Benchmark calculations of proton affinities and gas-phase basicities of molecules important in the study of biological phosphoryl transfer

Benchmark calculations of proton affinities and gas-phase basicities of molecules most relevant to biological phosphoryl transfer reactions are presented and compared with available experimental results. The accuracy of proton affinity and gas-phase basicity results obtained from several multi-level model chemistries (CBS-QB3, G3B3, and G3MP2B3) and density-functional quantum models (PBE0, B1B95, and B3LYP) are assessed and compared. From these data, a set of empirical bond enthalpy, entropy, and free energy corrections are introduced that considerably improve the accuracy and predictive capability of the methods. These corrections are applied to the prediction of proton affinity and gas-phase basicity values of important biological phosphates and phosphoranes for which experimental data does not currently exist. Comparison is made with results from semiempirical quantum models that are commonly employed in hybrid quantum mechanical/molecular mechanical simulations. Data suggest that the design of improved semiempirical quantum models with increased accuracy for relative proton affinity values is necessary to obtain quantitative accuracy for phosphoryl transfer reactions in solution, enzymes, and ribozymes.     

Hybrid QM/MM study of thio effects in transphosphorylation reactions

Results of a series of hybrid quantum mechanical/molecular mechanical (QM/MM) activated dynamics simulations of thio effects in the transphosphorylation (methanolysis) of a 2'-ribose, 5'-methyl phosphate-diester under basic conditions are presented. Single and double substitutions in the nonbridging oxygen positions exhibit thio effects in accord with experimental data and show the existence of a stable intermediate. Thio substitution at the 2' and 5' positions resulted in reactions having a single transition state with increased and decreased free energy barriers, respectively, relative to the unsubstituted reaction. In all of the reactions except for the 5' substitution, the rate-limiting step corresponds to exocyclic cleavage. In the 5' substitution reaction, the rate-limiting step corresponds to endocyclic cleavage and shows a considerable reverse thio effect, in accord with experimental observations of phosphates with enhanced leaving groups. Thio substitution at the 3' position results in a mild reverse thio effect that arises from electronic stabilization of the dianionic transition state. The results presented here provide an important step toward the development and application of new hybrid QM/MM methods that, combined with experiment, may provide a detailed picture of the molecular mechanisms of RNA catalysis.     

High-order discretization schemes for biochemical applications of boundary element solvation and variational electrostatic projection methods

A series of high-order surface element discretization schemes for variational boundary element methods are introduced. The surface elements are chosen in accord with angular quadrature rules for integration of spherical harmonics. Surface element interactions are modeled by Coulomb integrals between spherical Gaussian functions with exponents chosen to reproduce the exact variational energy and Gauss's law for a point charge in a spherical cavity. The present work allows high-order surface element expansions to be made for variational methods such as the conductorlike screening model for solvation and the variational electrostatic projection method for generalized solvent boundary potentials in molecular simulations.     

Polypeptide-templated synthesis of hexagonal silica platelets

Several studies have demonstrated the use of biomimetic approaches in the synthesis of a variety of inorganic materials. Poly-L-lysine (PLL) promotes the precipitation of silica from a silicic acid solution within minutes. The molecular weight of PLL was found to affect the morphology of the resulting silica precipitate. Larger-molecular weight PLL produced hexagonal silica platelets, whereas spherical silica particles were obtained using low-molecular weight PLL. Here we report on the polypeptide secondary-structure transition that occurs during the silicification reaction. The formation of the hexagonal silica platelets is attributed to the PLL helical chains that are formed in the presence of monosilicic acid and phosphate ions. Hexagonal PLL crystals can also serve as templates in directing the growth of the silica in a manner that generates a largely mesoporous silica phase that is oriented with respect to the protein crystal template.     

Pseudorotation barriers of biological oxyphosphoranes: a challenge for simulations of ribozyme catalysis

Pseudorotation reactions of biologically relevant oxyphosphoranes were studied by using density functional and continuum solvation methods. A series of 16 pseudorotation reactions involving acyclic and cyclic oxyphosphoranes in neutral and monoanionic (singly deprotonated) forms were studied, in addition to pseudorotation of PF5. The effect of solvent was treated by using three different solvation models for comparison. The barriers to pseudorotation ranged from 1.5 to 8.1 kcal mol(-1) and were influenced systematically by charge state, apicophilicity of ligands, intramolecular hydrogen bonding, cyclic structure and solvation. Barriers to pseudorotation for monoanionic phosphoranes occur with the anionic oxo ligand as the pivotal atom, and are generally lower than for neutral phosphoranes. The OCH3 groups were observed to be more apicophilic than OH groups, and hence pseudorotations that involve axial OCH3/equatorial OH exchange had higher reaction and activation free energy values. Solvent generally lowered barriers relative to the gas-phase reactions. These results, together with isotope 18O exchange experiments, support the assertion that dianionic phosphoranes are not sufficiently long-lived to undergo pseudorotation. Comparison of the density functional results with those from several semiempirical quantum models highlight a challenge for new-generation hybrid quantum mechanical/molecular mechanical potentials for non-enzymatic and enzymatic phosphoryl transfer reactions: the reliable modeling of pseudorotation processes.     

