Asymptotic stability of contraction-driven cell motion

C. Alex Safsten, Volodmyr Rybalko, Leonid Berlyand

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We study the onset of motion of a living cell (e.g., a keratocyte) driven by myosin contraction with focus on a transition from unstable radial stationary states to stable asymmetric moving states. We introduce a two- dimensional free-boundary model that generalizes a previous one-dimensional model [P. Recho, T. Putelat, and L. Truskinovsky, Phys. Rev. Lett. 111, 108102 (2013)10.1103/PhysRevLett.111.108102] by combining a Keller-Segel model, a Hele-Shaw boundary condition, and the Young-Laplace law with a regularizing term which precludes blowup or collapse by ensuring that membrane-cortex interaction is sufficiently strong. We find a family of asymmetric traveling solutions bifurcating from stationary solutions. Our main result is nonlinear asymptotic stability of traveling solutions that model observable steady cell motion. We derive an explicit asymptotic formula for the stability-determining eigenvalue via asymptotic expansions in small speed. This formula greatly simplifies computation of this eigenvalue and shows that stability is determined by the change in total myosin mass when stationary solutions bifurcate to traveling solutions. Our spectral analysis reveals the physical mechanisms of stability.

Original languageEnglish (US)
Article number024403
JournalPhysical Review E
Issue number2
StatePublished - Feb 2022

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


Dive into the research topics of 'Asymptotic stability of contraction-driven cell motion'. Together they form a unique fingerprint.

Cite this