Direct Derivation of Free Energies of Membrane Deformation and Other Solvent Density Variations From Enhanced Sampling Molecular Dynamics

We report a methodology to calculate the free energy of a shape transformation in a lipid membrane directly from a molecular dynamics simulation. The bilayer need not be homogeneous or symmetric and can be atomically detailed or coarse grained. The method is based on a collective variable that quantifies the similarity between the membrane and a set of predefined density distributions. Enhanced sampling of this “Multi-Map” variable re-shapes the bilayer and permits the derivation of the corresponding potential of mean force. Calculated energies thus reflect the dynamic interplay of atoms and molecules, rather than postulated effects. Evaluation of deformations of different shape, amplitude, and range demonstrates that the macroscopic bending modulus assumed by the Helfrich–Canham model is increasingly unsuitable below the 100-Å scale. In this range of major biological significance, direct free-energy calculations reveal a much greater plasticity. We also quantify the stiffening effect of cholesterol on bilayers of different composition and compare with experiments. Lastly, we illustrate how this approach facilitates analysis of other solvent reorganization processes, such as hydrophobic hydration. Published 2019. This article is a U.S. Government work and is in the public domain in the USA.     

Interaction with plasmid DNA of Hoechst-TACN conjugates

ABSTRACT

A new family of conjugates between the Hoechst minor groove binder and the TACN metal ion ligand connected through hydrophobic alkyl or more hydrophilic oxyethyl linkers of different length has been prepared. The linkers are connected to the convex side of the Hoechst skeleton thus forcing the TACN ligand to exit the minor groove and interact with the phosphate backbone of DNA. The conjugates preserve the binding mode of Hoechst with an affinity influenced by the nature of the linker, the more hydrophobic being the more efficient. Coordination of Cu(II) or Zn(II) poorly affect these parameters. Nevertheless, the Zn(II) complex bearing a C6 linear alkyl linker induced a modest but reproducible acceleration of the hydrolytic cleavage of DNA which can be ascribed to the ability of the conjugate to deliver the hydrolytic subunit close to the DNA phosphodiester bonds.     

Deep‐ultraviolet laser ablation electrospray ionization mass spectrometry

A 193‐nm wavelength deep ultraviolet laser was used for ambient laser ablation electrospray ionization mass spectrometry of biological samples. A pulsed ArF excimer laser was used to ablate solid samples, and the resulting plume of the desorbed material merged with charged electrospray droplets to form ions that were detected with a quadrupole time‐of‐flight mass spectrometer. Solutions containing peptide and protein standards up to 66‐kDa molecular weight were deposited on a metal target, dried, and analyzed. No fragmentation was observed from peptides and proteins as well as from the more easily fragmented vitamin B₁₂ molecule. The mass spectra contained peaks from multiply charged ions that were identical to conventional electrospray. Deep UV laser ablation of tissue allowed detection of lipids from untreated tissue. The mechanism of ionization is postulated to involve absorption of laser energy by a fraction of the analyte molecules that act as a sacrificial matrix or by residual water in the sample.     

Decay Estimates for Solutions of Porous Medium Equations with Advection

In this paper, we show that bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the form

$$ u_{t} + \operatorname{div}f(x,t,u) = \operatorname{div}\bigl( |u|^{\alpha } \nabla u\bigr), \quad x \in \mathbb{R}^{n} , \ t > 0, $$

where \(\alpha > 0 \) is constant, decrease to zero, under fairly broad conditions on the advection flux \(f\). Besides that, we derive a time decay rate for these solutions.

     

Pyroxene inclusions in paleo-Christian mosaic tesserae: a new tool for constraining the glass manufacturing temperature

The mineral inclusions of two orange glass tesserae from paleo-Christian mosaics were investigated in order to derive the melting temperature reached during their production (sourced from Padua and Vicenza, Veneto region, Italy). In particular, clinopyroxene crystals were studied by single-crystal X-ray diffraction and electron microprobe WDS analysis. The crystals show C2/c symmetry, typical of disordered Ca/Na and Mg/Al distributions indicating high-temperature of formation (>700°C). The cation site populations were obtained by combining results from the two experimental techniques enabled us to derive the following stoichiometric formula:

Multivariate Hierarchical Copulas with Shocks

A transformation to obtain new multivariate hierarchical copulas, starting with an arbitrary copula, is introduced. In addition to the hierarchical structure, the presented construction principle explicitly supports singular components. These may be interpreted as the effect of local or global shocks to the underlying random variables. A large spectrum of dependence patterns can be achieved by the presented transformation, which seems promising for practical applications. Moreover, copulas arising from this construction are similarly admissible with respect to analytical tractability and sampling routines as the original copula. Finally, several well-known families of copulas may be interpreted as special cases.     

Design of a Composite Membrane with Patches

This paper is concerned with minimization and maximization problems of eigenvalues. The principal eigenvalue of a differential operator is minimized or maximized over a set which is formed by intersecting a rearrangement class with an affine subspace of finite co-dimension. A solution represents an optimal design of a 2-dimensional composite membrane Ω, fixed at the boundary, built out of two different materials, where certain prescribed regions (patches) in Ω are occupied by both materials. We prove existence results, and present some features of optimal solutions. The special case of one patch is treated in detail.