Performance of efficient minimization algorithms as applied to models of peptides and proteins

We test the efficiency of three minimization algorithms as applied to models of peptides and proteins. These include: the limited memory quasi-Newton (L-BFGS) of Liu and Nocedal; the truncated Newton (TN) with automatic preconditioner of Nash; and the nonlinear conjugate gradients (CG) of Shanno and Phua. The molecules are modeled by two energy functions, one is the Gromos 87 united atoms force field (defining the energy E_GRO), which takes into account the intramolecular interactions only; the second is defined by the energy E_tot=E_GRO+E_solv, where E_solv is an implicit solvation free every term based on the solvent-accessible surface area of the atoms. The molecules studied are cyclo-(d -Pro¹–Ala²–Ala³–Ala⁴–Ala⁵) (31 atoms), axinastatin 2 [cyclo-(Asn¹–Pro²–Phe³–Val⁴–Leu⁵–Pro⁶–Val⁷), 62 atoms], and the protein bovine pancreatic trypsin inhibitor (58 residues, 568 atoms). With E_GRO, the performance of TN with respect to the CPU time is found to be ∼1.2 to 2 times better than that of both L-BFGS and CG, whereas, with E_tot, L-BFGS outperforms TN by a factor of 1.5 to 2.5, and CG by a larger factor. Still, the quality of the solution in terms of the value of the minimized energy and the gradient norm, obtained with TN, is always equivalent to, or better than, those obtained with L-BFGS and CG. The performance is analyzed in terms of criteria outlined by Nash and Nocedal. We find the distribution of the Hessian eigenvalues to be a reliable predictor of efficiency. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 354–364, 1999     

Electrocatalytic Oxidation of Calcium Folinate on Carboxyl Graphene Modified CuxO/Cu Electrode

Carboxyl graphene modified Cu_xO/Cu electrode was fabricated. The bare copper electrode was firstly anodic polarized in 1.0 mol/L NaOH solution in order to get Cu_xO nanoparticles, then the carboxyl graphene (CG) was electrodeposited on the Cu_xO/Cu electrode by cyclic potential sweeping. The electrocatalytic oxidation behaviors of calcium folinate (CF) at the graphene modified Cu_xO/Cu electrode were investigated by cyclic voltammetry. A positive scan polarization reverse catalytic voltammetry was used to obtain the pure catalytic oxidation current. The graphene modified Cu_xO/Cu electrode was served as the electrochemical sensor of CF, a highly sensitivity of 22.0 μA·(μmol/μL)^-1cm^-2 was achieved, and the current response was linear with increasing CF concentration in the range of 2.0×10^-7 mol/L to 2.0×10^-5 mol/L, which crossed three orders of magnitude, and the detection limit was found 7.6×10^-8 mol/L (S/N=3). In addition, the proposed sensor was successfully applied in determination of CF in drug sample.     

The Electropolymerization of 2,6‐Diaminopyridine and Its Application as Mercury Ion Selective Electrode

A composite graphite (CG) electrode modified with poly(2,6‐diaminopyridine) (PDAP) was used as solid state‐ion selective electrode for determination of mercury. The electrooxidation of monomer 2, 6 diaminopyridine (DAP) onto CG was accomplished from the 30 mM DAP in 5% H₂SO₄ and 0.5 M ZnSO₄. The electrode displayed Nernstian response with slope of 28.4±1 mV decade⁻¹ in concentration range of 1×10⁻⁶ to 1×10⁻¹ M and in solution of pH 3–5. The limit of detection for electrode was 3×10⁻⁸ M with response time of 25 s. The electrode was also suitable as an indicator electrode in the potentiometric titration of Hg²⁺ with iodide.     

Evidence of two relaxation processes in the photon correlation spectra of poly(methyl methacrylate) above Tg

Photon correlation functions of a high-molecular-weight PMMA (M_w = 1.06 × 10⁷, M_n = 2.2 × 10⁶, T_g = 103°C) have been studied in the temperature range 98 ? 149°C. In contrast to previous results, two relaxation modes are observed in relaxation functions. The observed relaxation functions of PMMA are analyzed for the first time in terms of a continuous spectrum representing the distribution of retardation times. Using a modified computer program originally developed by Provencher, we have computed the spectrum of retardation times at various temperatures. The appearance of two distinct relaxation modes is clearly evident in the distribution of the retardation times and in the time correlation functions below 123°C.     

