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Single-Molecule Diffusion and Assembly on Polymer-Crowded Lipid Membranes
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Pattern forming systems coupling linear bulk diffusion to dynamically active membranes or cells.

D Gomez1, S Iyaniwura1, F Paquin-Lefebvre1

  • 1Dept. of Mathematics, Univ. of British Columbia, Vancouver, British Columbia, Canada V6T 1Z2.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|November 8, 2021
PubMed
Summary
This summary is machine-generated.

This study explores novel reaction-diffusion (RD) systems coupling bulk diffusion with boundary or compartment nonlinearities. We analyze pattern formation, bifurcations, and intracellular oscillations in these complex systems.

Keywords:
Green’s functionbifurcationbulk-membrane coupled systemquorum and diffusion sensingspikessynchrony

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Area of Science:

  • Mathematical Biology
  • Chemical Physics
  • Pattern Formation

Background:

  • Reaction-diffusion (RD) systems are crucial for understanding pattern formation in biological and chemical systems.
  • Coupling bulk diffusion with boundary or localized nonlinear processes presents unique challenges and opportunities for novel pattern dynamics.
  • Turing's theory of morphogenesis provides a foundational framework for studying pattern emergence.

Purpose of the Study:

  • To investigate pattern formation properties in novel reaction-diffusion systems with coupled bulk-boundary or bulk-compartment nonlinearities.
  • To characterize Turing and Hopf bifurcations in a bulk-membrane system derived from asymptotic analysis.
  • To analyze the stability of localized patterns and study collective intracellular oscillations in coupled bulk-cell models.

Main Methods:

  • Asymptotic analysis in the limit of thin domains to derive bulk-membrane systems.
  • Weakly nonlinear analysis to study bifurcations from radially symmetric steady states.
  • Singularly perturbed analysis to investigate the stability of localized membrane-bound spike patterns.
  • Partial differential equation-ordinary differential equation (PDE-ODE) modeling for bulk-cell interactions.

Main Results:

  • Characterization of Turing and Hopf bifurcations in a 2D disk bulk-membrane system.
  • Analysis of the existence and linear stability of localized membrane-bound spike patterns in a Gierer-Meinhardt model.
  • Demonstration of collective intracellular oscillations in a bulk-cell model with localized active cells.

Conclusions:

  • The studied reaction-diffusion systems exhibit rich pattern formation capabilities through the coupling of bulk and localized nonlinear processes.
  • These models provide insights into biological pattern formation, with potential applications in developmental biology and cell signaling.
  • Further research is needed to explore the full range of emergent phenomena and open problems in these complex systems.