Stochastic Dynamics of Eukaryotic Flagellar Growth

Area of Science:

• Cell Biology
• Biophysics
• Mathematical Modeling

Background:

• Eukaryotic flagellar growth is essential for cellular motility and function.
• Intraflagellar transporters (IFT) are critical components regulating flagellar assembly and maintenance.
• Previous models, like the balance point model, provide a framework for understanding flagellar dynamics.

Purpose of the Study:

• To investigate the dynamics of flagellar growth using a stochastic approach.
• To compare and contrast detailed stochastic models with simplified ordinary differential equation (ODE) and stochastic differential equation (SDE) models.
• To analyze flagellar length distributions under different IFT transport models (isolated particles vs. particle trains).

Main Methods:

• Developed a discrete event vector-valued Markov process model for IFT dynamics.
• Compared stochastic simulations with ODE and derived SDE approximations.
• Utilized small noise approximations to derive analytical results for flagellar length distribution.

Main Results:

• Numerical simulations show that ODE models well approximate the steady-state mean of the detailed stochastic model.
• A small noise approximation of the SDE model predicts flagellar length to be Gaussian, with mean and variance governed by ODEs.
• Both original and revised balance point models, under small noise approximation, yield similar Gaussian length distributions.

Conclusions:

• Simplified mathematical models (ODEs and SDEs) can accurately capture key aspects of eukaryotic flagellar growth dynamics.
• Flagellar length is robustly approximated as a Gaussian distribution under various IFT transport mechanisms.
• The study provides a robust mathematical framework for understanding flagellar length regulation.