Autocatalytic microtubule nucleation determines the size and mass of spindles

Regulation of size and growth is a fundamental problem in biology. A prominent example is the formation of the mitotic spindle, where protein concentration gradients around chromosomes are thought to regulate spindle growth by controlling microtubule nucleation (1, 2). Previous evidence suggests that microtubules nucleate throughout the spindle structure (3-5). However, the mechanisms underlying microtubule nucleation and its spatial regulation are still unclear. Here, we developed an assay based on laser ablation to directly probe microtubule nucleation events in Xenopus laevis egg extracts. Combining this method with theory and quantitative microscopy, we show that the size of a spindle is controlled by autocatalytic growth of microtubules, driven by microtubule-stimulated microtubule nucleation. The autocatalytic activity of this nucleation system is spatially regulated by the limiting amounts of active microtubule nucleators, which decrease with distance from the chromosomes. Thus, the size of spindles is determined by the distance where one microtubule nucleates on average less than one new microtubule. This mechanism provides an upper limit to spindle size even when resources are not limiting and may have implications for spindle scaling during development (6, 7).

provides an upper limit to spindle size even when resources are not limiting and may have implications for spindle scaling during development (6,7).

Main text
A general class of problems in biology is related to the emergence of size and shape in cells and tissues. Reaction diffusion mechanisms have been broadly successful in explaining spatial patterns in developmental biology as well as some instances of intracellular structures (8,9). The mitotic spindle, a macromolecular machine responsible for segregating chromosomes during cell division, is thought to be a classic example of such reaction diffusion processes. A diffusible gradient of the small GTPase Ran emanating from chromosomes has been shown to trigger a cascade of events that result in the nucleation of microtubules, the main building blocks of the spindle (1,2). The spatial distribution of microtubule nucleation is key for understanding size and architecture of large spindles. This is because microtubules in these spindles are short and turnover rapidly (3,10,11). The mechanisms underlying the spatial regulation of microtubule nucleation, however, are still unclear (12,13).
One possibility is that the interplay between Ran-mediated nucleation and microtubule turnover governs spindle assembly (1,2). However, the role of the Ran gradient in determining spindle size is still controversial. For instance, in cell culture systems, the length scale of the Ran gradient does not correlate with spindle size (5).
A second possibility is that autocatalytic growth accounts for spindle assembly via microtubule-stimulated microtubule nucleation (4,(14)(15)(16). However, autocatalytic mechanisms suffer from the fact that their growth is hard to control. Although autocatalytic growth can be regulated by limiting the catalyst, such mechanisms are unlikely to function in the large cells of developing eggs such as Xenopus, where resources are not limiting (17). Understanding the role of microtubule nucleation in setting the size of spindles is limited by the fact that little is known about the rate, distribution, and regulation of microtubule nucleation in spindles (12,13). This is partly because of the lack of methods to measure microtubule nucleation in spindles.
Microtubules grow from the plus ends while minus ends remain stable (18). Thus, the location of minus ends functions as a marker for microtubule nucleation. However, in spindles microtubules constantly flux towards the poles (19), and measuring the location of a microtubule minus end at a particular time does not correspond to its original site of nucleation (3). To decouple microtubule transport from microtubule nucleation, we inhibited kinesin-5 (Eg5) in spindles assembled in Xenopus laevis egg extracts. This inhibition stops microtubule transport and leads to the formation of radially symmetric monopolar spindles (monopoles) that have a similar size as regular spindles (20,21) (Fig. 1A and S1). The location of minus ends in these monopoles exactly corresponds to the location of microtubule nucleation.
Three independent measurements show that inhibiting microtubule transport does not affect dynamic parameters of microtubules. First, microtubules in these structures polymerize at 20.9 ± 5.1 µm/min (N = 7 monopoles, Fig. 1A and movie S1), which is indistinguishable from the polymerization velocity in spindles, 22.7 ± 8.4 µm/min (N = 4 spindles). Second, microtubules from monopolar and control spindles depolymerize at the same velocity (33.5 ± 6.4 µm/min and 35.9 ± 7.3 µm/min respectively, see Fig. S2). Third, microtubule lifetime distributions of monopolar spindles, measured by single-molecule microscopy of tubulin dimers, give an average lifetime of 19.8 ± 2.2 s, consistent with similar measurements in regular spindles (11) (materials and methods and movie S2).
