Existence and positivity of solutions of a fourth-order nonlinear PDE describing interface fluctuations

We study the partial differential equation which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S¹. We establish existence, uniqueness, and regularity of solutions, locally in time, for positive initial data in H¹(S¹), and prove the existence of several families of Lyapunov functions for the evolution. From the latter we establish a sharp connection between existence globally in time and positivity preservation: if [0], T*) is a maximal half open interval of existence for a positive solution of the equation, with T* < ∞, then lim_tT* w(t,·) exists in C¹(S¹) but vanishes at some point. We show further that if T* > (1 + √3)/16π² √3 then T* = ∞ and lim_t∞ w(t,.) exists and is constant. We discuss also some explicit solutions and propose a generalization to higher dimensions. © 1994 John Wiley & Sons, Inc.     

Development of Molecular Mechanics Torsion Parameters for alpha,beta-Cyclopropyl Ketones and Conformational Analysis of Bicyclo[m.1.0]alkan-2-ones

Conformations of cyclopropyl methyl ketone have been studied using ab initio methods in an effort to quantify the effects of conjugative overlap between the cyclopropane ring and an adjacent ketone carbonyl. Results were comparable with previous experimental and theoretical studies. Cyclopropyl methyl ketone exhibits a global energy minimum in the s-cis conformer and a local energy minimum near the s-trans conformer. The potential energy curve obtained was used to derive torsion parameters which were employed in molecular mechanics studies of the conformations of the set of bicyclo[m.1.0]alkan-2-ones having larger ring sizes from five- to 16-membered. Similar conformations for the cyclopropyl ketone substructure are observed for all the medium and large ring systems examined. Possible synthetic ramifications of local conformational anchoring by this functional group array are discussed.     

Newton's method and periodic solutions of nonlinear wave equations

We prove the existence of periodic solutions of the nonlinear wave equation satisfying either Dirichlet or periodic boundary conditions on the interval [O, π]. The coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation. Using a version of Newton's method, we show that this equation has solutions provided the nonlinearity g(x, u) satisfies certain generic conditions of nonresonance and genuine nonlinearity. © 1993 John Wiley & Sons, Inc.     

Atomic force microscopy study for supermolecular microstructures in side-chain liquid crystalline polymer films

Atomic force microscopy (AFM) is employed to study the supermolecular microstructures of disclinations and inversion walls in thin films of a smectic side-chain liquid crystalline polymer. Two-dimensional nanostripes are formed in thin films when the material enters the smectic phase. A possible mechanism for their formation is also suggested. The stripes run parallel to the local director and thus decorate the overall patterns of nematic director around the disclinations and inversion walls. Three patterns involving radial, spiral, and circular supermolecular microstructures of a positive disclination with s = +1 and one hyperbolic pattern of a negative disclination with s = -1 are observed. The cores of all these microstructures exhibit circular dark centers in AFM height images. It is found that the specific configurations of a pair of (+1, -1) disclinations form during the late stage of annihilation and inversion walls always separate a pair of (+1, +1) disclinations. The analysis on the director fields around disclinations and inversion walls shows that the bend and splay elastic constants are of the same order of magnitude in the side-chain liquid crystalline polymer.     

Derivatives of 2,4-diamino-6-methylpteridine

Eighteen derivatives of 2,4-diamino-6-methylpteridine related to methotrexate and aminopterin have been prepared from 6-(bromomethyl)-2,4-pteridinediamine by nucleophilic displacement reactions. None of these compounds showed any antileukemic acitivity.     

Isotactic-b-syndiotactic stereoblock poly(methyl methacrylate) by chiral metallocene/Lewis acid hybrid catalysts

Stereoblock polymerization with chiral ansa-metallocene/strong Lewis acid hybrid catalysts capable of switching stereospecificity of the methyl methacrylate polymerization produces the highly stereoregular isotactic-b-syndiotactic stereoblock poly(methyl methacrylate).     

Nonpeptide inhibitors of cathepsin G: optimization of a novel beta-ketophosphonic acid lead by structure-based drug design

The serine protease cathepsin G (EC 3.4.21.20; Cat G), which is stored in the azurophilic granules of neutrophils (polymorphonuclear leukocytes) and released on degranulation, has been implicated in various pathological conditions associated with inflammation. By employing high-throughput screening, we identified beta-ketophosphonic acid 1 as a moderate inhibitor of Cat G (IC(50) = 4.1 microM). We were fortunate to obtain a cocrystal of 1 with Cat G and solve its structure by X-ray crystallography (3.5 A). Structural details from the X-ray analysis of 1.Cat G served as a platform for optimization of this lead compound by structure-based drug design. With the aid of molecular modeling, substituents were attached to the 3-position of the 2-naphthyl ring of 1, which occupies the S1 pocket of Cat G, to provide an extension into the hydrophobic S3 region. Thus, we arrived at analogue 7 with an 80-fold potency improvement over 1 (IC(50) = 53 nM). From these results, it is evident that the beta-ketophosphonic acid unit can form the basis for a novel class of serine protease inhibitors.     

Using molecular dynamics simulations to identify the key factors responsible for chiral recognition by an amino acid-based molecular micelle

Molecular dynamics (MD) simulations were used to investigate the binding of six chiral compounds to the amino acid-based molecular micelle (MM) poly-(sodium undecyl-(L)-leucine-leucine) or poly(SULL). The MM investigated is used as a chiral selector in capillary electrophoresis. The project goal was to characterize the chiral recognition mechanism in these separations and to move toward predictive models to identify the best amino acid-based MM for a given separation. Poly(SULL) was found to contain six binding sites into which chiral compounds could insert. Four sites had similar sizes, shapes, and electrostatic properties. Enantiomers of alprenolol, propranolol, 1,1′-bi-2-naphthyl-2,2′-diyl hydrogen phosphate, 1,1′-bi-2-naphthol, chlorthalidone, or lorazepam were separately docked into each binding pocket and MD simulations with the resulting intermolecular complexes were performed. Solvent-accessible surface area calculations showed the compounds preferentially associated with binding sites where they penetrated into the MM core and shielded their non-polar atoms from solvent. Furthermore, with five of the six compounds the enantiomer with the most favorable free energy of MM association also experienced the most favorable intermolecular hydrogen bonding interactions with the MM. This result suggests that stereoselective intermolecular hydrogen bonds play an important role in chiral discrimination in separations using amino acid-based MMs.GRAPHICAL ABSTRACT     

Folic acid analogs. Modifications in the benzene-ring region. 5. 2′,6′-diazafolic acid

The synthesis of 2′,6′-diazafolic acid was accomplished by the condensation of 2-acetylamino-4(3H)pteridinone-6-earboxaldehyde (XIV) with diethyl N-[(5-amino-2-pyrimidinyl)carbonyl]-L-glutamate (XIII) followed by reduction of the anil double bond and alkaline hydrolylic cleavage of the N²-acetyl and ethyl ester protecting groups. Intermediate XIII was prepared by starling with 5-nitro-2-styrylpyrimidine (VI) and proceeding via 5-arnino-2-styrylpyrimidine (IX). The henzyloxycarbonyl derivative of IX was prepared and oxidized to the corresponding 5-benzyloxycarbonylaminopyrimidine-2-carboxylic acid (XI). The coupling of XI with diethyl L-glutamate followed by hydrogenolysis of the henzyloxycarbonyl function afforded the desired intermediate XIII. 2′,6′-Diazafolic acid was a potent inhibitor of Streptococcus faecium and displayed marginal activity against leukemia 1,1210 in mice.