Active smectics on a sphere.

The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are spontaneously formed, and then annihilate during a coarsening process until a steady state is achieved. The coarsening process is highly complex involving several scaling laws of defect densities as a function of time where different dynamical exponents can be identified. In general the exponent for the final stage towards the steady state is significantly larger than that in the passive and in the planar case, i.e. the coarsening is getting accelerated both by activity and by the topological and geometrical properties of the sphere. A defect type characteristic for this active system is a rotating spiral of evolving smectic layering lines. On a sphere this defect type also determines the steady state. Our results can in principle be confirmed by dense systems of synthetic or biological active particles.

Axis convergence in C. elegans embryos.

Embryos develop in a surrounding that guides key aspects of their development. For example, the anteroposterior (AP) body axis is always aligned with the geometric long axis of the surrounding eggshell in fruit flies and worms. The mechanisms that ensure convergence of the AP axis with the long axis of the eggshell remain unresolved. We investigate axis convergence in early C. elegans development, where the nascent AP axis, when misaligned, actively re-aligns to converge with the long axis of the egg. We identify two physical mechanisms that underlie axis convergence. First, bulk cytoplasmic flows, driven by actomyosin cortical flows, can directly reposition the AP axis. Second, active forces generated within the pseudocleavage furrow, a transient actomyosin structure similar to a contractile ring, can drive a mechanical re-orientation such that it becomes positioned perpendicular to the long axis of the egg. This in turn ensures AP axis convergence. Numerical simulations, together with experiments that either abolish the pseudocleavage furrow or change the shape of the egg, demonstrate that the pseudocleavage-furrow-dependent mechanism is a major driver of axis convergence. We conclude that active force generation within the actomyosin cortical layer drives axis convergence in the early nematode.

Properties of surface Landau-de Gennes Q-tensor models.

Uniaxial nematic liquid crystals whose molecular orientation is subjected to tangential anchoring on a curved surface offer a non trivial interplay between the geometry and the topology of the surface and the orientational degree of freedom. We consider a general thin film limit of a Landau-de Gennes Q-tensor model which retains the characteristics of the 3D model. From this, previously proposed surface models follow as special cases. We compare fundamental properties, such as the alignment of the orientational degrees of freedom with principle curvature lines, order parameter symmetry and phase transition type for these models, and suggest experiments to identify suitable model assumptions.

Nematic liquid crystals on curved surfaces: a thin film limit.

We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process, we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. The main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Landau-de Gennes model, we consider an L2-gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.

Non-invasive perturbations of intracellular flow reveal physical principles of cell organization.

Recent advances in cell biology enable precise molecular perturbations. The spatiotemporal organization of cells and organisms, however, also depends on physical processes such as diffusion or cytoplasmic flows, and strategies to perturb physical transport inside cells are not yet available. Here, we demonstrate focused-light-induced cytoplasmic streaming (FLUCS). FLUCS is local, directional, dynamic, probe-free, physiological, and is even applicable through rigid egg shells or cell walls. We explain FLUCS via time-dependent modelling of thermoviscous flows. Using FLUCS, we demonstrate that cytoplasmic flows drive partitioning-defective protein (PAR) polarization in Caenorhabditis elegans zygotes, and that cortical flows are sufficient to transport PAR domains and invert PAR polarity. In addition, we find that asymmetric cell division is a binary decision based on gradually varying PAR polarization states. Furthermore, the use of FLUCS for active microrheology revealed a metabolically induced fluid-to-solid transition of the yeast cytoplasm. Our findings establish how a wide range of transport-dependent models of cellular organization become testable by FLUCS.