A simple non-chaotic map generating subdiffusive, diffusive and superdiffusive dynamics

Analytically tractable dynamical systems exhibiting a whole range of normal and anomalous deterministic diffusion are rare. Here we introduce a simple non-chaotic model in terms of an interval exchange transformation suitably lifted onto the whole real line which preserves distances except at a countable set of points. This property, which leads to vanishing Lyapunov exponents, is designed to mimic diffusion in non-chaotic polygonal billiards that give rise to normal and anomalous diffusion in a fully deterministic setting. As these billiards are typically too complicated to be analyzed from first principles, simplified models are needed to identify the minimal ingredients generating the different transport regimes. For our model, which we call the slicer map, we calculate all its moments in position analytically under variation of a single control parameter. We show that the slicer map exhibits a transition from subdiffusion over normal diffusion to superdiffusion under parameter variation. Our results may help to understand the delicate parameter dependence of the type of diffusion generated by polygonal billiards. We argue that in different parameter regions the transport properties of our simple model match to different classes of known stochastic processes. This may shed light on difficulties to match diffusion in polygonal billiards to a single anomalous stochastic process.Comment: 15 pages, 3 figure

Monitoring Microtubule Mechanical Vibrations via Optomechanical Coupling

The possible disruption of a microtubule during mitosis can control the duplication of a cancer cell. Cancer detection and treatment may be possible based on the detection and control of microtubule mechanical oscillations in cells through external fields (e.g. electromagnetic or ultrasound). However, little is known about the dynamic (high-frequency) mechanical properties of microtubules. Here we propose to control the vibrations of a doubly clamped microtubule by tip electrodes and to detect its motion via the optomechanical coupling between the vibrational modes of the microtubule and an optical cavity. In the presence of a red-detuned strong pump laser, this coupling leads to optomechanical induced transparency of an optical probe field, which can be detected with state-of the art technology. The center frequency and linewidth of the transparency peak give the resonance frequency and damping rate of the microtubule respectively, while the height of the peak reveals information about the microtubule-cavity field coupling. Our method should yield new knowledge about the physical properties of microtubules, which will enhance our capability to design physical cancer treatment protocols as alternatives to chemotherapeutic drugs

Interactions of L-3,5,3′-triiodothyronine, allopregnanolone, and ivermectin with the GABAA receptor: Evidence for overlapping intersubunit binding modes

Structural mechanisms of modulation of γ-aminobutyric acid (GABA) type A receptors by neurosteroids and hormones remain unclear. The thyroid hormone L-3,5,3'-triiodothyronine (T3) inhibits GABAA receptors at micromolar concentrations and has common features with neurosteroids such as allopregnanolone (ALLOP). Here we use functional experiments on α2β1γ2 GABAA receptors expressed in Xenopus oocytes to detect competitive interactions between T3 and an agonist (ivermectin, IVM) with a crystallographically determined binding site at subunit interfaces in the transmembrane domain of a homologous receptor (glutamate-gated chloride channel, GluCl). T3 and ALLOP also show competitive effects, supporting the presence of both a T3 and ALLOP binding site at one or more subunit interfaces. Molecular dynamics (MD) simulations over 200 ns are used to investigate the dynamics and energetics of T3 in the identified intersubunit sites. In these simulations, T3 molecules occupying all intersubunit sites (with the exception of the α-β interface) display numerous energetically favorable conformations with multiple hydrogen bonding partners, including previously implicated polar/acidic sidechains and a structurally conserved deformation in the M1 backbone

Study of gill and kidney tissue changes in Tenualosa ilisha during migration from sea to the Karun and Bahmanshir Rivers

In this research, histological changes of gill and kidney, as a basic and important organ in osmoregulation, during migration from Musa creek to Karun and Bahmanshir Rivers was studied. Ten fish from each station of Persian Gulf, Karun and Bahmanshir with similarity in biometric of size and weight were collected. After fixation in Bouin's solutions, routine procedure of tissue preparation was done and 6 μm sections stained with Hematoxylin and Eosin, studied by optical microscope equipped with a daynolit lenses. The greatest number and area of chloride cells were seen in sea samples but they decreased during migration to Karun and Bahmanshir Rivers (p0.05). In kidney, during migration from the sea to the river, the diameter of proximal and distal lumen increased. But in Karun samples, diameter of lumen of distal tubules were higher than others station. Also, there was no significant difference in other tubule between in Karun and Bahmanshir samples. Therefore according to this study, gill and kidney have active participation in osmoregulation. This fish can be a good model for study of osmoregulation in different salinities because of adaptation and response to different environmental salinities in gill that associated with histologic changes