IDSite: An accurate approach to predict P450-mediated drug metabolism

Accurate prediction of drug metabolism is crucial for drug design. Since a large majority of drugs metabolism involves P450 enzymes, we herein describe a computational approach, IDSite, to predict P450-mediated drug metabolism. To model induced-fit effects, IDSite samples the conformational space with flexible docking in Glide followed by two refinement stages using the Protein Local Optimization Program (PLOP). Sites of metabolism (SOMs) are predicted according to a physical-based score that evaluates the potential of atoms to react with the catalytic iron center. As a preliminary test, we present in this paper the prediction of hydroxylation and O-dealkylation sites mediated by CYP2D6 using two different models: a physical-based simulation model, and a modification of this model in which a small number of parameters are fit to a training set. Without fitting any parameters to experimental data, the Physical IDSite scoring recovers 83% of the experimental observations for 56 compounds with a very low false positive rate. With only 4 fitted parameters, the Fitted IDSite was trained with the subset of 36 compounds and successfully applied to the other 20 compounds, recovering 94% of the experimental observations with high sensitivity and specificity for both sets.     

Targeted analysis of glycomics liquid chromatography/mass spectrometry data

Hydrophilic interaction chromatography (HILIC) liquid chromatography/mass spectrometry (LC/MS) is appropriate for all native and reductively aminated glycan classes. HILIC carries the advantage that retention times vary predictably according to oligosaccharide composition. Chromatographic conditions are compatible with sensitive and reproducible glycomics analysis of large numbers of samples. The data are extremely useful for quantitative profiling of glycans expressed in biological tissues. With these analytical developments, the rate-limiting factor for widespread use of HILIC LC/MS in glycomics is the analysis of the data. In order to eliminate this problem, a Java-based open source software tool, Manatee, was developed for targeted analysis of HILIC LC/MS glycan datasets. This tool uses user-defined lists of compositions that specify the glycan chemical space in a given biological context. The program accepts high-resolution LC/MS data using the public mzXML format and is capable of processing a large data file in a few minutes on a standard desktop computer. The program allows mining of HILIC LC/MS data with an output compatible with multivariate statistical analysis. It is envisaged that the Manatee tool will complement more computationally intensive LC/MS processing tools based on deconvolution and deisotoping of LC/MS data. The capabilities of the tool were demonstrated using a set of HILIC LC/MS data on organ-specific heparan sulfates.     

The Hilbert-Chow morphism and the incidence divisor: Zero-cycles and divisors

For a smooth projective variety X of dimension n, on the product of Chow varieties C_a(X)×C_n−a−1(X) parameterizing pairs (A,B) of an a-cycle A and an (n−a−1)-cycle B in X, Barry Mazur raised the problem of constructing a Cartier divisor supported on the locus of pairs with A∩B≠0?. We introduce a new approach to this problem, and new techniques supporting this approach.     

Approximation theorems for total quasi-?-asymptotically nonexpansive mappings with applications

The purpose of this article is to prove some approximation theorems of common fixed points for countable families of total quasi-?-asymptotically nonexpansive mappings which contain several kinds of mappings as its special cases in Banach spaces. In order to get the approximation theorems, the hybrid algorithms are presented and are used to approximate the common fixed points. Using this result, we also discuss the problem of strong convergence concerning the maximal monotone operators in a Banach space. The results of this article extend and improve the results of Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theor. 134 (2005) 257-266], Plubtieng and Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces, J. Approx. Theor. 149 (2007) 103-115], Li, Su [H. Y. Li, Y. F. Su, Strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems, Nonlinear Anal. 72(2) (2010) 847-855], Su, Xu and Zhang [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890-3960], Wang et al. [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364-2371], Chang et al. [S.S. Chang, H.W. Joseph Lee, Chi Kin Chan, A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications, Nonlinear Anal. 73 (2010) 2260-2270], Chang et al. [S.S. Chang, C.K. Chan, H.W. Joseph Lee, Modified block iterative algorithm for quasi-?-asymptotically nonexpansive mappings and equilibrium problem in Banach spaces, Appl. Math. Comput. 217 (2011) 7520-7530], Ofoedu and Malonza [E.U. Ofoedu, D.M. Malonza, Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type, Appl. Math. Comput. 217 (2011) 6019-6030] and Yao et al. [Y.H. Yao, Y.C. Liou, S.M. Kang, Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings, Appl. Math. Comput. 208 (2009) 211-218].     

