We describe the large-scale collective behavior of solutions of polar biofilaments and both stationary and mobile crosslinkers. Both mobile and stationary crosslinkers induce filament alignment promoting either polar or nematic order. In addition, mobile crosslinkers, such as clusters of motor proteins, exchange forces and torques among the filaments and render the homogeneous states unstable via filament bundling. We start from a Smoluchowski equation for rigid filaments in solutions, where pairwise crosslink-mediated interactions among the filaments yield translational and rotational currents. The large-scale properties of the system are described in terms of continuum equations for filament and motor densities, polarization We make contact with work by other authors and show that our model allows for an estimate of the various parameters in the hydrodynamic equations in terms of physical properties of the crosslinkers.
Using a microscopic model of interacting polar biofilaments and motor proteins, we characterize the phase diagram of both homogeneous and inhomogeneous states in terms of experimental parameters. The polarity of motor clusters is key in determining the organization of the filaments in homogeneous isotropic, polarized, and nematic states, while motor-induced bundling yields spatially inhomogeneous structures.
In vertebrate eyes, the rod photoreceptor has a modified cilium with an extended cylindrical structure specialized for phototransduction called the outer segment (OS). The OS has numerous stacked membrane disks and can bend or break when subjected to mechanical forces. The OS exhibits axial structural variation, with extended bands composed of a few hundred membrane disks whose thickness is diurnally modulated. Using high-resolution confocal microscopy, we have observed OS flexing and disruption in live transgenic Xenopus rods. Based on the experimental observations, we introduce a coarse-grained model of OS mechanical rigidity using elasticity theory, representing the axial OS banding explicitly via a spring-bead model. We calculate a bending stiffness of ∼10(5) nN⋅μm2, which is seven orders-of-magnitude larger than that of typical cilia and flagella. This bending stiffness has a quadratic relation to OS radius, so that thinner OS have lower fragility. Furthermore, we find that increasing the spatial frequency of axial OS banding decreases OS rigidity, reducing its fragility. Moreover, the model predicts a tendency for OS to break in bands with higher spring number density, analogous to the experimental observation that transgenic rods tended to break preferentially in bands of high fluorescence. We discuss how pathological alterations of disk membrane properties by mutant proteins may lead to increased OS rigidity and thus increased breakage, ultimately contributing to retinal degeneration.
We investigate the total transmission probability of a nanoscale Aharonov-Bohm (AB) ring with an embedded quantum dot in one of its arms and a magnetic flux passing through its center. We find a peculiar quantum transport though this system such as a symmetric Breit-Wiper (BW) and an asymmetric Fano transmission resonance. The transition from BW to Fano resonance (or vice verse) occurs by tuning the magnetic AB flux threading through the AB ring, indicating the Fano asymmetric parameter is extended to a complex number. Unique properties of the AB phase coexistent with Fano interference are examined. I. IntroductionRecent advances ,in nanotechnologies have made it possible to fabricate quantum dot structures with gec+ metrical dimensions smaller than the elastic mean free paths. In these nanoscopic systems, electron transport is ballistic and phase coherence can be preserved. Many studies on measurement of the phase of the electron wavefunction have been performed both experimeutally[l]-[4] and theoretically[5]-[10]. Especially, a quantum interference experiment for a quantum dot embedded in an AB ring fabricated in a two-dimensional AlGaAslGaAs heterostructnre was recently performed by Kobayashi et al.[ll]. They studied unique properties of the Fano effect on the phase and coherence of electrons traversing the AB interferometer. This well-known Fano effect[l2], which arises &om the fact that interference between resonant transport through the quantum dot and the direct channel, gives ri& to asymmetric line shapes in the transmission as a function of gate or bias voltage. They also reported in this tunable Fano experiment that an external control, such as a magnetic field, of the relative phase between a discrete level in the QD and the continuum changes the Fano line shapes which is characterized by a complex number of the asymmetric parameter.In this article the total transmission probability of a
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