Multiple bound states in scissor-shaped waveguides

We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle $\theta$. Such a four-terminal junction with a tunable $\theta$ can realized experimentally if a right-angle structure is filled by a ferrite. It is known that for $\theta=90^o$ there is one proper bound state and one eigenvalue embedded in the continuum. We show that the number of eigenvalues becomes larger with increasing asymmetry and the bound-state energies are increasing as functions of $\theta$ in the interval $(0,90^o)$. Moreover, states which are sufficiently strongly bent exist in pairs with a small energy difference and opposite parities. Finally, we discuss how with increasing $\theta$ the bound states transform into the quasi-bound states with a complex wave vector.Comment: 6 pages, 6 figure

Comparison between three-dimensional linear and nonlinear tsunami generation models

The modeling of tsunami generation is an essential phase in understanding tsunamis. For tsunamis generated by underwater earthquakes, it involves the modeling of the sea bottom motion as well as the resulting motion of the water above it. A comparison between various models for three-dimensional water motion, ranging from linear theory to fully nonlinear theory, is performed. It is found that for most events the linear theory is sufficient. However, in some cases, more sophisticated theories are needed. Moreover, it is shown that the passive approach in which the seafloor deformation is simply translated to the ocean surface is not always equivalent to the active approach in which the bottom motion is taken into account, even if the deformation is supposed to be instantaneous.Comment: 39 pages, 16 figures; Accepted to Theoretical and Computational Fluid Dynamics. Several references have been adde

Polar Chemoreceptor Clustering by Coupled Trimers of Dimers

Receptors of bacterial chemotaxis form clusters at the cell poles, where clusters act as "antennas" to amplify small changes in ligand concentration. Interestingly, chemoreceptors cluster at multiple length scales. At the smallest scale, receptors form dimers, which assemble into stable timers of dimers. At a large scale, trimers form large polar clusters composed of thousands of receptors. Although much is known about the signaling properties emerging from receptor clusters, it is unknown how receptors localize at the cell poles and what the cluster-size determining factors are. Here, we present a model of polar receptor clustering based on coupled trimers of dimers, where cluster size is determined as a minimum of the cluster-membrane free energy. This energy has contributions from the cluster-membrane elastic energy, penalizing large clusters due to their high intrinsic curvature, and receptor-receptor coupling favoring large clusters. We find that the reduced cluster-membrane curvature mismatch at the curved cell poles leads to large and robust polar clusters in line with experimental observation, while lateral clusters are efficiently suppressed.Comment: 11 pages, 6 figures, and 1 tabl

Chemotactic response and adaptation dynamics in Escherichia coli

Adaptation of the chemotaxis sensory pathway of the bacterium Escherichia coli is integral for detecting chemicals over a wide range of background concentrations, ultimately allowing cells to swim towards sources of attractant and away from repellents. Its biochemical mechanism based on methylation and demethylation of chemoreceptors has long been known. Despite the importance of adaptation for cell memory and behavior, the dynamics of adaptation are difficult to reconcile with current models of precise adaptation. Here, we follow time courses of signaling in response to concentration step changes of attractant using in vivo fluorescence resonance energy transfer measurements. Specifically, we use a condensed representation of adaptation time courses for efficient evaluation of different adaptation models. To quantitatively explain the data, we finally develop a dynamic model for signaling and adaptation based on the attractant flow in the experiment, signaling by cooperative receptor complexes, and multiple layers of feedback regulation for adaptation. We experimentally confirm the predicted effects of changing the enzyme-expression level and bypassing the negative feedback for demethylation. Our data analysis suggests significant imprecision in adaptation for large additions. Furthermore, our model predicts highly regulated, ultrafast adaptation in response to removal of attractant, which may be useful for fast reorientation of the cell and noise reduction in adaptation.Comment: accepted for publication in PLoS Computational Biology; manuscript (19 pages, 5 figures) and supplementary information; added additional clarification on alternative adaptation models in supplementary informatio

Single-Cell Census of Mechanosensitive Channels in Living Bacteria

Bacteria are subjected to a host of different environmental stresses. One such insult occurs when cells encounter changes in the osmolarity of the surrounding media resulting in an osmotic shock. In recent years, a great deal has been learned about mechanosensitive (MS) channels which are thought to provide osmoprotection in these circumstances by opening emergency release valves in response to membrane tension. However, even the most elementary physiological parameters such as the number of MS channels per cell, how MS channel expression levels influence the physiological response of the cells, and how this mean number of channels varies from cell to cell remain unanswered. In this paper, we make a detailed quantitative study of the expression of the mechanosensitive channel of large conductance (MscL) in different media and at various stages in the growth history of bacterial cultures. Using both quantitative fluorescence microscopy and quantitative Western blots our study complements earlier electrophysiology-based estimates and results in the following key insights: i) the mean number of channels per cell is much higher than previously estimated, ii) measurement of the single-cell distributions of such channels reveals marked variability from cell to cell and iii) the mean number of channels varies under different environmental conditions. The regulation of MscL expression displays rich behaviors that depend strongly on culturing conditions and stress factors, which may give clues to the physiological role of MscL. The number of stress-induced MscL channels and the associated variability have far reaching implications for the in vivo response of the channels and for modeling of this response. As shown by numerous biophysical models, both the number of such channels and their variability can impact many physiological processes including osmoprotection, channel gating probability, and channel clustering

Linear Wave Interaction with a Vertical Cylinder of Arbitrary Cross Section: An Asymptotic Approach

