Taxol stabilized microtubules in Xenopus oocyte extracts self-organize into asters that can then coalesce.
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The mageneta channel depicts microtubules while the green channel depicts NUMA localization, here used as a proxy for microtubule minus ends. Time is shown in minutes : seconds. In other regions of the channel, microtubules organize into aster-like structures that exhibit large-scale movement on the minute timescale. To characterize these large-scale motions, we next imaged networks at lower magnification, obtaining a field of view spanning the entire channel width.
The contractile behavior of these microtubule networks is highly reminiscent of the contractions of actin networks in these extracts Bendix et al. We characterized the dynamics of microtubule network contractions by measuring the width, W t , of the network as a function of time Figure 2B. We then calculated the fraction contracted of the network:. Low magnification imaging of the channels reveals that microtubules organize into a macroscopic network that spontaneously contracts on the millimeter length scale.
During contraction, tears can develop in the microtubule network, causing the network to break. We next sought to investigate which processes determine the timescale of contraction and the extent that the network contracts. B Width of the networks as a function of time in channels with various widths. The networks all contract to a similar final fraction, while the timescale of contraction differs. The scaling is well described by an active fluid model green line analytic scaling, fit to Equation 6 ; green dots numerical solution. Devices were fabricated with different widths.
Each video panel depicts a representative experiment using channels of the given width. Since the Taxol concentration was held constant, all experiments started with the same initial density of microtubules, regardless of the dimensions of the channel. Thus, all networks contracted to the same final density. Remarkably, this is comparable to the concentration of microtubules in reconstituted meiotic spindles in Xenopus extracts Needleman et al.
As neither the simple viscoelastic nor poroelastic models are consistent with these results, we sought to construct an alternative model of the contraction process. As the contracting networks consist of microtubule asters Figure 1D, E , and microtubule asters in meiotic extracts are thought to assemble by the dynein-induced clustering of microtubule minus ends Verde et al.
A Microtubule sliding by dynein drives microtubule minus ends together. B Minus end clustering leads to the formation of aster-like structures. Due to steric interactions between microtubules, there is an upper limit to the local microtubule density. C The microtubule network is composed of interacting asters. Motor activity driving aster cores together leads to bulk contraction of the network. As only a finite number of microtubules can fit near the core of an aster, steric collisions will counteract the contractile stress at high densities Figure 4B.
Only the strength s of the active stress will be affected if the number of active motors could be changed. Taken together, Equations 3,4,5 constitute an active fluid theory of microtubule network contraction by minus end clustering. Isotropy of interactions remains a fundamental assumption. We first investigated if this active fluid theory can explain the dependence of the timescale of contraction on sample geometry.
An analysis of the equations of motion, Equations 3,4,5 , near equilibrium predicts that the timescale of contractions obeys. This predicted scaling is both consistent with the experimental data and simulations of the full theory Figure 3D. To further explore the validity of the active fluid theory of contraction by microtubule minus end clustering, we explored other testable predictions of the theory. Thus, reducing the number of motors should lead to slower contractions, but still yield the same final density.
We first examined prediction ii , that the stress discontinuity at the edge of the network should lead to a material buildup in the film. We next explored if the inhomogeneous density profile could be quantitatively explained by our active fluid theory. Within error, these values are the same as those determined from the dependence of the timescale of contraction on channel width Figure 3D. The simulated profiles closely match the experimental ones for most of the contraction Figure 5B , but at late times the simulated inhomogeneities dissipate in contrast to the experiments Figure 5—figure supplement 1.
This might be caused by a long-term aging of the network that is not incorporated into our simple model. A Time series of contraction showing intensity averaged along the length of the channel. The measured and simulated velocities increase superlinearly with distance from the center of the network, as can be seen by comparison to a linear velocity profile dashed black line.
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Finally, we sought to determine the molecular basis of the contraction process, and check prediction iii , that the number of motors driving the contraction affects the rate of contraction, but not the final density the network contracts to. Aster assembly is dynein-dependent in Xenopus egg extracts Gaglio et al.
