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A Dynamical Analysis of the Alignment Mechanism Between Two Interacting Cells.

Vivienne Leech1, Mohit P Dalwadi2,3, Angelika Manhart4,5

  • 1Department of Mathematics, University College London, London, UK.

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Summary
This summary is machine-generated.

Self-propelled ellipse-shaped cells can align through overlap avoidance. A critical balance of self-propulsion is needed; too little or too much hinders perfect cell alignment.

Keywords:
Asymptotic analysisCell alignmentDynamical systems

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Area of Science:

  • Cellular dynamics
  • Biophysics
  • Collective cell behavior

Background:

  • Understanding how individual cells interact and organize is crucial in developmental biology and tissue engineering.
  • Self-propelled particles offer a model system for studying emergent collective behaviors.
  • Cell shape and motility are key factors influencing cellular interactions.

Purpose of the Study:

  • To analytically investigate the alignment mechanism of self-propelled ellipse-shaped cells in 2D.
  • To determine the role of self-propulsion and overlap avoidance in achieving cell alignment.
  • To identify conditions leading to perfect cellular alignment.

Main Methods:

  • Analytical investigation of a two-cell system with imposed symmetries.
  • Mathematical analysis of a tractable dynamical system.
  • Phase space analysis to identify stable and unstable states.

Main Results:

  • A half-stable steady state for perfect alignment exists for elongated cells.
  • A separatrix divides initial conditions, determining alignment or non-alignment outcomes.
  • Optimal self-propulsion is necessary for alignment; excessive propulsion is detrimental.
  • Two distinct timescales govern cell movement: fast separation and slow alignment.

Conclusions:

  • The interplay between self-propulsion and overlap avoidance is sufficient to generate cell alignment.
  • Initial conditions critically determine whether cells achieve perfect alignment.
  • Cell shape and motility parameters significantly influence collective behavior.