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Numerical algorithm for morphogen synthesis region identification with indirect image-type measurement data.

Alexey Penenko1, Ulyana Zubairova2, Zhadyra Mukatova1

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Summary

This study uses diffusion-reaction models and inverse problems to identify morphogen synthesis regions. The approach helps understand biological tissue regulation by solving complex equations with a Newton-Kantorovich-type algorithm.

Keywords:
Inverse source problemadjoint equationsdiffusion–reaction modelimage analysismorphogen theorysensitivity operator

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Area of Science:

  • Mathematical Biology
  • Computational Biology
  • Systems Biology

Background:

  • Diffusion-reaction models are fundamental to morphogen theory in developmental biology.
  • Interpreting experimental concentration field data requires solving inverse problems.
  • Understanding morphogen dynamics is crucial for tissue development and regulation.

Purpose of the Study:

  • To develop a computational method for identifying morphogen synthesis regions.
  • To interpret concentration field data using diffusion-reaction models.
  • To apply the method to the regulation of biological tissue size.

Main Methods:

  • Stating the inverse source problem for diffusion-reaction models.
  • Utilizing a sensitivity operator derived from adjoint problem solutions.
  • Solving nonlinear ill-posed operator equations with a Newton-Kantorovich-type algorithm.

Main Results:

  • The inverse problem is transformed into a solvable family of operator equations.
  • The Newton-Kantorovich-type algorithm effectively solves these equations.
  • The approach successfully identifies morphogen synthesis regions in a tissue regulation model.

Conclusions:

  • The developed method provides a robust framework for parameter identification in diffusion-reaction models.
  • This technique enhances the interpretation of morphogen concentration data.
  • The findings contribute to understanding biological tissue size regulation mechanisms.