Manoj Gopalakrishnan

In the intracellular environment, the intrinsic dynamics of microtubule filaments is often hindered by the presence of barriers of various kind, such as kinetochore complexes and cell cortex, which impact their polymerisation force and dynamical properties such as catastrophe frequency. We present a theoretical study of the effect of a forced barrier, also subjected to thermal noise, on the statistics of catastrophe events in a single microtubule as well as a 'bundle' of two parallel microtubules. For microtubule dynamics, which includes growth, detachment, hydrolysis and the consequent dynamic instability, we employ a one-dimensional discrete stochastic model. The dynamics of the barrier is captured by over-damped Langevin equation, while its interaction with a growing filament is assumed to be hard-core repulsion. A unified treatment of the continuum dynamics of the barrier and the discrete dynamics of the filament is realized using a hybrid Fokker-Planck equation. An explicit mathematical formula for the force-dependent catastrophe frequency of a single microtubule is obtained by solving the above equation, under some assumptions. The prediction agrees well with results of numerical simulations in the appropriate parameter regime. More general situations are studied via numerical simulations. To investigate the extent of 'load-sharing' in a microtubule bundle, and its impact on the frequency of catastrophes, the dynamics of a two-filament bundle is also studied. Here, two parallel, non-interacting microtubules interact with a common, forced barrier. The equations for the two-filament model, when solved using a mean-field assumption, predicts equal sharing of load between the filaments. However, numerical results indicate the existence of a wide spectrum of load-sharing behaviour, which is characterized using a dimensionless parameter.

Motor-driven bidirectional transport inside a cell is an intriguing phenomenon where multiple dyneins and kinesins drag cargoes and deliver them to specific locations. Quite often, both anterograde (plus) and retrograde (minus) directed motors reside simultaneously on the cargo and co-ordinate their activity such that the motion of the cargo looks like spells of plus directed and minus directed segments, with pauses in between. The stochastic tug-of-war model is widely used to analyze this motion, largely studied by computer simulations. Here, we present some analytical results for this model, such as the average durations of plus and minus-run segments and tug-of-war events as well as probabilities of persistence and reversal of directions following a tug-of-war. We show that cargo motion has memory in case of 2 dyneins and 1 kinesin driving together, while it is absent when only a dynein and a kinesin is involved. © 2013 American Institute of Physics.