Analytical approach to viscous fingering in a cylindrical Hele-Shaw cell

We report analytical results for the development of the viscous fingering instability in a cylindrical Hele-Shaw cell of radius a and thickness b. We derive a generalized version of Darcy's law in such cylindrical background, and find it recovers the usual Darcy's law for flow in flat, rectangular cells, with corrections of higher order in b/a. We focus our interest on the influence of cell's radius of curvature on the instability characteristics. Linear and slightly nonlinear flow regimes are studied through a mode-coupling analysis. Our analytical results reveal that linear growth rates and finger competition are inhibited for increasingly larger radius of curvature. The absence of tip-splitting events in cylindrical cells is also discussed.Comment: 14 pages, 3 ps figures, Revte

Age-Related Changes in Cardiac Autonomic Modulation and Heart Rate Variability in Mice

Objective: The aim of this study was to assess age-related changes in cardiac autonomic modulation and heart rate variability (HRV) and their association with spontaneous and pharmacologically induced vulnerability to cardiac arrhythmias, to verify the translational relevance of mouse models for further in-depth evaluation of the link between autonomic changes and increased arrhythmic risk with advancing age. Methods: Heart rate (HR) and time- and frequency-domain indexes of HRV were calculated from Electrocardiogram (ECG) recordings in two groups of conscious mice of different ages (4 and 19 months old) (i) during daily undisturbed conditions, (ii) following peripheral β-adrenergic (atenolol), muscarinic (methylscopolamine), and β-adrenergic + muscarinic blockades, and (iii) following β-adrenergic (isoprenaline) stimulation. Vulnerability to arrhythmias was evaluated during daily undisturbed conditions and following β-adrenergic stimulation. Results: HRV analysis and HR responses to autonomic blockades revealed that 19-month-old mice had a lower vagal modulation of cardiac function compared with 4-month-old mice. This age-related autonomic effect was not reflected in changes in HR, since intrinsic HR was lower in 19-month-old compared with 4-month-old mice. Both time- and frequency-domain HRV indexes were reduced following muscarinic, but not β-adrenergic blockade in younger mice, and to a lesser extent in older mice, suggesting that HRV is largely modulated by vagal tone in mice. Finally, 19-month-old mice showed a larger vulnerability to both spontaneous and isoprenaline-induced arrhythmias. Conclusion: The present study combines HRV analysis and selective pharmacological autonomic blockades to document an age-related impairment in cardiac vagal modulation in mice which is consistent with the human condition. Given their short life span, mice could be further exploited as an aged model for studying the trajectory of vagal decline with advancing age using HRV measures, and the mechanisms underlying its association with proarrhythmic remodeling of the senescent heart

A caveolin-binding domain in the HCN4 channels mediates functional interaction with caveolin proteins

Pacemaker (HCN) channels have a key role in the generation and modulation of spontaneous activity of sinoatrial node myocytes. Previous work has shown that compartmentation of HCN4 pacemaker channels within caveolae regulates important functions, but the molecular mechanism responsible is still unknown. HCN channels have a conserved caveolin-binding domain (CBD) composed of three aromatic amino acids at the N-terminus; we sought to evaluate the role of this CBD in channel-protein interaction by mutational analysis. We generated two HCN4 mutants with a disrupted CBD (Y259S, F262V) and two with conservative mutations (Y259F, F262Y). In CHO cells expressing endogenous caveolin-1 (cav-1), alteration of the CBD shifted channels activation to more positive potentials, slowed deactivation and made Y259S and F262V mutants insensitive to cholesterol depletion-induced caveolar disorganization. CBD alteration also caused a significant decrease of current density, due to a weaker HCN4-cav-1 interaction and accumulation of cytoplasmic channels. These effects were absent in mutants with a preserved CBD. In caveolin-1-free fibroblasts, HCN4 trafficking was impaired and current density reduced with all constructs; the activation curve of F262V was not altered relative to wt, and that of Y259S displayed only half the shift than in CHO cells. The conserved CBD present in all HCN isoforms mediates their functional interaction with caveolins. The elucidation of the molecular details of HCN4-cav-1 interaction can provide novel information to understand the basis of cardiac phenotypes associated with some forms of caveolinopathies

Properties of the hyperpolarizing-activated current (if) in cells isolated from the rabbit sino-atrial node

