Modeling microtubule catastrophes

HFSP Young Investigator Grant holder Francois Nedelec and colleagues

Microtubules are micro-filaments made of a protein called tubulin. They are polarized tracks that allow molecular motors to move miniature cargoes inside the cell. Being one of the main components of the mitotic spindle, they also have an essential role in cell division. The dynamics of tubulin assembly at the tip of a microtubule is unusual since in contrast to conventional polymer, a microtubule may grow for a while and then switch to a shrinking phase even though the external conditions have not changed. Such a rapid transition from growth to shrinkage is called a catastrophe and the inverse transition is called a rescue. The term dynamic instability has been coined to describe this property of microtubule growth. Dynamic instability is a very important process that enables microtubules to sense and adapt to the cellular environment. For instance, microtubule length can be adjusted to the size of the cell, if a mechanism exists that induces catastrophes when microtubule tips contact the cell membrane.
 
Ever since its discovery in 1984 by Mitchison et al., dynamic instability has attracted a lot of attention from the scientific community, and in particular from theoreticians. More than 20 different models have been proposed, but we still do not have a complete understanding of this process. In particular, we cannot predict how dynamic instability is regulated by associated proteins even though we know how many of them interact with microtubules in the cell. Yet, this is essential to understand the role of microtubules in processes such as cell division or cell growth. Rather than studying the entire process of dynamic instability (catastrophes and rescues), we decided to focus solely on catastrophes. We also made use of recent measurements showing how catastrophes are regulated by a specific class of motor protein (kinesin-8) that controls microtubule length in many cell types.
 
The basis of our model was proposed previously by Mitchison and co-workers. They observed that dynamic instability consumes energy provided by the hydrolysis of Guanosine tri-Phosphate (GTP) to Guanosine di-Phosphate (GDP). Freshly incorporated tubulin is loaded with GTP, and the phosphate is released as tubulin undergoes a conformational change within the microtubule. They proposed that a catastrophe occurs when, by chance, GTP hydrolysis overcomes the continuous supply of GTP-tubulin at the tip of the microtubule. This was a brilliant insight, but Mitchison et al. did not specify the rules that dictated hydrolysis on the molecular scale. As always, the devil is in the details, and these rules indeed determine whether a certain model will match the experimental data.
 
In a recent publication (Brun et al. 2009), we considered a simplified microtubule, made of 13 parallel filaments arranged side-by-side forming a tubular structure. The microtubule grows by addition of GTP tubulin subunits at the tip of each filament at a rate g. Hydrolysis of the GTP to GDP then occurs within the lattice at a rate h. The model is based on the concepts of mini-catastrophes and gated rescues. A mini-catastrophe occurs when the N terminal units of a filament are all hydrolyzed, leading to the depolymerization of the filament. Gated rescue is a process by which filaments help each other: a shrinking filament will be rescued if it meets the growing end of a neighboring filament. Most mini-catastrophes are rescued, and the microtubule thus grows while its filaments alternate between periods of growth and shrinkage. In rare cases, however, a mini-catastrophe cannot be rescued, leading to a microtubule catastrophe. This occurs, for example, if a mini-catastrophe affects the shortest filament. The model is simple and has only three parameters: g, h and N. The values of these parameters are over-determined, which means that only one specific model can fit all of the data.
 
We show in particular that N=2, and this suggests that exactly two independent transitions are required to trigger catastrophe of the microtubule. The first transition is probably a conformational change that occurs in the terminal unit of a filament when another unit is added. The second transition may be the hydrolysis of GTP that occurs two units away from the tip. The model recapitulates the linear relationship between the catastrophe rate and microtubule length that is induced by the kinesin-8 homologue in fission yeast. It also accounts for the regulation by physical force and changes in the free tubulin concentration. This model was essential for studying the process of chromosome capture and the regulation of microtubules by kinetochores, as proposed in a HFSP young investigator grant, since dynamic instability is a fundamental part of this process.
 


 
Pubmed link
 
PNAS link

Reference:
A theory of microtubule catastrophes and their regulation. L Brun, B Rupp, J Ward, F Nédélec. Proc Natl Acad Sci USA, 2009 vol. 106 (50) pp. 21173-8.

Additional References:
Dynamic instability of microtubule growth. T Mitchison, M Kirschner. Nature, 1984 vol. 312 (5991) pp. 237-42.