Calculation of the conductance and selectivity of an ion-selective potassium channel (IRK1) from simulation of atomic scale models

We present the equations and methodology for the theoretical prediction of the conductance, permeability and selectivity of a K⁺ channel on the basis of atomic scale models for it. The methodology involves the use of Langevin dynamics and activated trajectories in order to obtain translocation free energies, rate constants and transmission coefficients for an ion going through the channel. The models are for the Inward Rectifier K⁺ channel (IRK1) which is a member of a family of ion-selective K⁺ channels. The IRK1 channel is biologically important because of its role in cardiac pacemaker function. The models we use for the IRK1 channel are developed from a model of the Shaker voltage-gated K⁺ channel. We find that the theoretically predicted conductance is too low by three orders of magnitude. We attribute this underestimate to a specific structural defect in the model used. Perhaps our most significant result is that the computed conductance is tremendously sensitive to the structural details of the so-called ‘P-loop’ that lines the outer half of the permeation pathway of the channel. This sensitivity may be useful in future studies on ion channel proteins for which the structure is not known from X-ray crystallography. In addition, this sensitivity may help determine whether X-ray structures of these proteins correspond to open or closed conformations.     

Complete characterization of the water dimer vibrational ground state and testing the VRT(ASP-W)III,SAPT-5st,and VRT(MCY-5f) surfaces

We report the observation of extensive a- and c-type rotation-tunnelling (RT) spectra of (H₂O)₂ for K_a = 0–3, and (D₂O)₂ for K_a = 0–4. These data allow a detailed characterization of the vibrational ground state to energies comparable to those of the low-lying (70–80 cm^?1) intermolecular vibrations. We present a comparison of the experimentally determined molecular constants and tunnelling splittings with those calculated on the VRT(ASP-W)III, SAPT-5st, and VRT(MCY-5f) intermolecular potential energy surfaces. The SAPT-5st potential reproduces the vibrational ground state properties of the water dimer very well. The VRT(MCY-5f) and especially the VRT(ASP-W)III potentials show larger disagreements, in particular for the bifurcation tunnelling splitting.     

Prediction of ion channel transport from Grote—Hynes and Kramers theories

Generalized Langevin equation based Grote—Hynes (GH) theory and Langevin equation based Kramers theory are used to calculate the transmission coefficient for K⁺ diffusion through a model of the biological potassium ion channel IRK1, which contains a high potential barrier in the selectivity filter. The ion friction kernel is determined from a molecular dynamics (MD) simulation of the force on a stationary ion at the barrier top. The GH and Kramers estimates of the transmission coefficient are compared with those obtained from MD simulations of ion diffusion at the barrier top of the IRK1 channel. It is found that the GH estimate agrees with the value determined by rigorous MD, but the Kramers estimate is about 40% too small. The success or failure of GH and Kramers theories for various other systems is discussed and compared with these results.     

PROPER AFFINE DEFORMATIONS OF THE ONE-HOLED TORUS

A Margulis spacetime is a complete at Lorentzian 3-manifold M with free fundamental group. Associated to M is a noncompact complete hyperbolic surface ∑ homotopy-equivalent to M. The purpose of this paper is to classify Margulis spacetimes when ∑ is homeomorphic to a one-holed torus. We show that every such M decomposes into polyhedra bounded by crooked planes, corresponding to an ideal triangulation of ∑. This paper classifies and analyzes the structure of crooked ideal triangles, which play the same role for Margulis spacetimes as ideal triangles play for hyperbolic surfaces.     

Test of rate theory transmission coefficient algorithms. An application to ion channels

The determination of rate constants is an important problem in many areas of chemical physics. Transition state theory (TST) is often used in estimating the rate constants. However TST neglects recrossings of the transition state by the reaction coordinate. The transmission coefficient is a correction to the TST estimate which accounts for the influence of recrossing dynamics. The transmission coefficient is calculated by generating activated trajectories which cross the transition state. This article investigates the correctness and efficiency of several current numerical algorithms for estimating the transmission coefficient, as well as a new one presented here. We use these algorithms to estimate the transmission coefficient for K⁺ diffusion through a model inward rectifier potassium (IRK1) ion channel.     

ChemInform Abstract: Observation of Two Structurally Distinct States in Ni-P Glasses Using EXAFS.

X-Ray absorption spectra above the Ni K-edge of samples prepared by pulsed electrodeposition (type I) and electrodeposition (type II) exhibit distinct differences which are related to a rearrangement of Ni-P and Ni-Ni bonds.