Second phase spinodal decomposition for the Cahn-Hilliard-Cook equation

We consider the dynamics of a nonlinear partial differential equation perturbed by additive noise. Assuming that the underlying deterministic equation has an unstable equilibrium, we show that the nonlinear stochastic partial differential equation exhibits essentially linear dynamics far from equilibrium. More precisely, we show that most trajectories starting at the unstable equilibrium are driven away in two stages. After passing through a cylindrical region, most trajectories diverge from the deterministic equilibrium through a cone-shaped region which is centered around a finite-dimensional subspace corresponding to strongly unstable eigenfunctions of the linearized equation, and on which the influence of the nonlinearity is surprisingly small.

This abstract result is then applied to explain spinodal decomposition in the stochastic Cahn-Hilliard-Cook equation on a domain . This equation depends on a small interaction parameter  , and one is generally interested in asymptotic results as  . Specifically, we show that linear behavior dominates the dynamics up to distances from the deterministic equilibrium which can reach  with respect to the -norm.

     

Synthesis,Biochemical Characterization,and Genetic Encoding of a 1,2,4-Triazole Amino Acid as an Acetyllysine Mimic for Bromodomains of the BET Family

Lysine acetylation is a charge-neutralizing post-translational modification of proteins bound by bromodomains (Brds). A 1,2,4-triazole amino acid (ApmTri) was established as acetyllysine (Kac) mimic recruiting Brds of the BET family in contrast to glutamine commonly used for simulating this modification. Optimization of triazole substituents and side chain spacing allowed BET Brd recruitment to ApmTri-containing peptides with affinities similar to native substrates. Crystal structures of ApmTri-containing peptides in complex with two BET Brds revealed the binding mode which mirrored that of Kac ligands. ApmTri was genetically encoded and recombinant ApmTri-containing proteins co-enriched BRD3(2) from cellular lysates. This interaction was blocked by BET inhibitor JQ1. With genetically encoded ApmTri, biochemistry is now provided with a stable Kac mimic reflecting charge neutralization and Brd recruitment, allowing new investigations into BET proteins in vitro and in vivo.     

Polyketide Synthase-Mediated O-Methyloxime Formation in the Biosynthesis of the Oximidine Anticancer Agents

Bacterial trans-acyltransferase polyketide synthases (trans-AT PKSs) are modular megaenzymes that employ unusual catalytic domains to assemble diverse bioactive natural products. One such PKS is responsible for the biosynthesis of the oximidine anticancer agents, oxime-substituted benzolactone enamides that inhibit vacuolar H⁺-ATPases. Here, we describe the identification of the oximidine gene cluster in Pseudomonas baetica and the characterization of four novel oximidine variants, including a structurally simpler intermediate that retains potent anticancer activity. Using a combination of in vivo, in vitro and computational approaches, we experimentally elucidate the oximidine biosynthetic pathway and reveal an unprecedented mechanism for O-methyloxime formation. We show that this process involves a specialized monooxygenase and methyltransferase domain and provide insight into their activity, mechanism and specificity. Our findings expand the catalytic capabilities of trans-AT PKSs and identify potential strategies for the production of novel oximidine analogues.     

Neutralizing the Impact of the Virulence Factor LecA from Pseudomonas aeruginosa on Human Cells with New Glycomimetic Inhibitors

Bacterial adhesion, biofilm formation and host cell invasion of the ESKAPE pathogen Pseudomonas aeruginosa require the tetravalent lectins LecA and LecB, which are therefore drug targets to fight these infections. Recently, we have reported highly potent divalent galactosides as specific LecA inhibitors. However, they suffered from very low solubility and an intrinsic chemical instability due to two acylhydrazone motifs, which precluded further biological evaluation. Here, we isosterically substituted the acylhydrazones and systematically varied linker identity and length between the two galactosides necessary for LecA binding. The optimized divalent LecA ligands showed improved stability and were up to 1000-fold more soluble. Importantly, these properties now enabled their biological characterization. The lead compound L2 potently inhibited LecA binding to lung epithelial cells, restored wound closure in a scratch assay and reduced the invasiveness of P. aeruginosa into host cells.     

