Many active processes in cells are driven by highly specialised motor proteins, which interact with the cytoskeleton: a network of filamentous structures, e.~g.~ actin filaments and microtubules, which organises intracellular transport and largely determines the cell shape. These motor proteins are able to transduce the chemical energy, stored in ATP molecules, to do mechanical work while interacting with a filament. Certain motor proteins, e.~g.~members of the KIN-13 kinesin subfamily, are able to interact specifically with filament ends and induce depolymerisation of the filament ends. One important role for KIN-13 family members is in the mitotic spindle, a microtubule structure that is formed in the process of cell division and is responsible for separation and distribution of the duplicated genetic material to the forming daughter cells. The aim of this work is to develop a theoretical framework capable of describing experimentally observed behaviour and shed light on underlying principles of motor induced filament depolymerisation. We use two different theoretical approaches to describe motor dynamics in this non- equilibrium situation: On the one hand we use phenomenological continuum equations which themselves are to a large extent independent of the underlying molecular details of the system. Molecular details of the system are incorporated in the equations through the specific values of macroscopic parameters which are determined by the underlying details. On the other hand, we use one- and two-dimensional discrete stochastic descriptions of motors on a filament. These kind of descriptions enable us to investigate the effects of different microscopic mechanisms of filament depolymerisation, and to investigate the role of fluctuations on the dynamic behaviour of motor proteins. We additionally discuss filament depolymerisation in the case where motors are not free to move but are fixed to a common anchoring point and depolymerise filaments under the influence of applied forces, mimicking the situation in the mitotic spindle. Our results can be related to recent experiments on members of the KIN-13 subfamily and predictions made in our theory can be tested by further experiments. Although motivated by experiments involving members of the KIN-13 subfamily, our theory is not restricted to these motors but applies in general to associated proteins which regulate dynamics of filament ends.

Many active processes in cells are driven by highly specialised motor proteins, which interact with the cytoskeleton: a network of filamentous structures, e.~g.~ actin filaments and microtubules, which organises intracellular transport and largely determines the cell shape. These motor proteins are able to transduce the chemical energy, stored in ATP molecules, to do mechanical work while interacting with a filament. Certain motor proteins, e.~g.~members of the KIN-13 kinesin subfamily, are able to interact specifically with filament ends and induce depolymerisation of the filament ends. One important role for KIN-13 family members is in the mitotic spindle, a microtubule structure that is formed in the process of cell division and is responsible for separation and distribution of the duplicated genetic material to the forming daughter cells. The aim of this work is to develop a theoretical framework capable of describing experimentally observed behaviour and shed light on underlying principles of motor induced filament depolymerisation. We use two different theoretical approaches to describe motor dynamics in this non- equilibrium situation: On the one hand we use phenomenological continuum equations which themselves are to a large extent independent of the underlying molecular details of the system. Molecular details of the system are incorporated in the equations through the specific values of macroscopic parameters which are determined by the underlying details. On the other hand, we use one- and two-dimensional discrete stochastic descriptions of motors on a filament. These kind of descriptions enable us to investigate the effects of different microscopic mechanisms of filament depolymerisation, and to investigate the role of fluctuations on the dynamic behaviour of motor proteins. We additionally discuss filament depolymerisation in the case where motors are not free to move but are fixed to a common anchoring point and depolymerise filaments under the influence of applied forces, mimicking the situation in the mitotic spindle. Our results can be related to recent experiments on members of the KIN-13 subfamily and predictions made in our theory can be tested by further experiments. Although motivated by experiments involving members of the KIN-13 subfamily, our theory is not restricted to these motors but applies in general to associated proteins which regulate dynamics of filament ends.