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Register a new userSwirling Instability of the Microtubule Cytoskeleton
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In the cellular phenomena of cytoplasmic streaming, molecular motors carrying cargo along a network of microtubules entrain the surrounding fluid. The piconewton forces produced by individual motors are sufficient to deform long microtubules, as are the collective fluid flows generated by many moving motors. Studies of streaming during oocyte development in the fruit fly $D.~melanogaster$ have shown a transition from a spatially-disordered cytoskeleton, supporting flows with only short-ranged correlations, to an ordered state with a cell-spanning vortical flow. To test the hypothesis that this transition is driven by fluid-structure interactions we study a discrete-filament model and a coarse-grained continuum theory for motors moving on a deformable cytoskeleton, both of which are shown to exhibit a $swirling~instability$ to spontaneous large-scale rotational motion, as observed.
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Biological activity gives rise to non-equilibrium fluctuations in the cytoplasm of cells; however, there are few methods to directly measure these fluctuations. Using a reconstituted actin cytoskeleton, we show that the bending dynamics of embedded microtubules can be used to probe local stress fluctuations. We add myosin motors that drive the network out of equilibrium, resulting in an increased amplitude and modified time-dependence of microtubule bending fluctuations. We show that this behavior results from step-like forces on the order of 10 pN driven by collective motor dynamics.
Following recent X-ray diffraction experiments by Wong, Li, and Safinya on biopolymer gels, we apply Onsager excluded volume theory to a nematic mixture of rigid rods and strong ``$pi/2$ cross-linkers obtaining a long-ranged, highly anisotropic depletion attraction between the linkers. This attraction leads to breakdown of the percolation theory for this class of gels, to breakdown of Onsagers second-order virial method, and to formation of heterogeneities in the form of raft-like ribbons.
The phase behavior of charged rods in the presence of inter-rod linkers is studied theoretically as a model for the equilibrium behavior underlying the organization of actin filaments by linker proteins in the cytoskeleton. The presence of linkers in the solution modifies the effective inter-rod interaction and can lead to inter-filament attraction. Depending on the systems composition and physical properties such as linker binding energies, filaments will either orient perpendicular or parallel to each other, leading to network-like or bundled structures. We show that such a system can have one of three generic phase diagrams, one dominated by bundles, another by networks, and the third containing both bundle and network-like phases. The first two diagrams can be found over a wide range of interaction energies, while the third occurs only for a narrow range. These results provide theoretical understanding of the classification of linker proteins as bundling proteins or crosslinking proteins. In addition, they suggest possible mechanisms by which the cell may control cytoskeletal morphology.
A two-dimensional granular packing under horizontally circular shaking exhibits various collective motion modes depending on the strength of the oscillation and the global packing density. For intermediate packing density and oscillation amplitude, a high density phase travels along the containers side wall in clockwise direction, while the oscillation itself is anti-clockwise. Further increasing packing density towards the hexagonal packing, the whole packing rotates collectively in clockwise direction. The core of the packing rotates as a solid and is separated from the boundary by a fluid-like layer. Both motion modes are associated with the asymmetric motion of particles close to the side wall.
Microtubules and motor proteins are building blocks of self-organized subcellular biological structures such as the mitotic spindle and the centrosomal microtubule array. These same ingredients can form new bioactive liquid-crystalline fluids that are intrinsically out of equilibrium and which display complex flows and defect dynamics. It is not yet well understood how microscopic activity, which involves polarity-dependent interactions between motor proteins and microtubules, yields such larger scale dynamical structures. In our multiscale theory, Brownian dynamics simulations of polar microtubule ensembles driven by crosslinking motors allow us to study microscopic organization and stresses. Polarity sorting and crosslink relaxation emerge as two polar-specific sources of active destabilizing stress. On larger length scales, our continuum Doi-Onsager theory captures the hydrodynamic flows generated by polarity-dependent active stresses. The results connect local polar structure to flow structures and defect dynamics.
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