Zero sets of bivariate Hermite polynomials

We establish various properties for the zero sets of three families of bivariate Hermite polynomials. Special emphasis is given to those bivariate orthogonal polynomials introduced by Hermite by means of a Rodrigues type formula related to a general positive definite quadratic form. For this family we prove that the zero set of the polynomial of total degree n+m$n+m$ consists of exactly n+m$n+m$ disjoint branches and possesses n+m$n+m$ asymptotes. A natural extension of the notion of interlacing is introduced and it is proved that the zero sets of the family under discussion obey this property. The results show that the properties of the zero sets, considered as affine algebraic curves in R²${\mathbb{R}}^2$, are completely different for the three families analyzed.     

Amplification free detection of herpes simplex virus DNA

Amplification-free detection of nucleic acids in complex biological samples is an important technology for clinical diagnostics, especially in the case where the detection is quantitative and highly sensitive. Here we present the detection of a synthetic DNA sequence from Herpes Simplex Virus-1 within swine cerebrospinal fluid (CSF), using a sandwich-like, magnetic nanoparticle pull-down assay. Magnetic nanoparticles and fluorescent polystyrene nanoparticles were both modified with DNA probes, able to hybridise either end of the target DNA, forming the sandwich-like complex which can be captured magnetically and detected by fluorescence. The concentration of the target DNA was determined by counting individual and aggregated fluorescent nanoparticles on a planar glass surface within a fluidic chamber. DNA probe coupling for both nanoparticles was optimized. Polystyrene reporter nanoparticles that had been modified with amine terminated DNA probes were also treated with amine terminated polyethylene glycol, in order to reduce non-specific aggregation and target independent adhesion to the magnetic particles. This way, a limit of detection for the target DNA of 0.8 pM and 1 pM could be achieved for hybridisation buffer and CSF respectively, corresponding to 0.072 and 0.090 femtomoles of target DNA, in a volume of 0.090 mL.     

Encaging the Verkade's superbases: thermodynamic and kinetic consequences

Proazaphosphatranes, also known as Verkade's superbases, are nonionic species, which exhibit catalytic properties for a wide range of reactions. The properly designed host molecule 3 and its protonated counterpart [3·H](+)Cl(-) were synthesized to study how confinement can modify the stability and the reactivity of a Verkade's superbase. The results show that the encapsulation does not alter the strong basicity of the proazaphosphatrane, but dramatically decreases the rate of proton transfer.     

Novel covalent bond in proteins: calculations on model systems question the bond stability

We have investigated the sulfilimine covalent link between methionine (Met) and lysine (Lys), recently identified in collagen IV (R. Vanacore, A.-J. L. Ham, M. Voehler, C. R. Sanders, T. P. Conrads, T. D. Veenstra, K. B. Sharpless, P. E. Dawson, B. G. Hudson, Science 2009, 325, 1230), and have explored its stability with respect to both the redox processes and UV radiation by means of advanced computational methods. We have concluded that the bond should be present in a protonated state, (-NH=S-)(+). The bond is characterized by a relatively high standard reduction potential, that is, the bond should not be stable in a typical cell environment; if the sulfilimine bond exists (as suggested by the experiment) then the bond has to be supported by the protein environment. The sulfilimine bond then destabilizes the protein structure with respect to the alternative tertiary structure. We discuss conditions under which the bond could be formed as well as other possible structural arrangements consistent with the Met-Lys stoichiometry; some of the alternative bond motifs are more thermodynamically stable than the sulfilimine bond. We suggest that the character of the Met-Lys contact could be approached via NEXAFS spectroscopy. Finally, we show that the protonation brings photostability to the sulfilimine bond.     

Log-gases on quadratic lattices via discrete loop equations and q-boxed plane partitions

We study a general class of log-gas ensembles on (shifted) quadratic lattices. We prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are Gaussian with a universal covariance. We apply our general results to analyze the asymptotic behavior of a q-boxed plane partition model introduced by Borodin, Gorin and Rains. In particular, we show that the global fluctuations of the height function on a fixed slice are described by a one-dimensional section of a pullback of the two-dimensional Gaussian free field.Our approach is based on a q-analogue of the Schwinger–Dyson (or loop) equations, which originate in the work of Nekrasov and his collaborators, and extends the methods developed by Borodin, Gorin and Guionnet to quadratic lattices.     

Solvent-mediated folding of a doubly charged anion

The microsolvation of the suberate dianion, -O2C(CH2)6CO2-, with two separate charge centers was studied by photoelectron spectroscopy and molecular dynamics simulation one solvent molecule at a time for up to 20 waters. It is shown that the two negative charges are solvated in the linear suberate alternately. As the solvent number increases, the negative charges are screened and a conformation change occurs at 16 waters, where the cooperative hydrogen bonding of water is large enough to overcome the Coulomb repulsion and pull the two negative charges closer through a water bridge. This conformation change, revealed both from the experiment and from the simulation, is a manifestation of the hydrophilic and hydrophobic forces at the molecular level.     

Computational identification of interface delaminations in layered composites based on surface measurements

One of the main contemporary challenges facing engineering sciences is how to identify the actual state of internal defects, their self-organized criticality, interaction, and thus influence on the overall strength and durability of a system. In this study we address one aspect in the panoply of problems emerging in this context, namely: how to identify a single delamination in a layered composite specimen performing measurements only on the surface. In rigor terms the answer to this question relates to the answer to the question of how to solve the nonlinear semi-inverse problem of the mathematical programming emerging from the minimization of an associated Kohn–Vogelius functional with respect to some set of design variables parameterizing the delamination region. Clearly, one methodological way to approach the solution is to use some classical, gradient-based, nonlinear programming technique, like SQP. One should not forget, however, that the identification problems of this class are per se ill-posed, nonsmooth, and highly sensitive to the initial boundary data. Three bottlenecks occur that cannot be trivially circumvented when the shape of the delamination region, its characteristic dimensions, and position are preliminarily unknown (or highly uncertain). Based on an appropriate split of the governing Kohn–Vogelius functional we succeed here in transforming the ill-posed local inverse problem into a coupled system of elliptic well-posed Euler–Lagrange equations and to derive a direct smooth iterative strategy for its numerical solution. The strategy leads to a semiempirical reconstruction method for finding isolated interlaminar cavities from the measurement of the displacement field performed on the surface of the specimen.     

сОДЕРжАНИь РАБОт, ОпУБлИкОВАННых тОлькО В ЧЕшскОМ ИжДАНИИ НАстОьЩЕгО жУРНАлА

---

Abstracts of Papers which have appeared only in the Czech Edition of this Journal