Longitudinally Grafting of Graphene with Iron Phthalocyanine-based Porous Organic Polymer to Boost Oxygen Electroreduction

Iron phthalocyanine-based polymers (PFePc) are attractive noble-metal-free candidates for catalyzing oxygen reduction reaction (ORR). However, the low site-exposure degree and poor electrical conductivity of bulk PFePc restricted their practical applications. Herein, laminar PFePc nanosheets covalently and longitudinally linked to graphene (3D-G-PFePc) was prepared. Such structural engineering qualifies 3D-G-PFePc with high site utilization and rapid mass transfer. Thence, 3D-G-PFePc demonstrates efficient ORR performance with a high specific activity of 69.31 μA cm⁻², a high mass activity of 81.88 A g⁻¹, and a high turnover frequency of 0.93 e s⁻¹ site⁻¹ at 0.90 V vs. reversible hydrogen electrode in O₂-saturated 0.1 M KOH, outperforming the lamellar PFePc wrapped graphene counterpart. Systematic electrochemical analyses integrating variable-frequency square wave voltammetry and in situ scanning electrochemical microscopy further underline the rapid kinetics of 3D-G-PFePc towards ORR.     

Chemical modification of colloidal masks for nanolithography

A method is presented to tune the holes in colloidal masks used for nanolithography. Using a simple wet-chemical method, a thin layer of silica is grown on masks of silica particles. The size of the holes is controlled by the amount of tetraethoxysilane (TEOS) added. More accurate tuning of the hole size is possible in the presence of a calibrated seed dispersion of silica colloids. We demonstrate modified masks that were used to create arrays of metal nanoparticles with a size ranging from 400 nm, for unmodified masks, down to tens of nanometers. The method is easy-to-use, fast, and inexpensive.     

On pattern transfer in replica molding

Nano- and micromolding of elastic materials produces smoothed replicas of the mold structures. This limits the technique's resolution. Here we identified surface tension as the cause of smoothing and derived explicit equations for calculating molded feature shapes. The characteristic length scale for smoothing is given by the ratio of the interface tension to Young's modulus of the molded material. This approach offers the possibility to correct for the smoothing caused by surface tension during mold design. Moreover, it can be exploited to measure interface tension.     

Pore-filling-dependent selectivity effects in the vapor-phase separation of xylene isomers on the metal-organic framework MIL-47

Vapor-phase adsorption and separation of the C8 alkylaromatic components p-xylene, m-xylene, o-xylene, and ethylbenzene on the metal-organic framework MIL-47 have been studied. Low coverage Henry adsorption constants and adsorption enthalpies were determined using the pulse chromatographic technique at temperatures between 230 and 290 degrees C. The four C8 alkylaromatic components have comparable Henry constants and adsorption enthalpies. Adsorption isotherms of the pure components were determined using the gravimetric technique at 70, 110, and 150 degrees C. The adsorption capacity and steepness of the isotherms differs among the components and are strongly temperature dependent. Breakthrough experiments with several binary mixtures were performed at 70-150 degrees C and varying total hydrocarbon pressure from 0.0004 to 0.05 bar. Separation of the different isomers could be achieved. In general, it was found that the adsorption selectivity increases with increasing partial pressure or degree of pore filling. The separation at a high degree of pore filling in the vapor phase is a result of differences in packing modes of the C8 alkylaromatic components in the pores of MIL-47.     

Charge transfer reactions along a supramolecular redox gradient

A rotaxane scaffold is used to align three photo/electroactive units along a supramolecular redox gradient leading to a cascade of through-space charge transfer reactions.     

Application of Quasi-Monte Carlo Methods to Elliptic PDEs with Random Diffusion Coefficients: A Survey of Analysis and Implementation

This article provides a survey of recent research efforts on the application of quasi-Monte Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion coefficients. It considers and contrasts the uniform case versus the lognormal case, single-level algorithms versus multi-level algorithms, first-order QMC rules versus higher-order QMC rules, and deterministic QMC methods versus randomized QMC methods. It gives a summary of the error analysis and proof techniques in a unified view, and provides a practical guide to the software for constructing and generating QMC points tailored to the PDE problems. The analysis for the uniform case can be generalized to cover a range of affine parametric operator equations.