The calculation of molecular similarity: alternative formulas,data manipulation and graphical display

The use of electrostatic potential comparisons between molecules for the elucidation of structure activity relationships is now a well-established modeling technique. The Carbo and Hodgkin similarity indices are used extensively to make quantitative comparisons of this nature; yet their roots are found in the overlap of electron density distribution, with both formulas utilizing a product-based numerator.Two new similarity indices are suggested that calculate the electrostatic potential similarity using a difference-based numerator. The form of the new indices allows the creation of additional software functions that enhance the flexibility of similarity calculations and permit the creation of similarity maps.The general properties of these software functions and all indices are discussed and applied to a series of dopamine D2 receptor agonists.     

Calculation and display of electrostatic potentials

A general methodology is developed for incorporating accurate electrostatic information from ab initio molecular orbital calculations into molecular mechanics calculations. Examples are given of the method applied to simple aromatic organic molecules. A program has been developed for displaying the results of the ab initio calculations on a Silicon Graphics workstation. The technique developed here provides an alternative method for including electrostatic interactions in molecular mechanics calculations and is compared with other methods for determining atomic charges.     

Evaluating molecular similarity using reduced representations of the electron density

A model system of four benzodiazepine-like ligands for the central benzodiazepine receptors (CBRs) and peripheral benzodiazepine receptors (PBRs)is examined using a genetic algorithm procedure (GAGS) designed for evaluating molecular similarity. The method is based on the alignment of reduced representations generated from the critical points of the electron density computed at medium crystallographic resolution. The results are further characterized by a comparison with alignments produced by MIMIC, a field-based superimposition method that matches both steric and electrostatic molecular fields. The alignments produced by the two methods are generally seen to be consistent. The relationships of the compounds' binding affinities for both CBRs and PBRs to the alignments determined by GAGS yield a set of structural features required for significant binding to benzodiazepine receptors. Benefits of using reduced representations for evaluating molecular similarities and for constructing pharmacophore models are discussed.     

Statistical analysis and graphical display of multivariate data on the Macintosh

Two Macintosh programs written for multivariate data analysisand multivariate data graphical display are presented. MacMulincludes principal component analysis (PCA), correspondenceanalysis (CA) and multiple correspondence analysis (MCA), witha complete, original and unified set of numerical aids to interpretation.GraphMu is designed for drawing collections of elementary graphics(curves, maps, graphical models) thus allowing comparisons betweenvariables, individuals, and principal axes planes of multivariatemethods. Both programs are self-documented applications andmake full use of the user-oriented graphical interface of theMacintosh to simplify the process of analysing data sets. Anexample is described to show the results obtained on a smallecological data set. Received on January 24, 1989; accepted on July 17, 1989     

A graphical theory of competition on spatial resource gradients

Resource competition is a fundamental interaction in natural communities. However, little remains known about competition in spatial environments where organisms are able to regulate resource distributions. Here, we analyse the competition of two consumers for two resources in a one-dimensional habitat in which the resources are supplied from opposite sides. We show that the success of an invading species crucially depends on the slope of the resource gradients shaped by the resident. Our analysis reveals that parameter combinations, which lead to coexistence in a uniform environment, may favour alternative stable states in a spatial system, and vice versa. Furthermore, differences in growth rate, mortality or dispersal abilities allow a consumer to coexist stationarily with - or even outcompete - a competitor with lower resource requirements. Applying our theory to a phytoplankton model, we explain shifts in the community structure that are induced by environmental changes.     

Topological analysis of aromatic halogen/hydrogen bonds by electron charge density and electrostatic potentials

In this work, the intermolecular distribution of the electronic charge density in the aromatic hydrogen/halogen bonds is studied within the framework of the atoms in molecules (AIM) theory and the molecular electrostatic potentials (MEP) analysis. The study is carried out in nine complexes formed between benzene and simple lineal molecules, where hydrogen, fluorine and chlorine atoms act as bridge atoms. All the results are obtained at MP2 level theory using cc-pVTZ basis set. Attention is focused on topological features observed at the intermolecular region such as bond, ring and cage critical points of the electron density, as well as the bond path, the gradient of the density maps, molecular graphs and interatomic surfaces. The strength of the interaction increases in the following order: F⋅⋅⋅π < Cl⋅⋅⋅π < H⋅⋅⋅π. Our results show that the fluorine atom has the capability to interact with the π−cloud to form an aromatic halogen bond, as long as the donor group is highly electron withdrawing. The Laplacian topology allows us to state that the halogen atoms can act as nucleophiles as well as electrophiles, showing clearly their dual character.     

