On wavelets interpolated from a pair of wavelet sets

We show that any wavelet, with the support of its Fourier transform small enough, can be interpolated from a pair of wavelet sets. In particular, the support of the Fourier transform of such wavelets must contain a wavelet set, answering a special case of an open problem of Larson. The interpolation procedure, which was introduced by X. Dai and D. Larson, allows us also to prove the extension property.

     

Poly(L‐lysine) and clay nanocomposite with desired matrix secondary structure: Effects of polypeptide molecular weight

Nanocomposites (NC) were formed using cationic poly(L ‐lysine) (PLL), a semicrystalline polypeptide, that was reinforced by sodium montmorillonite (MMT) clay via solution intercalation technique. By varying solution conditions such as pH, temperature, and polypeptide concentration in the presence of clay platelets, the secondary structure of PLL was controllably altered into α‐helical, β‐sheet, and random coil. The high molecular weight polypeptide shows a strong propensity to fold into the β‐sheet structure when cast as films, irrespective of the initial secondary structure in solution. Nanocomposite local morphology confirms intercalated MMT platelets with PLL over a wide range of compositions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 239–252, 2007.     

Spectroscopic properties of tyrosyl radicals in dipeptides

Redox-active tyrosine residues play important roles in long-distance electron reactions in enzymes, including prostaglandin H synthase, galactose oxidase, ribonucleotide reductase, and photosystem II. Magnetic resonance and vibrational spectroscopy provide methods with which to study the structures of redox-active amino acids in proteins. In this report, ultraviolet photolysis was used to generate tyrosyl radicals from polycrystalline tyrosinate or dipeptides, and the structure of the radical was investigated with EPR and reaction-induced FT-IR spectroscopy at 77 K. Photolysis at 77 K is expected to generate a neutral tyrosyl radical through oxidation of the aromatic ring. EPR and FT-IR results obtained from (13)C-labeled tyrosine were consistent with that expectation. Surprisingly, labeling of the tyrosyl amino group with (15)N also resulted in isotope-shifted bands in the photolysis spectrum. The force constant of a NH deformation mode increased when the tyrosyl radical was generated. These data suggest an interaction between the pi system of the tyrosyl radical and the amino group. In spectra acquired from the dipeptides, evidence for a sequence-dependent interaction between the tyrosyl radical and the amide bond of the dipeptide was also obtained. We postulate that perturbation of the amino or the amide/imide groups may occur through a spin polarization mechanism, which is indirectly detected as a change in NH force constant. This conclusion is supported by density functional calculations, which suggest a conformationally sensitive delocalization of spin density onto the amino and carboxylate groups of the tyrosyl radical. These experiments provide a step toward a detailed spectral interpretation for protein-based tyrosyl radicals.     

Theoretical studies of dissociative phosphoryl transfer in interconversion of phosphoenolpyruvate to phosphonopyruvate: solvent effects, thio effects, and implications for enzymatic reactions

The conversion of phosphoenolpyruvate (PEP) to phosphonopyruvate (P-pyr) is catalyzed by PEP mutase via a dissociative mechanism. In this work, we investigate the uncatalyzed reaction using ab initio methods, density functional theory, and the semiempirical MNDO/d method. Comparisons of geometries and relative energies of stationary points (minima and transition states) with density functional results indicate that the semiempirical method is reasonably accurate. Solvent effects are examined using implicit solvent models, including the recently extended smooth conductor-like screening model. Due to the large negative charge carried by the system, solvation is found to drastically alter the location and energy of stationary points along the dissociative reaction pathways. The influence of substituting a nonbridging phosphoryl oxygen by sulfur (thio effects) was also investigated. Implications of these results for the enzymatic reaction are discussed.     

Variational electrostatic projection (VEP) methods for efficient modeling of the macromolecular electrostatic and solvation environment in activated dynamics simulations

New methods for the calculation of electrostatic interactions between the active dynamical region and surrounding external solvated macromolecular environment in hybrid quantum mechanical/molecular mechanical (QM/MM) simulations are presented. The variational electrostatic projection (VEP) method, and related variational reverse-mapping procedure (VEP-RVM) utilize an expansion in Gaussian surface elements for representation of electrostatic interactions. The use of a discretized surface that surrounds the active dynamical region greatly reduces the number of interactions with the particles of the external environment. The methods are tested on two catalytic RNA systems: the hammerhead and the hairpin ribozymes. It is shown that with surface elements numbering from 302 to 1202 points the direct VEP and VEP-RVM methods are able to obtain relative force errors in the range of 0.5-0.05% and 0.09-0.0001%, respectively, using a 4.0 A projection buffer. These results are encouraging and provide an essential step in the development of new variational macromolecular solvent-boundary methods for QM/MM calculations of enzyme reactions.     

Complete basis set extrapolated potential energy, dipole, and polarizability surfaces of alkali halide ion-neutral weakly avoided crossings with and without applied electric fields

Complete basis set extrapolations of alkali halide (LiF, LiCl, NaF, NaCl) energy, dipole, and polarizability surfaces are performed with and without applied fields along the internuclear axis using state-averaged multireference configuration interaction. Comparison between properties (equilibrium separation, dissociation energy, crossing distance, diabatic coupling constant, dipole, and polarizability) derived from the extrapolated potential energy (or dipole) surfaces are made with those obtained from direct extrapolation from the basis set trends. The two extrapolation procedures are generally found to agree well for these systems. Crossing distances from this work are compared to those of previous work and values obtained from the Rittner potential. Complete basis set extrapolated crossing distances agree well with those derived from the Rittner potential for LiF, but were significantly larger for LiCl, NaF, and NaCl. The results presented here serve as an important set of benchmark data for the development of new-generation many-body force fields that are able to model charge transfer.     

