Minimal Mechanisms of Microtubule Length Regulation in Living Cells

The microtubule cytoskeleton is responsible for sustained, long-range intracellular transport of mRNAs and proteins in neurons. Neuronal microtubules must be stable enough to ensure reliable transport, but they also undergo dynamic instability, as their plus and minus ends continuously switch between growth and shrinking. This process allows for continuous rebuilding of the cytoskeleton and for flexibility in injury settings. Motivated by \textit{in vivo} experimental data on microtubule behavior in \textit{Drosophila} neurons, we propose a spatially-explicit mathematical model of dendritic microtubule dynamics. We find that experimental parameters predict unbounded microtubule growth. We therefore investigate two minimal length-limiting factors (limitation due to resource constraints and limitation due to large length instability) for microtubule growth using a stochastic modeling framework. We show that steady-state analysis of a mean-field model using ordinary differential equations model aids in parameterizing the stochastic model. This framework enables investigation of qualitatively different parameter regimes and provides predictions for both observable and unobservable biological measurements, such as tubulin allocation and tubulin photoconversion measurements.