EB3-informed dynamics of the microtubule stabilizing cap during stalled growth

Microtubule stability is known to be governed by a stabilizing GTP/GDP-Pi cap, but the exact relation between growth velocity, GTP hydrolysis and catastrophes remains unclear. We investigate the dynamics of the stabilizing cap through in vitro reconstitution of microtubule dynamics in contact with micro-fabricated barriers, using the plus-end binding protein GFP-EB3 as a marker for the nucleotide state of the tip. The interaction of growing microtubules with steric objects is known to slow down microtubule growth and accelerate catastrophes. We show that the lifetime distributions of stalled microtubules, as well as the corresponding lifetime distributions of freely growing microtubules, can be fully described with a simple phenomenological 1D model based on noisy microtubule growth and a single EB3-dependent hydrolysis rate. This same model is furthermore capable of explaining both the previously reported mild catastrophe dependence on microtubule growth rates and the catastrophe statistics during tubulin washout experiments.


INTRODUCTION
(normalized) similarity parameters for each compared distribution (Fig. 4A). We also included 283 a comparison between the simulated GTP/GDP-Pi decay and the experimental EB decay rate 284 during stalling (Fig. 2D). The resulting range of ℎ values that captured the experimental     show that free microtubule lifetimes and microtubule stalling can indeed be simultaneously 334 captured with a 1D model comprising three parameters (Fig 5A-C). From the fits, we find that 335 with increasing EB3 concentration, ℎ increases and decreases (Fig. 5C).

336
Additionally, we find both fully and partially decayed GTP/GDP-Pi intensities at the where is the size of a dimer, the tubulin addition rate, and the tubulin dissociation rate. 416 We thus conclude that our 1D model can describe the reported mild dependence of the 417 microtubule lifetimes on the growth velocity.   the observable optical resolution (Fig. S6D). 476 We furthermore showed that our model can capture tubulin washout and reproduces a that the onset of a catastrophe is not fully coupled to the presence of an observable comet.

495
To determine the stretch of hydrolysed subunits at the microtubule tip required to initiate 496 a catastrophe ( ), we measured the ratio between the EB3 comet intensity at the moment of catastrophe and the mean EB3 comet intensity during steady-state growth (Fig.   498   4BC). In parallel, we evaluated the decay rates of EB3 comets after initial barrier contact. Both subunits equal or greater than ( Fig. 8A and S5AB). The distance between the microtubule tip and this position is equal to the size of the stabilizing cap, which means we can 525 obtain the relation between the size of the stabilizing cap and the parameters , ℎ , 526 and 〈 〉 (Fig. 8BC and S5B). We find that the size of the stabilizing cap scales linearly with the 527 growth velocity 〈 〉 (Fig. 8B). The addition of EB3 however affects both the growth velocity 528 and the hydrolysis rate, the combined effect of which results in a decreasing cap size with 529 increasing EB concentration (Fig. 8C). We can calculate the mean size of the stabilizing cap in lifetimes are successfully reproduced with the analytical solution (Fig 7A and S5D). This holds 546 true for catastrophes during free growth and after tubulin washout ( Fig 8D left and middle).

Microtubule ageing is not required to describe microtubule lifetimes
An observed feature of microtubule stability lacking in our model is an age-dependent 575 catastrophe frequency. It has been reported that "younger" microtubules are more stable than 576 "older" ones (Gardner et al., 2011b;Odde et al., 1995). Ageing has also been observed through     used to fit the EB3 comet to obtain its position and intensity, using the intensity profile: where ( ) is the fluorescence intensity, is the background intensity, is the intensity 732 amplitude, is the position of the peak of the EB3 comet, and σ is the width of the EB3 comet.

733
As EB3 comet decay at the barrier makes fitting impossible, the intensity during contact was 734 determined by calculating the average intensity value in a region around the comet position and around the barrier (Fig. S1C) Each microtubule simulation started from a few initial subunits (a 'seed') that were excluded 747 from hydrolysis, and that were not allowed to be removed during microtubule tip fluctuations.

748
Microtubule growth was simulated as a discrete, biased, Gaussian random walk. This means 749 that for each time-step , the microtubule length was changed by a discretized random number as the dimer directly preceding the sequence needs to be unhydrolyzed to initiate the sequence 799 ( Fig S5A). 800 We can now obtain an expression for the probability of finding this sequence for the first time where and are coefficients that depend on the hydrolysis rate and the growth velocity.

815
Similarly, we can calculate the dependence of the cap size on the parameters ℎ and 〈 〉 (Fig.   816 8BC).

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Analytical expression for the catastrophe probability and microtubule lifetimes 819 The probability for a microtubule to undergo a catastrophe within time window ∆ is defined 820 as (∆ ) and is equal to the probability of reducing the cap size to zero during ∆ . The The growth fluctuations at the microtubule tip can be described by a biased random walk with 835 Gaussian distributed steps ∆ within ∆ (Fig 3B).