Localization of the K+ Lock-in and the Ba2+ Binding Sites in a Voltage-Gated Calcium-Modulated Channel: Implications for Survival of K+ Permeability

Using Ba2+ as a probe, we performed a detailed characterization of an external K+ binding site located in the pore of a large conductance Ca2+-activated K+ (BKCa) channel from skeletal muscle incorporated into planar lipid bilayers. Internal Ba2+ blocks BKCa channels and decreasing external K+ using a K+ chelator, (+)-18-Crown-6-tetracarboxylic acid, dramatically reduces the duration of the Ba2+-blocked events. Average Ba2+ dwell time changes from 10 s at 10 mM external K+ to 100 ms in the limit of very low [K+]. Using a model where external K+ binds to a site hindering the exit of Ba2+ toward the external side (Neyton, J., and C. Miller. 1988. J. Gen. Physiol. 92:549–568), we calculated a dissociation constant of 2.7 μM for K+ at this lock-in site. We also found that BKCa channels enter into a long-lasting nonconductive state when the external [K+] is reduced below 4 μM using the crown ether. Channel activity can be recovered by adding K+, Rb+, Cs+, or NH4 + to the external solution. These results suggest that the BKCa channel stability in solutions of very low [K+] is due to K+ binding to a site having a very high affinity. Occupancy of this site by K+ avoids the channel conductance collapse and the exit of Ba2+ toward the external side. External tetraethylammonium also reduced the Ba2+ off rate and impeded the channel from entering into the long-lasting nonconductive state. This effect requires the presence of external K+. It is explained in terms of a model in which the conduction pore contains Ba2+, K+, and tetraethylammonium simultaneously, with the K+ binding site located internal to the tetraethylammonium site. Altogether, these results and the known potassium channel structure (Doyle, D.A., J.M. Cabral, R.A. Pfuetzner, A. Kuo, J.M. Gulbis, S.L. Cohen, B.T. Chait, and R. MacKinnon. 1998. Science. 280:69–77) imply that the lock-in site and the Ba2+ sites are the external and internal ion sites of the selectivity filter, respectively

n2 of dissipative couplings are sufficient to guarantee the exponential decay in elasticity

In this paper, we prove that the solutions to the problem determined by an elastic material with n2 coupling dissipative mechanisms decay in an exponential way for every (bounded) geometry of the body, where n is the dimension of the domain, and whenever the coupling coefficients satisfy a suitable condition. We also give several examples where the solutions do not decay when the rank of the matrix of the coupling mechanisms is less than n2 (2 in dimension 2 and 6 in dimension 3)Peer ReviewedPostprint (published version

Anisotropy can imply exponential decay in micropolar elasticity

In this note, two problems arisen in micropolar elasticity are considered from the analytical point of view. Following the Kelvin–Voigt theory of micropolar viscoelasticity, two dissipative mechanisms are imposed: in the first problem, it is defined on the microscopic structure and, for the second problem, on the macroscopic structure. Then, an existence and uniqueness result, as well as an exponential energy decay, are proved for the first problem. Since similar arguments can be used for the second problem, only the main key points are commentedPeer ReviewedPostprint (published version

Capillary jumps of fluid-fluid fronts across an elementary constriction in a model open fracture

We study experimentally the quasistatic displacement of an oil-air front across a localized constriction in a model open fracture. The front experiences capillary jumps at one end of the constriction in both imbibition and drainage, leading to a microscale pressure-saturation hysteresis cycle. At the other end the front is reversibly pinned. A condition of local mechanical equilibrium between the restoring elasticity of the front and the distortion produced by the local change in aperture captures all we measure quantitatively, in terms of material and geometrical properties only

Analysis of two thermoelastic problems with the Green–Lindsay model

In this paper, we analyze, from the numerical point of view, two thermo-elastic problems involving the Green–Lindsay theory. The coupling term is different for each case, involving second order or first order spatial derivatives, respectively. The variational formulation leads to a linear coupled system which is written in terms of the velocity and temperature speed. An existence and uniqueness results and the exponential energy decay for the problem with the stronger coupling are recalled. The polynomial energy decay for the weaker coupling is then proved but using the theory of linear semigroups. Then, a fully discrete approximation is introduced using the finite element method and an implicit scheme. A discrete stability property and a main a priori error estimates result are shown, from which we can derive the linear convergence of the approximations. Finally, some numerical simulations are presented to demonstrate the accuracy of the algorithm, the discrete energy decay and the dependence on the relaxation parameterPeer ReviewedPostprint (published version

Modulation of the Shaker K+Channel Gating Kinetics by the S3–S4 Linker

In Shaker K+ channels depolarization displaces outwardly the positively charged residues of the S4 segment. The amount of this displacement is unknown, but large movements of the S4 segment should be constrained by the length and flexibility of the S3–S4 linker. To investigate the role of the S3–S4 linker in the ShakerH4Δ(6–46) (ShakerΔ) K+ channel activation, we constructed S3–S4 linker deletion mutants. Using macropatches of Xenopus oocytes, we tested three constructs: a deletion mutant with no linker (0 aa linker), a mutant containing a linker 5 amino acids in length, and a 10 amino acid linker mutant. Each of the three mutants tested yielded robust K+ currents. The half-activation voltage was shifted to the right along the voltage axis, and the shift was +45 mV in the case of the 0 aa linker channel. In the 0 aa linker, mutant deactivation kinetics were sixfold slower than in ShakerΔ. The apparent number of gating charges was 12.6 ± 0.6 eo in ShakerΔ, 12.7 ± 0.5 in 10 aa linker, and 12.3 ± 0.9 in 5 aa linker channels, but it was only 5.6 ± 0.3 eo in the 0 aa linker mutant channel. The maximum probability of opening (Pomax) as measured using noise analysis was not altered by the linker deletions. Activation kinetics were most affected by linker deletions; at 0 mV, the 5 and 0 aa linker channels' activation time constants were 89× and 45× slower than that of the ShakerΔ K+ channel, respectively. The initial lag of ionic currents when the prepulse was varied from −130 to −60 mV was 0.5, 14, and 2 ms for the 10, 5, and 0 aa linker mutant channels, respectively. These results suggest that: (a) the S4 segment moves only a short distance during activation since an S3–S4 linker consisting of only 5 amino acid residues allows for the total charge displacement to occur, and (b) the length of the S3–S4 linker plays an important role in setting ShakerΔ channel activation and deactivation kinetics