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# Regulation of Microtubule Dynamics by Reaction Cascades Around Chromosomes

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Science  21 Nov 2008:
Vol. 322, Issue 5905, pp. 1243-1247
DOI: 10.1126/science.1161820

## Abstract

During spindle assembly, chromosomes generate gradients of microtubule stabilization through a reaction-diffusion process, but how this is achieved is not well understood. We measured the spatial distribution of microtubule aster asymmetry around chromosomes by incubating centrosomes and micropatterned chromatin patches in frog egg extracts. We then screened for microtubule stabilization gradient shapes that would generate such spatial distributions with the use of computer simulations. Only a long-range, sharply decaying microtubule stabilization gradient could generate aster asymmetries fitting the experimental data. We propose a reaction-diffusion model that combines the chromosome generated Ran–guanosine triphosphate–Importin reaction network to a secondary phosphorylation network as a potential mechanism for the generation of such gradients.

In eukaryotic cells, chromosomes regulate spindle assembly by generating a gradient of Ran–guanosine triphosphate (RanGTP) in their vicinity (15). In frog eggs and egg extracts, it has been shown that this gradient triggers the nucleation of spindle microtubules (MTs) by activating the protein TPX2 (6) and stabilizes the plus ends of centrosomal MTs by activating the kinase CDK11 (7). When centrosomes are incubated together with chromatin stripes or beads in those extracts, the centrosomal asters are asymmetric, sending longer microtubules preferentially toward chromatin, presumably because of their increased stability in this region (8, 9). However, the exact distribution of the CDK11-dependent MT stabilization activity and how this could translate into a defined asymmetry of centrosomal asters in the vicinity of chromosomes has remained unclear.

To visualize the shape of the stabilization gradient, we designed an experimental system allowing the precise measurement of centrosomal MT asymmetry as a function of centrosome distance from chromatin (10). We immobilized chromatin beads on patches of defined sizes and distributions and incubated them in Xenopus egg extracts containing purified human centrosomes (Fig. 1, A and B). The chromatin patches nucleated MTs actively, and spindles assembled robustly on practically all patches. In the experiments designed to assay aster asymmetry, we added anti-TPX2 antibodies to the extract to prevent chromatin mediated MT nucleation around the beads and their interaction with centrosome-nucleated MTs (7). In this assay, centrosomal MTs displayed a radial symmetric distribution when far away from chromatin patches and became asymmetric when closer, whereas no obvious interactions between astral microtubules and the beads could be detected (Fig. 1B).

In parallel to this experimental setup, we developed a simple generic model to carry out computer simulations. It includes a centrosome with dynamic MTs, circular chromatin, and a MT stabilization gradient (Fig. 1, C and D). The centrosome nucleates a finite number of MTs from equally spaced points on its periphery. According to the MT dynamic instability model, MTs are allowed to grow and shrink with parameter values vg and vs (velocities of growth and shrinkage, respectively) and fcat and fres (frequencies of catastrophe and rescue, respectively), derived from measurements in mitotic Xenopus extracts (table S1) (Fig. 1C). In the absence of a gradient, the average MT length (<L>) rises rapidly and achieves a symmetric steady-state value of 4.23 μm within 100 s. This matches the value obtained from an analytical solution (4.25 μm) (11). The stabilization gradient is modeled as a two-dimensional spatial change in fcat and fres scaled between values measured in mitotic extracts and extracts containing RanQ69L (12) (Fig. 1D and table S1). The RanQ69L values are assumed to correspond to the situation around chromatin. For a gradient with a range of ∼20 μm and an aster located at 20 μm from the surface of chromatin, mean MT lengths also achieve a steady state within 100 s. These asters are, however, asymmetric and polarized toward chromatin with MT mean lengths of ∼7 μm toward chromatin and 5 μm away from it (Fig. 1D).

Using the experimental setup, we measured the maximal aster asymmetry (Cα) as a function of centrosome position relative to chromatin (Fig. 2A). Cα reached a maximum value (∼2) when centrosomes were ∼20 μm from chromatin, in agreement with previous results (8). When centrosomes were further away (between 50 and 100 μm), Cα was close to 1 (symmetric asters). We found a linear correlation between the Cα value of each aster and the length of its longest MT pointing toward chromatin (Fig. 2B), indicating that the change in Cα was due to a lengthening of MTs toward chromatin and not to a possible shortening of MTs away from it. A few astral MTs were longer than the chromatin-centrosome distance (Fig. 2C). Although we do not rule out that they physically contact the chromatin, we can explain the MT lengthening simply by the stabilizing effects of diffusible factors generated by chromatin. Such weak asymmetries were generated by a highly stochastic process involving MT dynamic instability (movies S1 and S2).

We thus screened for fcat and fres gradient shapes that would generate the aster asymmetry observed experimentally. A long-range shallow gradient, a short exponential, and a long-range step gradient were tested (Fig. 2, D to F). Of these, only the step gradient with a cutoff distance of Rc = 22 μm reproduced the asymmetry measured in the experiments (Fig. 2F). The long-range step gradient reproduced the experimental values better than any other tested model because the asymmetry is expected to be maximal at the edge of the decaying stabilization gradient. On either side of this edge, asymmetry should tend toward the minimum; i.e., Cα ∼1.

