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Register a new userChirality and Equilibrium Biopolymer Bundles
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We use continuum theory to show that chirality is a key thermodynamic control parameter for the aggregation of biopolymers: chirality produces a stable disperse phase of hexagonal bundles under moderately poor solvent conditions, as has been observed in {it in-vitro} studies of F-actin [O. Pelletier {it et al.}, Phys. Rev. Lett. {bf 91}, 148102 (2003)]. The large characteristic radius of these chiral bundles is not determined by a mysterious long-range molecular interaction but by in-plane shear elastic stresses generated by the interplay between a chiral torque and an unusual, but universal, non-linear gauge term in the strain tensor of ordered chains that is imposed by rotational invariance.
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Bundles of stiff filaments are ubiquitous in the living world, found both in the cytoskeleton and in the extracellular medium. These bundles are typically held together by smaller cross-linking molecules. We demonstrate analytically, numerically and experimentally that such bundles can be kinked, i.e., have localized regions of high curvature that are long-lived metastable states. We propose three possible mechanisms of kink stabilization: a difference in trapped length of the filament segments between two cross links; a dislocation where the endpoint of a filament occurs within the bundle, and the braiding of the filaments in the bundle. At a high concentration of cross links, the last two effects lead to the topologically protected kinked states. Finally, we explore numerically and analytically the transition of the metastable kinked state to the stable straight bundle.
We present the results of extensive computer simulations performed on solutions of monodisperse charged rod-like polyelectrolytes in the presence of trivalent counterions. To overcome energy barriers we used a combination of parallel tempering and hybrid Monte Carlo techniques. Our results show that for small values of the electrostatic interaction the solution mostly consists of dispersed single rods. The potential of mean force between the polyelectrolyte monomers yields an attractive interaction at short distances. For a range of larger values of the Bjerrum length, we find finite size polyelectrolyte bundles at thermodynamic equilibrium. Further increase of the Bjerrum length eventually leads to phase separation and precipitation. We discuss the origin of the observed thermodynamic stability of the finite size aggregates.
We explore the behavior of neon, xenon, and methane filmas adsorbed on the external surface of a bundle of carbon nanotubes. The methods used are classical: a ground state calculation, by grand potential energy minimization, and the grand canonical Monte Carlo (GCMC) method of simulation. Our results are similar to those found recently in a GCMC study of Ar and Kr. At low chemical potential (pressure) the particles form a quasi-one dimensional phase within the groove formed by two contiguous tubes. At higher chemical potential, there occurs a three-stripe phase aligned parallel to the groove (except for xenon). This is followed by monolayer and bilayer phases. The low temperature monolayer phase is striped; the number of stripes per nanotube is a quantized function of the adatom size. In the neon case, the bilayer regime also includes a second layer groove phase. Our results are compared with recent thermal and diffraction experiments. We find no evidence of a zig-zag phase reported recently.
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.
We present a Landau type theory for the non-linear elasticity of biopolymer gels with a part of the order parameter describing induced nematic order of fibers in the gel. We attribute the non-linear elastic behavior of these materials to fiber alignment induced by strain. We suggest an application to contact guidance of cell motility in tissue. We compare our theory to simulation of a disordered lattice model for biopolymers. We treat homogeneous deformations such as simple shear, hydrostatic expansion, and simple extension, and obtain good agreement between theory and simulation. We also consider a localized perturbation which is a simple model for a contracting cell in a medium.
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