Energetics of ion competition in the DEKA selectivity filter of neuronal sodium channels

The energetics of ionic selectivity in the neuronal sodium channels is studied. A simple model constructed for the selectivity filter of the channel is used. The selectivity filter of this channel type contains aspartate (D), glutamate (E), lysine (K), and alanine (A) residues (the DEKA locus). We use Grand Canonical Monte Carlo simulations to compute equilibrium binding selectivity in the selectivity filter and to obtain various terms of the excess chemical potential from a particle insertion procedure based on Widom's method. We show that K$^{+}$ ions in competition with Na$^{+}$ are efficiently excluded from the selectivity filter due to entropic hard sphere exclusion. The dielectric constant of protein has no effect on this selectivity. Ca$^{2+}$ ions, on the other hand, are excluded from the filter due to a free energetic penalty which is enhanced by the low dielectric constant of protein.Comment: 14 pages, 7 figure

A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equations: Validation and model problems

An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction

Applications systems verification and transfer project. Volume 4: Operational applications of satellite snow cover observations. Colorado Field Test Center

The study was conducted on six watersheds ranging in size from 277 km to 3460 km in the Rio Grande and Arkansas River basins of southwestern Colorado. Six years of satellite data in the period 1973-78 were analyzed and snowcover maps prepared for all available image dates. Seven snowmapping techniques were explored; the photointerpretative method was selected as the most accurate. Three schemes to forecast snowmelt runoff employing satellite snowcover observations were investigated. They included a conceptual hydrologic model, a statistical model, and a graphical method. A reduction of 10% in the current average forecast error is estimated when snowcover data in snowmelt runoff forecasting is shown to be extremely promising. Inability to obtain repetitive coverage due to the 18 day cycle of LANDSAT, the occurrence of cloud cover and slow image delivery are obstacles to the immediate implementation of satellite derived snowcover in operational streamflow forecasting programs

Improved error estimates for the perturbed Galerkin method applied to a class of generalized eigenvalue problems

AbstractWe consider the generalized eigenvalue problem x-Kx = μBx in a complex Banach space E. Here, K and B are bounded linear operators, B is compact, and 1 is not in the spectrum of K. If {En: n = 1, 2,…} is a sequence of closed subspaces of E and Pn: E → En is a linear projection which maps E onto En, then we consider the sequence of approximate eigenvalue problems {xn-PnKxn = μPnBxn in En: n = 1, 2,…}. Assuming that ‖K-PnK‖ → 0 and ‖B-PnB‖ → 0 as n → ∞, we prove the convergence of sequences of eigenvalues and eigenelements of the approximate eigenvalue problem to eigenvalues and eigenelements of the original eigenvalue problem, and establish upper bounds for the errors. These error bounds are sharper than those given by Vainikko in Ref. 2 for the more general problem x = μTx in E, T linear and compact, and the sequence of approximate problems {xn = μTnxn in En: n=l, 2,…}, and do not involve the operator Sn=Tn-PnT/En

Orthogonal, solenoidal, three-dimensional vector fields for no-slip boundary conditions

Viscous fluid dynamical calculations require no-slip boundary conditions. Numerical calculations of turbulence, as well as theoretical turbulence closure techniques, often depend upon a spectral decomposition of the flow fields. However, such calculations have been limited to two-dimensional situations. Here we present a method that yields orthogonal decompositions of incompressible, three-dimensional flow fields and apply it to periodic cylindrical and spherical no-slip boundaries.Comment: 16 pages, 2 three-part figure