Evaluation of two-center,two- and three-electron integrals involving correlation factors over Slater-type orbitals. II. Kinetic and potential energy integrals and examples of numerical results

This article is concerned with the construction of the general algorithm for evaluating two-center, two- and three-electron integrals occurring in matrix elements of one-electron operators in the basis of variational correlated functions. This problem has been solved here in prolate spherical coordinates, using the modified and extended form of the Neumann expansion of the interelectronic distance function r^k_ij derived in Part I of this series for k = ?1, 0, 1, 2. This work expands the method proposed by one of us in the preceding paper for integrals of the types mentioned above. The results of numerical calculations for different types of the two- and three-electron integrals are presented. The problem of convergence of the proposed procedures used is also discussed.     

Application of modified Neumann expansion for analytical evaluation of two-center,two-electron integrals over slater-type orbitals

A modified form of the Neumann expansion in terms of products of orthogonal polynomials for the inverse interelectronic distance r¹₁₂ is proposed. This expansion has been applied in order to derive a unified analytical formula for two-center and two-electron integrals over Slater-type orbitals. The results are equivalent to those given recently by Yasui and Saika, but the expansion itself can be used for building up a realistic algorithm for evaluation of three- and four-electron integrals determined by using correlated variational wave functions.     

Fluorescence Quenching over Short Range in a Donor‐DNA‐Acceptor System

A new donor‐DNA‐acceptor system has been synthesized containing Nile red‐modified 2′‐deoxyuridine as charge donor and 6‐N,N‐dimethylaminopyrene‐modified 2′‐deoxyuridine as acceptor to investigate the charge transfer in DNA duplexes using fluorescence spectroscopy and time‐resolved femtosecond pump‐probe techniques. Fluorescence quenching experiments revealed that the quenching efficiency of Nile red depends on two components: 1) the presence of a charge acceptor and 2) the number of intervening CG and AT base pairs between donor and acceptor. Surprisingly, the quenching efficiency of two base pairs (73 % for CG and the same for AT) is higher than that for one base pair (68 % for CG and 37 % for AT), while at a separation of three base pairs less than 10 % quenching is observed. A comparison with the results of time‐resolved measurements revealed a correlation between quenching efficiency and the first ultrafast time constant suggesting that quenching proceeds via a charge transfer from the donor to the acceptor. All transients are satisfactorily described with two decays: a rapid charge transfer with 600 fs (～10¹² s^?1) that depends strongly and in a non‐linear fashion on the distance between donor and acceptor, and a slower time constant of a few picoseconds (～10¹¹ s^?1) with weak distance dependence. A third time constant on a nanosecond time scale represents the fluorescence lifetime of the donor molecule. According to these results and time‐dependent density functional theory (TDDFT) calculations a combination of single‐step superexchange and multistep hopping mechanisms can be proposed for this short‐range charge transfer. Furthermore, significantly less quenching efficiency and slower charge transfer rates at very short distances indicate that the direct interaction between donor and acceptor leads to a local structural distortion of DNA duplexes which may provide some uncertainty in identifying the charge transfer rates in short‐range systems.     

Molecular integrals in the generalized hylleraas–CI method

In the generalized Hylleraas–CI method, the original correlation factor r^v_ij is multiplied by a Gaussian geminal. Using the approach of generating functions, the general formulas of molecular integrals in this method are derived over Cartesian Gaussian orbitals. From differentiations of the generating functions, the expanding length in the incomplete Gamma functions is reduced, and some cancellations presented in other approaches are avoided. Preliminary calculations for H₂ and H₂—H₂ systems are carried out over STO -3G basis. The results are encouraging.     

