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Related Concept Videos

Cell Migration01:19

Cell Migration

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Cell migration is a process by which the cells move from one location to another, playing an essential role in embryological development, repair and regeneration, immune response, and metastasis. Cells migrate in response to chemical or mechanical signals generated by specific organs or tissues. The overall mechanism includes three steps - polarization, protrusion, and release. Polarization involves the formation of a distinct cell front and rear, which determines the direction of movement.
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Proteins show rotational as well as lateral diffusion across the membrane. The lateral diffusion of proteins was confirmed through the cell fusion experiment where mouse and human cells were fused, resulting in hybrid cells. When the human and mouse cells fused, the specific membrane proteins on human and mouse cells were marked with the red and green-fluorescent markers, respectively. Initially, the red and green fluorescence was located on the respective hemisphere of the cell. As time...
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Updated: Jun 24, 2025

Image Processing Protocol for the Analysis of the Diffusion and Cluster Size of Membrane Receptors by Fluorescence Microscopy
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Bayesian inverse problem for a fractional diffusion model of cell migration.

Francisco Julian Ariza-Hernandez1, Juan Carlos Najera-Tinoco1, Martin Patricio Arciga-Alejandre1

  • 1Faculty of Mathematics, Autonomous University of Guerrero, Mexico.

Mathematical Biosciences and Engineering : MBE
|June 14, 2024
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Summary

This study models cell migration using a fractional diffusion equation. We solved direct and inverse problems, estimating model parameters from experimental wound closure data using Bayesian inference and Markov Chain Monte Carlo methods.

Keywords:
Bayesian estimationcell migrationfractional derivative

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Area of Science:

  • Mathematical Biology
  • Biophysics
  • Computational Biology

Background:

  • Cell migration is a fundamental biological process crucial for development and disease.
  • Mathematical models, particularly diffusion equations, are used to describe cell movement.
  • Fractional diffusion equations offer a more nuanced approach to modeling complex transport phenomena like cell migration.

Purpose of the Study:

  • To analyze a Fisher-type fractional diffusion equation for modeling cell migration.
  • To solve both the direct problem (predicting migration) and the inverse problem (estimating parameters) of the model.
  • To validate the model using experimental data from a wound closure assay.

Main Methods:

  • The direct problem was solved using the Fourier method and Laplace transform.
  • The inverse problem was addressed within a Bayesian statistical framework.
  • Model parameters were estimated using Markov Chain Monte Carlo (MCMC) simulations.

Main Results:

  • The study successfully applied Fourier and Laplace methods to solve the direct problem.
  • Bayesian inference combined with MCMC enabled robust estimation of model parameters.
  • The model parameters were successfully estimated using experimental cell migration data.

Conclusions:

  • The Fisher-type fractional diffusion equation is a viable model for cell migration.
  • The Bayesian framework provides an effective approach for solving the inverse problem in cell migration modeling.
  • This work demonstrates the utility of computational methods for understanding biological processes.