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Modeling microtubule dynamic instability: Microtubule growth, shortening and pause

Frederick Laud Amoah-Darko1, Diana White1

  • 1Clarkson University, 8 Clarkson Avenue, Potsdam, NY, United States of America.

Journal of Theoretical Biology
|September 3, 2022
PubMed

Insights

This study introduces a new mathematical model for microtubule (MT) dynamics, incorporating pausing alongside growth and shortening. The model enhances understanding of MT behavior and the effects of drugs and proteins.

Area of Science:

  • Cell Biology
  • Biophysics
  • Mathematical Modeling

Background:

  • Microtubules (MTs) are essential protein polymers in eukaryotic cells, vital for cell structure and intracellular transport.
  • MT dynamics are characterized by polymerization (growth) and depolymerization (shortening), with transitions termed catastrophe and rescue.
  • Extended periods of MT pausing are observed but not well understood, necessitating new modeling approaches.

Purpose of the Study:

  • To develop a novel mathematical model describing microtubule dynamics, including growth, shortening, and pausing.
  • To derive expressions for catastrophe frequency and time spent in growth and pause states.
  • To investigate the influence of microtubule-associated proteins (MAPs) and chemotherapeutic drugs on MT dynamics.

Main Methods:

  • Development of a new mathematical model for microtubule dynamics.
  • Derivation of mathematical expressions for catastrophe frequency and time spent in different dynamic states.
  • Simulation and analysis of model parameters to reflect effects of MAPs and drugs.

Main Results:

  • A mathematical framework was established to model MT dynamics incorporating pausing.
  • Expressions were derived to quantify catastrophe frequency and the duration of growth and pause phases.
  • The model demonstrates how MAPs and chemotherapeutic agents implicitly alter MT dynamics by modulating model parameters.

Conclusions:

  • The new model provides a more comprehensive description of microtubule dynamic instability by including pausing.
  • This framework allows for a quantitative analysis of how cellular factors and drugs affect microtubule behavior.
  • The study offers insights into the mechanisms underlying microtubule regulation and drug interactions.
Keywords:
Hyperbolic systemsMAPsModeling microtubule dynamicsPDEsPaused state

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