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A Growth-Fragmentation Approach for Modeling Microtubule Dynamic Instability

Stéphane Honoré1,2, Florence Hubert3, Magali Tournus3

  • 1CNRS, INP, Inst Neurophysiopathol, Faculté de Pharmacie de Marseille, Aix Marseille University, 13385, Marseille, France.

Bulletin of Mathematical Biology
|November 29, 2018
PubMed

Insights

This study introduces a new mathematical model for microtubule (MT) dynamics to investigate cancer chemotherapy drugs. The model simulates how drugs like vinca alkaloids affect MTs, aiding in the development of new cancer treatments.

Area of Science:

  • Cell Biology
  • Mathematical Biology
  • Biophysics

Background:

  • Microtubules (MTs) are vital protein filaments in eukaryotic cells, essential for cell division and movement.
  • Their role in cell division makes them a key target for cancer chemotherapy drugs.
  • Existing experimental studies lack a complete description of MT dynamics, hindering drug development.

Purpose of the Study:

  • To propose a novel mathematical model for microtubule dynamics.
  • To analyze the effects of chemotherapy drugs on microtubule dynamics.
  • To provide a framework for understanding drug-induced alterations in microtubule behavior.

Main Methods:

  • Developed a mathematical model combining a growth-fragmentation equation for MT length distribution.
  • Coupled the equation with two ODEs for free GTP- and GDP-tubulin concentrations.
  • Proved the system's well-posedness and performed numerical simulations to explore parameter influences.

Main Results:

  • Demonstrated the model's capability to simulate MT dynamics under varying parameters.
  • Provided a qualitative description of how vinca alkaloids, a class of destabilizing drugs, alter MT dynamics.
  • Validated simulation results against in vitro observations by adjusting model parameters.

Conclusions:

  • The proposed mathematical model offers a valuable tool for studying microtubule dynamics and chemotherapy drug effects.
  • The model facilitates a deeper understanding of how specific drugs impact microtubule stability and function.
  • This work contributes to the ongoing development of novel cancer therapeutics targeting microtubules.
Keywords:
Banach fixed pointGrowth-fragmentation modelMicrotubules dynamics

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