Influence of Gemini Surfactant with Modified TiO2 Nanoparticles on the Interfacial Tension of Oil/Water

The research on the impacts of modified TiO₂ nanoparticles (NPs) on interfacial tension (IFT) is in its infancy. Our work focuses on the IFT of the modified TiO₂ and Gemini surfactant N,N,N′,N′-tetramethyl-N,N′-dimyristyl-1,2-ethane diammonium dichlone (YND1233) complex solutions for reservoir stimulation purposes. The factors of YND1233, modified TiO₂ NPs, temperature, aging stability, adsorption loss, and mineralized degree were explored with the comparison of unmodified TiO₂ NPs and YND1233 as contrast samples. The results indicate that the dynamic IFTs decrease and then increase with the concentrations of YND1233 and modified TiO₂ NPs, and the minimum IFT appears at 0.200 and 0.010 wt%, respectively. YND1233/modified TiO₂ complex solutions show lower and more stable IFTs, better temperature resistance, longer aging time, and lower adsorption on the surface of quartz sand. The modified TiO₂ NPs and YND1233 in the YND1233/modified TiO₂ complex solution can be adsorbed to the interface and decrease the IFTs through synergistic effect. A mixed diffusion-kinetic mechanism is provided for the adsorption and interactions with Ca²⁺/Mg²⁺ involved in YND1233/modified TiO₂ complex solution.     

Electrochemical determination of <Emphasis Type="Italic">p</Emphasis>-cresol using mesoporous TiO<Subscript>2</Subscript>-modified carbon paste electrode

A mesoporous TiO₂ (meso-TiO₂) was synthesized, and used to prepare modified carbon paste electrode (CPE). The electrochemical sensing properties were characterized using K₃[Fe(CN)₆], showing that meso-TiO₂ modified CPE possesses larger surface area and higher electron transfer rate. The electrochemical behavior of p-cresol was investigated. At the meso-TiO₂ modified CPE, the oxidation peak current of p-cresol remarkably increases, and the oxidation peak potential shifts negatively, suggesting that meso- TiO₂ exhibits highly efficient catalytic activity to the oxidation of p-cresol. Based on this, a sensitive, rapid and convenient electrochemical method was developed for the detection of p-cresol. The linear range is from 1.5 × 10⁻⁷ and 2.0 × 10⁻⁵ mol l⁻¹, and the limit of detection is as low as 8.0 × 10⁻⁸ mol l⁻¹. Finally, the new method was successfully used to determine p-cresol in water samples.     

Bestimmung der Stabilit?tskonstanten von mehrkernigen Komplexen mit Hilfe einer spektrophotometrischen Methode

Zusammenfassung Es wurde eine allgemeine Gleichung für die Berechnung der Stabilitätskonstante von Komplexen L _mH_iM_nZ_j (Z=OH^–, usw.) abgeleitet und für Maximumbedingungen der Jobschen Kurve die Schwarzenbachsche graphische Methode so modifiziert, daß sie die allgemeine Bestimmung der Zusammensetzung und Stabilität von Komplexen L _mH_iM_nZ_j ermöglicht.

---

Summary A general equation has been derived for the calculation of stability constants of complexes L _mH_iM_nZ_j (Z=OH^–, etc.). The graphic method of Schwarzenbach has been modified for maximum conditions of Job's curve in order to make possible the general determination of the composition and stability of complexes L _mH_iM_nZ_j.

     

Solubility of gases in liquids. XVI. Henry's law coefficients for nitrogen in water at 5 to 50°C

The solubility of nitrogen in pure liquid water was measured in the pressure range 45 to 115 kPa and in the temperature range 5 to 50°C. These data are used to obtain Henry coefficients H _2,1 (T,P _s,1 ) at the vapor pressure P _s,1 of water. The temperature dependence of H _2,1 (T,P _s,1 ) is accounted for by both a Clarke-Glew (CG) type fitting equation, and a power series in T^–1, as suggested by Benson and Krause (BK). The imprecision of our measurements is characterized by an average deviation of ±0.038% from a four-term CG equation, and by an average deviation of ±0.042% from a three-term BK equation. From the temperature variation of H _2,1 (T,P _s,1 ) partial molar quantities referring to the solution process, such as enthalpies and heat capacities of solution, are obtained. They are given in tabular form, together with H _2,1 (T,P _s,1 ) and derived Ostwald coefficients L, at rounded temperatures. Finally, experimental results are compared with values calculated via scaled particle theory.     