To localize microtubule nucleation events, we measured the density of minus ends in monopolar spindles by analyzing synchronous waves of microtubule depolymerization from laser cuts similar to (3). Briefly, the minus end density at the location of the cut can be obtained from the decrease of the microtubule depolymerization wave, but as opposed to Ref. Several mechanisms have been proposed to regulate microtubule nucleation. From a biophysical perspective, these mechanisms can be categorized into two scenarios: (1) microtubule-dependent nucleation, in which a pre-existing microtubule stimulates the nucleation of a new microtubule, or (2) microtubule-independent nucleation, in which factors other than pre-existing microtubules (e.g. diffusible cues in the cytoplasm) stimulate nucleation (12)(13)(14)(15)(22)(23)(24).
If microtubule nucleation depends on pre-existing microtubules, altering microtubule stability should change the nucleation profile-a microtubule that exists for a longer time would have a higher probability to stimulate the creation of more microtubules.
To test this scenario, we increased microtubule stability by inhibiting the depolymerizing kinesin MCAK (25) using antibodies. MCAK inhibition led to a dramatic increase in monopole size (see Fig. 2A). Both the average length and stability of microtubules increased threefold after inhibition ( Fig. 2B (25,26). We measured microtubule nucleation in this perturbed condition and found that the nucleation profile extends further from the center of the monopole, has a larger amplitude, and decays over a larger distance with respect to control monopoles (Fig. 2D). Therefore, the number and spatial distribution of nucleated microtubules does indeed scale with microtubule stability in monopolar spindles, which is inconsistent with microtubule-independent nucleation. Thus, microtubule nucleation in these structures depends on the presence and dynamics of microtubules.
The presence and dynamics of microtubules could alter microtubule nucleation in two ways: microtubules could nucleate indiscriminately in the cytoplasm without requiring microtubules, but their presence concentrate active nucleators through transient interactions with microtubules as previously proposed (5), or alternatively, microtubules could directly nucleate new microtubules, requiring active nucleators to bind to microtubules to initiate nucleation. In the latter case, the presence of a microtubule is essential for the nucleation process, whereas in the former, microtubules can still nucleate in the absence of microtubules. To test whether microtubule nucleation requires physical proximity to pre-existing microtubules (e.g., a branching process (14) For a microtubule structure to have a finite size through an autocatalytic process, each microtubule at the periphery must create on average less than one microtubule at steady state, otherwise the number of microtubules would increase exponentially and the structure would grow unbounded (16). However, measurements of the temporal evolution of microtubule mass in spindles show indeed an initial phase of exponential growth ( Fig. S4 and (22, 27)). This is also consistent with the observation of microtubules creating more than one microtubule on average when inducing bulk microtubule branching by adding TPX2 and constitutively active Ran (RanQ69L) in extracts (14). These observations raise the question of how spindles reach a finite size through autocatalytic growth (as in the control and MCAK-inhibited monopoles). One possibility is that microtubule dynamics change as a result of limiting amounts of tubulin or microtubule-associated proteins (6,7). However, since our cell-free system is not confined, availability of tubulin and microtubule-associated proteins is not limiting. Furthermore, inhibiting MCAK leads to microtubule growth with a polymerization velocity that is indistinguishable from control monopoles (20.9 ± 5.1 µm/min and 18.8 ± 5.4 µm/min respectively, movie S1 and S6), suggesting that the availability of tubulin appears not to be diffusion-limited. Finally, microtubule dynamics do not change spatially throughout MCAK-inhibited monopoles (Fig. S5), indicating that spatial variations of tubulin amount or microtubule dynamics cannot explain the finite size of these structures.
Another possibility is that microtubule nucleation is limiting. It has been shown that  (Fig. 4C). To test the model beyond scaling, we fit the MCAKinhibited profile with the other two remaining parameters and the arbitrary amplitude of the microtubule density profile, which agrees quantitatively with the data (Fig. 4B).
By fixing all parameters to the values obtained by this fit and using the measured average microtubule length, the model predicts the control monopole microtubule profile. Finally, we can also predict the MCAK-inhibited and control microtubule nucleation profiles from the fitted parameters up to an arbitrary amplitude (common for both profiles) (Fig. 4D). Remarkably, this prediction is also consistent with flux-    , where ρ C , l C and ρ M , l M are the density and length of microtubules for the control (blue) and MCAK-inhibited (gray) structures, respectively, and x is the distance from the center of the structure. (D) Data and predictions (orange) for the nucleation profiles of control (blue) and MCAK monopoles (gray) up to a global nucleation amplitude, and flux-corrected regular spindles (green) (mean ± SD, N control = 117, N a-MCAK = 74, N spindle = 36 cuts).