We then simulated the functional consequence of the astral asymmetry caused by a long-range step gradient on the first capture time (tc) of a single microtubule by chromatin. Previous models such as random (13) or biased (14) “search and capture” have predicted biologically unreasonable tc values (>30 min) for centrosomes located farther than ∼30 μm from chromatin. In the presence of the step gradient described here, tc remains on the order of a few minutes for centrosome-chromatin distances as large as 45 μm (fig. S2). In addition, the capture-time values appear less variable in the presence of a step gradient. This is consistent with the previous finding that tc is sensitive to location of the centrosome with respect to the edge of a sharply decaying stabilization gradient (14). Thus, long-range, abruptly decaying stabilization gradients efficiently reduce tc and increase the robustness of the search and capture mechanism.

What kind of molecular mechanism could produce a long-range, sharp decaying gradient of fres and fcat values around chromatin in the cytoplasm? In developmental biology (1517), eukaryotic cells (18), and bacteria (19), step gradients (boundaries) are modeled by zero-order (15, 20) ultrasensitive reaction networks, but other possibilities could be thought of (such as cooperativity or positive feedback) (17). In frog egg extracts, the stabilization effect around chromosomes involves the local activation of a kinase (CDK11), which dissociates from importins in response to high RanGTP concentration (17). We therefore built a reaction-diffusion model downstream of the previously modeled Ran gradient (2), which involves a protein kinase (E1) and a phosphatase (E2) (Fig. 3A). The locally activated kinase (E1) converts the substrate (W) into a phosphorylated form (Wp) locally, whereas the phosphatase (E2), free to diffuse in the cytoplasmic space, dephosphorylates Wp globally (Fig. 3A and fig. S3). We modeled Wp as stabilizing MTs directly while W is inactive. The reaction parameters are given in table S1 and were chosen to reflect realistic kinetic constants and diffusion rates for proteins. We tested the following scenarios (Fig. 3B): (i) a linear network where [W] is not saturating, (ii) a network where WE1 interaction is cooperative, (iii) a positive feedback network where Wp inhibits the phosphatase, and (iv) a zero-order ultrasensitive network where [W] is saturating for both enzymes (15, 20). The reactions between the components are described by the following partial differential equations $Math$(1) $Math$ $Math$(2) $Math$ $Math$(3) $Math$ $Math$(4) $Math$ $Math$(5) $Math$ $Math$(6) $Math$

The term S in Eq. 1 connects this network to the RanGTP-Importin gradient-forming reaction system (supporting online material text). Also, in the above equations, d is the dissociation rate, k is the rate of product formation, a is the association rate, n is the Hill coefficient, and D is the diffusion coefficient of each species (16). In the positive feedback network, the parameter k2 is replaced by avariable k2, such that k2 = k2 · Kf/(Kf +[Wp]), where Kf is the feedback strength (17). Wp reaches steady-state concentration within 150 s for all models (Fig. 3C). Gradients of RanGTP and Importin-E1 complexes extend over 4 to 10 μm away from chromosomes with amplitudes between 0.5 and 1μM. Gradients of E1, WE1, and WpE2 extend over similar distances away from chromosomes but have lower amplitudes on the order of 0.05 to 0.1 μM. Both gradient extents and amplitudes vary somewhat according to network topology. All networks generated gradients of Wp extending over 20 to 25 μm with amplitudes ranging from 0.2 to 0.8 μM, depending on the topology of the network. Only the zero order network produced a relatively long-range, sharply decaying gradient.

To examine whether some of these gradients could generate distributions of aster asymmetries as a function of chromatin distance similar to those observed experimentally, we made Wp stabilize MT plus ends by affecting MT dynamics transition frequencies as a function of chromatin distance (r) as follows $Math$(7) $Math$ $Math$(8) $Math$

The gradients of MT dynamic instability parameters generated by the linear network produced an asymmetry pattern that is a poor fit to the experimental results (Fig. 4). The positive feedback network did not generate any asymmetry pattern, as expected from the shape of the Wp gradient that is too shallow (Fig. 4, A and B). The Hill cooperative and the zero-order ultrasensitive networks generated asymmetry patterns that were best fit to the experimental results, both for the amplitude and extent of the gradients (Fig. 4). The distance from chromatin at which asters showed half maximum asymmetry was on the order of 20 μm in both cases. The fit of the asymmetry generated by the ultrasensitive or Hill-cooperative networks is not as good as with the pure step gradient (compare Figs. 2C and 4B). It is possible that alternative, additional, or more complex mechanisms are at work or that we did not find the exact parameters combination. However, the present results demonstrate that it is possible to generate gradients of microtubule dynamic instability around chromosomes having an extent of ∼20 μm with enzymatic networks composed of proteins having realistic diffusivity and kinetic constants.

Our hypothetical network consists of a kinase-phosphatase-substrate system regulated by RanGTP. Small heterotrimeric GTP-binding protein systems are involved in various processes, ranging from signal transduction (21) to cell polarity (22) and membrane trafficking (23). In almost all cases, they are coupled to the downstream modulation of kinase activities (2426). Such systems may also generate local gradients involved in a variety of morphogenetic processes at the subcellular level.

Supporting Online Material

Materials and Methods

SOM Text

Figs. S1 to S4

Tables S1 and S2

References

Movies S1 and S2

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