Monday 16 Oct 2017: Dynamics Seminar: Modelling Microtubule Rings in Gliding Assays
Simon Pearce - Manchester
LSI Seminar Room B 14:30-15:30
Microtubules are one of the main components of the cells, and are essential for many biological functions such as mitosis and intracellular transport. As the stiffest cytoskeletal polymer, they are generally seen to be very straight over cellular length-scales, with a persistence length of 2-4mm. However, in areas of neurodegeneration highly curved microtubules are seen, with radius of curvature of a micron. Similarly sized microtubule rings are sometimes seen in gliding assays, where microtubules are moved over a surface by the motor protein kinesin, amongst other microtubules translocating as rigid rods.
Recent evidence suggests that some microtubule-associated proteins such as kinesin are able to sense and alter MT curvature, and so we model MTs moving on gliding assays as inextensible rods with a preferred curvature which is controlled by the differential binding of the kinesin. We find that there exist parameter regimes wherein metastable rings can form, and hence offer this differential binding as an explanation for these highly curved microtubules seen in vitro and in vivo.
The compound matrix method for solving eigenvalue boundary value problems will also be discussed, including showing a Mathematica implementation.