QSAR models using a large diverse set of estrogens

Endocrine disruptors (EDs) have a variety of adverse effects in humans and animals. About 58,000 chemicals, most having little safety data, must be tested in a group of tiered assays. As assays will take years, it is important to develop rapid methods to help in priority setting. For application to large data sets, we have developed an integrated system that contains sequential four phases to predict the ability of chemicals to bind to the estrogen receptor (ER), a prevalent mechanism for estrogenic EDs. Here we report the results of evaluating two types of QSAR models for inclusion in phase III to quantitatively predict chemical binding to the ER. Our data set for the relative binding affinities (RBAs) to the ER consists of 130 chemicals covering a wide range of structural diversity and a 6 orders of magnitude spread of RBAs. CoMFA and HQSAR models were constructed and compared for performance. The CoMFA model had a r2 = 0.91 and a q2LOO = 0.66. HQSAR showed reduced performance compared to CoMFA with r2 = 0.76 and q2LOO = 0.59. A number of parameters were examined to improve the CoMFA model. Of these, a phenol indicator increased the q2LOO to 0.71. When up to 50% of the chemicals were left out in the leave-N-out cross-validation, the q2 remained significant. Finally, the models were tested by using two test sets; the q2pred for these were 0.71 and 0.62, a significant result which demonstrates the utility of the CoMFA model for predicting the RBAs of chemicals not included in the training set. If used in conjunction with phases I and II, which reduced the size of the data set dramatically by eliminating most inactive chemicals, the current CoMFA model (phase III) can be used to predict the RBA of chemicals with sufficient accuracy and to provide quantitative information for priority setting.     

Entropy-enthalpy compensations in solutions of dual character molecules with polymeric chromatographic liquid phases

Careful gas chromatographic studies provide thermodynamic data for insights into solution processes in nonvolatile solvents. Using 24 solutes and five stationary phases, several entropy-enthalpy compensation effects in the thermodynamics of solution were identified. Despite solute structure differences, when excess enthalpy and entropy of solutions were examined, entropy-enthalpy compensation effects were found in solvents dominated by single types of interaction: squalane and, to some extent, methoxy poly(ethylene oxide) (PEO). The main reason for the absence of linearity in other solvents is pure solute state interactions in the reference state and the multicharacter nature of solvents. In this study, consideration of solute state interactions was removed through examination of the thermodynamics of transfer between solvent pairs. It was found that solute transfers from squalane to poly[methyl(trifluoropropyl)siloxane] (QF-1) and to poly(methylphenyl) (DC-550) also gave linear relationships. The former system contains a second correlation for ester type solutes. The transfer data for squalane to poly(methylsiloxane) (DC-200) had smaller ranges and were more scattered. The effects of derivatizing groups on the transfer enthalpy and entropy were treated as a summation of hydrocarbon cores with the derivative groups. The group properties of transfer then also show entropy-enthalpy compensation effects. Many solution effects could be explained on the basis of solvent composition and local interactions with solutes.     

Size Ramsey numbers involving stars

We calculate some size Ramsey numbers involving stars. For example we prove that for t ? k ? 2 and n sufficiently large the size Ramsey number.

$\text{r}{}_{\mathrm{n}}\text{(K}{}_{\mathrm{1,k}}\text{K}{}_{\mathrm{t}}\text{+}\text{K}{}_{\mathrm{n}}\text{=}\text{k(t?1)+1}\text{2}\text{+(k(t?1)+1)(n+k?1).}$

     

Supramolecular Chemistry In Silico

Computational protocols capable of modelling supramolecular complexes have been evaluated. The complexation of cations by crown ethers and quaternary ammonium ions by an oxacalix[3]arene are presented as examples. In the latter case reliable qualitative results were obtained using the semi-empirical PM3 method where guest LUMO and electrostatic potential energies have been shown to correlate with experimental binding data. The optimal method for more accurate results combines semi-empirical equilibrium geometry and property calculations with single point energy calculations at the HF/6–31G* or BP/6–31G* quantum mechanical level.     

2‐factors with prescribed and proscribed edges

Let G be a finite k‐edge‐connected simple graph. We consider when a set of independent edges can be extended to a 2‐factor such that this 2‐factor avoids a fixed set of independent edges. A complete characterization is provided in those cases, where this is feasible. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 48–58, 2005