The simplified partial digest problem: Approximation and a graph-theoretic model

The goal of the simplified partial digest problem (SPDP) is motivated by the reconstruction of the linear structure of a DNA chain with respect to a given nucleotide pattern, based on the multiset of distances between the adjacent patterns (interpoint distances) and the multiset of distances between each pattern and the two unlabeled endpoints of the DNA chain (end distances). We consider optimization versions of the problem, called SPDP-Min and SPDP-Max. The aim of SPDP-Min (SPDP-Max) is to find a DNA linear structure with the same multiset of end distances and the minimum (maximum) number of incorrect (correct) interpoint distances. Results are presented on the worst-case efficiency of approximation algorithms for these problems. We suggest a graph-theoretic model for SPDP-Min and SPDP-Max, which can be used to reduce the search space for an optimal solution in either of these problems. We also present heuristic polynomial time algorithms based on this model. In computational experiments with randomly generated and real-life input data, our best algorithm delivered an optimal solution in 100% of the instances for a number of restriction sites not greater than 50.     

Evolution of pattern formation under ion bombardment of substrate

Processes of self-organization described by a nonlinear evolution equation of sixth order are considered on substrate surfaces after ion beam bombardment. Five families of exact solutions are found for the nonlinear evolution equation. A numerical method enabling one to solve the boundary value problem is presented. Simulation of the pattern formation and classification of their profiles are given. The influence of the third, fifth order dispersion terms and a nonlinear diffusion term on processes of the pattern formation is discussed.     

Decomposition of Sparse Graphs into Forests and a Graph with Bounded Degree

For a loopless multigraph G, the fractional arboricity Arb(G) is the maximum of over all subgraphs H with at least two vertices. Generalizing the Nash‐Williams Arboricity Theorem, the Nine Dragon Tree Conjecture asserts that if , then G decomposes into forests with one having maximum degree at most d. The conjecture was previously proved for ; we prove it for and when and . For , we can further restrict one forest to have at most two edges in each component. For general , we prove weaker conclusions. If , then implies that G decomposes into k forests plus a multigraph (not necessarily a forest) with maximum degree at most d. If , then implies that G decomposes into forests, one having maximum degree at most d. Our results generalize earlier results about decomposition of sparse planar graphs.     

Facile synthesis of digermylene oxide and its reactivity towards vanadocene: the first example of Cp2V–germylene coordination

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Conformational Dynamics of Sensory Rhodopsin II in Nanolipoprotein and Styrene–Maleic Acid Lipid Particles

Styrene–maleic acid lipid particles (SMALPs) provide stable water‐soluble nanocontainers for lipid‐encased membrane proteins. Possible effects of the SMA‐stabilized lipid environment on the interaction dynamics between functionally coupled membrane proteins remain to be elucidated. The photoreceptor sensory rhodopsin II, NpSRII and its cognate transducer, NpHtrII, of Natronomonas pharaonis form a transmembrane complex, NpSRII₂/NpHtrII₂ that plays a key role in negative phototaxis and provides a unique model system to study the light‐induced transfer of a conformational signal between two integral membrane proteins. Photon absorption induces transient structural changes in NpSRII comprising an outward movement of helix F that cause further conformational alterations in NpHtrII. We applied site‐directed spin labeling and time‐resolved optical and EPR spectroscopy to compare the conformational dynamics of NpSRII₂/NpHtrII₂ reconstituted in SMALPs with that of nanolipoprotein particle and liposome preparations. NpSRII and NpSRII₂/NpHtrII₂ show similar photocycles in liposomes and nanolipoprotein particles. An accelerated decay of the M photointermediate found for SMALPs can be explained by a high local proton concentration provided by the carboxylic groups of the SMA polymer. Light‐induced large‐scale conformational changes of NpSRII₂/NpHtrII₂ observed in liposomes and nanolipoprotein particles are affected in SMALPs, indicating restrictions of the protein's conformational freedom.     

Al3+ solvation in solutions of aluminum nitrate in a protic ionic liquid: Nuclear magnetic resonance verification of the solvation shell composition

The closest environment of Al³⁺ cations was analyzed in detail in solutions of aluminum nitrate in the prototypical protic ionic liquid ethyl ammonium nitrate (EAN) using ¹H and ¹⁴N nuclear magnetic resonance (NMR) spectra. For Al (NO₃)₃–EAN mixtures with different water content, a quantitative analysis of the integral intensities of the ¹H and ¹⁴N signals was carried out and the composition of the first solvation shell of the aluminum cation was refined.     

Theory for the determination of activity coefficients of strong electrolytes with regard to concentration dependence of hydration numbers

A new theory of electrolyte solutions is discussed which, as opposed to the Debye–Huckel method valid for relatively small concentrations only, enables one to describe the thermodynamic properties of electrolyte solutions over a wide range of state parameters. The novelty of the proposed theory is that it takes into account the dependence of hydration numbers upon concentration, the fact that failed to attract much attention before. The applicability of the theory to the calculation of activity coefficients of some electrolytes (LiCl, NaCl, KCl, RbCl, and CsCl) is demonstrated. A method is proposed for the determination of the thermodynamic parameters of solvation of separate ions.     

Packing chromatic number of cubic graphs

A packing$k$-coloring of a graph $G$ is a partition of $V\left(G\right)$ into sets $V_1,\dots ,V_k$ such that for each $1\le i\le k$ the distance between any two distinct $x,y\in V_i$ is at least $i+1$. The packing chromatic number, ${\chi }_p\left(G\right)$, of a graph $G$ is the minimum $k$ such that $G$ has a packing $k$-coloring. Sloper showed that there are $4$-regular graphs with arbitrarily large packing chromatic number. The question whether the packing chromatic number of subcubic graphs is bounded appears in several papers. We answer this question in the negative. Moreover, we show that for every fixed $k$ and $g\ge 2k+2$, almost every $n$-vertex cubic graph of girth at least $g$ has the packing chromatic number greater than $k$.     

Exploring benzylic gem-C(sp3)–boron–silicon and boron–tin centers as a synthetic platform

A stepwise build-up of multi-substituted C_sp³ carbon centers is an attractive, conceptually simple, but often synthetically challenging type of disconnection. To this end, this report describes how gem-α,α-dimetalloid-substituted benzylic reagents bearing boron/silicon or boron/tin substituent sets are an excellent stepping stone towards diverse substitution patterns. These gem-dimetalloids were readily accessed, either by known carbenoid insertion into C–B bonds or by the newly developed scalable deprotonation/metallation approach. Highly chemoselective transformations of either the C–Si (or C–Sn) or the C–B bonds in the newly formed gem-C_sp³ centers have been achieved through a set of approaches, with a particular focus on exploiting the synthetically versatile polarity reversal in organometalloids by λ³-aryliodanes. Of particular note is the metal-free arylation of the C–Si (or C–Sn) bonds in such gem-dimetalloids via the iodane-guided C–H coupling approach. DFT calculations show that this transfer of the (α-Bpin)benzyl group proceeds via unusual [5,5]-sigmatropic rearrangement and is driven by the high-energy iodine(iii) center. As a complementary tool, the gem-dimetalloid C–B bond is shown to undergo a potent and chemoselective Suzuki–Miyaura arylation with diverse Ar–Cl, thanks to the development of the reactive gem-α,α-silyl/BF₃K building blocks.

This work explores divergent reactivity of the benzylic gem-boron–silicon and boron–tin double nucleophiles, including the arylation of the C–B bond with Ar–Cl, along with a complementary oxidative λ³-iodane-guided arylation of the C–Si/Sn moiety.