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In biological cells, the long-range intracellular traffic is powered by molecular motors which transport various cargos along microtubule filaments. The microtubules possess an intrinsic direction, having a 'plus' and a 'minus' end. Some molecular motors such as cytoplasmic dynein walk to the minus end, while others such as conventional kinesin walk to the plus end. Cells typically have an isopolar microtubule network. This is most pronounced in neuronal axons or fungal hyphae. In these long and thin tubular protrusions, the microtubules are arranged parallel to the tube axis with the minus ends pointing to the cell body and the plus ends pointing to the tip. In such a tubular compartment, transport by only one motor type leads to 'motor traffic jams'. Kinesin-driven cargos accumulate at the tip, while dynein-driven cargos accumulate near the cell body. We identify the relevant length scales and characterize the jamming behaviour in these tube geometries by using both Monte Carlo simulations and analytical calculations. A possible solution to this jamming problem is to transport cargos with a team of plus and a team of minus motors simultaneously, so that they can travel bidirectionally, as observed in cells. The presumably simplest mechanism for such bidirectional transport is provided by a 'tug-of-war' between the two motor teams which is governed by mechanical motor interactions only. We develop a stochastic tug-of-war model and study it with numerical and analytical calculations. We find a surprisingly complex cooperative motility behaviour. We compare our results to the available experimental data, which we reproduce qualitatively and quantitatively.
Movements of processive cytoskeletal motors are characterized by an interplay between directed motion along filament and diffusion in the surrounding solution. In the present work, these peculiar movements are studied by modeling them as random walks on a lattice. An additional subject of our studies is the effect of motor-motor interactions on these movements. In detail, four transport phenomena are studied: (i) Random walks of single motors in compartments of various geometries, (ii) stationary concentration profiles which build up as a result of these movements in closed compartments, (iii) boundary-induced phase transitions in open tube-like compartments coupled to reservoirs of motors, and (iv) the influence of cooperative effects in motor-filament binding on the movements. All these phenomena are experimentally accessible and possible experimental realizations are discussed.