Individual cells were isolated from the sino-atrial node area of the rabbit heart using an enzyme medium containing collagenase and elastase. After enzymatic treatment the cells were placed in normal Tyrode solution, where beating resumed in a fraction of them. Isolated cells were studied in the whole cell configuration. Action potentials as well as membrane currents under voltage-clamp conditions were similar to those in multicellular preparations. Pulses to voltages more negative than about -50 mV caused activation of the hyperpolarizing-activated current, if. Investigation of the properties of this current was carried out under conditions that limited the influence of other current systems during voltage clamp. The if current activation range usually extended approximately from -50 to -100 mV, but varied from cell to cell. In several cases, pulsing to the region of -40 mV elicited a sizeable if. Both current activation and deactivation during voltage steps had S-shaped time courses. A high variability was however observed in the sigmoidal behaviour of if kinetics. Plots of the fully-activated current-voltage (I-V) relation in different extracellular Na and K concentrations showed that both ions carry the current if. While changes in the external Na concentration caused the current I-V relation to undergo simple shifts along the voltage axis, changes in extracellular K concentration were also associated with changes in its slope. Again, a large variability was observed in the increase of I-V slope on raising the external K concentration. The current if was strongly depressed by Cs, and the block induced by 5 mM-Cs was markedly voltage dependent. Adrenaline (1-5 microM) and noradrenaline (1 microM) increased the current if around the half-activation voltage range and accelerated its activation at more negative voltages. Often, however, drug application failed to elicit any modification of if. Current run-down was observed in nearly all cells, although at a highly variable rate. It was accelerated by raising the extracellular K concentration but did not show a marked use dependence. Both the if activation curve and the fully activated I-V relation were affected by run-down, the former being shifted to more negative values along the voltage axis and the latter being depressed with no apparent change of the if reversal potential

Boundary states for a free boson defined on finite geometries

Langlands recently constructed a map that factorizes the partition function of a free boson on a cylinder with boundary condition given by two arbitrary functions in the form of a scalar product of boundary states. We rewrite these boundary states in a compact form, getting rid of technical assumptions necessary in his construction. This simpler form allows us to show explicitly that the map between boundary conditions and states commutes with conformal transformations preserving the boundary and the reality condition on the scalar field.Comment: 16 pages, LaTeX (uses AMS components). Revised version; an analogy with string theory computations is discussed and references adde

Perturbation Theory in Two Dimensional Open String Field Theory

In this paper we develop the covariant string field theory approach to open 2d strings. Upon constructing the vertices, we apply the formalism to calculate the lowest order contributions to the 4- and 5- point tachyon--tachyon tree amplitudes. Our results are shown to match the `bulk' amplitude calculations of Bershadsky and Kutasov. In the present approach the pole structure of the amplitudes becomes manifest and their origin as coming from the higher string modes transparent.Comment: 26 page

SU(m) non-Abelian anyons in the Jain hierarchy of quantum Hall states

We show that different classes of topological order can be distinguished by the dynamical symmetry algebra of edge excitations. Fundamental topological order is realized when this algebra is the largest possible, the algebra of quantum area-preserving diffeomorphisms, called $W_{1+\infty}$. We argue that this order is realized in the Jain hierarchy of fractional quantum Hall states and show that it is more robust than the standard Abelian Chern-Simons order since it has a lower entanglement entropy due to the non-Abelian character of the quasi-particle anyon excitations. These behave as SU($m$) quarks, where $m$ is the number of components in the hierarchy. We propose the topological entanglement entropy as the experimental measure to detect the existence of these quantum Hall quarks. Non-Abelian anyons in the $\nu = 2/5$ fractional quantum Hall states could be the primary candidates to realize qbits for topological quantum computation.Comment: 5 pages, no figures, a few typos corrected, a reference adde

Cyclic dinucleotides bind the C-linker of HCN4 to control channel cAMP responsiveness

cAMP mediates autonomic regulation of heart rate by means of hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which underlie the pacemaker current If. cAMP binding to the C-terminal cyclic nucleotide binding domain enhances HCN open probability through a conformational change that reaches the pore via the C-linker. Using structural and functional analysis, we identified a binding pocket in the C-linker of HCN4. Cyclic dinucleotides, an emerging class of second messengers in mammals, bind the C-linker pocket (CLP) and antagonize cAMP regulation of the channel. Accordingly, cyclic dinucleotides prevent cAMP regulation of If in sinoatrial node myocytes, reducing heart rate by 30%. Occupancy of the CLP hence constitutes an efficient mechanism to hinder β-adrenergic stimulation on If. Our results highlight the regulative role of the C-linker and identify a potential drug target in HCN4. Furthermore, these data extend the signaling scope of cyclic dinucleotides in mammals beyond their first reported role in innate immune system