Properties of contact matrices induced by pairwise interactions in proteins

The total conformational energy is assumed to consist of pairwise interaction energies between atoms or residues, each of which is expressed as a product of a conformation-dependent function (an element of a contact matrix, C-matrix) and a sequence-dependent energy parameter (an element of a contact energy matrix, E-matrix). Such pairwise interactions in proteins force native C-matrices to be in a relationship as if the interactions are a Go-like potential [N. Go, Annu. Rev. Biophys. Bioeng. 12. 183 (1983)] for the native C-matrix, because the lowest bound of the total energy function is equal to the total energy of the native conformation interacting in a Go-like pairwise potential. This relationship between C- and E-matrices corresponds to (a) a parallel relationship between the eigenvectors of the C- and E-matrices and a linear relationship between their eigenvalues, and (b) a parallel relationship between a contact number vector and the principal eigenvectors of the C- and E-matrices; the E-matrix is expanded in a series of eigenspaces with an additional constant term, which corresponds to a threshold of contact energy that approximately separates native contacts from non-native ones. These relationships are confirmed in 182 representatives from each family of the SCOP database by examining inner products between the principal eigenvector of the C-matrix, that of the E-matrix evaluated with a statistical contact potential, and a contact number vector. In addition, the spectral representation of C- and E-matrices reveals that pairwise residue-residue interactions, which depends only on the types of interacting amino acids but not on other residues in a protein, are insufficient and other interactions including residue connectivities and steric hindrance are needed to make native structures the unique lowest energy conformations.Comment: Errata in DOI:10.1103/PhysRevE.77.051910 has been corrected in the present versio

Face- and Cell-Averaged Nodal-Gradient Approach to Cell-Centered Finite-Volume Method on Mixed Grids

In this paper, the averaged nodal-gradient approach previously developed for triangular grids is extended to mixed triangular-quadrilateral grids. It is shown that the face- averaged approach leads to deteriorated iterative convergence on quadrilateral grids. To develop a convergent solver, we consider cell-averaging instead of face-averaging for quadri- lateral cells. We show that the cell-averaged approach leads to a convergent solver and can be efficiently combined with the face-averaged approach on mixed grids. The method is demonstrated for various inviscid and viscous problems from low to high Mach numbers on two-dimensional mixed grids

Efficient and Robust Weighted Least-Squares Cell-Average Gradient Construction Methods for the Simulation of Scramjet Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use of these gradients in the construction of the inviscid fluxes is the focus of this paper. A comparison of least-squares stencil construction methodologies is presented and approaches designed to minimize the number of cells used to augment/stabilize the least-squares stencil while preserving accuracy are explored. Due to our interest in hypersonic flow, a robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cellaverage gradients is described. Canonical problems are computed to illustrate the challenges and investigate the accuracy, robustness and convergence behavior of the cell-average gradient methods on unstructured cell-centered finite-volume grids. Finally, thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet engine flowpath is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the preferred gradient method for a realistic 3-D geometry on a non-hex-dominant grid

Renormalized parameters and perturbation theory for an n-channel Anderson model with Hund's rule coupling: Asymmetric case

We explore the predictions of the renormalized perturbation theory for an n-channel Anderson model, both with and without Hund's rule coupling, in the regime away from particle-hole symmetry. For the model with n=2 we deduce the renormalized parameters from numerical renormalization group calculations, and plot them as a function of the occupation at the impurity site, nd. From these we deduce the spin, orbital and charge susceptibilities, Wilson ratios and quasiparticle density of states at T=0, in the different parameter regimes, which gives a comprehensive overview of the low energy behavior of the model. We compare the difference in Kondo behaviors at the points where nd=1 and nd=2. One unexpected feature of the results is the suppression of the charge susceptibility in the strong correlation regime over the occupation number range 1 <nd <3.Comment: 9 pages, 17 figure

Fermi Liquids and the Luttinger Integral

The Luttinger Theorem, which relates the electron density to the volume of the Fermi surface in an itinerant electron system, is taken to be one of the essential features of a Fermi liquid. The microscopic derivation of this result depends on the vanishing of a certain integral, the Luttinger integral $I_{\rm L}$, which is also the basis of the Friedel sum rule for impurity models, relating the impurity occupation number to the scattering phase shift of the conduction electrons. It is known that non-zero values of $I_{\rm L}$ with $I_{\rm L}=\pm\pi/2$, occur in impurity models in phases with non-analytic low energy scattering, classified as singular Fermi liquids. Here we show the same values, $I_{\rm L}=\pm\pi/2$, occur in an impurity model in phases with regular low energy Fermi liquid behavior. Consequently the Luttinger integral can be taken to characterize these phases, and the quantum critical points separating them interpreted as topological.Comment: 5 pages 7 figure