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Statistical description of mobile oscillators in embryonic pattern formation.

Koichiro Uriu1,2, Luis G Morelli3

  • 1School of Life Science and Technology, Institute of Science Tokyo, 2-12-1, Ookayama, Meguro-ku Tokyo 152-8550, Japan.

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Summary
This summary is machine-generated.

Mobile oscillators synchronize biological patterns, but cell mobility can disrupt segment formation. This study develops a framework linking mobility fluctuations to synchronization and pattern stability in developing vertebrates.

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Area of Science:

  • Biological Physics
  • Developmental Biology
  • Complex Systems

Background:

  • Synchronization of mobile oscillators is crucial in various systems, including vertebrate embryonic development.
  • Segmental body structures form via mobile cells with autonomous gene expression rhythms and local signaling.
  • Gradients in frequency and cell mobility exist in developing vertebrate tissues, influencing kinematic waves and segment patterning.

Purpose of the Study:

  • To derive a general framework relating local mobility fluctuations to synchronization dynamics and pattern robustness in mobile oscillators.
  • To analyze the impact of cell mobility on the synchronization and patterning of vertebrate segment formation.
  • To extend the statistical description to inhomogeneous systems relevant to developmental tissues.

Main Methods:

  • Formulation of a statistical description for mobile phase oscillators using probability density.
  • Solving diffusion equations for average phase and variance to link fluctuations and synchronization.
  • Analysis of probability density for large mobility to identify mean-field behavior.
  • Extension of the statistical description to inhomogeneous systems with gradients.

Main Results:

  • Revealed a relationship between local fluctuations and global synchronization in homogeneous oscillator populations.
  • Identified a mean-field onset for large mobility, where oscillators behave as if globally coupled.
  • Related pattern stability to mobility, coupling strength, and pattern wavelength in inhomogeneous systems.

Conclusions:

  • Oscillator mobility's impact on synchronization and pattern robustness is quantified.
  • The framework provides insights into how cell mobility influences vertebrate segment formation.
  • The statistical description approach is applicable to other mobile oscillator systems and patterning contexts.