Charged polypeptide vesicles with controllable diameter

We report the preparation and characterization of charged, amphiphilic block copolypeptides that form stable vesicles and micelles in aqueous solution. Specifically, we prepared and studied the aqueous self-assembly of a series of poly(L-lysine)-b-poly(L-leucine) block copolypeptides, KxLy, where x ranged from 20 to 80 and y ranged from 10 to 30 residues, as well as the poly(L-glutamatic acid)-b-poly(L-leucine) block copolypeptide, E60L20. Furthermore, the vesicular assemblies show dynamic properties, indicating a high degree of membrane fluidity. This characteristic provides stimuli-responsive properties to the vesicles and allows fine adjustment of vesicle size using liposome-based extrusion techniques. Vesicle extrusion also provides a straightforward means to trap solutes, making the vesicles promising biomimetic encapsulants.     

Disk morphology and disk-to-cylinder tunability of poly(acrylic acid)-b-poly(methyl acrylate)-b-polystyrene triblock copolymer solution-state assemblies

Disk and cylindrical micellar assemblies were formed through self-organization of poly(acrylic acid)-b-poly(methyl acrylate)-b-polystyrene (PAA-b-PMA-b-PS) amphiphilic triblock copolymers with organic diamines as counterions in water/ tetrahydrofuran (THF) solvent mixtures. The system was investigated by means of transmission electron microscopy and cryogenic transmission electron microscopy. It was found that the assembled-state morphologies could be modified by alteration of the type and concentration of cationic diamine counterion undergoing interaction with the negatively charged, polyelectrolyte PAA corona block, the relative amount of water in the water/THF mixture, and the hydrophobic block chain length. Multivalency of the organic amine counterion was critical for disk formation. It was further demonstrated that a single block copolymer underwent disc-to-cylindrical micellar transitions reversibly with variation in the relative water/THF ratio. The ability to form disks beginning from either THF-rich or water-rich solutions indicated that the disk morphology was thermodynamically stable and that THF was important in keeping the micellar structure from becoming kinetically frozen. The nanoassemblies were produced having low size dispersities and were stable for at least one month. Intermediate structures between disks and cylinders were also observed, indicating two distinct kinetic pathways between the two micelle structures.     

Synthesis and molecular and extended structures for a diaminonaphthalene-derived bis(amido)stannylene

The cyclic bis(amido)tin(II) compound Sn[1,8-((iPrN)2C10H6] (2) was isolated from the reaction of Li2[1,8-((iPrN)2C10H6] (1) and SnCl2. Solid-state structural analysis of 2 showed it to be a mononuclear species with a pyramidal Sn center as part of a nonplanar metallaheterocycle. The packing diagram of 2 revealed an extended one-dimensional head-to-tail chain structure with short intermolecular Sn/arene-C interactions. Computational examination of 2 (DFT/PW91 and MP2 with 6-31G* and 6-311G** basis functions) indicated that the optimum gas-phase structure of 2,which displays a Sn center in the plane of the naphthyl backbone with a slightly twisted metallaheterocycle, is approximately 24 kcal/mol lower in energy than the X-ray structure. The solid-state geometry of 2 is attributed to the intermolecular donation of the naphthalene pi-electrons to a Lewis acidic Sn center, which leads to the observed supramolecular structure. The crystal structure of 1 is also reported.     

Synthesis and structural investigation of N,N',N' '-trialkylguanidinato-supported zirconium(IV) complexes

The addition of 2 equiv of N,N',N' '-triisopropylguanidine (guanH(2)) to Zr(CH(2)Ph)(4) produced the bis(guanidinato)bis(benzyl)zirconium complex [((i)PrNH)C(N(i)Pr)(2)](2)Zr(CH(2)Ph)(2) (1). The mono(guanidinato) complex [((i)PrN)(2)C(NH(i)Pr)]ZrCl(3) (2) was accessible by the reaction of 2 equiv of guanH(2) with ZrCl(4). Guanidinium hydrochloride, [C(NH(i)Pr)(3)]Cl, is a byproduct of this reaction. When crystallized from THF, complex 2 was isolated as the THF adduct [((i)PrNH)C(N(i)Pr)(2)]ZrCl(3)(THF) (2-THF). The mixed cyclopentadienyl guanidinato complex [eta(5)-1,3-(Me(3)Si)(2)C(5)H(3)][((i)PrNH)C(N(i)Pr)(2)]ZrCl(2) (3) was prepared by treatment of [1,3-(Me(3)Si)(2)C(5)H(3)]ZrCl(3) with the in situ generated lithium triisopropylguanidinate salt. The reaction of guanH(2) with [1,3-(Me(3)Si)(2)C(5)H(3)]ZrMe(3) affords the dimethyl derivative [eta(5)-1,3-(Me(3)Si)(2)C(5)H(3)][((i)PrNH)C(N(i)Pr)(2)]ZrMe(2) (4). Definitive evidence for the molecular structures of these products is provided through single-crystal X-ray characterization of 1, 2-THF, and 3, which are presented. The extent of pi delocalization within the guanidinato ligand is discussed in the context of the metrical parameters obtained from these structural studies.