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Multiscale Asymptotic Analysis Reveals How Cell Growth and Subcellular Compartments Affect Tissue-Scale Hormone

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Summary

This study models hormone transport in plant tissues, revealing how cell growth and internal compartments influence movement. Cell growth induces directional transport, while vacuoles act as storage, altering effective transport properties.

Keywords:
Cell growth and divisionHormone transportMultiscale analysisReaction–advection–diffusion equationSubcellular compartment

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Area of Science:

  • Multiscale modeling of biological systems
  • Mathematical biology and biophysics
  • Plant development and physiology

Background:

  • Understanding tissue-scale patterns requires linking cell-scale processes to macro-level phenomena.
  • Hormone and morphogen distribution is crucial for biological development.
  • Plant tissues present unique challenges for modeling transport due to cellular structure.

Purpose of the Study:

  • To derive a continuum approximation for hormone transport in plant tissues using multiscale asymptotic analysis.
  • To investigate the impact of subcellular compartments, cell growth, and cell division on tissue-scale hormone transport.
  • To reveal how these factors influence effective transport properties like diffusivity and velocity.

Main Methods:

  • Development of a discrete multicellular ODE model tracking hormone concentration in cytoplasm, vacuole, and apoplast.
  • Application of multiscale asymptotic analysis to derive a continuum model from the discrete model.
  • Analysis of the effective reaction-advection-diffusion equation and its parameters.

Main Results:

  • Subcellular compartments (vacuoles) act as storage, significantly altering effective transport properties.
  • Cell growth induces an effective velocity in the direction of growth.
  • Spatial variance in cell lengths and compartment sizes creates effective velocities, with transport faster across decreasing cell lengths.

Conclusions:

  • The derived continuum model accurately captures tissue-scale hormone transport influenced by cell-scale dynamics.
  • Cellular structure and dynamics, including growth and division, fundamentally shape hormone distribution in plant tissues.
  • The findings are applicable to various plant hormones, such as gibberellic acid in Arabidopsis roots, and other cell transport systems.