Analysis and display of the size dependence of chemical similarity coefficients

We discuss the size-bias inherent in several chemical similarity coefficients when used for the similarity searching or diversity selection of compound collections. Limits to the upper bounds of 14 standard similarity coefficients are investigated, and the results are used to identify some exceptional characteristics of a few of the coefficients. An additional numerical contribution to the known size bias in the Tanimoto coefficient is identified. Graphical plots with respect to relative bit density are introduced to further assess the coefficients. Our methods reveal the asymmetries inherent in most similarity coefficients that lead to bias in selection, most notably with the Forbes and Russell-Rao coefficients. Conversely, when applied to the recently introduced Modified Tanimoto coefficient our methods provide support for the view that it is less biased toward molecular size than most. In this work we focus our discussion on fragment-based bit strings, but we demonstrate how our approach can be generalized to continuous representations.     

Evaluation of similarity measures for searching the dictionary of natural products database

Similarity searches using combinations of seven different similarity coefficients and six different representations have been carried out on the Dictionary of Natural Products database. The objective was to discover if any special methods of searching apply to this database, which is very different in nature from the many synthetic databases that have been the subject of previous studies of similarity searching. Search effectiveness was assessed by a recall analysis of the search outputs from sets of pharmacologically active target structures. The different target sets produce exceptional but contradictory results for the Russell-Rao and Forbes coefficients, which have been shown to be due to a dependence on molecular size; these are the coefficients of choice in the case of large and small structures, respectively. Rankings from these results have been combined using a data fusion scheme and some small gains in performance were normally obtained by using substructural fingerprints and molecular holograms in combination with the Squared Euclidean or Tanimoto coefficients.     

On Matroids Representable over and other Fields

The matroids that are representable over and some other fields depend on the choice of field. This paper gives matrix characterisations of the classes that arise. These characterisations are analogues of the characterisation of regular matroids as the ones that can be represented over the rationals by a totally-unimodular matrix. Some consequences of the theory are as follows. A matroid is representable over and if and only if it is representable over and the rationals, and this holds if and only if it is representable over for all odd primes . A matroid is representable over and the complex numbers if and only if it is representable over and . A matroid is representable over , and if and only if it is representable over every field except possibly . If a matroid is representable over for all odd primes , then it is representable over the rationals.

     

A new class of iridium complexes suitable for stepwise incorporation into linear assemblies: synthesis, electrochemistry, and luminescence

A new family of cationic iridium(III) complexes is reported that contain two cyclometalating terdentate ligands. The complex [Ir(N--C--N-dpyx)(N--N--C-phbpy)]+ (1) contains one N--C--N-coordinating ligand, cyclometalating through the central phenyl ring, and one N--N--C-coordinated ligand, cyclometalated at the peripheral phenyl ring [dpyxH = 1,3-di(2-pyridyl)-4,6-dimethylbenzene; phbpyH = 6-phenyl-2,2'-bipyridine]. This binding mode dictates a mutually cis arrangement of the cyclometalated carbon atoms: the complexes are thus bis-terdentate analogues of the well-known [Ir(N--C-ppy)2(N--N-bpy)]+ family of complexes, which similarly contain a cis-C2N4 coordination environment. The dpyx ligand can be brominated regioselectively at the carbon atom para to the metal under mild conditions. Starting from a modified complex, [Ir(N--C--N-dpyx)(N--N--C-mtbpy-phi-Br)]+ (2), which incorporates a pendent bromophenyl group, a sequential cross-coupling-bromination-cross-coupling strategy can be applied for the stepwise introduction of aryl groups into the ligands, using in situ palladium-catalyzed Suzuki reactions with arylboronic acids [mtbpyH-phi-Br = 4-(p-bromophenyl)-6-(m-tolyl)bipyridine]. Dimetallic complexes 6 and 7 have similarly been prepared by a palladium-catalyzed reaction of complex 2 with 1,4-benzenediboronic acid and 4,4'-biphenyldiboronic acid, respectively. All five monometallic complexes and both dimetallic systems are luminescent in solution, emitting around 630 nm in MeCN at 298 K, with quantum yields in the range of 0.02-0.06, superior to [Ir(ppy)2(bpy)]+. The luminescence, electrochemistry, and singlet-oxygen-sensitizing abilities of the new family of complexes are discussed in the context of the tris-bidentate analogues and related bis-terdentate compounds that contain a trans arrangement of cyclometalated carbon atoms.     

A comparison of field-based similarity searching methods: CatShape, FBSS, and ROCS

Three field-based similarity methods are compared in retrospective virtual screening experiments. The methods are the CatShape module of CATALYST, ROCS, and an in-house program developed at the University of Sheffield called FBSS. The programs are used in both rigid and flexible searches carried out in the MDL Drug Data Report. UNITY 2D fingerprints are also used to provide a comparison with a more traditional approach to similarity searching, and similarity based on simple whole-molecule properties is used to provide a baseline for the more sophisticated searches. Overall, UNITY 2D fingerprints and ROCS with the chemical force field option gave comparable performance and were superior to the shape-only 3D methods. When the flexible methods were compared with the rigid methods, it was generally found that the flexible methods gave slightly better results than their respective rigid methods; however, the increased performance did not justify the additional computational cost required.     