Determination of kinetic parameters for pyrolysis of cellulose and cellulose treated with ammonium phosphate by differential thermal analysis and thermal gravimetric analysis

Activation energy E, pre-exponential factor k₀, and reaction order n for the pyrolysis of α-cellulose and cellulose modified with dihydrogen ammonium phosphate were determined by means of TGA and DTA. The results obtained are E = 53.5 kcal./mole, k₀ = 10^18.8 min.^?1, n = 1 for α-cellulose and E = 32 kcal./mole, k₀ = 10¹² min.^?1, n = 1 for modified cellulose. A new theory of DTA was also developed. This theory, in which it is concluded that the peak value of DTA curve coincides with the maximum rate of reaction, may be used not only for the present work but is generally applicable to DTA studies. Detailed procedures of experiment and theory are described.     

Anisotropy in the dimensional and elastic parameters of confined macromolecules

Using lattice simulations the effect of confinement on the size, orientation and elastic properties of athermal chains was investigated. For chains confined in a slit or in a “cylinder” with square profile a minimum was observed in the dependence of the mean‐square end‐to‐end distance 〈R²〉 on the plate distance D. However, the components of the mean chain dimensions perpendicular and parallel to the walls, 〈R²_⟂〉 and 〈R²_∥〉, steadily diverge with reduction of the pore size. In a slit the distribution functions of the chain vector perpendicular and parallel to the plates, W〈R²_⟂ 〉 and W〈R²_∥〉, respectively, were computed. The marked difference between these distribution functions is interpreted as a sign of enhanced alignment of chains of the shape of elongated ellipsoids along the pore walls. A major part of the free energy of confinement ΔA_cf stems from this mechanism of pore‐induced macromolecular orientation. A striking anisotropy was observed in the elastic free energies A^el_⟂ and A^el_∥ of chains deformed in the direction perpendicular and parallel to the walls and in the corresponding force‐displacement functions. Finally, the relation between the elastic free energy A^el and the free energy of confinement ΔA_cf and between the forces f and f_solv derived thereof is analysed.     

Estimation of the agglomeration structure for conductive particles and fiber‐filled high‐density polyethylene through dynamic rheological measurements

A study on the correlation between electrical percolation and viscoelastic percolation for carbon black (CB) and carbon fiber (CF) filled high‐density polyethylene (HDPE) conductive composites was carried out through an examination of the filler concentration (?) dependence of the volume resistivity (ρ) and dynamic viscoelastic functions. For CB/HDPE composites, when ? was higher than the modulus percolation threshold (?_G ～ 15 vol %), the dynamic storage modulus (G′) reached a plateau at low frequencies. The relationship between ρ and the normalized dynamic storage modulus (G_c^′/G_p^′, where G_c^′ and G_p^′ are the dynamic storage moduli of the composites and the polymer matrix, respectively) was studied. When ? approached a critical value (?_r), a characteristic change in G_c^′/G_p^′ appeared. The critical value (G_c^′/G^′_p)c was 9.80, and the corresponding ?_r value was 10 vol %. There also existed a ? dependence of the dynamic loss tangent (tan δ) and a peak in a plot of tan δ versus the frequency when ? approached a loss‐angle percolation (?_δ = 9 vol %). With parameter K substituted for A, a modified Kerner–Nielson equation was obtained and used to analyze the formation of the network structure. The viscoelastic percolation for CB/HDPE composites could be verified on the basis of the modified equation, whereas no similar percolation was found for CF/HDPE composites. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1199–1205, 2004     

Preparation, Electrochemical Behavior and Electrocatalytic Activity of a Copper Hexacyanoferrate Modified Ceramic Carbon Electrode