An asymptotic approach to the linear problem of regular water waves interacting with a vertical cylinder of an arbitrary cross section is presented. The incident regular wave was one-dimensional, water was of finite depth, and the rigid cylinder extended from the bottom to the water surface. The nondimensional maximum deviation of the cylinder cross section from a circular one plays the role of a small parameter of the problem. A fifth-order asymptotic solution of the problem was obtained. The problems at each order were solved by the Fourier method. It is shown that the first-order velocity potential is a linear function of the Fourier coefficients of the shape function of the cylinder, the second-order velocity potential is a quadratic function of these coefficients, and so on. The hydrodynamic forces acting on the cylinder and the water surface elevations on the cylinder are presented. The present asymptotic results show good agreement with numerical and experimental results of previous investigations. Long-wave approximation of the hydrodynamic forces was derived and used for validation of the asymptotic solutions. The obtained values of the forces are exact in the limit of zero wave numbers within the linear wave theory. An advantage of the present approach compared with the numerical solution of the problem by an integral equation method is that it provides the forces and the diffracted wave field in terms of the coefficients of the Fourier series of the deviation of the cylinder shape from the circular one. The resulting asymptotic formula can be used for optimization of the cylinder shape in terms of the wave loads and diffracted wave fields

Intimal Hyperplasia in Balloon Dilated Coronary Arteries is Reduced by Local Delivery of the NO Donor, SIN-1 Via a cGMP-Dependent Pathway

<p>Abstract</p> <p>Background</p> <p>To elucidate the mechanism by which local delivery of 3-morpholino-sydnonimine (SIN-1) affects intimal hyperplasia after percutaneous transluminal coronary angioplasty (PTCA).</p> <p>Methods</p> <p>Porcine coronary arteries were treated with PTCA and immediately afterwards locally treated for 5 minutes, with a selective cytosolic guanylate cyclase inhibitor, 1 H-(1,2,4)oxadiazole(4,3-alpha)quinoxaline-1-one (ODQ) + SIN-1 or only SIN-1 using a drug delivery-balloon. Arteries were angiographically depicted, morphologically evaluated and analyzed after one and eight weeks for actin, myosin and intermediate filaments (IF) and nitric oxide synthase (NOS) contents.</p> <p>Results</p> <p>Luminal diameter after PCI in arteries treated with SIN-1 alone and corrected for age-growth was significantly larger as compared to ODQ + SIN-1 or to controls (p < 0.01). IF/actin ratio after one week in SIN-1 treated segments was not different compared to untreated segments, but was significantly reduced compared to ODQ + SIN-1 treated vessels (p < 0.05). Expression of endothelial NADPH diaphorase activity was significantly lower in untreated segments and in SIN-1 treated segments compared to controls and SIN-1 + ODQ treated arteries (p < 0.01). Restenosis index (p < 0.01) and intimal hyperplasia (p < 0.01) were significantly reduced while the residual lumen was increased (p < 0.01) in SIN-1 segments compared to controls and ODQ + SIN-1 treated vessels.</p> <p>Conclusions</p> <p>After PTCA local delivery of high concentrations of the NO donor SIN-1 for 5 minutes inhibited injury induced neointimal hyperplasia. This favorable effect was abolished by inhibition of guanylyl cyclase indicating mediation of a cyclic guanosine 3',5'-monophosphate (cGMP)-dependent pathway. The momentary events at the time of injury play crucial role in the ensuring development of intimal hyperplasia.</p

Piston-driven numerical wave tank based on WENO solver of well-balanced shallow water equations

A numerical wave tank equipped with a piston type wave-maker is presented for long-duration simulations of long waves in shallow water. Both wave maker and tank are modelled using the nonlinear shallow water equations, with motions of the numerical piston paddle accomplished via a linear mapping technique. Three approaches are used to increase computational efficiency and accuracy. First, the model satisfies the exact conservation property (C-property), a stepping stone towards properly balancing each term in the governing equation. Second, a high-order weighted essentially non-oscillatory (WENO) method is used to reduce accumulation of truncation error. Third, a cut-off algorithm is implemented to handle contaminated digits arising from round-off error. If not treated, such errors could prevent a numerical scheme from satisfying the exact C-property in long-duration simulations. Extensive numerical tests are performed to examine the well-balanced property, high order accuracy, and shock-capturing ability of the present scheme. Correct implementation of the wave paddle generator is verified by comparing numerical predictions against analytical solutions of sinusoidal, solitary, and cnoidal waves. In all cases, the model gives satisfactory results for small-amplitude, low frequency waves. Error analysis is used to investigate model limitations and derive a user criterion for long wave generation by the model

Membrane-mediated interactions

Interactions mediated by the cell membrane between inclusions, such as membrane proteins or antimicrobial peptides, play important roles in their biological activity. They also constitute a fascinating challenge for physicists, since they test the boundaries of our understanding of self-assembled lipid membranes, which are remarkable examples of two-dimensional complex fluids. Inclusions can couple to various degrees of freedom of the membrane, resulting in different types of interactions. In this chapter, we review the membrane-mediated interactions that arise from direct constraints imposed by inclusions on the shape of the membrane. These effects are generic and do not depend on specific chemical interactions. Hence, they can be studied using coarse-grained soft matter descriptions. We deal with long-range membrane-mediated interactions due to the constraints imposed by inclusions on membrane curvature and on its fluctuations. We also discuss the shorter-range interactions that arise from the constraints on membrane thickness imposed by inclusions presenting a hydrophobic mismatch with the membrane.Comment: 38 pages, 10 figures, pre-submission version. In: Bassereau P., Sens P. (eds) Physics of Biological Membranes. Springer, Cha