Strong convergence theorems for countable families of asymptotically relatively nonexpansive mappings with applications

The purpose of this paper is by using the hybrid iterative method to prove some strong convergence theorems for approximating a common element of the set of solutions to a system of generalized mixed equilibrium problems and the set of common fixed points for two countable families of closed and asymptotically relatively nonexpansive mappings in Banach space. The results presented in the paper improve and extend the corresponding results of Su et al. [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890-3906], Li and Su [H.Y. Li, Y.F. Su, Strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems, Nonlinear Anal. 72 (2) (2010) 847-855], Chang et al. [S.S. Chang, H.W. Joseph Lee, Chi Kin Chan, A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications, Nonlinear Anal. TMA 73 (2010) 2260-2270], Kang et al. [J. Kang, Y. Su, X. Zhang, Hybrid algorithm for fixed points of weak relatively nonexpansive mappings and applications, Nonlinear Anal. HS 4 (4) (2010) 755-765], Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theory 134 (2005) 257-266], Tan et al. [J.F. Tan, S.S. Chang, M. Liu, J.I. Liu, Strong convergence theorems of a hybrid projection algorithm for a family of quasi-?-asymptotically nonexpansive mappings, Opuscula Math. 30 (3) (2010) 341-348], Takahashia and Zembayashi [W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal. 70 (2009) 45-57] and Wattanawitoon and Kumam [K. Wattanawitoon, P. Kumam, Strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Anal. Hybrid Systems 3 (2009) 11-20] and others.     

SOME EXACT SOLUTIONS OF 3-DIMENSIONAL ZERO-PRESSURE GAS DYNAMICS SYSTEM

The 3-dimensional zero-pressure gas dynamics system appears in the modeling for the large scale structure formation in the universe. The aim of this paper is to construct spherically symmetric solutions to the system. The radial component of the velocity and density satisfy a simpler one dimensional problem. First we construct explicit solutions of this one dimensional case with initial and boundary conditions. Then we get special radial solutions with different behaviours at the origin.     

How ordinary elimination became Gaussian elimination

Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method — which Euler did not recommend, which Legendre called “ordinary,” and which Gauss called “common” — is now named after Gauss: “Gaussian” elimination. Gauss’s name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least-squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices.     

The steady boundary value problem for charged incompressible fluids: PNP/Navier–Stokes systems

The initial-boundary value problem for the Poisson–Nernst–Planck/Navier–Stokes model was investigated in [J.W. Jerome, R. Sacco, Global weak solutions for an incompressible charged fluid with multi-scale couplings: initial-boundary-value problem, Nonlinear Anal. 71 (2009) e2487–e2497], where an existence theory was demonstrated, based upon Rothe’s method of horizontal lines. In this article, the steady case is considered, and the existence of a weak solution is established for the boundary-value problem. This solution satisfies a weak maximum principle for the concentrations relative to the boundary values. As noted in the above-mentioned citation, the model assumes significance because of its connection to the electrophysiology of the cell, including neuronal cell monitoring and microfluidic devices in biochip technology. The model has also been used in other applications, including electro-osmosis. The steady model is especially important in ion channel modeling, because the channel remains open for milliseconds, and the transients appear to decay on the scale of tens of nanoseconds.     

The Inverse Commutant Lifting Problem. I: Coordinate-Free Formalism

It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal unitary extensions of a partially defined isometry constructed explicitly from the problem data. A special role is played by a particular unitary extension, called the central or universal unitary extension. The coefficient matrix for the Redheffer linear-fractional map has a simple expression in terms of the universal unitary extension. The universal unitary extension can be seen as a unitary coupling of four unitary operators (two bilateral shift operators together with two unitary operators coming from the problem data) which has special geometric structure. We use this special geometric structure to obtain an inverse theorem (Theorem 8.4) which characterizes the coefficient matrices for a Redheffer linear-fractional map arising in this way from a lifting problem. The main tool is the formalism of unitary scattering systems developed in Boiko et al. (Operator theory, system theory and related topics (Beer-Sheva/Rehovot 1997), pp. 89–138, 2001) and Kheifets (Interpolation theory, systems theory and related topics, pp. 287–317, 2002)