A copper hexacyanoferrate modified ceramic carbon electrode （CuHCF/CCE） had been prepared by two-step sol-gel technique and characterized using electrochemical methods. The resulting modified electrode showed a pair of well-defined surface waves in the potential range of 0.40 to 1.0 V with the formal potential of 0.682 V （vs. SCE） in 0.050 mol·dm^-3 HOAc-NaOAc buffer containing 0.30 mol·dm^-3 KCl. The charge transfer coefficient （a） and charge transfer rate constant （ks） for the modified electrode were calculated. The electrocatalytic activity of this modified electrode to hydrazine was also investigated, and chronoamperometry was exploited to conveniently determine the diffusion coefficient （D） of hydrazine in solution and the catalytic rate constant （kcat）. Finally, hydrazine was determined with amperometry using the resulting modified electrode. The calibration plot for hydrazine determination was linear in 3.0 × 10^-6--7.5 × 10^-4 mol·dm^-3 with the detection limit of 8.0 × 10^-7 molodm^-3. This modified electrode had some advantages over the modified film electrodes constructed by the conventional methods, such as renewable surface, good long-term stability, excellent catalytic activity and short response time to hydrazine.     

High Performance Oxide Functionalized Nitrogen‐Doped Mesocellular Carbon Foam for Biosensor Construction

Nitrogen‐doped mesocellular carbon foam (denoted as MCF? CN_x) with high surface area and large pore volume was prepared and characterized in detail. The MCF? CN_x was further functionalized by oxidation with HNO₃ (denoted as MCF? CN_x‐O) in order to effectively improve its hydrophilicity and biocompatibility. Both MCF? CN_x and MCF? CN_x‐O were used for immobilization of Hb and design of electrochemical biosensors. The activity of Hb immobilized on MCF? CN_x‐O is two times higher than that of Hb immobilized on MCF? CN_x. The Hb‐MCF? CN_x‐O‐Nafion modified electrode displays fast response, high sensitivity and low detection limit to the detection of hydrogen peroxide. The sensitivity of Hb‐MCF? CN_x‐O‐Nafion modified electrode (477 μA mM^?1 cm^?2) is twice that of Hb‐MCF? CN_x‐Nafion modified electrode.     

Trace Level Determination of Hydrogen Peroxide at a Carbon Ceramic Electrode Modified with Copper Oxide Nanostructures

An electrochemical sensor was developed for determination of hydrogen peroxide based on nanocopper oxides modified carbon sol‐gel or carbon ceramic electrode (CCE). The modified electrode was prepared by electrodeposition of metallic copper on the CCE surface and derivatized in situ to copper oxides nanostructures and characterized by scanning electron microscopy (SEM) and X‐ray diffraction (XRD) techniques. The modified electrode responded linearly to the hydrogen peroxide (H₂O₂) concentration over the range 0.78–193.98 µmol L^?1 with a detection limit of 71 nmol L^?1 (S/N=3) and the sensitivity of 0.697 A mol^?1 L cm^?2. This electrode was used as selective amperometric sensor for determination of H₂O₂ contents in hair coloring creams.     

Optimization of virtual orbitals in the framework of a multiconfiguration spin-coupled wave function

A new method is introduced for the optimization of nonorthogonal virtual orbitals for use in general multiconfiguration spin-coupled wave functions. The use of a number of highly effective approximations greatly reduces the computational effort involved, the most important being the use of a second-order perturbation expression for the energy and an approximate expression for the elements of the Hessian. As a result, the overall scheme scales very favourably with respect to the numbers of active electrons and of basis functions, making it suitable for the accurate study of large systems. Benchmark calculations are presented for the dissociation of LiH(X¹Σ⁺) and Li₂(X¹Σ⁺ _g ) using a highly compact four-configuration wave function. Standard spin-coupled valence bond expansions in the same virtual space are required to be significantly larger before equivalent results are obtained. The results are shown to compare very favourably with full valence complete active space self-consistent field calculations using an identical basis, and binding energies are within 4% of the values obtained from full configuration interaction calculations in the same basis set. Received: 10 June 1997 / Accepted: 7 October 1997