At Least n – 1 Intersection Points in a Connected Family of n Unit Circles in the Plane

Let C be a family of n different unit circles in the plane. We show that C determines at least n - c intersection points, where c is the number of connected components in ∪_{C ∈ C}C. This proves a conjecture of A. Bezdek.     

Highly efficient antibody-catalyzed deuteration of carbonyl compounds

Antibody 38C2 efficiently catalyzes deuterium-exchange reactions at the alpha position of a variety of ketones and aldehydes, including substrates that have a variety of sensitive functional groups. In addition to the regio- and chemoselectivity of these reactions, the catalytic rates (kcat) and rate-enhancement values (kcat/kun) are among the highest values ever observed with catalytic antibodies. Comparison of the substrate range of the catalytic antibody with highly evolved aldolase enzymes, such as rabbit-muscle aldolase, highlights the much broader practical scope of the antibody, which accepts a wide range of substrates. The hydrogen-exchange reaction was used for calibration and mapping of the antibody active site. Isotope-exchange experiments with cycloheptanone reveal that the formation of the Schiff base species (as concluded from the 16O/18O exchange rate at the carbonyl oxygen) is much faster than the formation of the enamine intermediate (as concluded from the H/D exchange rate), and both steps are faster than the antibody-catalyzed aldol addition reaction.     

A versatile toolbox for variable DNA functionalization at high density

To broaden the applicability of chemically modified DNAs in nano- and biotechnology, material science, sensor development, and molecular recognition, strategies are required for introducing a large variety of different modifications into the same nucleic acid sequence at once. Here, we investigate the scope and limits for obtaining functionalized dsDNA by primer extension and PCR, using a broad variety of chemically modified deoxynucleotide triphosphates (dNTPs), DNA polymerases, and templates. All natural nucleobases in each strand were substituted with up to four different base-modified analogues. We studied the sequence dependence of enzymatic amplification to yield high-density functionalized DNA (fDNA) from modified dNTPs, and of fDNA templates, and found that GC-rich sequences are amplified with decreased efficiency as compared to AT-rich ones. There is also a strong dependence on the polymerase used. While family A polymerases generally performed poorly on "demanding" templates containing consecutive stretches of a particular base, family B polymerases were better suited for this purpose, in particular Pwo and Vent (exo-) DNA polymerase. A systematic analysis of fDNAs modified at increasing densities by CD spectroscopy revealed that single modified bases do not alter the overall B-type DNA structure, regardless of their chemical nature. A density of three modified bases induces conformational changes in the double helix, reflected by an inversion of the CD spectra. Our study provides a basis for establishing a generally applicable toolbox of enzymes, templates, and monomers for generating high-density functionalized DNAs for a broad range of applications.     

Modified Eulerian–Lagrangian formulation for hydrodynamic modeling

We present the modified Eulerian–Lagrangian (MEL) formulation, based on non-divergent forms of partial differential balance equations, for simulating transport of extensive quantities in a porous medium. Hydrodynamic derivatives are written in terms of modified velocities for particles propagating phase and component quantities along their respective paths. The particles physically interpreted velocities also address the heterogeneity of the matrix and fluid properties. The MEL formulation is also implemented to parabolic Partial Differential Equations (PDE’s) as these are shown to be interchangeable with equivalent PDE’s having hyperbolic – parabolic characteristics, without violating the same physical concepts. We prove that the MEL schemes provide a convergent and monotone approximation also to PDE’s with discontinuous coefficients. An extension to the Peclet number is presented that also accounts for advective dominant PDE’s with no reference to the fluid velocity or even when this velocity is not introduced.In Sorek et al. [27], a mathematical analysis for a linear system of coupled PDE’s and an example of nonlinear PDE’s, proved that the finite difference MEL, unlike an Eulerian scheme, guaranties the absence of spurious oscillations. Currently, we present notions of monotone interpolation associated with the MEL particle tracking procedure and prove the convergence of the MEL schemes to the original balance equation also for discontinuous coefficients on the basis of difference schemes approximating PDE’s. We provide numerical examples, also with highly random fields of permeabilities and/or dispersivities, suggesting that the MEL scheme produces resolutions that are more consistent with the physical phenomenon in comparison to the Eulerian and the Eulerian–Lagrangian (EL) schemes.     

