The affine equivariant sign covariance matrix: asymptotic behavior and efficiencies.

We consider the affine equivariant sign covariance matrix (SCM) introduced by Visuri et al. (J. Statist. Plann. Inference 91 (2000) 557). The population SCM is shown to be proportional to the inverse of the regular covariance matrix. The eigenvectors and standardized eigenvalues of the covariance, matrix can thus be derived from the SCM. We also construct an estimate of the covariance and correlation matrix based on the SCM. The influence functions and limiting distributions of the SCM and its eigenvectors and eigenvalues are found. Limiting efficiencies are given in multivariate normal and t-distribution cases. The estimates are highly efficient in the multivariate normal case and perform better than estimates based on the sample covariance matrix for heavy-tailed distributions. Simulations confirmed these findings for finite-sample efficiencies. (C) 2003 Elsevier Science (USA). All rights reserved.affine equivariance; covariance and correlation matrices; efficiency; eigenvectors and eigenvalues; influence function; multivariate median; multivariate sign; robustness; multivariate location; discriminant-analysis; principal components; dispersion matrices; tests; estimators;

Influence function and asymptotic efficiency of the affine equivariant rank covariance matrix.

Visuri et al (2001) proposed and illustrated the use of the affine equivariant rank covariance matrix (RCM) in classical multivariate inference problems. The RCM was shown to be asymptotically multinormal but explicit formulas for the limiting variances and covariances were not given yet. In this paper the influence functions and the limiting variances and covariances of the RCM and the corresponding scatter estimate are derived in the multivariate elliptic case. Limiting efficiencies are given in the multivariate normal and t-distribution cases. The estimates based on the RCM are highly efficient in the multinormal case, and for heavy tailed distribution, perform better than those based on the regular covariance matrix.Efficiency;

Effect of Recycling Cooking Liquor and Eliminating the Washing Stage During Chemical Deinking

The purpose of this investigation was two-fold--first to determine what effects recycling the cooking liquor in varying percentages had upon the final pulp quality, and second to find out what effect eliminating the washing stage had upon the final pulp. The results are not as definite as would have been desired due to variation in the data. Generally, the results showed recycling the cooking liquor left more fines in the pulp resulting in higher tensile, burst, and fold strength. Eliminating the washing stage left more ink particles, pigments, and fines in the pulp which resulted in higher yields, better opacity, lower brightness, and increased physical strengths

Canonical analysis based on scatter matrices.

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix are considered in more detail. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimator and S-estimates through theoretical and simulation studies. The theory is illustrated by an example.Canonical correlations; Canonical variables; Canonical vectors; Covariance; Covariance determinant estimator; Determinant estimator; Distribution; Efficiency; Estimator; Functions; Influence function; Matrix; Scatter; Shape matrix; Sign covariance mix; Simulation; Studies; Theory; Tyler's estimate;

Charged Small Molecule Binding to Membranes in MD Simulations Evaluated against NMR Experiments

Interactions of charged molecules with biomembranes regulate many of their biological activities, but their binding affinities to lipid bilayers are difficult to measure experimentally and model theoretically. Classical molecular dynamics (MD) simulations have the potential to capture the complex interactions determining how charged biomolecules interact with membranes, but systematic overbinding of sodium and calcium cations in standard MD simulations raises the question of how accurately force fields capture the interactions between lipid membranes and charged biomolecules. Here, we evaluate the binding of positively charged small molecules, etidocaine, and tetraphenylphosphonium to a phosphatidylcholine (POPC) lipid bilayer using the changes in lipid head-group order parameters. We observed that these molecules behave oppositely to calcium and sodium ions when binding to membranes: (i) their binding affinities are not overestimated by standard force field parameters, (ii) implicit inclusion of electronic polarizability increases their binding affinity, and (iii) they penetrate into the hydrophobic membrane core. Our results can be explained by distinct binding mechanisms of charged small molecules with hydrophobic moieties and monoatomic ions. The binding of the former is driven by hydrophobic effects, while the latter has direct electrostatic interactions with lipids. In addition to elucidating how different kinds of charged biomolecules bind to membranes, we deliver tools for further development of MD simulation parameters and methodology.Peer reviewe

Accurate Simulations of Lipid Monolayers Require a Water Model with Correct Surface Tension

