title: Polar patterns of driven filaments.
abstract: The emergence of collective motion exhibited by systems ranging from flocks of animals to self-propelled microorganisms to the cytoskeleton is a ubiquitous and fascinating self-organization phenomenon. Similarities between these systems, such as the inherent polarity of the constituents, a density-dependent transition to ordered phases or the existence of very large density fluctuations, suggest universal principles underlying pattern formation. This idea is followed by theoretical models at all levels of description: micro- or mesoscopic models directly map local forces and interactions using only a few, preferably simple, interaction rules, and more macroscopic approaches in the hydrodynamic limit rely on the systems' generic symmetries. All these models characteristically have a broad parameter space with a manifold of possible patterns, most of which have not yet been experimentally verified. The complexity of interactions and the limited parameter control of existing experimental systems are major obstacles to our understanding of the underlying ordering principles. Here we demonstrate the emergence of collective motion in a high-density motility assay that consists of highly concentrated actin filaments propelled by immobilized molecular motors in a planar geometry. Above a critical density, the filaments self-organize to form coherently moving structures with persistent density modulations, such as clusters, swirls and interconnected bands. These polar nematic structures are long lived and can span length scales orders of magnitudes larger than their constituents. Our experimental approach, which offers control of all relevant system parameters, complemented by agent-based simulations, allows backtracking of the assembly and disassembly pathways to the underlying local interactions. We identify weak and local alignment interactions to be essential for the observed formation of patterns and their dynamics. The presented minimal polar-pattern-forming system may thus provide new insight into emerging order in the broad class of active fluids and self-propelled particles.
authors.affiliation: Lehrstuhl für Biophysik-E27, Technische Universität München, 85748 Garching, Germany.
authors.forename: Volker
authors.initials: V
authors.lastname: Schaller
authors.forename: Christoph
authors.initials: C
authors.lastname: Weber
authors.forename: Christine
authors.initials: C
authors.lastname: Semmrich
authors.forename: Erwin
authors.initials: E
authors.lastname: Frey
authors.forename: Andreas R
authors.initials: AR
authors.lastname: Bausch
mesh_terms: D008841:Actin Cytoskeleton / Q000378:metabolism*; D000818:Animals; D003599:Cytoskeleton / Q000737:chemistry*; D008870:Microtubules / Q000737:chemistry; D008954:Models, Biological; D015879:Myosin Subfragments / Q000378:metabolism*
chemical_list: D015879:Myosin Subfragments
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 Aug;54(2):1791-1801
references.pmid: 9965259
references.citation: Science. 2007 Jul 20;317(5836):333-6
references.pmid: 17641191
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jun;81(6 Pt 1):061916
references.pmid: 20866449
references.citation: Phys Rev Lett. 1995 Aug 7;75(6):1226-1229
references.pmid: 10060237
references.citation: Integr Biol (Camb). 2009 Feb;1(2):150-69
references.pmid: 20023800
references.citation: Nature. 2005 Feb 3;433(7025):513-6
references.pmid: 15690039
references.citation: Phys Rev Lett. 2004 Feb 20;92(7):078101
references.pmid: 14995891
references.citation: Phys Biol. 2006 Dec 04;3(4):264-73
references.pmid: 17200602
references.citation: Phys Rev Lett. 2010 May 7;104(18):184502
references.pmid: 20482178
references.citation: Phys Rev Lett. 2002 Jul 29;89(5):058101
references.pmid: 12144468
references.citation: Nat Rev Mol Cell Biol. 2008 Mar;9(3):255-62
references.pmid: 18292780
references.citation: Phys Rev Lett. 2008 Dec 31;101(26):268101
references.pmid: 19113789
references.citation: Science. 2008 May 9;320(5877):789-92
references.pmid: 18467587
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2005 May;71(5 Pt 1):050901
references.pmid: 16089514
references.citation: Proc Natl Acad Sci U S A. 2009 Sep 15;106(37):15567-72
references.pmid: 19717428
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Apr;77(4 Pt 2):046113
references.pmid: 18517696
references.citation: Nature. 1997 Sep 18;389(6648):305-8
references.pmid: 9305848
references.citation: J Cell Biol. 1984 Nov;99(5):1867-71
references.pmid: 6490724
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jan;77(1 Pt 1):011920
references.pmid: 18351889
references.citation: Science. 2001 May 11;292(5519):1167-71
references.pmid: 11349149
references.citation: Science. 2005 Jul 8;309(5732):300-3
references.pmid: 16002619
references.citation: Phys Rev Lett. 2004 Aug 27;93(9):098103
references.pmid: 15447144
references.citation: Phys Rev Lett. 2006 Jun 30;96(25):258103
references.pmid: 16907349
references.citation: Science. 2007 Jul 6;317(5834):105-8
references.pmid: 17615353