A high-resolution shape fitting and simulation demonstrated equatorial cell surface softening during cytokinesis and its promotive role in cytokinesis.

Different models for animal cell cytokinesis posit that the stiffness of the equatorial cortex is either increased or decreased relative to the stiffness of the polar cortex. A recent work has suggested that the critical cytokinesis signaling complex centralspindlin may reduce the stiffness of the equatorial cortex by inactivating the small GTPase Rac. To determine if such a reduction occurs and if it depends on centralspindlin, we devised a method to estimate cortical bending stiffness with high spatio-temporal resolution from in vivo cell shapes.

Formation and maintenance of tubular membrane projections: experiments and numerical calculations.

To study the mechanical properties of lipid membranes, we manipulated liposomes by using a system comprising polystyrene beads and laser tweezers, and measured the force required to transform their shapes. When two beads pushed the membrane from inside, spherical liposomes transformed into a lemon-shape. Then a discontinuous shape transformation occurred to form a membrane tube from either end of the liposomes, and the force dropped drastically.

Theoretical analysis of opening-up vesicles with single and two holes.

Cuplike lipid vesicles with a single hole and tubelike vesicles with two holes were theoretically analyzed by taking into account the line tension of membrane holes and the bending energy of membranes, using the area difference elasticity model. We numerically solved the Euler-Lagrange equation and the boundary conditions holding on the membrane edge to obtain axisymmetric vesicle shapes that minimize the total energy. The numerical results showed that when the line tension is very low, and for appropriate values of the relaxed area difference between the two monolayers of bilayer membranes, the model yields cup-, tube-, and funnel-shaped vesicles that closely resemble previously observed shapes of opening-up vesicles with additive guest molecules such as the protein talin and some detergents.

Cell sorting by differential cell motility: a model for pattern formation in Dictyostelium.

In the slug stage of the cellular slime mold Dictyostelium discoideum, prespore cells and four types of prestalk cells show a well-defined spatial distribution in a migrating slug. We have developed a continuous mathematical model for the distribution pattern of these cell types based on the balance of force in individual cells. In the model, cell types are assumed to have different properties in cell motility, i.

Possible role of contact following in the generation of coherent motion of Dictyostelium cells.

After aggregation by chemotaxis, cells of the cellular slime mold Dictyostelium discoideum form a multicellular structure and show coherent motion such as vortices. Here, we present a mathematical model to explain both aggregation and coherent motion of cells in two-dimensional space. The model incorporates chemotactic response of cells and the cell's property, called "contact following", to follow the other cells with which they are in contact.