Nucleation feedback can drive establishment and maintenance of biased microtubule polarity in neurites

Abstract

The microtubule cytoskeleton is comprised of dynamic, polarized filaments that facilitate transport within the cell. Polarized microtubule arrays are key to facilitating cargo transport in long cells such as neurons. Microtubules also undergo dynamic instability, where the plus and minus ends of the filaments switch between growth and shrinking phases, leading to frequent microtubule turnover. Although microtubules often completely disassemble and new filaments nucleate, microtubule arrays have been observed to both maintain their biased orientation throughout the cell lifetime and to rearrange their polarity as an adaptive response to injury. Motivated by cytoskeleton organization in neurites, we propose a spatially-explicit stochastic model of microtubule arrays and investigate how nucleation of new filaments could generate biased polarity in a simple linear domain. Using a continuous-time Markov chain model of microtubule growth dynamics, we model and parameterize two experimentally-validated nucleation mechanisms: nucleation feedback, where the direction of filament growth depends on existing microtubule content, and a checkpoint mechanism, where microtubules that nucleate in a direction opposite to the majority experience frequent catastrophe. When incorporating these validated mechanisms into the spatial model, we find that nucleation feedback is sufficient to establish biased polarity in neurites of different lengths, and that the emergence and maintenance of biased polarity is relatively stable in spite of stochastic fluctuations. This work provides a framework to study the relationship between microtubule nucleation and polarity, and could extend to give insights into mechanisms that drive the formation of polarized filament arrays in other biological settings.

Keywords: Stochastic simulation; microtubule turnover; nucleation feedback; parameterization.

Figure 1:

Nucleation direction of new microtubules is dependent on pre-existing microtubule orientation. (a) Drosophila Class I sensory neuron ddaE. (b) Example kymograph of EB1-GFP in control and Kap3 RNAi conditions. (c) Percentage of MT plus ends growing towards the cell body. Numbers on the bars represent the number of cells analyzed and p < 0.00001 using Pearson’s chi-squared test. (d) Dendrite branch point in ddaE neuron with labeled nucleation directions: proximal, distal, peripheral and opposite wall. (e) Percentage of nucleation events in each direction in control and Kap3 RNAi conditions. Numbers on the bars represent the number of nucleation events identified and p < 0.00063 using Pearson’s chi-squared test. (f) Schematics showing the influence of pre-existing microtubules on new nucleation directions.

Figure 2:

Checkpoint mechanism data, design and validation: (a) experimental checkpoint success rates data from [9] for PEO and MEO nucleation directions in control (Ctrl) and Patronin knockdown (Pat) background environments; (b) simple mechanism design and calculated success rates which do not match experimental data, (c) proposed mechanism design and derivation with calculated success rates which match experimental data.

Figure 3:

Schematic of the model and mechanism designs. Panel (a) illustrates our short and long domains, which are defined by the number of nucleation locations included in the spatial model. Panel (b) shows the MT end states (growth or shrinking) and how the the free tubulin pool depends on MT growth dynamics. Panel (c) depicts the two polarity mechanisms that depend on local MT content, $n^{+/-}$.

Figure 4:

Microtubule polarity results for 100 runs of 5-day simulations with a single nucleation location and $N=20$ MTs in a 20 μm domain. The simulations are initialized with 50% MEO polarity for each combination of mechanisms: neither (blue), checkpoint-only (purple), feedback-only (red), and both (yellow). The average MEO polarity over time is shown in panel (a) as a solid curve, with a cloud representing the interquartile range. Panel (b) shows the polarity distribution at the end of 5 days, and (c) shows the MEO polarity percentage for each simulation over time. The inset figures for feedback-only (red) and both mechanisms (yellow) show how the MEO polarity percentage changes on a shorter time scale of 5 hours.

Figure 5:

Microtubule polarity results for 100 runs of 5-day simulations with six nucleation locations and $N=60$ MTs in a 70 μm domain. The simulations are initialized with 50% MEO polarity for each combination of mechanisms: neither (blue), checkpoint-only (purple), feedback-only (red), and both (yellow). The average MEO polarity over time is shown in panel (a) as a solid curve, with a cloud representing the interquartile range. Panel (b) shows the polarity distribution at the end of 5 days, and (c) shows the MEO polarity percentage over time for each simulation.

Figure 6:

Schematic illustrating how polarity varies spatially across nucleation locations. Without any additional nucleation mechanism, (a) shows how MEO polarity varies spatially due to MT growth dynamics alone, with MEO polarity percentage shown for each nucleation location to the right of the figure. With nucleation mechanisms, (b) illustrates the phase separation behavior between MEO and PEO nucleation locations, where polarity is spatially-biased and consistent with the growth bias from (a). Over time, this phase separation front moves until one polarity bias is established globally.

Figure 7:

Distributions of MEO polarity percentages at each nucleation location. Panel (a) shows an example initial condition (I.C.) from one set of simulations. Each remaining subpanel captures the resulting polarity for one mechanism combination: (b) neither mechanism, (c) checkpoint-only, (d) feedback-only, (e) both mechanisms. For each scenario, we show the distributions of MEO polarity at 3 hours and 5 days of simulation time, with the color bar corresponding to the percentage of MEO polarity.

Figure 8:

Cumulative distribution functions (CDFs) of data from 100 model runs for the first time to hit (blue), to depart (yellow) and to return to (red) a fully-biased MT polarity distribution (100% or 0% MEO) for feedback-only (dotted) and both mechanism (solid) combinations. The CDFs include data from simulations which achieved each metric, and percentages of such runs are shown for each category in the inset table.