A Self-Organized Vortex Array of Hydrodynamically Entrained Sperm Cells

TLDR

Biological pattern formation often relies on intercellular chemical signaling. The authors employed an order‑parameter model and estimated hydrodynamic forces (~0.03 pN) to show that vortex arrays arise only above a critical sperm density. Spermatozoa on planar surfaces self‑organize into dynamic, hexagonally ordered vortices driven solely by hydrodynamic interactions, without the need for chemical signaling.

Abstract

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 approximately 0.03 piconewtons. Thus, large-scale coordination of cells can be regulated hydrodynamically, and chemical signals are not required.