Mathematical modeling of Myosin induced bistability of Lamellipodial fragments.

For various cell types and for lamellipodial fragments on flat surfaces, externally induced and spontaneous transitions between symmetric nonmoving states and polarized migration have been observed. This behavior is indicative of bistability of the cytoskeleton dynamics. In this work, the Filament Based Lamellipodium Model (FBLM), a two-dimensional, anisotropic, two-phase continuum model for the dynamics of the actin filament network in lamellipodia, is extended by a new description of actin-myosin interaction. For appropriately chosen parameter values, the resulting model has bistable dynamics with stable states showing the qualitative features observed in experiments. This is demonstrated by numerical simulations and by an analysis of a strongly simplified version of the FBLM with rigid filaments and planar lamellipodia at the cell front and rear.

A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion.

We develop and analyse a discrete model of cell motility in one dimension which incorporates the effects of volume filling and cell-to-cell adhesion. The formal continuum limit of the model is a nonlinear diffusion equation with a diffusivity which can become negative if the adhesion coefficient is sufficiently large. This appears to be related to the presence of spatial oscillations and the development of plateaus (pattern formation) in numerical solutions of the discrete model. A combination of stability analysis of the discrete equations and steady-state analysis of the limiting PDE (and a higher-order correction thereof) can be used to shed light on these and other qualitative predictions of the model.

Kinetic models for chemotaxis: hydrodynamic limits and spatio-temporal mechanisms.

We study kinetic models for chemotaxis, incorporating the ability of cells to assess temporal changes of the chemoattractant concentration as well as its spatial variations. For prescribed smooth chemoattractant density, the macroscopic limit is carried out rigorously. It leads to a drift equation with a chemotactic sensitivity depending on the time derivative of the chemoattractant density. As an application it is shown by numerical experiments that the new model can resolve the chemotactic wave paradox. For this purpose, the macroscopic equation is coupled to a simple activation-inhibition model for the chemoattractant which produces the chemoattractant waves typical for the slime mold Dictyostelium discoideum.

Specificity patterns indicate that auxin exporters and receptors are the same proteins.

A study of transport and action of synthetic auxin analogues can help to identify transporters and receptors of this plant hormone. Both aspects--transportability and action on growth--were tested with 2-naphthoxyacetic acid (2-NOA) and compared across several plant species. 2-NOA stimulates elongation effectively at low concentrations in petioles of the gymnosperm Ginkgo biloba L., in hypocotyls or internodes of the dicot legumes, mung bean (Vigna mungo L.) and pea (Pisum sativum L.), in cotyledons of onion (Allium cepa L.) and in leaf bases of chive (Allium schoenoprasum L.), the latter two of the monocot order Asparagales. In contrast, elongation of coleoptile segments of maize (Zea mays L.) is poorly responsive to 2-NOA. Significant auxin-like transport of 2-NOA was observed in segments of mung bean hypocotyls, pea internodes, and chive leaf bases, but not in segments of the grass coleoptiles. Thus, for the two assays, elongation and polar transportability, the same difference in ligand specificity was observed between the grass and all other species assayed. This finding supports the hypothesis that a common protein mediates auxin efflux as well as auxin action on elongation.