Self-organization of waves and pulse trains by molecular motors in cellular protrusions.

Actin-based cellular protrusions are an ubiquitous feature of cells, performing a variety of critical functions ranging from cell-cell communication to cell motility. The formation and maintenance of these protrusions relies on the transport of proteins via myosin motors, to the protrusion tip. While tip-directed motion leads to accumulation of motors (and their molecular cargo) at the protrusion tip, it is observed that motors also form rearward moving, periodic and isolated aggregates. The origins and mechanisms of these aggregates, and whether they are important for the recycling of motors, remain open puzzles. Motivated by novel myosin-XV experiments, a mass conserving reaction-diffusion-advection model is proposed. The model incorporates a non-linear cooperative interaction between motors, which converts them between an active and an inactive state. Specifically, the type of aggregate formed (traveling waves or pulse-trains) is linked to the kinetics of motors at the protrusion tip which is introduced by a boundary condition. These pattern selection mechanisms are found not only to qualitatively agree with empirical observations but open new vistas to the transport phenomena by molecular motors in general.

Generation of finite wave trains in excitable media.

Spatiotemporal control of excitable media is of paramount importance in the development of new applications, ranging from biology to physics. To this end, we identify and describe a qualitative property of excitable media that enables us to generate a sequence of traveling pulses of any desired length, using a one-time initial stimulus. The wave trains are produced by a transient pacemaker generated by a one-time suitably tailored spatially localized finite amplitude stimulus, and belong to a family of fast pulse trains. A second family, of slow pulse trains, is also present. The latter are created through a clumping instability of a traveling wave state (in an excitable regime) and are inaccessible to single localized stimuli of the type we use. The results indicate that the presence of a large multiplicity of stable, accessible, multi-pulse states is a general property of simple models of excitable media.

Formation and mobility of droplets on composite layered substrates.

A mesoscale fluid film placed on a solid support may break up and form droplets. In addition, droplets may exhibit spontaneous translation by modifying the wetting properties of the substrate, resulting in asymmetry in the contact angles. We examine mechanisms for droplet formation and motion on uniform and terraced landscapes, i.e., composite substrates. The fluid film stability, droplet formation and velocity are studied theoretically in the isothermal case using a lubrication approach in one spatial dimension. The droplet properties are found to involve contributions from both the terraced layer thickness and molecular interactions via the disjoining potential.

Oscillon formation as an initial pattern state.

Following Venkataramani and Ott [Phys. Rev. Lett. 80, 3495 (1998)], we consider oscillons (local excitations) as spatiotemporal subcritical bifurcation phenomena. We show in a series of numerical experiments that the appearance of oscillons is highly dependent on the initial pattern state. This finding has led to a new patterning mechanism. In this Brief Report we describe the instabilities that govern the mutual interaction of oscillons/extended patterns.