Theoretical description of the bulk movement of kinesin motors
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During growth, a nerve cell creates protrusions that are called neurites. The intracellular active transport of the proteins is based on kinesin molecules walking on microtubules that have a chiral symmetry and thus a direction. The direction of this movement is towards the +END of the microtubule. Estimates suggest that in neurites 80% of microtubules are aligned in such a way that kinesin molecules walk to the tip of the neurite. In sharp con- trast, recent experiments found that kinesin molecules move collectively toward the cell body, away from the tip of the neurite. So far, there is no explanation on this unexpected observation. In this thesis, we introduce a mathematical description of the collective ki- nesin movement and investigate three different possible underlying mechanisms for the observed reversal. The most possible mechanism assumes that through cell signaling ki- nesin molecules exclusively can bind to different subsets of microtubules pointing either toward or away from the cell body. For this model, we approximate the full mathemati- cal system of transport-reaction equations with an equation for biased diffusion and fit the parameters so we reproduce the experimental data and describe quantitatively the environ- ment changes that the cell induces.