Moment-Based Approximations of Distributions Using Mixtures: Theory and Applications

There are a number of cases where the moments of a distribution are easily obtained, but theoretical distributions are not available in closed form. This paper shows how to use moment methods to approximate a theoretical univariate distribution with mixtures of known distributions. The methods are illustrated with gamma mixtures. It is shown that for a certain class of mixture distributions, which include the normal and gamma mixture families, one can solve for a p-point mixing distribution such that the corresponding mixture has exactly the same first 2p moments as the targeted univariate distribution. The gamma mixture approximation to the distribution of a positive weighted sums of independent central ² variables is demonstrated and compared with a number of existing approximations. The numerical results show that the new approximation is generally superior to these alternatives.     

SAMPL7 blind challenge: quantum–mechanical prediction of partition coefficients and acid dissociation constants for small drug-like molecules

The physicochemical properties of a drug molecule determine the therapeutic effectiveness of the drug. Thus, the development of fast and accurate theoretical approaches for the prediction of such properties is inevitable. The participation to the SAMPL7 challenge is based on the estimation of logP coefficients and pK_a values of small drug-like sulfonamide derivatives. Thereby, quantum mechanical calculations were carried out in order to calculate the free energy of solvation and the transfer energy of 22 drug-like compounds in different environments (water and n-octanol) by employing the SMD solvation model. For logP calculations, we studied eleven different methodologies to calculate the transfer free energies, the lowest RMSE value was obtained for the M06L/def2-TZVP//M06L/def2-SVP level of theory. On the other hand, we employed an isodesmic reaction scheme within the macro pK_a framework; this was based on selecting reference molecules similar to the SAMPL7 challenge molecules. Consequently, highly well correlated pK_a values were obtained with the M062X/6–311+G(2df,2p)//M052X/6–31+G(d,p) level of theory.

     

pH-induced structural transitions of caseins

Caseins are relatively small (molecular mass approximately 20 kDa), unstructured milk proteins of which the main components are referred to as alpha(s)-, beta- and kappa-casein. All three components lack a compact folded conformation, which can be ascribed to a combination of their low overall hydrophobicity and high net charge. Structural transitions of the three caseins in response to variation of pH were investigated using fluorescence and circular dichroism (CD) spectroscopy. Tryptophan emission parameters (intensity and wavelength of emission maximum) and CD spectra showed that at neutral and alkaline pH the caseins exist predominantly in random coil conformation. As the solvent is made acidic the added protons compensate the negative charges on the caseins and reduce the repulsion between like charged residues, allowing the casein chains to fold. At the pI (pH 4-5), the net charge on the protein tends to zero and the protein should approach its maximally structured state. Below pI, the uncompensated charges and their interactions reappear, resulting in slackening of the compact structure and formation of a partially unfolded intermediate. These conclusions were borne out by the biphasic pH-dependence of the fluorescence emission parameters of Trp as well as of ANS incubated with the caseins. Measurement of the efficiency of energy transfer between Trp (donor) and ANS (acceptor) and of the CD spectra of caseins as functions of pH were also consistent with this scenario.     

Enantioselective total synthesis of 1-epi-pathylactone A

[structure: see text]. The first enantioselective total synthesis of 1-epi-pathylactone A, 3, has been accomplished using a PhI(OAc)2-mediated domino reaction as a key step. No diastereomeric separation was required throughout the whole synthetic scheme presented in this paper. Comparison of 1H and 13C NMR spectral data of the synthetic product with the reported spectral data of natural pathylactone A, coupled with an X-ray crystallographic analysis, led to the conclusion that the C1 configuration in the original paper was erroneously ascribed to (R).     

Complexation and coacervation of polyelectrolytes with oppositely charged colloids

Polyelectrolyte-colloid coacervation could be viewed as a sub-category of complex coacervation, but is unique in (1) retaining the structure and properties of the colloid, and (2) reducing the heterogeneity and configurational complexity of polyelectrolyte-polyelectrolyte (PE-PE) systems. Interest in protein-polyelectrolyte coacervates arises from preservation of biofunctionality; in addition, the geometric and charge isotropy of micelles allows for better comparison with theory, taking into account the central role of colloid charge density. In the context of these two systems, we describe critical conditions for complex formation and for coacervation with regard to colloid and polyelectrolyte charge densities, ionic strength, PE molecular weight (MW), and stoichiometry; and effects of temperature and shear, which are unique to the PE-micelle systems. The coacervation process is discussed in terms of theoretical treatments and models, as supported by experimental findings. We point out how soluble aggregates, subject to various equilibria and disproportionation effects, can self-assemble leading to heterogeneity in macroscopically homogeneous coacervates, on multiple length scales.     

