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Summary
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This study develops new methods to analyze cell migration data using partial differential equation (PDE) models. A novel multinomial measurement error model improves parameter estimation and yields physically realistic predictions for collective cell migration.

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Area of Science:

  • * Mathematical biology and computational biophysics.
  • * Statistical modeling and data analysis in cell biology.

Background:

  • * In vitro cell migration experiments are crucial for understanding cell behavior.
  • * Lattice-based random walk models and their continuum partial differential equation (PDE) limits offer efficient analysis of cell migration.
  • * Relating discrete, noisy cell count data to continuous PDE models is a significant challenge for parameter estimation.

Purpose of the Study:

  • * To develop and implement likelihood-based methods for parameter estimation, identifiability, and prediction in collective cell migration models.
  • * To compare a standard additive Gaussian measurement error model with a new, physically motivated multinomial measurement error model.
  • * To assess the impact of different measurement error models on the accuracy and physical realism of model predictions.

Main Methods:

  • * Development of likelihood-based inference frameworks for lattice-based collective cell migration models.
  • * Implementation and comparison of an additive Gaussian measurement error model and a novel multinomial measurement error model.
  • * Application of these methods to analyze quantitative cell count data from in vitro experiments.

Main Results:

  • * Both Gaussian and multinomial error models provide similar results for parameter estimation and identifiability.
  • * The standard Gaussian error model produces nonphysical predictions for cell migration.
  • * The new multinomial error model results in physically meaningful predictions and offers lower computational overhead.

Conclusions:

  • * A novel multinomial measurement error model effectively bridges discrete cell count data and continuous PDE models for collective migration.
  • * This approach enhances the reliability of parameter estimation, identifiability analysis, and predictive modeling in cell migration studies.
  • * The developed methods provide a more robust and computationally efficient framework for analyzing complex cell migration dynamics.