How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Molecular simulation to characterize the adsorption behavior of a fibrinogen gamma-chain fragment

Implants invoke inflammatory responses from the body even if they are chemically inert and nontoxic. It has been shown that a crucial precedent event in the inflammatory process is the spontaneous adsorption of fibrinogen (Fg) on implant surfaces, which is typically followed by the presence of phagocytic cells. Interactions between the phagocyte integrin Mac-1 and two short sequences within the fibrinogen gamma chain, gamma190-202 and gamma377-395, may partially explain phagocyte accumulation at implant surfaces. These two sequences are believed to form an integrin binding site that is inaccessible when Fg is in its soluble-state structure but then becomes available for Mac-1 binding following adsorption, presumably due to adsorption-induced conformational changes. The objective of this research was to theoretically investigate this possibility by using molecular dynamics simulations of the gamma-chain fragment of Fg over self-assembled monolayer (SAM) surfaces presenting different types of surface chemistry. The GROMACS software package was used to carry out the molecular simulations in an explicit solvation environment over a 5 ns period of time. The adsorption of the gamma-chain of fibrinogen was simulated on five types of SAM surfaces. The simulations showed that this protein fragment exhibits distinctly different adsorption behavior on the different surface chemistries. Although the trajectory files showed that significant conformational changes did not occur in this protein fragment over the time frame of the simulations, it was predicted that the protein does undergo substantial rotational and translational motions over the surface prior to stabilizing in various preferred orientations. This suggests that the kinetics of surface-induced conformational changes in a protein's structure might be much slower than the kinetics of orientational changes, thus enabling the principles of adsorption thermodynamics to be used to guide adsorbing proteins into defined orientations on surfaces before large conformational changes can occur. This finding may be very important for biomaterial surface design as it suggests that surface chemistry can potentially be used to directly control the orientation of adsorbing proteins in a manner that either presents or hides specific bioactive sites contained within a protein's structure, thereby providing a mechanism to control cellular responses to the adsorbed protein layer.     

Alkyl- and aryl-substituted corroles. 5. Synthesis, physicochemical properties, and X-ray structural characterization of copper biscorroles and porphyrin-corrole dyads

The synthesis and characterization of cofacial copper biscorroles and porphyrin-corroles linked by a biphenylenyl or anthracenyl spacer are described. The investigated compounds are represented as (BCA)Cu(2) and (BCB)Cu(2) in the case of the biscorrole (BC) derivatives and (PCA)Cu(2) and (PCB)Cu(2) in the case of porphyrin (P)-corrole (C) dyads, where A and B represent the anthracenyl and biphenylenyl bridges, respectively. A related monomeric corrole (Me(4)Ph(5)Cor)Cu and monomeric porphyrin (Me(2)Et(6)PhP)Cu that comprise the two halves of the porphyrin-corrole dyads were also studied. Electron spin resonance (ESR), (1)H NMR, and magnetic measurements data demonstrate that the copper corrole macrocycle, when linked to another copper corrole or copper(II) porphyrin, can be considered to be a Cu(III) complex in equilibrium with a Cu(II) radical species, copper(III) corrole being the main oxidation state of the corrole species at all temperatures. The cofacial orientation of (BCB)Cu(2), (BCA)Cu(2), and (PCB)Cu(2) was confirmed by X-ray crystallography. Structural data: (BCB)Cu(2)(C(110)H(82)N(8)Cu(2).3CDCl(3)), triclinic, space group P, a = 10.2550(2) A, b = 16.3890(3) A, c = 29.7910(8) A, alpha = 74.792(1) degrees , beta = 81.681(1) degrees , gamma = 72.504(2) degrees , Z = 2; (BCA)Cu(2)(C(112)H(84)N(8)Cu(2).C(7)H(8).1.5H(2)O), monoclinic, space group P 2(1)/c, a = 16.0870(4) A, b = 35.109(2) A, c = 19.1390(8) A, beta = 95.183(3) degrees , Z = 4; (PCB)Cu(2)(C(89)H(71)N(8)Cu(2).CHCl(3)), monoclinic, space group P2(1)/n, a = 16.7071(3) A, b = 10.6719(2) A, c = 40.8555(8) A, beta = 100.870(1) degrees , Z = 4. The two cofacial biscorroles, (BCA)Cu(2) and (BCB)Cu(2), both show three electrooxidations under the same solution conditions. The reduction of (BCA)Cu(2) involves a reversible electron addition to each macrocycle at the same potential of E(1/2) = -0.20 V although (BCB)Cu(2) is reversibly reduced in two steps to give first [(BCB)Cu(2)](-) and then [(BCB)Cu(2)](2)(-), each of which was characterized by ESR spectroscopy as containing a Cu(II) center. These latter electrode reactions occur at E(1/2) = -0.36 and -0.51 V versus a saturated calomel reference electrode. The half-reduced and fully reduced (BCB)Cu(2) show similar Cu(II) ESR spectra, and no evidence of a triplet signal is observed. The two well-separated reductions of (BCB)Cu(2) to give [(BCB)Cu(2)](2)(-) can be attributed to a stronger pi-pi interaction between the two macrocycles of this dimer as compared to those of (BCA)Cu(2). The copper porphyrin-corrole dyads, (PCA)Cu(2) and (PCB)Cu(2), show five reversible oxidations and two reversible reductions, and these potentials are compared with corresponding values for electrochemical reactions of the porphyrin and corrole monomers under the same solution conditions.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

