Modelling Microtubule Organisation in Axons

Abstract

The organisation of microtubule filaments in neurites is starkly different from each other. In vertebrates, the microtubules in the axon are almost organised with their plus ends directing towards the cell periphery/axon terminus (plus-end distal). At the same time, the dendrites have an equal number of microtubules oriented towards the cell periphery and cell body. The uniform microtubule organisation is essential for the targeted cargo trafficking in an elongating axon. Disruption in this uniform polarity of microtubules will be detrimental to the axon. Several intra-cellular events and pathological conditions can cause the production of shorter microtubules in axoplasm, which may eventually flip and mis orient. The negatively directed motor protein dynein is proposed to be the main component of polarity sorting machinery. Dynein, when immobilised on a rigid structure with its cargo domain, can slide microtubules with its plus ends leading. Thus, immobilised dynein can clear out the short misoriented minus-end distal microtubules to the cell body. The previous model approached the question with a one-dimensional system, and the motor proteins were modelled as identical particles. The model was unable to distinguish between the proposed substrates of motor protein immobilisation and the role of thermal energy in polarity sorting. Here, we are building a computational model of polarity sorting with insights from previous studies. A basic 3D model with immobilised dynein and microtubules is simulated in `Cytosim', a cytoskeletal simulation software. The motor protein-filament interaction is modelled as discrete stochastic events rather than being modelling the interaction as a continuous process. The effect of thermal energy in properly aligning MTs longer than the axon diameter was revealed. By studying a 3D model, we could differentiate between 2 proposed sites of dynein immobilisation in axons. The model revealed that dynein immobilised on long microtubules present in the axoplasm is more efficient in polarity sorting than dynein immobilised on the actin network. The velocity of microtubule movement increases and reach a steady-state as microtubule length increases. This is in check with \textit{in vitro} observations. The features of microtubule movement in axons include frequent pauses and occasional change of direction. The pauses in MT movement increased as the rate of binding of dynein to the microtubule was reduced. Addition of immobilised kinesin to the model with immobilised dynein, induced change of direction of Microtubule movements. More studies exploring the components and initial conditions of the model can reveal more insights regarding the polarity sorting.