Unique toroidal morphology from composition and sequence control of triblock copolymers

The mechanism by which the unique toroidal supramolecular assemblies were formed for triblock copolymers of acrylic acid (AA), methyl acrylate (MA), and styrene (S), PAA99-b-PMA73-b-PS66, was probed in this study by investigating the influences of the block copolymer compositions and sequences. Two triblock copolymers, PAA99-b-PMA73-b-PS66 and PAA99-b-PS76-b-PMA62, and two diblock copolymers, PAA99-b-PMA155 and PAA99-b-PS133, were studied under experimental solution-state conditions that involved a range of solvent/nonsolvent (tetrahydrofuran/water) compositions, each in the presence of 2,2'-(ethylenedioxy)bis(ethylamine). The resulting morphologies were determined by transmission electron microscopy. The failures to afford toroidal supramolecular assemblies from both diblock copolymers having comparable lengths of the total hydrophobic chain segment, either entirely PMA or entirely PS, and from the triblock copolymer having a reversed connection sequence for the hydrophobic (PMA and PS) segments demonstrate the unique self-assembly behaviors of triblock copolymers and the importance of the block copolymer sequence.     

De novo design of strand-swapped beta-hairpin hydrogels

De novo designed peptides, capable of undergoing a thermally triggered beta-strand-swapped self-assembly event leading to hydrogel formation were prepared. Strand-swapping peptide 1 (SSP1) incorporates an exchangeable beta-strand domain composed of eight residues appended to a nonexchangeable beta-hairpin domain. CD shows that, at pH 9 and temperatures less than 35 degrees C, this peptide adopts a random coil conformation, rendering it soluble in aqueous solution. On heating to 37 degrees C or greater, SSP1 adopts a beta-hairpin that displays an exchangeable beta-strand region. The exchangeable strand domain participates in swapping with the exchangeable domain of another peptide, affording a strand-swapped dimer. These dimers further assemble into fibrils that define the hydrogel. A second peptide (SSP2) containing an exchangeable strand composed of only four residues was also studied. Microscopy and scattering data show that the length of the exchangeable domain directly influences the fibril nanostructure and can be used as a design element to construct either twisted (SSP1) or nontwisted (SSP2) fibril morphologies. CD, FTIR, and WAXS confirm that both peptides adopt beta-sheet secondary structure when assembled into fibrils. Fibril dimensions, as measured by TEM, AFM, and SANS indicate a fibril diameter of 6.4 nm, a height of 6.0 nm, and a pitch of 50.4 nm for the twisted SSP1 fibrils. The nontwisted SSP2 fibrils are 6.2 nm in diameter and 2.5 nm in height. Oscillatory rheology, used to measure bulk hydrogel rigidity, showed that the gel composed of the nontwisted fibrils is more mechanically rigid (517 Pa at 6 rad/s) than the gel composed of twisted fibrils (367 Pa at 6 rad/s). This work demonstrates that beta-strand-swapping can be used to fabricate biomaterials with tunable fibril nanostructure and bulk hydrogel rheological properties.     

Atom efficient cyclotrimerization of dimethylcyanamide catalyzed by aluminium amide: a combined experimental and theoretical investigation

A novel method for the cyclotrimerization of dimethylcyanamide to form hexamethylmelamine has been developed using an aluminium amide catalyst; detailed DFT modelling of the catalytic cycle supports a triple insertion, nucleophilic ring closure, deinsertion mechanism.     

Uniform partitions of frames of exponentials into Riesz sequences

The Feichtinger conjecture, if true, would have as a corollary that for each set E⊂[0,1] and Λ⊂Z, there is a partition Λ₁,…,ΛN of Z such that for each 1?i?N, is a Riesz sequence. In this paper, sufficient conditions on sets E⊂[0,1] and Λ⊂R are given so that can be uniformly partitioned into Riesz sequences.     

A decomposition theorem for frames and the Feichtinger Conjecture

In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in -Algebras. We will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. This construction is then used to answer two open problems concerning the Feichtinger Conjecture: 1. The Feichtinger Conjecture is equivalent to the conjecture that every unit norm Bessel sequence is a finite union of frame sequences. 2. Every unit norm Bessel sequence is a finite union of sets each of which is -independent for -sequences.