Determination of the adsorption free energy for peptide-surface interactions by SPR spectroscopy

To understand and predict protein adsorption behavior, we must first understand the fundamental interactions between the functional groups presented by the amino acid residues making up a protein and the functional groups presented by the surface. Limited quantitative information is available, however, on these types of submolecular interactions. The objective of this study was therefore to develop a reliable method to determine the standard state adsorption free energy (delta Go ads) of amino acid residue-surface interactions using surface plasma resonance (SPR) spectroscopy. Two problems are commonly encountered when using SPR for peptide adsorption studies: the need to account for "bulk-shift" effects and the influence of peptide-peptide interactions at the surface. Bulk-shift effects represent the contribution of the bulk solute concentration to the SPR response that occurs in addition to the response due to adsorption. Peptide-peptide interactions, which are assumed to be zero for Langmuir adsorption, can greatly skew the isotherm shape and result in erroneous calculated values of delta Go ads. To address these issues, we have developed a new approach for the determination of delta Go ads using SPR that is based on the chemical potential. In this article, we present the development of this new approach and its application for the calculation of delta Go ads for a set of peptide-surface systems where the peptide has a host-guest amino acid sequence of TGTG-X-GTGT (where G and T are glycine and threonine residues and X represents a variable residue) and the surface consists of alkanethiol self-assembled monolayers (SAMs) with methyl (CH 3) and hydroxyl (OH) functionality. This new approach enables bulk-shift effects to be directly determined from the raw SPR versus peptide concentration data plots and the influence of peptide-peptide interaction effects to be minimized, thus providing a very straightforward and accurate method for the determination of delta Go ads for peptide adsorption. Further studies are underway to characterize delta Go ads for a large library of peptide-SAM combinations.     

Carboxylate ligands drastically enhance the rates of oxo exchange and hydrogen peroxide disproportionation by oxo manganese compounds of potential biological significance

To mimic the carboxylate-rich active site of the manganese catalases more closely we introduced carboxylate groups into dimanganese complexes in place of nitrogen ligands. The series of dimanganese(III,IV) complexes of tripodal ligands [Mn(2)(L)(2)(O)(2)](3+/+/-/3-) was extended from those of tpa (1) and H(bpg) (2) to those of H(2)(pda) (3) and H(3)(nta) (4) (tpa=tris-picolylamine, H(bpg)=bis-picolylglycylamine, H(2)(pda)=picolyldiglycylamine, H(3)(nta)=nitrilotriacetic acid). While 3 [Mn(2)(pda)(2)(O)(2)][Na(H(2)O)(3)] could be synthesized at -20 degrees C and characterized in the solid state, 4 [Mn(2)(nta)(2)(O)(2)](3-) could be obtained and studied only in solution at -60 degrees C. A new synthetic procedure for the dimanganese(III,III) complexes was devised, using stoichiometric reduction of the dimanganese(III,IV) precursor by the benzil radical with EPR monitoring. This enabled the preparation of the parent dimanganese(III,III) complex 5 [Mn(2)(tpa)(2)(O)(2)](ClO(4))(2), which was structurally characterized. The UV/visible, IR, EPR, magnetic, and electrochemical properties of complexes 1-3 and 5 were analyzed to assess the electronic changes brought about by the carboxylate replacement of pyridine ligands. The kinetics of the oxo ligand exchanges with labeled water was examined in acetonitrile solution. A dramatic effect of the number of carboxylates was evidenced. Interestingly, the influence of the second carboxylate substitution differs from that of the first one probably because this substitution occurs on an out-of-plane coordination while the former occurs in the plane of the [Mn(2)O(2)] core. Indeed, on going from 1 to 3 the exchange rate was increased by a factor of 50. Addition of triethylamine caused a rate increase for 1, but not for 3. The abilities of 1-3 to disproportionate H(2)O(2) were assessed volumetrically. The disproportionation exhibited a sensitivity corresponding to the carboxylate substitution. These observations strongly suggest that the carboxylate ligands in 2 and 3 act as internal bases.     

Temperature distribution and thermal-induced defects in photorefractive barium titanate crystals illuminated with intense cw or pulsed laser irradiations

The temperature distribution in a parallelepipedic crystal irradiated with a Gaussian repartition of light is calculated by solving the three-dimensional heat equation and taking into account the losses through the sides of the samples. The theoretical and experimental maps of temperature are satisfactorily compared. For barium titanate crystals, the resistance to intense cw laser (25.7 kW/mm² at 514.5 nm) and to Nd:YAG pulsed laser (peak power of 9.2 MW at 532 nm) is investigated. The defects induced by the irradiation are analysed. Under pulsed illumination, the damage threshold is found to be 0.54 GW/cm² in a nominally undoped BaTiO₃ and 0.44 GW/cm² in a rhodium-cobalt doped BaTiO₃ crystal. Received: 7 March 2000 / Revised version: 14 April 2000 / Published online: 16 August 2000