Lipid monolayers provide our lungs and eyes their functionality and serve as proxy systems in biomembrane research. Therefore, lipid monolayers have been studied intensively including using molecular dynamics simulations, which are able to probe their lateral structure and interactions with, e.g., pharmaceuticals or nanoparticles. However, such simulations have struggled in describing the forces at the air-water interface. Particularly, the surface tension of water and long-range van der Waals interactions have been considered critical, but their importance in monolayer simulations has been evaluated only separately. Here, we combine the recent C36/LJ-PME lipid force field that includes long-range van der Waals forces with water models that reproduce experimental surface tensions to elucidate the importance of these contributions in monolayer simulations. Our results suggest that a water model with correct surface tension is necessary to reproduce experimental surface pressure-area isotherms and monolayer phase behavior. The latter includes the liquid expanded and liquid condensed phases, their coexistence, and the opening of pores at the correct area per lipid upon expansion. Despite these improvements of the C36/LJ-PME with certain water models, the standard cutoff-based CHARMM36 lipid model with the 4-point OPC water model still provides the best agreement with experiments. Our results emphasize the importance of using high-quality water models in applications and parameter development in molecular dynamics simulations of biomolecules.Peer reviewe

Canonical analysis based on scatter matrices.

In this paper, the influence functions and limiting distributions of the canonical correlations and coefficients based on affine equivariant scatter matrices are developed for elliptically symmetric distributions. General formulas for limiting variances and covariances of the canonical correlations and canonical vectors based on scatter matrices are obtained. Also the use of the so-called shape matrices in canonical analysis is investigated. The scatter and shape matrices based on the affine equivariant Sign Covariance Matrix as well as the Tyler's shape matrix serve as examples. Their finite sample and limiting efficiencies are compared to those of the Minimum Covariance Determinant estimators and S-estimator through theoretical and simulation studies. The theory is illustrated by an example.Canonical correlations; Canonical variables; Canonical vectors; Covariance; Covariance determinant estimator; Determinant estimator; Distribution; Efficiency; Estimator; Functions; Influence function; Matrix; Principal components; Scatter; Shape matrix; Sign; Sign covariance mix; Simulation; Studies; Theory; Tyler's estimate; Variance;

Interfacial Tension and Surface Pressure of High Density Lipoprotein, Low Density Lipoprotein, and Related Lipid Droplets

AbstractLipid droplets play a central role in energy storage and metabolism on a cellular scale. Their core is comprised of hydrophobic lipids covered by a surface region consisting of amphiphilic lipids and proteins. For example, high and low density lipoproteins (HDL and LDL, respectively) are essentially lipid droplets surrounded by specific proteins, their main function being to transport cholesterol. Interfacial tension and surface pressure of these particles are of great interest because they are related to the shape and the stability of the droplets and to protein adsorption at the interface. Here we use coarse-grained molecular-dynamics simulations to consider a number of related issues by calculating the interfacial tension in protein-free lipid droplets, and in HDL and LDL particles mimicking physiological conditions. First, our results suggest that the curvature dependence of interfacial tension becomes significant for particles with a radius of ∼5 nm, when the area per molecule in the surface region is <1.4 nm2. Further, interfacial tensions in the used HDL and LDL models are essentially unaffected by single apo-proteins at the surface. Finally, interfacial tensions of lipoproteins are higher than in thermodynamically stable droplets, suggesting that HDL and LDL are kinetically trapped into a metastable state

Calcium Sensing by Recoverin : Effect of Protein Conformation on Ion Affinity

The detailed functional mechanism of recoverin, which acts as a myristoyl switch at the rod outer-segment disk membrane, is elucidated by direct and replica-exchange molecular dynamics. In accord with NMR structural evidence and calcium binding assays, simulations point to the key role of enhanced calcium binding to the EF3 loop of the semiopen state of recoverin as compared to the closed state. This 2-4-order decrease in calcium dissociation constant stabilizes the semiopen state in response to the increase of cytosolic calcium concentration in the vicinity of recoverin. A second calcium ion then binds to the EF2 loop and, consequently, the structure of the protein changes from the semiopen to the open state. The latter has the myristoyl chain extruded to the cytosol, ready to act as a membrane anchor of recoverin.Peer reviewe