We inhibited these motors to test their involvement in the contraction process. Inhibiting Kinesin-5 had little effect on the contraction process Figure 6—figure supplement 1. In contrast, inhibiting dynein caused a dose-dependent slowdown of the contraction Figure 6A. In spindle assembly, inhibiting Kinesin-5 suppresses the morphological changes caused by dynein inhibition Mitchison et al.
We, therefore, tested how simultaneously inhibiting both motors influences the contraction process, but found that the effects of dynein inhibition were not rescued by the simultaneous inhibition of Kinesin-5 Figure 6—figure supplement 1 , suggesting that in this context, Kinesin-5 is not generating a counteracting extensile stress.
This further suggests the possibility that in the spindle, the role of Kinesin-5 may be in orienting, polarity sorting, and sliding microtubules as opposed to active stress generation. Thus, the microtubule networks contract to approximately the same final density irrespective of the concentration of pCC1.
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The observation that inhibiting dynein affects the timescale of contraction but not the final density to which the network contracts is consistent with the predictions of our model. We note that even at the highest pCC1 concentrations used, the network still undergoes a bulk contraction. This could possibly be due to incomplete inhibition of dynein by pCC1, or by another motor protein present in the extract that also contributes to the contraction process. Solid green line indicates fit of sigmoid function. Here, we have shown that networks of stabilized microtubules in Xenopus egg extracts undergo a bulk contraction.
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By systematically varying the width of the microfluidic channel in which the network forms, we demonstrated that the timescale of contraction is not a poroelastic or viscoelastic timescale. A simple active fluid model of network contraction by dynein-driven clustering of microtubule minus ends correctly predicts the dependence of the contraction timescale on channel width, the nonuniform density profile in the network during contraction, and that inhibiting dynein affects the timescale of contraction but not the final density that the network contracts to. Parameters of this model can be measured by the scaling of the contraction timescale with channel width and by a detailed analysis of the inhomogeneities in the network that develop during contraction.
Both methods give similar values. Our results demonstrate that the behaviors of a complex biological system can be quantitatively described by a simple active matter continuum theory. Previously, these theories have been predominately applied to describe biological systems near non-equilibrium steady states Prost et al. In the present work, we augment previous theories with a nonlinear active stress term derived from microscopic considerations to capture the far from steady state dynamics of the contraction process.
This approach allows us to quantitatively explain our experimental results using a theory with only four parameters, while a complete microscopic model would require understanding the behavior of the thousands of different proteins present in Xenopus egg extracts. Furthermore, the considerations of the model are general, and it will be interesting to consider whether the end clustering mechanism proposed here could contribute to contraction in actin networks as well. In our model, the active stress which drives network contraction results from the motor-induced clustering of microtubule minus ends, the same process thought to be responsible for aster formation and spindle pole focusing Gaglio et al.
Our results, and previous data Verde et al. The ability of dynein to cluster microtubule minus ends could result from dynein being able to accumulate on the minus end of one microtubule, while simultaneously walking towards the minus end of another Hyman and Karsenti, ; McKenney et al. There is indication that such behaviors may indeed occur in spindles Elting et al.
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The contribution of dynein to spindle pole focusing may ultimately be due to these contractile stresses. The presence of contractile stresses from dynein might also explain both the observation that the fusion of spindles is dynein-dependent Gatlin et al. It is unclear what processes set the density of microtubules in the spindle, and the finding that the active stress generated from minus end clustering saturates at a preferred microtubule density could play an important role.
CSF-arrested extracts were prepared from Xenopus llaevis oocytes as previously described Hannak and Heald, Crude extracts were sequentially filtered through 2. Devices and coverslips were each corona treated with air plasma for 1 min before bonding. Baker, Center Valley, PA supplemented with 2. Unless stated otherwise, the microfluidic devices had a length of 18 mm, a height of 0.
After a brief lag time, the microtubule networks spontaneously begin contraction.
The final density was estimated using contraction experiments with 2. The fluorescence intensity in the channel but outside the network comes from monomeric fluorescently labeled tubulin and was assumed to be constant throughout the channel. Images from contraction experiments were corrected for the camera offset and inhomogeneous laser illumination before being thresholded in order to segment the microtubule network from background fluorescence.
