The twisted tauopathies: surface interactions of helically patterned filaments seen in alzheimer's disease and elsewhere

Bistability of a helical filament confined on a cylinder

The natural configuration of an intrinsically curved and twisted filament is uniquely a helix so that it can be referred to as a helical filament. We find that confining a helical filament on a cylinder can create a bistable state. When c_{0}R=0.5, where c_{0} is the intrinsic curvature of filament and R is the radius of cylinder, the phase diagram for the stability of a helix contains three regimes. Regime I has a small intrinsic twisting rate (ITR) and exhibits a bistable state which consists of two isoenergic helices. In regime II, the filament has a moderate ITR and the bistable state consists of a metastable low-pitch helix and a stable nonhelix. In regime III, the helix is unstable, owing to a large ITR. A similar phenomenon occurs when c_{0}R∼0.5. Monte Carlo simulation confirms these conclusions and indicates further that there are bistable nonhelices in regime III. This bistable system offers a prospective green material since the wide range of parameters and distinctive configurations for bistable states favor its realization and application.

Mutual Sliding Motion of Wrapped Filaments for Biomedical and Engineering Applications

Here we aim at understanding and modeling of macroscopic interactions and sliding motion of curved filaments during muscles' isometric action in which tension is developed without overall contraction. A generic dynamic model of a curved elastic filament undergoing sliding, twisting, and unraveling around a cylindrical filament affected by the interfilament friction force is developed in full detail. In particular, the dynamic equations describing the general sliding motion of a curved filament wrapped around a cylindrical filament and pulled by a constant force applied to a free end are derived and solved numerically; the other end of the curved filament is considered to be fixed at the cylindrical one. The model predicts propagation of an elastic wave over the wrapped filament determined by the filament stiffness and the interfilament friction. The wrapped filament deformation and its ultimate arrest are predicted, and the final configurations of such filaments are revealed. Accordingly, the wrapped filament strain is predicted as a function of time for different values of the friction coefficient. The potential applications and possible biomechanical links of the proposed generic model are also discussed.

Super-helical filaments at surfaces: dynamics and elastic responses

Bio-filaments often behave in a way unexpected from the standard semi-flexible polymer chain model (WLC), when squeezed to a surface, confined in microfluidic channels or clamped by their end. This calls for the super-helical filament model, going beyond WLC, where the filament forms a helix much wider than its diameter. We study this model using Brownian dynamics simulations, focusing on filaments confined to a surface by a strong potential. We analyze shapes and shape fluctuations under tension where excited states comprising a number of inflection points (twist-kink) can be stabilized. Pulling/releasing experiments during a cycle of increasing/decreasing tension show hysteresis. We find that the excited state, once established, is long-lived and the life time grows with the filament length cubed. Twist-kink diffusion involves position (filament shape) dependent friction for which we provide analytical expression. Dynamic responses to tension are investigated via numerical simulations and several mechanisms of shape relaxation are found and rationalized.

Shape Selection of Surface-Bound Helical Filaments: Biopolymers on Curved Membranes

Motivated to understand the behavior of biological filaments interacting with membranes of various types, we employ a theoretical model for the shape and thermodynamics of intrinsically helical filaments bound to curved membranes. We show that filament-surface interactions lead to a host of nonuniform shape equilibria, in which filaments progressively unwind from their native twist with increasing surface interaction and surface curvature, ultimately adopting uniform-contact curved shapes. The latter effect is due to nonlinear coupling between elastic twist and bending of filaments on anisotropically curved surfaces such as the cylindrical surfaces considered here. Via a combination of numerical solutions and asymptotic analysis of shape equilibria, we show that filament conformations are critically sensitive to the surface curvature in both the strong- and weak-binding limits. These results suggest that local structure of membrane-bound chiral filaments is generically sensitive to the curvature radius of the surface to which it is bound, even when that radius is much larger than the filament's intrinsic pitch. Typical values of elastic parameters and interaction energies for several prokaryotic and eukaryotic filaments indicate that biopolymers are inherently very sensitive to the coupling between twist, interactions, and geometry and that this could be exploited for regulation of a variety of processes such as the targeted exertion of forces, signaling, and self-assembly in response to geometric cues including the local mean and Gaussian curvatures.

How bio-filaments twist membranes

We study the deformations of a fluid membrane imposed by adhering stiff bio-filaments due to the torques they apply. In the limit of small deformations, we derive a general expression for the energy and the deformation field of the membrane. This expression is specialised to different important cases including closed and helical bio-filaments. In particular, we analyse interface-mediated interactions and membrane wrapping when the filaments apply a local torque distribution on a tubular membrane.