Mathematical models of the cytoskeleton

Cell crawling is an important biological phenomenon because it underlies coordinated cell movement in morphogenesis, cancer and wound healing. This phenomenon is based on protrusion at the cell's leading edge, retraction at the rear, contraction and graded adhesion powered by the dynamics of actin and myosin protein networks. A few one-dimensional models successfully explain an anteroposterior organization of the motile cell, but don't sufficiently explore the viscoelastic nature of the actin-myosin gel. We develop and numerically solve a model of a treadmilling strip of viscoelastic actin-myosin gel. The results show that the strip translocates steadily as a traveling pulse, without changing length, and that protein densities, velocities and stresses become stationary. The simulations closely match the observed forces, movements and protein distributions in the living cell. We also model a stationary fragment and compare our results with a biological experiment.; Cell division is another example of intricate cell movements which rely on cytoskeleton elements. We focus particularly on the elastic forces generated in the mitotic spindle by overlapping interpolar microtubules. We describe a model that allows forces in the spindle to be estimated by using measurements for angles and pole distances from microscopy data.