Mean-field theory approach to three-dimensional nematic phase transitions in microtubules.

Microtubules are dynamic intracellular fibers that have been observed experimentally to undergo spontaneous self-alignment. We formulate a three-dimensional (3D) mean-field theory model to analyze the nematic phase transition of microtubules growing and interacting within a 3D space, then make a comparison with computational simulations. We identify a control parameter G_{eff} and predict a unique critical value G_{eff}=1.56 for which a phase transition can occur. Furthermore, we show both analytically and using simulations that this predicted critical value does not depend on the presence of zippering. The mean-field theory developed here provides an analytical estimate of microtubule patterning characteristics without running time-consuming simulations and is a step towards bridging scales from microtubule behavior to multicellular simulations.

Cytoskeletal organization in isolated plant cells under geometry control.

The cytoskeleton plays a key role in establishing robust cell shape. In animals, it is well established that cell shape can also influence cytoskeletal organization. Cytoskeletal proteins are well conserved between animal and plant kingdoms; nevertheless, because plant cells exhibit major structural differences to animal cells, the question arises whether the plant cytoskeleton also responds to geometrical cues. Recent numerical simulations predicted that a geometry-based rule is sufficient to explain the microtubule (MT) organization observed in cells. Due to their high flexural rigidity and persistence length of the order of a few millimeters, MTs are rigid over cellular dimensions and are thus expected to align along their long axis if constrained in specific geometries. This hypothesis remains to be tested in cellulo Here, we explore the relative contribution of geometry to the final organization of actin and MT cytoskeletons in single plant cells of Arabidopsis thaliana We show that the cytoskeleton aligns with the long axis of the cells. We find that actin organization relies on MTs but not the opposite. We develop a model of self-organizing MTs in three dimensions, which predicts the importance of MT severing, which we confirm experimentally. This work is a first step toward assessing quantitatively how cellular geometry contributes to the control of cytoskeletal organization in living plant cells.

Multi-directional bubble generated streaming flows.

In previous work, we have demonstrated the use of single-holed Armoured Microbubbles (AMBs) for microfluidic mixing and self-propulsion. AMBs are hollow partial spheres, inside which we capture a bubble. Under ultrasound, the bubble oscillates, generating a streaming flow with velocities of 1-100 mm/s in water. In this paper, inspired by our successful fabrication of a C60 geometry (buckyball), we study AMBs with multiple surface holes. We show more holes generate additional pairs of fast circulations around the AMB. However, as the number of holes increases further, the circulations become small and the in-plane flow is dominated by a source or sink flow. For an AMB with two different sized holes, we demonstrate each hole can be independently activated, potentially useful for multi-directional swimming.

Bubble-based acoustic micropropulsors: active surfaces and mixers.

Acoustic micropropulsors present great potential for microfluidic applications. The propulsion is based on encapsulated 20 µm bubbles excited by a contacless ultrasonic transducer. The vibrating bubbles then generate a powerful streaming flow, with speeds 1-100 mm s-1 in water, through the action of viscous stresses. In this paper we introduce a full toolbox of micropropulsors using a versatile three-dimensional (3D) microfabrication setup. Doublets and triplets of propulsors are introduced, and the flows they generate are predicted by a theoretical hydrodynamic model. We then introduce whole surfaces covered with propulsors, which we term active surfaces. These surfaces are excited by a single ultrasonic wave, can generate collective flows and may be harnessed for mixing purposes. Several patterns of propulsors are tested, and the flows produced by the two most efficient mixers are predicted by a simple theoretical model based on flow singularities. In particular, the vortices generated by the most efficient pattern, an L-shaped mixer, are analysed in detail.