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Mobility, fitness accumulation, and the breakdown of cooperation

By Anatolij Gelimson (11.01.2013)

A living cell is more than just a collection of randomly distributed proteins and molecules. In order to perform its various functions, a well-defined yet dynamical structure is needed. Microtubules are therefore important parts of the cellular cytoskeleton. With their high stiffness these polymers of tubulin serve for the stabilization of the cell shape as well as for various other cellular functions. Particularly fascinating is the interplay between microtubules and molecular motors like kinesin. These miniature machines are able to walk on a microtubule by undergoing stochastic cyclic deformations. For example, motor proteins from the kinesin-8 family (e.g. Kip3p in budding yeast and Klp5/6 in fission yeast) have been shown to walk on microtubules towards the plus-end, and to depolymerize them into single tubulin monomers in a length-dependent manner. It was argued that this could provide a mechanism for nuclear positioning during interphase or, in combination with microtubule polymerization, allow a cell to regulate microtubule length.

Various theoretical and experimental studies suggest that this is possible because of a length-dependent accumulation of kinesin motors towards the plus-end. In  particular, crowding effects have been shown to be a key regulatory mechanism. This suggests that spatial organization of kinesin motors plays a prominent role in regulating microtubule length, and hence, cell size. Given that cells have a relatively sharp size distribution — they are always typically around 10 μm — it is natural to wonder whether there are universal contributing factors to the process of motor accumulation, and consequently size selection.

Together with Prof. Ramin Golestanian and Prof. Erwin Frey I examined the interplay between the motion of colloids on a surface (e.g. motors on a microtubule) and the fluid flow field in the surrounding created by this motion in a generic model. The dynamics of the model is illustrated in Fig. 1. Colloids suspended in the bulk can associate to and dissociate from the surface (which is chosen to be in the x-y plane).

Fig. 1: The schematics of the model.[Bildunterschrift / Subline]: Fig. 1: The schematics of the model. Colloids solved in the surrounding can bind and unbind, with rates rac and rd. Bound colloids move at a velocity v0 = v0ex (large arrows). The movement of the colloids on the surface induces a hydrodynamic velocity field v(r) in the bulk, which in turn attracts more dissolved colloids to the surface (small arrows), hence creating a self-feedback mechanism.

Bound colloids move into the x-direction at the constant velocity v0. The hydrodynamic and transport equations for this model can be solved exactly. Interestingly, we find that the interplay between hydrodynamic interactions, binding, and near-surface active motion could lead to a self-feedback mechanism: the velocity flow field created by the movement of the colloids attracts further colloids from the surrounding. These, again, will also bind to the surface and further amplify the fluid flow. This mechanism leads to the accumulation of the colloids over a sharply selected length scale that depends on the bulk diffusion coefficient and the surface velocity of the colloids. Remarkably, we find that this lengthscale is of approximately the same size as the typical microtubule length of 10 μm in cells. Since some types of motors depolymerize microtubules when they come to their end, this effect could help regulate the microtubule length in cells.

Further evidence will be needed to investigate our theoretical findings. In a lab environment, we expect hydrodynamic effects to be most pronounced provided sufficiently long segments of microtubule or actin are stabilized and aligned perhaps using a substrate with grooves, or sufficiently fast motors are used. Surface-assisted motion could also be realized using engineered systems such as magnetic garnet films, and surface hydrophobicity gradient. It will be interesting to probe whether this mechanisms might be exploited in biological systems as a contributing factor in size selection.


Anatolij Gelimson (LMU Munich, Univ. of Oxford), Erwin Frey (LMU Munich), and Ramin Golestanian (Univ. of Oxford)



Anatolij Gelimson
* 25.08.1986 in Sumy/Ukraine

Scientific Career
  • 2007-2010
  • Bachelor Studies of Physics, LMU Munich
  • 2010-2012
  • Master Studies of Theoretical and Mathematical Physics, LMU Munich
  • 2011-2012
  • Visiting Research Student (Masterthesis), University of Oxford

Awards and Scholarships
  • 2008-2012
  • Studienstiftung des Deutschen Volkes Scholarship
  • 2011-2012
  • Year Abroad Scholarship, Studienstiftung des Deutschen Volkes