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

State-Dependent Accessibility of the P-S6 Linker of Pacemaker (HCN) Channels Supports a Dynamic Pore-to-Gate Coupling Model

The hyperpolarization-activated cyclic nucleotide-modulated channel gene family (HCN1-4) encodes the membrane depolarizing current that underlies pacemaking. Although the topology of HCN resembles Kv channels, much less is known about their structure-function correlation. Previously, we identified several pore residues in the S5-P linker and P-loop that are externally accessible and/or influence HCN gating, and proposed an evolutionarily conserved pore-to-gate mechanism. Here we sought dynamic evidence by assessing the functional consequences of Cys-scanning substitutions in the unexplored P-S6 linker (residues 352–359), the HCN1-R background (that is, resistant to sulfhydryl-reactive agents). None of A352C, Q353C, A354C, P355C, V356C, S357C, M358C, or S359C produced functional currents; the loss-of-function of Q353C, A354C, S357C, and M358C could be rescued by the reducing agent dithiothreitol. Q353C, A354C, and S357C, but not M358C and HCN1-R, were sensitive to Cd2+ blockade (IC50 = 3–12 μM vs. >1 mM). External application of the positively charged covalent sulfhydryl modifier MTSET irreversibly reduced I−140mV of Q353C and A354C to 27.9 ± 3.4% and 58.2 ± 13.1% of the control, respectively, and caused significant steady-state activation shifts (∆V1/2 = –21.1 ± 1.6 for Q353C and −10.0 ± 2.9 mV for A354C). Interestingly, MTSET reactivity was also state dependent. MTSET, however, affected neither S357C nor M358C, indicating site specificity. Collectively, we have identified novel P-S6 residues whose extracellular accessibility was sterically and state dependent and have provided the first functional evidence consistent with a dynamic HCN pore-to-gate model

Microscopic Selection of Fluid Fingering Pattern

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accord with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.Comment: 6 pages, 5 figure

Efficient Numerical Schemes for Computing Cardiac Electrical Activation over Realistic Purkinje Networks: Method and Verification

We present a numerical solver for the fast conduction system in the heart using both a CPU and a hybrid CPU/GPU implementation. To verify both implementations, we construct analytical solutions and show that the L2-error is similar in both implementations and decreases linearly with the spatial step size. Finally, we test the performance of the implementations with networks of varying complexity, where the hybrid implementation is, on average, 5.8 times faster

K+ Channel Regulator KCR1 Suppresses Heart Rhythm by Modulating the Pacemaker Current If

Hyperpolarization-activated, cyclic nucleotide sensitive (HCN) channels underlie the pacemaker current If, which plays an essential role in spontaneous cardiac activity. HCN channel subunits (HCN1-4) are believed to be modulated by additional regulatory proteins, which still have to be identified. Using biochemistry, molecularbiology and electrophysiology methods we demonstrate a protein-protein interaction between HCN2 and the K+ channel regulator protein 1, named KCR1. In coimmunoprecipitation experiments we show that KCR1 and HCN2 proteins are able to associate. Heterologously expressed HCN2 whole-cell current density was significantly decreased by KCR1. KCR1 profoundly suppressed IHCN2 single-channel activity, indicating a functional interaction between KCR1 and the HCN2 channel subunit. Endogenous KCR1 expression could be detected in adult and neonatal rat ventriculocytes. Adenoviral-mediated overexpression of KCR1 in rat cardiomyocytes (i) reduced If whole-cell currents, (ii) suppressed most single-channel gating parameters, (iii) altered the activation kinetics, (iv) suppressed spontaneous action potential activity, and (v) the beating rate. More importantly, siRNA-based knock-down of endogenous KCR1 increased the native If current size and single-channel activity and accelerated spontaneous beating rate, supporting an inhibitory action of endogenous KCR1 on native If. Our observations demonstrate for the first time that KCR1 modulates IHCN2/If channel gating and indicate that KCR1 serves as a regulator of cardiac automaticity

A gain-of-function mutation in the cardiac pacemaker HCN4 channel increasing cAMP sensitivity is associated with familial Inappropriate Sinus Tachycardia

