Theoretical studies of biological cell motility

In crawling cells, the polymerisation of actin into a filamentaus network generates lamellar pro­trusion into the direction of locomotion. Only recently it was discovered, that Arp2/3 nucleates the branching of actin filaments, by allowing new filaments to grow from old ones at an angle of roughly $\varphi$ = 70°. Topic of the present work is the amoeboid cell motility. Using computerbased models, the general mechanism of locomotion, and the special relevance of branched networks is studied.First the treadmilling of actin filaments is focused on. By Monte Carlo simulations on a lattice, in a two dimensional model the kind of locomotion is studied, that is generated by treadmillingfilaments inside a cell membrane. It is show, that the membrane and the filament tips cooperate tomaximise the effect of polymerisation. The interaction between the model cell and the substrate is looked at in a treadmilling based model by continuous Langevin simulations. In two dimensions the model can be specialised to describe the phenomena of chemotaxis and durotaxis.Furthermore, the consequences of Arp2/3 induced branching near the cell's periphery is analysed, both by means of Langevin simulations and analytical calculations. The antagonism between filament branching and pointed end capping leads to the phenomenon of the cellular persistent random walk. In an effectively one dimensionl computer model, the cell membrane supplies Arp2/3 to actin filaments within a certain range, thus polarising the cell. The resulting autocatalytic polymerisation amplifies this spatial polarisation and generates a persistent actin distribution, that leads to the persistent random walk of amoeboid cells