Aerobic Iron‐Based Cross‐Dehydrogenative Coupling Enables Efficient Diversity‐Oriented Synthesis of Coumestrol‐Based Selective Estrogen Receptor Modulators

An iron‐based cross‐dehydrogenative coupling (CDC) approach was applied for the diversity‐oriented synthesis of coumestrol‐based selective estrogen receptor modulators (SERMs), representing the first application of CDC chemistry in natural product synthesis. The first stage of the two‐step synthesis of coumestrol involved a modified aerobic oxidative cross‐coupling between ethyl 2‐(2,4‐dimethoxybenzoyl)acetate and 3‐methoxyphenol, with FeCl₃ (10 mol %) as the catalyst. The benzofuran coupling product was then subjected to sequential deprotection and lactonization steps, affording the natural product in 59 % overall yield. Based on this new methodology other coumestrol analogues were prepared, and their effects on the proliferation of the estrogen receptor (ER)‐dependent MCF‐7 and of the ER‐independent MDA‐MB‐231 breast cancer cells were tested. As a result, new types of estrogen receptor ligands having an acetamide group instead of the 9‐hydroxyl group of coumestrol were discovered. Both 9‐acetamido‐coumestrol and 8‐acetamidocoumestrol were found more active than the natural product against estrogen‐dependent MCF‐7 breast cancer cells, with IC₅₀ values of 30 and 9 nM , respectively.     

Erratum to: Preserving the activity of enzymes under harsh oxidizing conditions: sol–gel entrapped alkaline phosphatase exposed to bromine

Chemically reactive sol–gel matrices hold the ability of protecting entrapped enzymes from destruction by external harsh chemicals. We show this concept by exposing alkaline phosphatase (AlP) to a strong oxidizing agent—bromine. In solution, AlP is immediately destroyed by this oxidant. When AlP was entrapped in hybrid silica sol–gel materials carrying double bonds, the reactivity of AlP was preserved after exposure to bromine under conditions which totally destroy it in solution. The matrices studied were vinylated and allylated silicas, and their protectability was compared to n-alkylated silicas and to silica itself. For instance, the reactivity of AlP entrapped in allylated silica after exposure to 25.6 mM bromine solution is 40 times higher than its reactivity when entrapped in pure silica; and in solution the enzyme is totally destroyed at this concentration. Molecular level mechanisms for these observations are proposed.     

Structural elucidation of V‐type nerve agents by liquid chromatography/electrospray ionization mass spectrometry

V‐nerve agents present information‐poor spectra, both in GC‐EI‐MS and LC‐ESI‐MS/MS, with dominant fragments/product ions corresponding to the amine‐containing residue. Hence, derivatives/isomers with the same amine residue exhibit similar mass spectral patterns, leading to ambiguity in the phosphonate structure. We present a simple approach for their structural elucidation based on two complementary experiments: ESI‐MS/MS of the original compound, which provides information about the amine moiety, and ESI‐MS/MS of the phosphonic acid hydrolysis products generated by N‐iodosuccinimide, which provides ions' characteristic of the phosphonate structure. This approach enables the structural elucidation of the original V‐agents with a higher degree of certainty.     

Shock waves in saturated thermoelastic porous media

The objective of this paper is to develop and present the macroscopic motion equations for the fluid and the solid matrix, in the case of a saturated porous medium, in the form of coupled, nonlinear wave equations for the fluid and solid velocities. The nonlinearity in the equations enables the generation of shock waves. The complete set of equations required for determining phase velocities in the case of a thermoelastic solid matrix, includes also the energy balance equation for the porous medium as a whole, as well as mass balance equations for the two phase. In the special case of a rigid solid matrix, the wave after an abrupt change in pressure propagates only through the fluid.     

Two-dimensional adaptive Eulerian-Lagrangian method for mass transport with spatial velocity distribution

A Eulerian-Lagrangian scheme is used to solve the two-dimensional advection-dispersion equation. Concentration and its partial differential operator are decomposed into advection and dispersion terms. Thus, advection is formally decoupled from dispersion and solved by continuous forward particle tracking. Dispersion is handled by implicit finite elements on a fixed Eulerian grid. Translation of steep gradients of concentration in advection-dominated flow regimes, is done without numerical distortion. Continuous spatial distribution of velocities are evaluated by using Galerkin's approach in conjunction with Darcy's law based on hydraulic input data from each element. The method was implemented on coarse FE grid with linear shape functions, demonstrating no over/under shooting and practically no numerical dispersion. Simulations, covering a wide range of Peclet numbers, yield high agreement with analytic and practical results.