A Multi-Scale Approach to Model K+ Permeation Through the KcsA Channel.

K+ channels allow a very efficient passage of K+ ions through the membrane while excluding Na+ ions, and these properties are essential for life. The 3D structure of the KcsA K+ channel, solved more than 20 years ago, allows to address many relevant aspects of K+ permeation and selectivity mechanisms at the molecular level. Recent crystallographic data and molecular dynamics (MD) studies suggest that no water is normally present inside the selectivity filter (SF), which can instead accommodate four adjacent K+ ions. Using a multi-scale approach, whereby information taken from a low-level simulation approach is used to feed a high-level model, we studied the mechanism of K+ permeation through KcsA channels. More specifically, we used MD to find stable ion configurations under physiological conditions. They were characterized by two adjacent K+ ions occupying the more central positions of the SF (sites S2 and S3), while the other two K+ ions could be found at the external and internal entrances to the SF. Sites S1 and S4 were instead not occupied by K+. A continuum Bikerman-Poisson-Boltzmann model that takes into account the volume of the ions and their dehydration when entering the SF fully confirmed the MD results, showing peaks of K+ occupancy at S2, S3, and the external and internal entrances, with S1 and S4 sites being virtually never occupied by K+. Inspired by the newly found ion configuration in the SF at equilibrium, we developed a simple kinetic permeation model which, fed with kinetic rate constants assessed from molecular meta-dynamics, reproduced the main permeation properties of the KcsA channel found experimentally, including sublinear current-voltage and saturating conductance-concentration relationships. This good agreement with the experimental data also implies that the ion configuration in the SF we identified at equilibrium would also be a key configuration during permeation.

Turbulence in a matter-wave supersolid.

Quantum turbulence associated with wave and vortex dynamics is numerically investigated for a two-dimensional trapped atomic Rydberg-dressed Bose-Einstein condensate (BEC). When the coupling constant of the soft-core interaction is over a critical value, the superfluid (SF) system can transition into a hexagonal supersolid (SS) state. Based on the Gross-Pitaevskii equation approach, we have discovered a new characteristic k-13/3 scaling law for wave turbulence in the SS state, that coexists with the waveaction k-1/3 and energy k-1 cascades commonly existing in a SF BEC. The new k-13/3 scaling law implies that the SS system exhibits a negative, minus-one power energy dispersion (E ~ k-1) at the wavevector consistent with the radius of the SS droplet. For vortex turbulence, in addition to the presence of the Kolmogorov energy k-5/3 and Saffman enstrophy k-4 cascades, it is found that large amount of independent vortices and antivortices pinned to the interior of the oscillating SS results in a strong k-1 scaling at the wavevector consistent with the SS lattice constant.

Undular bore theory for the Gardner equation.

We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations.

Synthesis of Pt doped Bi2O3/RuO2 photocatalysts for hydrogen production from water splitting using visible light.

This study was focused on the preparation of modified bismuth oxide photocatalysts, including Ru and Pt doped Bi2O3, using sonochemically assisted method to enhance their photocatalytic activity. The crystalline phase composition and surface structure of Bi2O3 photocatalysts were examined using SEM, XRD, UV-visible spectroscopy, and XPS. Optical characterizations have indicated that the Bi2O3 presents the photoabsorption properties shifting from UV light region into visible light which is approaching towards the edge of 470 nm. According to the experimental results, visible-light-driven photocatalysis for water splitting with the addition of 0.3 M Na2SO3 and 0.03 M H2C2O4 as sacrificing agents demonstrates that Pt/Bi2O3-RuO2 catalyst could increase the amount of hydrogen evolution, which is around 11.6 and 14.5 micromol g(-1) h(-1), respectively. Plausible formation mechanisms of modified bismuth oxide and reaction mechanisms of photocatalytic water splitting have been proposed.