Automated segmentation of molecular subunits in electron cryomicroscopy density maps

Electron cryomicroscopy (cryoEM) is capable of imaging large macromolecular machines composed of multiple components. However, it is currently only possible to achieve moderate resolution at which it may be possible to computationally extract the individual components in the machine. In this work, we present application details of an automated method for detecting and segmenting the components of a large machine in an experimentally determined density map. This method is applicable to object with and without symmetry and takes advantage of global and local symmetry axes if present. We have applied this segmentation algorithm to several cryoEM data sets already deposited in EMDB with various complexities, symmetries and resolutions and validated the results using manually segmented density and available structures of the components in the PDB. As such, automated segmentation could become a useful tool for the analysis of the ever-increasing number of structures of macromolecular machines derived from cryoEM.     

distruct: a program for the graphical display of population structure

In analysis of multilocus genotypes from structured populations, individual coefficients of membership in subpopulations are often estimated using programs such as structure . distruct provides a general method for visualizing these estimated membership coefficients. Subpopulations are represented as colours, and individuals are depicted as bars partitioned into coloured segments that correspond to membership coefficients in the subgroups. distruct , available at http://www.cmb.usc.edu/~noahr/distruct.html , can also be used to display subpopulation assignment probabilities when individuals are assumed to have ancestry in only one group.     

On the functional significance of electron density protein structure alignments

Electron density protein alignments are analyzed in terms of their underlying similarity measure, the density overlap. These alignments are conceptually unrelated to biochemical structural elements and, therefore, are appropriate in structure-only similarity studies. The analysis is focused on the low sequence similarity subset of protein domains. A remarkable association is found between simple, density overlap measures and the expert designed Structural Classification of Proteins (SCOP) for which functional and evolutive analogies prevail. The association found validates the functional significance of electron density alignments.     

Formation of supported phospholipid bilayers on molecular surfaces: role of surface charge density and electrostatic interaction

Electrostatic interaction is known to play important roles in the adsorption of charged lipids on oppositely charged surfaces. Here we show that, even for charge neutral (zwitterionic) lipids, electrostatic interaction is critical in controlling the adsorption and fusion of lipid vesicles to form supported phospholipid bilayers (SPBs) on surfaces. We use terminally functionalized alkanethiol self-assembled monolayers (SAMs) to systematically control the surface charge density. Charge neutral egg phophatidylcholine (eggPC) vesicles readily fuse into SPBs on either a positively charged 11-aminino-1-undecanethiol SAM or a negatively charged 10-carboxy-1-decanethiol SAM when the density of surface charge groups is > or = 80%. These processes depend critically on the buffer environment: fusion of adsorbed vesicles to form SPBs on each charged molecular surface does not occur when the molecular ion of the buffer used is of the opposite charge type. We attribute this to the high entropic repulsion (electric double layer repulsion) due to the large size of molecular counterions. On the other hand, such a critical dependence on buffer type is not observed when charged lipids are used. This study suggests the general importance of controlling electrostatic interaction in the formation of stable SPBs.     

Understanding the conformational flexibility and electrostatic properties of curcumin in the active site of rhAChE via molecular docking,molecular dynamics,and charge density analysis

Acetylcholinesterase (AChE) is an important enzyme responsible for Alzheimer’s disease, as per report, keto-enol form of curcumin inhibits this enzyme. The present study aims to understand the binding mechanism of keto-enol curcumin with the recombinant human Acetylcholinesterase (rhAChE) from its conformational flexibility, intermolecular interactions, charge density distribution, and the electrostatic properties at the active site of rhAChE. To accomplish this, a molecular docking analysis of curcumin with the rhAChE was performed, which gives the structure and conformation of curcumin in the active site of rhAChE. Further, the charge density distribution and the electrostatic properties of curcumin molecule (lifted from the active site of rhAChE) were determined from the high level density functional theory (DFT) calculations coupled with the charge density analysis. On the other hand, the curcumin molecule was optimized (gas phase) using DFT method and further, the structure and charge density analysis were also carried out. On comparing the conformation, charge density distribution and the electrostatic potential of the active site form of curcumin with the corresponding gas phase form reveals that the above said properties are significantly altered when curcumin is present in the active site of rhAChE. The conformational stability and the interaction of curcumin in the active site are also studied using molecular dynamics simulation, which shows a large variation in the conformational geometry of curcumin as well as the intermolecular interactions.     

Simple and inexpensive fabrication of small-volume density gradients

A method is described for high speed centrifugation of small volumes of homogenates, tissue extracts, or body fluids without the use of expensive adapters. The procedure consists of introducing the samples into light polyethylene microcentrifuge tubes and then floating them in a medium contained in standard cellulose nitrate tubes. This assembly can be centrifuged at 198,000g for 90 min with no visible distortion of the sample tubes.     

Generation of density gradients. Approximations to equivolumetric gradients for zonal rotors

The use of a “density gradient generating function” allows the concentration profile of a density gradient to be written explicitly in terms of the required distribution of sedimentation coefficients in place of the previous implicit formulations. This function, which is easily implemented in a computer program, permits calculation of density gradients for a number of applications. This approach is applied to computation of a variety of equivolumetric gradients of sucrose for zonal rotors and yields a formula for the calibration of such gradients. An accurate approximation has been found which allows the generation of virtually all equivolumetric gradients of sucrose for a given rotor using a single program for the gradient generator employed; the adjustment for different particle densities and for different concentrations at the top of the gradient is made by varying only the initial and final concentrations of sucrose used.