental, omnipresent principles in nature—from small cellsup to geological scales. InE. colibacteria, for example, self-organized pole-to-pole oscillations of Minproteins—resembling a short standing wave—ensure correct positioning of the cell division site. Thesame biochemical reaction leads to traveling protein waves on extended membranes inin vitroexperiments. Are these seemingly contradictory observations of system-spanning importance? Weshow that a transition of nonlinear traveling wave patterns to reflection-induced standing waves inshort systems is a generic and robust phenomenon. It results from a competition between two basicphenomena in pattern formation theory. We confirm the genericfindings for the cell-biological Minreaction and for a chemical reaction–diffusion system. These standing waves show bistability andadapt to varying system lengths similar as pole-to-pole oscillations in growingE. coli.Our genericresults highlight key functions of universal principles for pattern formation in nature.