Spindle mechanics

The mitotic spindle self-assembles within the cell and reliably segregates chromosomes during cell division. During metaphase, the spindle aligns all chromosomes at the midplane of the cell. During this period the spindle maintains its size and shape. If all chromosomes are properly connected to the two poles, the spindle assembly checkpoint gets activated and the spindle enters anaphase during which the spindle elongates and pulls the chromosomes apart. The spindle itself is made up of microtubules, stiff filaments of tubulin that assemble with the help of hundreds of associated proteins. So far, it remains unclear how a spindle can maintain a robust steady-state size during metaphase, although the building blocks—dynamic microtubules—turn over rapidly.

We do not build houses for a century with bricks that have an average lifetime of a year.
The spindle is in this counterintuitive regime and, as such, is both flexible and dynamic.

I conduct my research in the biophysics division at the Max Planck Institute for the Physics of Complex Systems working with Frank Jülicher. I combine data analysis of electron tomography and light microscopy data with numerical simulations and modeling to gain insights into this self-assembly process and the mechanics of the metaphase spindle.

 

Estimating dynamic properties of microtubules in the spindle


Mass balance allows us to connect the light microscopy picture of the spindle with our knowledge about the building blocks: stiff microtubules, which turnover rapidly. It is so far not possible to track individual microtubules in living samples, as the density is high, the microtubules diffuse around, and the optical quality is poor.

Based on tracking of the growing microtubule tips, marked by EB1-GFP, we were able to show in a perturbation experiment that: XMAP215 activity sets spindle length by controlling the total mass of spindle microtubules. The experimental work was mainly performed by Anthony Hyman and Simone Reber. Simone Reber started in the meantime her own lab. The theoretical modeling part and data analysis were conducted by Frank Jülicher and myself.

Tracking individual EB1 tracks in the dense spindle is prone to artifacts. With the lab of Jan Brugués, we work on a new concept of the data analysis based on spatial-temporal correlations. With this approach, we give up on information of individual tracks for the sake of less parameter-dependent tracking method.

 

The architecture of the metaphase spindle described by the arrangement of microtubules

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The poles of the spindle are singularities where the orientation of the microtubules, the main structural component of the spindle, is not well defined. I analyze the local microtubule arrangement to retrieve precise quantitative measures, such as the local density, local ordering, and length distributions.

Large-scale serial electron tomography provides a complete geometrical description of the microtubules in three-dimensional space. The major part of data acquisition was performed by Thomas Müller-Reichert and Stefanie Redemann and by the lab of Anthony Hyman with Jean-Marc Verbavatz. The segmentation of the data was supported by Steffen Prohaska and Norbert Lindow. We gain further insights by incorporating our findings in models together with Jan Brugués and the lab of Michael Shelley with Sebastian Fürthauer and Ehssan Nazockdast.

Our paper C. elegans chromosomes connect to centrosomes by anchoring into the spindle network is available here. Currently, I use this detailed information on local microtubule densities to study the local concentration of tubulin polymerized into microtubules and in solution with Frank Jülicher, Jan Brugués, Anthony Hyman, Jeffrey Woodruff, Jean-Marc Verbavatz, Thomas Müller-Reichert, Marcel Kirchner, Stefanie Redemann, Steffen Prohaska, and Norbert Lindow.

 

The metaphase spindle as an active liquid-like drop


In cells the spindle apparatus reliably segregates chromosomes. The spindle’s main sub-units are hundreds of thousands of dynamic microtubules, which are well-studied. Despite this detailed knowledge, an understanding of how their collective properties give rise to a spindle with a defined size and shape is still lacking. To investigate how the self-organization of microtubules relates to the characteristic shape of the spindle, we use active liquid crystal theory. This approach is motivated by the rapid turnover of microtubules, their steric interactions, and the motor proteins acting between pairs of microtubules.

Such a description allows us to analyze spindle mechanics by nematic field equations in an active fluid. Here, we study a description including the orientation field, active stresses due to motors, and a source term to account for microtubule nucleation. We solve the set of differential equations by means of the finite element method.

On this theoretical project, I work with Frank Jülicher, Jan Brugués, David Oriola, Benjamin Dalton, Jean-François Joanny, and Christoph Erlenkämper.

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