A Self-Organized Vortex Array of Hydrodynamically Entrained Sperm Cells

Ingmar H. Riedel, Karsten Kruse, Jonathon Howard

Many patterns in biological systems depend on the exchange of chemical
signals between cells. We report a spatio-temporal 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. A model
allowed us to estimate the hydrodynamic interaction force between
spermatozoa to be ~0.03 pN. Thus, large-scale coordination of cells can
be regulated hydrodynamically, without chemical signals being required.
(Science, 2005)