  The microtubule cytoskeleton is responsible for sustained, long-range
intracellular transport of mRNAs, proteins, and organelles 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 mathematical model of dendritic
microtubule dynamics, with a focus on understanding microtubule length,
velocity, and state-duration distributions. We find that limitations on
microtubule growth phases are needed for realistic dynamics, but the type of
limiting mechanism leads to qualitatively different responses to plausible
experimental perturbations. We therefore propose and investigate two
minimally-complex length-limiting factors: limitation due to resource (tubulin)
constraints and limitation due to catastrophe of large-length microtubules. We
combine simulations of a detailed stochastic model with steady-state analysis
of a mean-field ordinary differential equations model to map out qualitatively
distinct parameter regimes. This provides a basis for predicting changes in
microtubule dynamics, tubulin allocation, and the turnover rate of tubulin
within microtubules in different experimental environments.
