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Multisolitons-like patterns in a one-dimensional MARCKS protein cyclic model.

Chenceline Fouedji1, Armand Sylvin Etémé1, Conrad Bertrand Tabi2

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Summary

The study investigates the nonlinear dynamics of the MARCKS protein using modulational instability. It reveals how phosphorylation, binding rates, and diffusion influence protein localization and transport, potentially forming multisoliton patterns.

Keywords:
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Area of Science:

  • Biophysics
  • Nonlinear Dynamics
  • Cell Biology

Background:

  • The Myristoylated Alanine-Rich C-Kinase Substrate (MARCKS) protein plays a crucial role in cellular processes, involving dynamic translocation between the cytosol and cytoplasmic membrane.
  • Understanding the complex nonlinear dynamics governing MARCKS protein behavior is essential for elucidating its functions in cell signaling and membrane trafficking.

Purpose of the Study:

  • To analyze the nonlinear dynamics of the MARCKS protein using the modulational instability (MI) phenomenon.
  • To identify parameter domains predicting the formation of nonlinear patterns in MARCKS protein distribution.
  • To investigate the influence of phosphorylation, binding rates, and self-diffusion on MARCKS protein dynamics.

Main Methods:

  • Transformation of a generic reaction-diffusion model for MARCKS protein into a cubic complex Ginzburg-Landau equation.
  • Application of modulational instability analysis to derive criteria and predict growth rates.
  • Confirmation of analytical predictions through numerical simulations.

Main Results:

  • Modulational instability criteria were derived, defining parameter spaces where nonlinear patterns emerge.
  • Phosphorylation rate promotes localized MARCKS structures, while binding rate inhibits them.
  • Self-diffusion consistently amplifies the modulational instability phenomenon.

Conclusions:

  • The interplay between phosphorylation, binding, and diffusion rates dictates the formation of localized MARCKS protein structures.
  • Cyclic transport of MARCKS protein between the membrane and cytosol may occur via multisoliton-like patterns.
  • The study provides a theoretical framework for understanding MARCKS protein dynamics at the membrane-cytosol interface.