We investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal constrained to a curved surface. Using a combination of hydrodynamic and particle-based simulations, we... Show moreWe investigate the turbulent dynamics of a two-dimensional active nematic liquid crystal constrained to a curved surface. Using a combination of hydrodynamic and particle-based simulations, we demonstrate that the fundamental structural features of the fluid, such as the topological charge density, the defect number density, the nematic order parameter, and defect creation and annihilation rates, are approximately linear functions of the substrate Gaussian curvature, which then acts as a control parameter for the chaotic flow. Our theoretical predictions are then compared with experiments on microtubule-kinesin suspensions confined on toroidal droplets, finding excellent qualitative agreement. Show less
We study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil–water interface. Kinesin motors continuously inject mechanical... Show moreWe study the dynamics of a tunable 2D active nematic liquid crystal composed of microtubules and kinesin motors confined to an oil–water interface. Kinesin motors continuously inject mechanical energy into the system through ATP hydrolysis, powering the relative microscopic sliding of adjacent microtubules, which in turn generates macroscale autonomous flows and chaotic dynamics. We use particle image velocimetry to quantify two-dimensional flows of active nematics and extract their statistical properties. In agreement with the hydrodynamic theory, we find that the vortex areas comprising the chaotic flows are exponentially distributed, which allows us to extract the characteristic system length scale. We probe the dependence of this length scale on the ATP concentration, which is the experimental knob that tunes the magnitude of the active stress. Our data suggest a possible mapping between the ATP concentration and the active stress that is based on the Michaelis–Menten kinetics that governs the motion of individual kinesin motors. Show less
Fonda, P.; Rinaldin, M.; Kraft, D.J.; Giomi, L. 2019
We introduce a simple mechanical model for adherent cells that quantitatively relates cell shape, internal cell stresses and cell forces as generated by an anisotropic cytoskeleton. We perform ex-... Show moreWe introduce a simple mechanical model for adherent cells that quantitatively relates cell shape, internal cell stresses and cell forces as generated by an anisotropic cytoskeleton. We perform ex- periments on the shape and traction forces of different types of cells with anisotropic morphologies, cultured on microfabricated elastomeric pillar arrays. We demonstrate that, irrespectively of the cell type, the shape of the cell edge between focal adhesions is accurately described by elliptical arcs, whose eccentricity expresses the ratio between directed and isotropic stresses. Our work paves the way toward the reconstruction of cellular forces from geometrical data available via optical microscopy. Show less
You, Z.; Pearce, D.J.G.; Sengupta, A.; Giomi, L. 2018
The shape of a cell membrane is largely defined by the underlying actin cytoskeleton and membrane mechanics. The actin cytoskeleton asserts contractile forces on the membrane that can be divided... Show moreThe shape of a cell membrane is largely defined by the underlying actin cytoskeleton and membrane mechanics. The actin cytoskeleton asserts contractile forces on the membrane that can be divided in isotropic and directed forces. We present a theory which is an extension of the Young-Laplace equation. It models cell edges as parts of one uniform ellipse, which changes from cell to cell. The ellipse parameters are characterized by the ratio of isotropic to directed contractility of the cell. We demonstrate the capabilities of this model using fibroblasts seeded on an elastic micro-pillar array. In this way adhesion forces exerted by the cell at single adhesion sites are measured. We show that isotropic and directed forces balance the line tension in cortical actin. Furthermore, for cells with homogeneous contractile forces and a single orientation of stress-fibers any part of the cell edge follows a universal ellipse, enabling us to calculate the magnitude of isotropic and directed contractility in a single cell. We show that in 3T3 fibroblasts the directed contractility is about three times as strong as the isotropic contractility. If myosin motors are inhibited, however, directed contractility decreases, effectively disabling forces generated by stress-fibers, and the elliptical cell cortex turns into a circular shape predicted for an isotropic contractile cytoskeleton. Our analysis shows that a simple two-parameter model explains polarity, shape of the cell cortex and cellular forces as experimentally observed. Potentially this model can be used to predict stresses and forces on the extracellular matrix and tissue. Show less
