Three-dimensional cell migration does not follow a random walk

Pei Hsun Wu, Anjil Giri, Sean X. Sun, Denis Wirtz

Research output: Contribution to journalArticlepeer-review

154 Scopus citations


Cell migration through 3D extracellular matrices is critical to the normal development of tissues and organs and in disease processes, yet adequate analytical tools to characterize 3D migration are lacking. Here, we quantified the migration patterns of individual fibrosarcoma cells on 2D substrates and in 3D collagen matrices and found that 3D migration does not follow a random walk. Both 2D and 3D migration features a non-Gaussian, exponential mean cell velocity distribution, which we show is primarily a result of cellto- cell variations. Unlike in the 2D case, 3D cell migration is anisotropic: velocity profiles display different speed and selfcorrelation processes in different directions, rendering the classical persistent random walk (PRW) model of cell migration inadequate. By incorporating cell heterogeneity and local anisotropy to the PRW model, we predict 3D cell motility over a wide range of matrix densities, which identifies density-independent emerging migratory properties. This analysis also reveals the unexpected robust relation between cell speed and persistence of migration over a wide range of matrix densities.

Original languageEnglish (US)
Pages (from-to)3949-3954
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number11
StatePublished - Mar 18 2014


  • 3D motility
  • Cancer
  • Theory

ASJC Scopus subject areas

  • General


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