Torque and rotation rate of the bacterial flagellar motor

This paper describes an analysis of microscopic models for the coupling between ion flow and rotation of bacterial flagella. In model I it is assumed that intersecting half-channels exist on the rotor and the stator and that the driving ion is constrained to move together with the intersection site. Model II is based on the assumption that ion flow drives a cycle of conformational transitions in a channel-like stator subunit that are coupled to the motion of the rotor. Analysis of both mechanisms yields closed expressions relating the torque M generated by the flagellar motor to the rotation rate v. Model I (and also, under certain assumptions, model II) accounts for the experimentally observed linear relationship between M and v. The theoretical equations lead to predictions on the relationship between rotation rate and driving force which can be tested experimentally

Relative humidity as a new parameter in rheological testing

Besides temperature and pressure the water content of a sample as well as the relative humidity of the ambient air are important parameter influencing the rheological behavior of many complex fluids such as for example gels, biomaterials, polymeric systems, food products, and adhesives. The aim of this contribution is to introduce a newly designed environmental control chamber for the use with a rotational rheometer. A combination of a modified convection oven and an external humidity generator enables to work under defined relative humidity (RH) and temperature (T) in the ranges of RH = 5 to 95 % and T = 5 to 120°C. Traditional convection ovens are mainly equipped with electrical heaters. For lower temperatures a cold gas (e.g. LN2) is brought into the chamber and the oven heats against the cold gas. In the new humidity system the convection oven is based on Peltier elements allowing to set temperatures below ambient without the need of a cold gas as input to the oven chamber. In order to control the relative humidity a humidity sensor is located in the oven and the external humidity generator provides the needed moisture of the gas flowing into the chamber. The humidity sensor and the humidity generator are fully integrated into the operating software for the rheometer, allowing the programing of combinations of T and RH including ramps in RH at constant T or ramps in T at constant RH, respectively. Various standard geometries like parallel-plate, cone-and-plate, solid bar for torsional DMTA, extensional tools for extensional DMTA and steady extensional rheological testing, a ball on three plate geometry for tribological investigations, as well as a newly designed modified ring geometry can be used in the humidity system. The later consists of two hollow cylinders, which build a ring geometry. Because the upper cylinder has three rectangular notches only the sample below these notches is used to characterize the sample properties. Hence the characterized sample has a large surface to volume ratio, enabling a fast and homogeneous diffusion of moisture in the sample. Applications examples in the different geometries are presented and show the importance of the relative humidity on a broad variety of samples. The new humidity system allows an easy control of the relative humidity and makes this parameter readily available in advanced rheological testing

Unidirectional hopping transport of interacting particles on a finite chain

Particle transport through an open, discrete 1-D channel against a mechanical or chemical bias is analyzed within a master equation approach. The channel, externally driven by time dependent site energies, allows multiple occupation due to the coupling to reservoirs. Performance criteria and optimization of active transport in a two-site channel are discussed as a function of reservoir chemical potentials, the load potential, interparticle interaction strength, driving mode and driving period. Our results, derived from exact rate equations, are used in addition to test a previously developed time-dependent density functional theory, suggesting a wider applicability of that method in investigations of many particle systems far from equilibrium.Comment: 33 pages, 8 figure

The role of conformational diffusion in ion channel gating

We consider an exactly tractable model of the Kramers type for the voltage-dependent gating dynamics of single ion channels. It is assumed that the gating dynamics is caused by the thermally activated transitions in a bistable potential. Moreover, the closed state of the channel is highly degenerate and embraces the whole manifold of closed substates. Opening of the ion channel is energetically prohibited from most of the closed substates and requires a special conformation where the voltage sensor can move along an activation pathway and trigger the transition into the open conformation. When the corresponding activation barrier towards the channel's opening is removed by the applied voltage, the statistics of non-conducting time intervals become strongly influenced by the conformational diffusion. For the corresponding supra-threshold voltages, our model explains the origin of the power law distribution of the closed time intervals. The exponential-linear dependence of the opening rate on voltage, often used as an experimental fit, is also reproduced by our model

Interface Fluctuations under Shear

Coarsening systems under uniform shear display a long time regime characterized by the presence of highly stretched and thin domains. The question then arises whether thermal fluctuations may actually destroy this layered structure. To address this problem in the case of non-conserved dynamics we study an anisotropic version of the Burgers equation, constructed to describe thermal fluctuations of an interface in the presence of a uniform shear flow. As a result, we find that stretched domains are only marginally stable against thermal fluctuations in $d=2$, whereas they are stable in $d=3$.Comment: 3 pages, shorter version, additional reference

The Effect of Shear on Phase-Ordering Dynamics with Order-Parameter-Dependent Mobility: The Large-n Limit