Aims Inappropriate Sinus Tachycardia (IST), a syndrome characterized by abnormally fast sinus rates and multisystem symptoms, is still poorly understood. Because of the relevance of HCN4 channels to pacemaker activity, we used a candidate-gene approach and screened IST patients for the presence of disease-causing HCN4 mutations. Methods and results Forty-eight IST patients, four of whom of known familial history, were enrolled in the study. We initially identified in one of the patients with familial history the R524Q mutation in HCN4. Investigation extended to the family members showed that the mutation co-segregated with IST-related symptoms. The R524Q mutation is located in the C-linker, a region known to couple cAMP binding to channel activation. The functional relevance of the mutation was investigated in heterologous expression systems by patch-clamp experiments. We found that mutant HCN4 channels were more sensitive to cAMP than wild-type channels, in agreement with increased sensitivity to basal and stimulated adrenergic input and with a faster than normal pacemaker rate. The properties of variant channels indicate therefore that R524Q is a gain-of-function mutation. Increased channel contribution to activity was confirmed by evidence that when spontaneously beating rat newborn myocytes were transfected with R524Q mutant HCN4 channels, they exhibited a faster rate than when transfected with wild-type HCN4 channels. Conclusion This is the first report of a gain-of-function HCN4 mutation associated with IST through increased sensitivity to cAMP-dependent activation

The JCMT Plane Survey: First complete data release - emission maps and compact source catalogue

We present the first data release of the James Clerk Maxwell Telescope (JCMT) Plane Survey (JPS), the JPS Public Release 1 (JPSPR1). JPS is an 850-µm continuum survey of six fields in the northern inner Galactic Plane in a longitude range of ℓ = 7°–63°, made with the Sub-millimetre Common-User Bolometer Array 2 (SCUBA-2). This first data release consists of emission maps of the six JPS regions with an average pixel-to-pixel noise of 7.19 mJy beam−1, when smoothed over the beam, and a compact-source catalogue containing 7,813 sources. The 95 per cent completeness limits of the catalogue are estimated at 0.04 Jy beam−1 and 0.3 Jy for the peak and integrated flux densities, respectively. The emission contained in the compact-source catalogue is 42 ± 5 per cent of the total and, apart from the large-scale (greater than 8 arcmin) emission, there is excellent correspondence with features in the 500-µm Herschel maps. We find that, with two-dimensional matching, 98 ± 2 per cent of sources within the fields centred at ℓ = 20°, 30°, 40° and 50° are associated with molecular clouds, with 91 ± 3 per cent of the ℓ = 30° and 40° sources associated with dense molecular clumps. Matching the JPS catalogue to Herschel 70-µm sources, we find that 38 ± 1 per cent of sources show evidence of ongoing star formation. The images and catalogue will be a valuable resource for studies of star formation in the Galaxy and the role of environment and spiral arms in the star formation process

High-Pass Filtering of Input Signals by the Ih Current in a Non-Spiking Neuron, the Retinal Rod Bipolar Cell

Hyperpolarization–activated cyclic nucleotide–sensitive (HCN) channels mediate the If current in heart and Ih throughout the nervous system. In spiking neurons Ih participates primarily in different forms of rhythmic activity. Little is known, however, about its role in neurons operating with graded potentials as in the retina, where all four channel isoforms are expressed. Intriguing evidence for an involvement of Ih in early visual processing are the side effects reported, in dim light or darkness, by cardiac patients treated with HCN inhibitors. Moreover, electroretinographic recordings indicate that these drugs affect temporal processing in the outer retina. Here we analyzed the functional role of HCN channels in rod bipolar cells (RBCs) of the mouse. Perforated–patch recordings in the dark–adapted slice found that RBCs exhibit Ih, and that this is sensitive to the specific blocker ZD7288. RBC input impedance, explored by sinusoidal frequency–modulated current stimuli (0.1–30 Hz), displays band–pass behavior in the range of Ih activation. Theoretical modeling and pharmacological blockade demonstrate that high–pass filtering of input signals by Ih, in combination with low–pass filtering by passive properties, fully accounts for this frequency–tuning. Correcting for the depolarization introduced by shunting through the pipette–membrane seal, leads to predict that in darkness Ih is tonically active in RBCs and quickens their responses to dim light stimuli. Immunohistochemistry targeting candidate subunit isoforms HCN1–2, in combination with markers of RBCs (PKC) and rod–RBC synaptic contacts (bassoon, mGluR6, Kv1.3), suggests that RBCs express HCN2 on the tip of their dendrites. The functional properties conferred by Ih onto RBCs may contribute to shape the retina's light response and explain the visual side effects of HCN inhibitors

Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio