In using spinor representation for the electron field, the charge density is given by a 2 × 2 matrix in the spin space. The propagator is also a 2 × 2 matrix. The diagonal term gives the usual many electron problem, and the off-diagonal term gives the superconductive state. The SCF equation for the usual many-electron problem turns out to be the gap equation for the superconductivity problem. This treatment presents a new theory for the high temperature superconductivity by using the multi-band treatment from which the attractive electron-electron coupling is effectively derived. This coupling is electronic, but not phonon associated. The energy region for making superconductivity possible is a hundred times larger than the phonon frequency.
The ability to assess the toxicity of a chemical substance depends on the available information on the compound and/or its related compounds. Among chemicals currently in commerce, very few are ascertained on their toxicity, and especially reliable data on the carcinogenicity are very limited for pharmaceutical chemicals. Therefore, attempts on the basis of quantitative structure-activity relationship (QSAR) models for estimating the carcinogenicity have been performed. But none of the models so far developed shows satisfactory performance for predicting the carcinogenicity of noncongeneric chemicals from their structures. The support vector machine (SVM) technique was applied to develop a QSAR model that relates the structures of diverse chemicals to their carcinogenicity, and its predictability was compared with that of our previous artificial neural network (ANN) model. The relationship between experimental carcinogenicity data used in the Predictive Toxicology Challenge (PTC) 2000-2001 contest on 454 chemicals and 37 molecular descriptors calculated from their structures alone was analyzed with a software LIBSVM ver.2.85 for support vector regression (SVR). Models were optimized using a cross-validation test for the training dataset, and their performances were evaluated using the test dataset. The training of ANN models took several months using seven PCs to solve the problems such as over-training, over-fitting and local minima, while SVM gave a just comparable predictability of 74 % with that by ANN, within much shorter computation time. It comes from the advantage of SVM that gives only one global optimum solution after training while ANN gives numerous local minimum solutions. Moreover the prediction accuracy of the SVM model was higher than the best predictability value of 71 % reported in the literature for the same dataset. It is concluded that the support vector machine, a novel nonlinear machine learning approach, leads to a model for predicting the carcinogenicity of noncongeneric chemicals from information on the molecular structure alone with a higher performance than any of the so-far proposed approaches.
F-ATPase is a membrane protein and catalyzes to synthesize ATP in the cell. It is well known that the ATPase (γ-subunit) rotates in coupling with hydrolysis of ATP. The rotating unit of ATPase for its function is α3β3γ subunit complex, and each of three β-subunits in the complex has the catalytic site. X-ray crystallographic study has revealed that there are three types of β-subunit conformations, ATP bound form (βTP), ADP bound form (βDP), and ligand free form (βE). These three types of β-subunit conformations show different ligand (ATP and ADP) binding affinities, however, ADP binding affinities and the conformational change of them accompanying the rotation of γ-subunit have not been extensively investigated. Here, we estimated the ADP binding affinities of three types of the β-subunits by using molecular dynamics/free energy calculations. From simulations, the βDP was the dominant β-subunit conformation to bind ADP with the highest affinity. Our free energy profile of the ATP hydrolysis by β-subunit supported thermodynamically the ATP hydrolysis model, which has been predicted from single molecule experiments. Furthermore, in our simulations, the conformational change of Phe418∼Gly426 was observed accompanying ligand change from ATP to ADP or vice versa. This result indicates that Phe418∼Gly426 are key residues to couple catalysis, conformational change and rotation of the F-ATPase.