The effect of shear on the ordering-kinetics of a conserved order-parameter system with O(n) symmetry and order-parameter-dependent mobility \Gamma({\vec\phi}) \propto (1- {\vec\phi} ^2/n)^\alpha is studied analytically within the large-n limit. In the late stage, the structure factor becomes anisotropic and exhibits multiscaling behavior with characteristic length scales (t^{2\alpha+5}/\ln t)^{1/2(\alpha+2)} in the flow direction and (t/\ln t)^{1/2(\alpha+2)} in directions perpendicular to the flow. As in the \alpha=0 case, the structure factor in the shear-flow plane has two parallel ridges.Comment: 6 pages, 2 figure

Two-scale competition in phase separation with shear

The behavior of a phase separating binary mixture in uniform shear flow is investigated by numerical simulations and in a renormalization group (RG) approach. Results show the simultaneous existence of domains of two characteristic scales. Stretching and cooperative ruptures of the network produce a rich interplay where the recurrent prevalence of thick and thin domains determines log-time periodic oscillations. A power law growth $R(t) \sim t^{\alpha}$ of the average domain size, with $\alpha =4/3$ and $\alpha = 1/3$ in the flow and shear direction respectively, is shown to be obeyed.Comment: 5 Revtex pages, 4 figure

Effect of Shear Flow on the Stability of Domains in Two Dimensional Phase-Separating Binary Fluids

We perform a linear stability analysis of extended domains in phase-separating fluids of equal viscosity, in two dimensions. Using the coupled Cahn-Hilliard and Stokes equations, we derive analytically the stability eigenvalues for long wavelength fluctuations. In the quiescent state we find an unstable varicose mode which corresponds to an instability towards coarsening. This mode is stabilized when an external shear flow is imposed on the fluid. The effect of the shear is seen to be qualitatively similar to that found in experiments.Comment: 13 pages, RevTeX, 8 eps figures included. Submitted to Phys. Rev.

Pore dimensions and the role of occupancy in unitary conductance of Shaker K channels

Indexación: Web of Science; Scopus.K channels mediate the selective passage of K+ across the plasma membrane by means of intimate interactions with ions at the pore selectivity filter located near the external face. Despite high conservation of the selectivity filter, the K+ transport properties of different K channels vary widely, with the unitary conductance spanning a range of over two orders of magnitude. Mutation of Pro475, a residue located at the cytoplasmic entrance of the pore of the small-intermediate conductance K channel Shaker (Pro475Asp (P475D) or Pro475Gln (P475Q)), increases Shaker's reported. 20-pS conductance by approximately six-and approximately threefold, respectively, without any detectable effect on its selectivity. These findings suggest that the structural determinants underlying the diversity of K channel conductance are distinct from the selectivity filter, making P475D and P475Q excellent probes to identify key determinants of the K channel unitary conductance. By measuring diffusion-limited unitary outward currents after unilateral addition of 2 M sucrose to the internal solution to increase its viscosity, we estimated a pore internal radius of capture of 0.82 for all the three Shaker variants (wild type, P475D, and P475Q). This estimate is consistent with the internal entrance of the Kv1.2/2.1 structure if the effective radius of hydrated K+ is set to 4 A. Unilateral exposure to sucrose allowed us to estimate the internal and external access resistances together with that of the inner pore. We determined that Shaker resistance resides mainly in the inner cavity, whereas only similar to 8% resides in the selectivity filter. To reduce the inner resistance, we introduced additional aspartate residues into the internal vestibule to favor ion occupancy. No aspartate addition raised the maximum unitary conductance, measured at saturating [K+], beyond that of P475D, suggesting an similar to 200-pS conductance ceiling for Shaker. This value is approximately one third of the maximum conductance of the large conductance K (BK) channel (the K channel of highest conductance), reducing the energy gap between their K+ transport rates to similar to 1 kT. Thus, although Shaker's pore sustains ion translocation as the BK channel's does, higher energetic costs of ion stabilization or higher friction with the ion's rigid hydration cage in its narrower aqueous cavity may entail higher resistance.http://jgp.rupress.org/content/146/2/13

Ohta-Jasnow-Kawasaki Approximation for Nonconserved Coarsening under Shear

We analytically study coarsening dynamics in a system with nonconserved scalar order parameter, when a uniform time-independent shear flow is present. We use an anisotropic version of the Ohta-Jasnow-Kawasaki approximation to calculate the growth exponents in two and three dimensions: for d=3 the exponents we find are the same as expected on the basis of simple scaling arguments, that is 3/2 in the flow direction and 1/2 in all the other directions, while for d=2 we find an unusual behavior, in that the domains experience an unlimited narrowing for very large times and a nontrivial dynamical scaling appears. In addition, we consider the case where an oscillatory shear is applied to a two-dimensional system, finding in this case a standard t^1/2 growth, modulated by periodic oscillations. We support our two-dimensional results by means of numerical simulations and we propose to test our predictions by experiments on twisted nematic liquid crystals.Comment: 25 RevTeX pages, 7 EPS figures. To be published in Phys. Rev.