Rotations of the channel relative to the CCD were detected by fitting linear equations to edges of the microtubule network. Frames were averaged along the length of the channel before background signal subtraction. For density profiles compared with simulations, the edge peaks of the density profile were identified and pixels between the two peaks were retained.
Profiles were normalized such that the integral of the profile was set to 1. Particle Imaging Velocimetry was performed using PIVLab software Thielicke and Stamhuis, using the FFT window deformation algorithm with a pixel interrogation area and 8 pixel step for the first pass and an 8 pixel interrogation area with a 4-pixel step for the second pass.
We introduce a theoretical description of a confined active microtubule-motor gel immersed in a Newtonian fluid. We obtain generic equations of motion for this system closely following the logic outlined in Doi and Onuki, ; Joanny et al. This generic description is augmented by including a density-dependent active stress, which is derived from a minimal microscopic description of microtubule-dynein interactions. Here, we present the equations of motion for the one dimensional system.
We begin by stating the conservation laws an active gel permeated by a Newtonian fluid obeys. Similarly the fluid permeating the gel obeys,. Force balance in the gel requires. The momentum continuity equation of the permeating fluid is. Furthermore, there is little observed motion of the extract surrounding the film. We thus simplify Equation 9 to.
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Equation 11 is the force balance equation we henceforth use for the gel to quantitatively capture the experimental dynamics. We next seek to obtain an expression for the active stress by coarse-graining a microscopic model of interactions between dynein molecular motors and microtubules. Here, we assume that dynein builds up near microtubule minus ends as previously suggested Elting et al. We introduce the positions of microtubule minus ends x i , such that the film density can be written as. Note that averaging Equation 15 over an appropriate mesoscopic volume yields the well-known Kirkwood formula.
Generically, A i j and R i j depend on the relative positions and orientations of microtubules i and j. Since we are concerned with a disordered assembly of microtubules in which all orientations occur with the same likelihood it is sufficient for our purposes to only think of microtubule positions, and orientation effects average out.
The average attractive force A i j that motors bound to the minus end of filament i exert on filament j can be expressed locally as the product. Since each dynein can link at most two filaments,. We next discuss the average steric force that filament i exerts on filament j. Given the force r i j of a collision event we find. Equation 19 is linear in the motor density m , since only filaments that are being actively moved will sterically displace their neighbors. The total active stress is thus given by,.
Together with Equations 7,11,21 are the equations of motions of our system. We asked how the characteristic time of contractions scales as a function of the width W 0 of the confining chamber, according to our theory. For this, we rewrite the equations of motion, Equations 7,11 , in dimensionless form. The boundary condition then becomes. We next linearize around this steady state, i. To linear order the equations of motion then become. To determine the timescale of the width contractions we need to remember the conservation of mass.
Thus, the dynamics is governed by multiple relaxation processes with varying timescales. In particular. In the experimental parameter regime, the timescale we measure is presumably intermediate,. We then fit the results to the functional form of Equation The instantaneous film velocity is determined from Equation 11 using a second order finite difference scheme.
We determine the time derivative of density using Equation 26 with the boundary condition specified in Equation 27 , which account for the grid contracting with the width of the film. Jump to an artist page. A Hawk and A Hacksaw A. Facebook Twitter Instagram. This field is intended to catch out spammers - please leave it blank. Ground Control Touring. This perspective is highlighted as a cover article. Innsbruck, Austria and submitted his diploma thesis. M hydrogen bonding " Competitive NH Seidel, Univ. Rostock publish a paper on the unexpected excited state behaviour of cyclometallated ruthenium II complexes " Understanding the excited state behavior of cyclometalated bis tridentate ruthenium II complexes: a combined experimental and theoretical study " Inorg.
The paper is featured as a cover article. Waldvogel and K. Polanski, Jan. This has been highlighted in local media Allgemeine Zeitung , Dec. Fe hydrogen bond " Diferrocenyl tosyl hydrazone with an ultrastrong NH Fe hydrogen bond as double click switch " Chem. Thomas Deufel in Trier. The research project has also been highlighted in several media Allgemeine Zeitung , Nov.