Pattern formation in active model C with anchoring: bands, aster networks, and foams

We study the dynamics of pattern formation in a minimal model for active mixtures made of microtubules and molecular motors. We monitor the evolution of the (conserved) microtubule density and of the (non-conserved) nematic order parameter, focusing on the effects of an "anchoring" term that provides a direct coupling between the preferred microtubule direction and their density gradient. The key control parameter is the ratio between activity and elasticity. When elasticity dominates, the interplay between activity and anchoring leads to formation of banded structures that can undergo additional bending or rotational instabilities. When activity dominates, the nature of anchoring instead gives rise to a range of active cellular solids, including aster-like networks, disordered foams and spindle-like patterns. We speculate that the introduced "active model C" with anchoring is a minimal model to describe pattern formation in a biomimetic analogue of the microtubule cytoskeleton

Kinetic theory of pattern formation in mixtures of microtubules and molecular motors

In this study we formulate a theoretical approach, based on a Boltzmann-like kinetic equation, to describe pattern formation in two-dimensional mixtures of microtubular filaments and molecular motors. Following the previous work by Aranson and Tsimring [Phys. Rev. E {\bf 74}, 031915 (2006)] we model the motor-induced reorientation of microtubules as collision rules, and devise a semi-analytical method to calculate the corresponding interaction integrals. This procedure yields an infinite hierarchy of kinetic equations that we terminate by employing a well-established closure strategy, developed in the pattern-formation community and based on a power-counting argument. We thus arrive at a closed set of coupled equations for slowly varying local density and orientation of the microtubules, and study its behaviour by performing a linear stability analysis and direct numerical simulations. By comparing our method with the work of Aranson and Tsimring, we assess the validity of the assumptions required to derive their and our theories. We demonstrate that our approximation-free evaluation of the interaction integrals and our choice of a systematic closure strategy result in a rather different dynamical behaviour than was previously reported. Based on our theory, we discuss the ensuing phase diagram and the patterns observed.Comment: 18 pages, 11 figures, Simulation movies can be found at http://dx.doi.org/10.7488/ds/224

Cortical contraction drives the 3D patterning of epithelial cell surfaces

Cellular protrusions create complex cell surface topographies, but biomechanical mechanisms regulating their formation and arrangement are largely unknown. To study how protrusions form, we focused on the morphogenesis of microridges, elongated actin-based structures that are arranged in maze-like patterns on the apical surfaces of zebrafish skin cells. Microridges form by accreting simple finger-like precursors. Live imaging demonstrated that microridge morphogenesis is linked to apical constriction. A nonmuscle myosin II (NMII) reporter revealed pulsatile contractions of the actomyosin cortex, and inhibiting NMII blocked apical constriction and microridge formation. A biomechanical model suggested that contraction reduces surface tension to permit the fusion of precursors into microridges. Indeed, reducing surface tension with hyperosmolar media promoted microridge formation. In anisotropically stretched cells, microridges formed by precursor fusion along the stretch axis, which computational modeling explained as a consequence of stretch-induced cortical flow. Collectively, our results demonstrate how contraction within the 2D plane of the cortex can pattern 3D cell surfaces

A Non-Linear Model for Solute Transport, Accounting for Sub-diffusive Concentration Decline and Sorption Saturation

Solute transport in porous media is very often complicated by solute immobilization on a solid matrix of porous media. Usually, immobilization is accounted by the mobile/immobile media approach (MIM). However, solute immobilization is very complicated phenomena with a variety of specific features. Therefore, in the literature there have been a lot of specific MIM-type models. Usually each model is constructed for to account one specific feature. Examples are the power decline of concentration in the large time limit at small concentration and the limitation of the immobilization process at high concentrations. Both effects have been evidenced by experiments. The present paper develops a hybrid nonlinear fractional MIM model potentially able to describe the above two features. A step-by-step process of constructing the nonlinear fractional MIM model is presented, and the main properties of the new model are discussed. Two limiting cases describe power law decline and sorption saturation have predicted by the new model equations. Numerical simulations illustrate limiting cases and the capabilities of new nonlinear fractional model

Laplace-transform based inversion method for fractional dispersion.

International audienc

Laplace-Transform Based Inversion Method for Fractional Dispersion

International audiencePartial differential equations with memory are challenging models for mass transport in porous media where fluid and tracer may be stored by the solid matrix, and then released. Moreover, integral transforms (generalizing time moments) of solutions to such models are linked to the corresponding transport parameters. Inverting that link provides a method to determine model parameters on the basis of solutions. It is checked using numerically generated profiles before passing to experimental data