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ReportsA Self-Organized Vortex Array of Hydrodynamically Entrained Sperm Cells
Many patterns in biological systems depend on the exchange of chemical signals between cells. We report a spatiotemporal pattern mediated by hydrodynamic interactions. At planar surfaces, spermatozoa self-organized into dynamic vortices resembling quantized rotating waves. These vortices formed an array with local hexagonal order. Introducing an order parameter that quantifies cooperativity, we found that the array appeared only above a critical sperm density. Using a model, we estimated the hydrodynamic interaction force between spermatozoa to be
1 Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstrasse 108, D-01307 Dresden, Germany. * To whom correspondence should be addressed. E-mail: riedel{at}mpi-cbg.de (I.H.R.); howard{at}mpi-cbg.de (J.H.)
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0.03 piconewtons. Thus, large-scale coordination of cells can be regulated hydrodynamically, and chemical signals are not required. 
Science. ISSN 0036-8075 (print), 1095-9203 (online)
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