Asimafoetidnol: a new sesquiterpenoid coumarin from the gum resin of Ferula assa-foetida

Chemical investigation of the gum resin of Ferula assa-foetida L. resulted in the isolation of a new sesquiterpenoid coumarin, 7-(((E)-5-((1S,3S,6S)-3,6-dihydroxy-2,2,6-trimethylcyclohexyl)-3-methylpent-2-en-1-yl)oxy)-2H-chromen-2-one (asimafoetidnol), together with several other known compounds. The structure of asimafoetidnol was established on the basis of spectroscopic analyses. Geometry optimization of the compound has been carried out using a DFT/B3LYP/3-21G* method.     

Modeling energy landscapes of proton motion in nonaqueous, tethered proton wires

We have modeled structures and energetics of anhydrous proton-conducting wires: tethered hydrogen-bonded chains of the form ···HX···HX···HX···, with functional groups HX = imidazole, triazole, and formamidine; formic, sulfonic, and phosphonic acids. We have applied density functional theory (DFT) to model proton wires up to 19 units long, where each proton carrier is linked to an effective backbone to mimic polymer tethering. This approach allows the direct calculation of hydrogen bond strengths. The proton wires were found to be stabilized by strong hydrogen bonds (up to 50 kJ/mol) whose strength correlates with the proton affinity of HX [related to pK(b)(HX)] and not to pK(a)(HX) as is often assumed. Geometry optimizations and ab initio molecular dynamics near 400 K on imidazole-based proton wires both predict that adding a proton to the end of such wires causes the excess charge to embed into the interior segments of these wires. Proton translocation energy landscapes for imidazole-based wires are sensitive to the imidazole attachment point (head or feet) and to wire architecture (linear or interdigitated). Linear imidazole wires with head-attachment exhibit low barriers for intrawire proton motion, rivaling proton diffusion in liquid imidazole. Excess charge relaxation from the edge of wires is found to be dominated by long-range Grotthuss shuttling for distances as long as 42 ?, especially for interdigitated wires. For imidazole, we predict that proton translocation is controlled by the energetics of desorption from the proton wire, even for relatively long wires (600 imidazole units). Proton desorption energies show no correlation with functional group properties, suggesting that proton desorption is a collective process in proton wires.     

Ordered dispersion of ZnO quantum dots in SiO2 matrix and its strong emission properties

ZnO nanoparticles in the form of quantum dots (QDs) have been dispersed in SiO₂ matrix using StÖber method to form ZnO QDs-SiO₂ nanocomposites. Addition of tetraethyl orthosilicate (TEOS) to an ethanolic solution of ZnO nanoparticles produces random dispersion. On the other hand, addition of ZnO nanoparticles to an already hydrolyzed ethanolic TEOS solution results in a chain-like ordered dispersion. The photoluminescence spectra of the as-grown nanocomposites show strong emission in the ultraviolet region. When annealed at higher temperature, depending on the sample type, these show strong red or white emission. Interestingly, when the excitation is removed, the orderly dispersed ZnO QDs-SiO₂ composite shows a very bright blue fluorescence visible by naked eyes for few seconds indicating their promise for display applications. The emission property has been explained in the light of structure–property relationship.     

Spectroscopic investigations and quantum chemical computational study of (E)-4-methoxy-2-[(p-tolylimino)methyl]phenol

In this work the electronic structure of (E)-4-methoxy-2-[(p-tolylimino)methyl]phenol has been characterized by the B3LYP/6-31G(d) level by using density functional theory. The experimental infrared and electronic absorption spectra have been obtained and compared with the theoretically obtained ones. Molecular electrostatic potential map has been evaluated; natural bond orbital and frontier molecular orbitals analysis have been performed from the optimized geometry. The energetic behavior of the title compound has been examined in solvent media using polarizable continuum model. The non-linear optical properties have been computed with the same level of theory. In addition, the changes of thermodynamic properties have been obtained in the range of 100-500 K.