Lanthanum pyrochlores and the effect of yttrium addition in the systems La2−xYxZr2O7 and La2−xYxHf2O7

The crystal structures of the compounds La_2−xY_xZr₂O₇ and La_2−xY_xHf₂O₇ with x=0.0, 0.4, 0.8, 1.2, 1.6, and 2.0 have been studied using neutron powder diffraction and electron microscopy to determine the stability fields of the pyrochlore and fluorite solid solutions. The limits of pyrochlore stability in these solid solutions are found to be close to La_0.8Y_1.2Zr₂O₇ and La_0.4Y_1.6Hf₂O₇, respectively. In both systems the unit cell parameter is found to vary linearly with Y content across those compositions where the pyrochlore phase is stable, as does the x-coordinate of the oxygen atoms on the 48f (x,,) sites. In both systems, linear extrapolations of the pyrochlore data suggest that the disordering is accompanied by a small decrease in the lattice parameter of approximately 0.4%. After the pyrochlore solid solution limit is reached, a sharp change is observed from x∼0.41 to 0.375 as the disordered defect fluorite structure is favoured. Electron diffraction patterns illustrate that some short-range order remains in the disordered defect fluorite phases.     

Quasi‐graphic matroids*

Frame matroids and lifted‐graphic matroids are two interesting generalizations of graphic matroids. Here, we introduce a new generalization, quasi‐graphic matroids, that unifies these two existing classes. Unlike frame matroids and lifted‐graphic matroids, it is easy to certify that a 3‐connected matroid is quasi‐graphic. The main result is that every 3‐connected representable quasi‐graphic matroid is either a lifted‐graphic matroid or a frame matroid.     

Cholesterol degradation in archaeological pottery mediated by fired clay and fatty acid pro-oxidants

Cholesterol is generally absent in animal fat residues preserved in archaeological ceramic vessels. It is known from edible oil refining that during bleaching with activated clay sterols are degraded, largely via oxidation. Laboratory heating experiments using fired clay from replica pottery vessels promoted rapid degradation of cholesterol via oxidation. Furthermore, heating cholesterol with fatty acids (saturated and unsaturated) revealed additional degradation to occur independently of the ceramic matrix. As both conditions are met in archaeological pottery during animal (and plant) product processing involving heating, the very rare detection of sterols in organic residues can be explained.     

Polymer models and generalized Potts-Kasteleyn models

The well-established relation between Potts models withv spin values and random-cluster models (with intracluster bonding favored over intercluster bonding by a factorv) is explored, but with the random-cluster model replaced by a much generalized polymer model, implying a corresponding generalization of the Potts model. The analysis is carried out in terms a given defined functionR(), an entropy/free-energy density for the polymer model in the casev=1, expressed as a function of the density of units. The aim of the analysis is to determine the analogR _v () ofR() for general nonnegativev in terms ofR(), and thence to determine the critical value of density _vg at which gelation occurs. This critical value is independent ofv up to a valuev _P, the Potts-critical value. What is principally required ofR() is that it should show a certain given concave/convex behavior, although differentiability and another regularizing condition are required for complete conclusions. Under these conditions the unique evaluation ofR _v () in terms ofR() is given in a form known to hold for integralv but not previously extended. The analysis is carried out in terms of the Legendre transforms of these functions, in terms of which the phenomena of criticality (gelation) and Potts criticality appear very transparently andv _P is easily determined. The value ofv _P is 2 under mild conditions onR. Special interest attaches to the functionR ₀(), which is shown to be the greatest concave minorant ofR(). The naturalness of the approach is demonstrated by explicit treatment of the first-shell model.     

Filtration in a Porous Granular Medium: 1. Simulation of Pore-Scale Particle Deposition and Clogging

This paper presents a numerical model for simulating the pore-scale transport and infiltration of dilute suspensions of particles in a granular porous medium under the action of hydrodynamic and gravitational forces. The formulation solves the Stokes’ flow equations for an incompressible fluid using a fixed grid, multigrid finite difference method and an embedded boundary technique for modeling particle–fluid coupling. The analyses simulate a constant flux of the fluid suspension through a cylindrical model pore. Randomly generated particles are collected within the model pore, initially through contact and attachment at the grain surface (pore wall) and later through mounding close to the pore inlet. Simple correlations have been derived from extensive numerical simulations in order to estimate the volume of filtered particles that accumulate in the pore and the differential pressure needed to maintain a constant flux through the pore. The results show that particle collection efficiency is correlated with the Stokes’ settling velocity and indirectly through the attachment probability with the particle–grain surface roughness. The differential pressure is correlated directly with the maximum mound height and indirectly with particle size and settling velocity that affect mound packing density. Simple modification factors are introduced to account for pore length and dip angle. These parameters are used to characterize pore-scale infiltration processes within larger scale network models of particle transport in granular porous media in a companion paper. Articlenote: Currently at GZA GeoEnvironmental Inc., 1 Edgewater Drive, Norwood, MA 02062, U.S.A.