Probing the Geometry of the Inner Vestibule of BK Channels with Sugars

The geometry of the inner vestibule of BK channels was probed by examining the effects of different sugars in the intracellular solution on single-channel current amplitude (unitary current). Glycerol, glucose, and sucrose decreased unitary current through BK channels in a concentration- and size-dependent manner, in the order sucrose > glucose > glycerol, with outward currents being reduced more than inward currents. The fractional decrease of outward current was more directly related to the fractional hydrodynamic volume occupied by the sugars than to changes in osmolality. For concentrations of sugars ≤1 M, the i/V plots for outward currents in the presence and absence of sugar superimposed after scaling, and increasing K+i from 150 mM to 2 M increased the magnitudes of the i/V plots with little effect on the shape of the scaled curves. These observations suggest that sugars ≤1 M reduce outward currents mainly by entering the inner vestibule and reducing the movement of K+ through the vestibule, rather than by limiting diffusion-controlled access of K+ to the vestibule. With 2 M sucrose, the movement of K+ into the inner vestibule became diffusion limited for 150 mM K+i and voltages >+100 mV. Increasing K+i then relieved the diffusion limitation. An estimate of the capture radius based on the 5 pA diffusion-limited current for channels without the ring of negative charge at the entrance to the inner vestibule was 2.2 Å. Adding the radius of a hydrated K+ (6–8 Å) then gave an effective radius for the entrance to the inner vestibule of 8–10 Å. Such a functionally wide entrance to the inner vestibule together with our observation that even small concentrations of sugar in the inner vestibule reduce unitary current suggest that a wide inner vestibule is required for the large conductance of BK channels

The HCN domain is required for HCN channel cell-surface expression and couples voltage- and cAMP-dependent gating mechanisms

Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels are major regulators of synaptic plasticity, and rhythmic activity in the heart and brain. Opening of HCN channels requires membrane hyperpolarization and is further facilitated by intracellular cyclic nucleotides (cNMPs). In HCN channels, membrane hyperpolarization is sensed by the membrane-spanning voltage sensor domain (VSD) and the cNMP-dependent gating is mediated by the intracellular cyclic nucleotide-binding domain (CNBD) connected to the pore-forming S6 transmembrane segment via the C-linker. Previous functional analysis of HCN channels has suggested a direct or allosteric coupling between the voltage- and cNMP-dependent activation mechanisms. However, the specifics of this coupling remain unclear. The first cryo-EM structure of an HCN1 channel revealed that a novel structural element, dubbed the HCN domain (HCND), forms a direct structural link between the VSD and C-linker/CNBD. In this study, we investigated the functional significance of the HCND. Deletion of the HCND prevented surface expression of HCN2 channels. Based on the HCN1 structure analysis, we identified R237 and G239 residues on the S2 of the VSD that form direct interactions with I135 on the HCND. Disrupting these interactions abolished HCN2 currents. We also identified three residues on the C-linker/CNBD (E478, Q382 and H559) that form direct interactions with residues R154 and S158 on the HCND. Disrupting these interactions affected both voltage- and cAMP-dependent gating of HCN2 channels. These findings indicate that the HCND is necessary for the cell-surface expression of HCN channels, and provides a functional link between voltage- and cAMP-dependent mechanisms of HCN channel gating

Eigenvalues and Eigenfunctions of the Scalar Laplace Operator on Calabi-Yau Manifolds

A numerical algorithm for explicitly computing the spectrum of the Laplace-Beltrami operator on Calabi-Yau threefolds is presented. The requisite Ricci-flat metrics are calculated using a method introduced in previous papers. To illustrate our algorithm, the eigenvalues and eigenfunctions of the Laplacian are computed numerically on two different quintic hypersurfaces, some Z_5 x Z_5 quotients of quintics, and the Calabi-Yau threefold with Z_3 x Z_3 fundamental group of the heterotic standard model. The multiplicities of the eigenvalues are explained in detail in terms of the irreducible representations of the finite isometry groups of the threefolds.Comment: 67 pages, 16 figures, 9 tables. v2: References adde

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

Deletion of cytosolic gating ring decreases gate and voltage sensor coupling in BK channels

Large conductance Ca(2+)-activated K(+) channels (BK channels) gate open in response to both membrane voltage and intracellular Ca(2+). The channel is formed by a central pore-gate domain (PGD), which spans the membrane, plus transmembrane voltage sensors and a cytoplasmic gating ring that acts as a Ca(2+) sensor. How these voltage and Ca(2+) sensors influence the common activation gate, and interact with each other, is unclear. A previous study showed that a BK channel core lacking the entire cytoplasmic gating ring (Core-MT) was devoid of Ca(2+) activation but retained voltage sensitivity (Budelli et al. 2013. Proc. Natl. Acad. Sci. USA. http://dx.doi.org/10.1073/pnas.1313433110). In this study, we measure voltage sensor activation and pore opening in this Core-MT channel over a wide range of voltages. We record gating currents and find that voltage sensor activation in this truncated channel is similar to WT but that the coupling between voltage sensor activation and gating of the pore is reduced. These results suggest that the gating ring, in addition to being the Ca(2+) sensor, enhances the effective coupling between voltage sensors and the PGD. We also find that removal of the gating ring alters modulation of the channels by the BK channel’s β1 and β2 subunits

B-L Cosmic Strings in Heterotic Standard Models

E_{8} X E_{8} heterotic string and M-theory, when compactified on smooth Calabi-Yau manifolds with SU(4) vector bundles, can give rise to softly broken N=1 supersymmetric theories with the exact matter spectrum of the MSSM, including three right-handed neutrinos and one Higgs-Higgs conjugate pair of supermultiplets. These vacua have the SU(3)_{C} X SU(2)_{L} X U(1)_{Y} gauge group of the standard model augmented by an additional gauged U(1)_{B-L}. Their minimal content requires that the B-L symmetry be spontaneously broken by a vacuum expectation value of at least one right-handed sneutrino. The soft supersymmetry breaking operators can induce radiative breaking of the B-L gauge symmetry with an acceptable B-L/electroweak hierarchy. In this paper, it is shown that U(1)_{B-L} cosmic strings occur in this context, potentially with both bosonic and fermionic superconductivity. We present a numerical analysis that demonstrates that boson condensates can, in principle, form for theories of this type. However, the weak Yukawa and gauge couplings of the right-handed sneutrino suggests that bosonic superconductivity will not occur in the simplest vacua in this context. The electroweak phase transition also disallows fermion superconductivity, although substantial bound state fermion currents can exist.Comment: 41 pages, 5 figure

Wilson Lines and a Canonical Basis of SU(4) Heterotic Standard Models

The spontaneous breaking of SU(4) heterotic standard models by Z_3 x Z_3 Wilson lines to the MSSM with three right-handed neutrino supermultiplets and gauge group SU(3)_C x SU(2)_L x U(1) x U(1) is explored. The two-dimensional subspace of the Spin(10) Lie algebra that commutes with su(3)_C + su(2)_L is analyzed. It is shown that there is a unique basis for which the initial soft supersymmetry breaking parameters are uncorrelated and for which the U(1) x U(1) field strengths have no kinetic mixing at any scale. If the Wilson lines "turn on" at different scales, there is an intermediate regime with either a left-right or a Pati-Salam type model. We compute their spectra directly from string theory, and adjust the associated mass parameter so that all gauge parameters exactly unify. A detailed analysis of the running gauge couplings and soft gaugino masses is presented.Comment: 59 pages, 9 figure