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Related Experiment Videos

Stochastic models for cell motion and taxis.

Edward L Ionides1, Kathy S Fang, R Rivkah Isseroff

  • 1Department of Statistics, University of Michigan, Ann Arbor, MI 48109, USA. ionides@umich.edu

Journal of Mathematical Biology
|December 20, 2003
PubMed
Summary

New models using stochastic differential equations enhance the analysis of cell motion data from time lapse video microscopy. This approach improves understanding of cell behavior and biophysical mechanisms in response to stimuli.

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Area of Science:

  • * Biophysics
  • * Cell Biology
  • * Mathematical Biology

Background:

  • * Cell motion analysis often uses time lapse video microscopy, generating data modeled by stochastic differential equations.
  • * Taxis, or directional cell motion, is typically modeled by the Keller-Segel diffusion equation, which has limitations in distinguishing taxis modes.
  • * There is a need for richer models that maintain statistical tractability for analyzing cell behavior.

Purpose of the Study:

  • * To introduce and analyze a richer class of models for cell velocity beyond the Keller-Segel equation.
  • * To develop statistical methods for parameter estimation and hypothesis testing in cell motion studies.
  • * To apply these models to experimental data, specifically cell responses to electric fields.

Main Methods:

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  • * State space model formulation to connect cell velocity models with observed microscopy data.
  • * Sequential Monte Carlo methods for maximum likelihood parameter estimation.
  • * Application and comparison of Ornstein-Uhlenbeck and nonlinear diffusion models for cell velocity.

Main Results:

  • * Developed a state space modeling framework applicable to stochastic differential equation models of cell velocity.
  • * Demonstrated the utility of Sequential Monte Carlo methods for parameter estimation in these models.
  • * Found that an Ornstein-Uhlenbeck model provided a favorable fit compared to a nonlinear diffusion model for cell behavior in an electric field.

Conclusions:

  • * Stochastic differential equation models offer a more nuanced approach to analyzing cell motion data than traditional methods.
  • * The proposed modeling framework and estimation techniques are effective for quantifying cell behavior and testing hypotheses.
  • * The Ornstein-Uhlenbeck model shows promise for describing cell responses to external stimuli like electric fields.