Filamentous active matter: Band formation, bending, buckling, and defects.

Motor proteins drive persistent motion and self-organization of cytoskeletal filaments. However, state-of-the-art microscopy techniques and continuum modeling approaches focus on large length and time scales. Here, we perform component-based computer simulations of polar filaments and molecular motors linking microscopic interactions and activity to self-organization and dynamics from the filament level up to the mesoscopic domain level. Dynamic filament cross-linking and sliding and excluded-volume interactions promote formation of bundles at small densities and of active polar nematics at high densities. A buckling-type instability sets the size of polar domains and the density of topological defects. We predict a universal scaling of the active diffusion coefficient and the domain size with activity, and its dependence on parameters like motor concentration and filament persistence length. Our results provide a microscopic understanding of cytoplasmic streaming in cells and help to develop design strategies for novel engineered active materials.

Chronology of motor-mediated microtubule streaming.

We introduce a filament-based simulation model for coarse-grained, effective motor-mediated interaction between microtubule pairs to study the time-scales that compose cytoplasmic streaming. We characterise microtubule dynamics in two-dimensional systems by chronologically arranging five distinct processes of varying duration that make up streaming, from microtubule pairs to collective dynamics. The structures found were polarity sorted due to the propulsion of antialigned microtubules. This also gave rise to the formation of large polar-aligned domains, and streaming at the domain boundaries. Correlation functions, mean squared displacements, and velocity distributions reveal a cascade of processes ultimately leading to microtubule streaming and advection, spanning multiple microtubule lengths. The characteristic times for the processes extend over three orders of magnitude from fast single-microtubule processes to slow collective processes. Our approach can be used to directly test the importance of molecular components, such as motors and crosslinking proteins between microtubules, on the collective dynamics at cellular scale.

Dramatic influence of patchy attractions on short-time protein diffusion under crowded conditions.

In the dense and crowded environment of the cell cytoplasm, an individual protein feels the presence of and interacts with all surrounding proteins. While we expect this to strongly influence the short-time diffusion coefficient Ds of proteins on length scales comparable to the nearest-neighbor distance, this quantity is difficult to assess experimentally. We demonstrate that quantitative information about Ds can be obtained from quasi-elastic neutron scattering experiments using the neutron spin echo technique. We choose two well-characterized and highly stable eye lens proteins, bovine α-crystallin and γB-crystallin, and measure their diffusion at concentrations comparable to those present in the eye lens. While diffusion slows down with increasing concentration for both proteins, we find marked variations that are directly linked to subtle differences in their interaction potentials. A comparison with computer simulations shows that anisotropic and patchy interactions play an essential role in determining the local short-time dynamics. Hence, our study clearly demonstrates the enormous effect that weak attractions can have on the short-time diffusion of proteins at concentrations comparable to those in the cellular cytosol.

Trains, tails and loops of partially adsorbed semi-flexible filaments.

Polymer adsorption is a fundamental problem in statistical mechanics that has direct relevance to diverse disciplines ranging from biological lubrication to stability of colloidal suspensions. We combine experiments with computer simulations to investigate depletion induced adsorption of semi-flexible polymers onto a hard-wall. Three dimensional filament configurations of partially adsorbed F-actin polymers are visualized with total internal reflection fluorescence microscopy. This information is used to determine the location of the adsorption/desorption transition and extract the statistics of trains, tails and loops of partially adsorbed filament configurations. In contrast to long flexible filaments which primarily desorb by the formation of loops, the desorption of stiff, finite-sized filaments is largely driven by fluctuating filament tails. Simulations quantitatively reproduce our experimental data and allow us to extract universal laws that explain scaling of the adsorption-desorption transition with relevant microscopic parameters. Our results demonstrate how the adhesion strength, filament stiffness, length, as well as the configurational space accessible to the desorbed filament can be used to design the characteristics of filament adsorption and thus engineer properties of composite biopolymeric materials.

Fluctuating shells under pressure.

Thermal fluctuations strongly modify the large length-scale elastic behavior of cross-linked membranes, giving rise to scale-dependent elastic moduli. Whereas thermal effects in flat membranes are well understood, many natural and artificial microstructures are modeled as thin elastic shells. Shells are distinguished from flat membranes by their nonzero curvature, which provides a size-dependent coupling between the in-plane stretching modes and the out-of-plane undulations. In addition, a shell can support a pressure difference between its interior and its exterior. Little is known about the effect of thermal fluctuations on the elastic properties of shells. Here, we study the statistical mechanics of shape fluctuations in a pressurized spherical shell, using perturbation theory and Monte Carlo computer simulations, explicitly including the effects of curvature and an inward pressure. We predict novel properties of fluctuating thin shells under point indentations and pressure-induced deformations. The contribution due to thermal fluctuations increases with increasing ratio of shell radius to thickness and dominates the response when the product of this ratio and the thermal energy becomes large compared with the bending rigidity of the shell. Thermal effects are enhanced when a large uniform inward pressure acts on the shell and diverge as this pressure approaches the classical buckling transition of the shell. Our results are relevant for the elasticity and osmotic collapse of microcapsules.

Orientational ordering in solid C60 fullerene-cubane.

We study the structure and phase behavior of fullerene-cubane C(60) x C(8)H(8) by Monte Carlo simulation. Using a simple potential model capturing the icosahedral and cubic symmetries of its molecular constituents, we reproduce the experimentally observed phase transition from a cubic to an orthorhombic crystal lattice and the accompanying rotational freezing of the C(60) molecules. We elaborate a scheme to identify the low-temperature orientations of individual molecules and to detect a pattern of orientational ordering similar to the arrangement of C(60) molecules in solid C(60). Our configuration of orientations supports a doubled periodicity along one of the crystal axes.