TROSY-based z-exchange spectroscopy: application to the determination of the activation energy for intermolecular protein translocation between specific sites on different DNA molecules

A two-dimensional TROSY-based z-exchange 1H-15N correlation experiment for the quantitative analysis of kinetic processes in the slow exchange regime is presented. The pulse scheme converts the product operator terms Nz into 2NzHz and 2NzHz into -Nz in the middle of the z-mixing period, thereby suppressing the buildup of spurious semi-TROSY peaks arising from the different relaxation rates for the Nz and 2NzHz terms and simplifying the behavior of longitudinal magnetization for an exchanging system during the mixing period. Theoretical considerations and experimental data demonstrate that the TROSY-based z-exchange experiment permits quantitative determination of rate constants using the same procedure as that for the conventional non-TROSY 15Nz-exchange experiment. Line narrowing as a consequence of the use of the TROSY principle makes the method particularly suitable for kinetic studies at low temperature, thereby permitting activation energies to be extracted from data acquired over a wider temperature range. We applied this method to the investigation of the process whereby the HoxD9 homeodomain translocates between specific target sites on different DNA molecules via a direct transfer mechanism without going through the intermediary of free protein. The activation enthalpy for intermolecular translocation was determined to be 17 kcal/mol.     

13-tungstoborate stabilized by an organostannoxane hexamer

The novel dimethyltin-containing polyanion [{(CH3)2Sn}6(OH)2O2(H2BW13O46)2]12- (1) is composed of two [H2BW13O46]9- clusters linked by an unprecedented planar, hexameric [{(CH3)2Sn}6(OH)2O2]8+ organostannoxane moiety, representing the first X-ray structural characterization of a molecular hybrid organic-inorganic tungstoborate and of the elusive [HnBW13O46](11-n)- species.     

Generalized complex structures and Lie brackets

We remark that the equations underlying the notion of generalized complex structure have simple geometric meaning when passing to Lie algebroids/groupoids.     

Translocation of DNA molecules through nanopores with salt gradients: the role of osmotic flow

Recent experiments of translocation of double-stranded DNA through nanopores [M. Wanunu et al., Nature Nanotech. 5, 160 (2009)] reveal that the DNA capture rate can be significantly influenced by a salt gradient across the pore. We show that osmotic flow combined with electrophoretic effects can quantitatively explain the experimental data on the salt-gradient dependence of the capture rate.     

Steiner transitive-closure spanners of low-dimensional posets

Given a directed graph G=(V, E) and an integer k ≥ 1, a k-transitive-closure spanner (k-TC-spanner) of G is a directed graph H=(V, E _H ) that has (1) the same transitive closure as G and (2) diameter at most k. In some applications, the shortcut paths added to the graph in order to obtain small diameter can use Steiner vertices, that is, vertices not in the original graph G. The resulting spanner is called a Steiner transitive-closure spanner (Steiner TC-spanner). Motivated by applications to property reconstruction and access control hierarchies, we concentrate on Steiner TC-spanners of directed acyclic graphs or, equivalently, partially ordered sets. In these applications, the goal is to find a sparsest Steiner k-TC-spanner of a poset G for a given k and G. The focus of this paper is the relationship between the dimension of a poset and the size of its sparsest Steiner TC-spanner. The dimension of a poset G is the smallest d such that G can be embedded into a d-dimensional directed hypergrid via an order-preserving embedding. We present a nearly tight lower bound on the size of Steiner 2-TC-spanners of d- dimensional directed hypergrids. It implies better lower bounds on the complexity of local reconstructors of monotone functions and functions with small Lipschitz constant. The lower bound is derived from an explicit dual solution to a linear programming relaxation of the Steiner 2-TC-spanner problem. We also give an efficient construction of Steiner 2-TC-spanners, of size matching the lower bound, for all low-dimensional posets. Finally, we present a lower bound on the size of Steiner k-TC-spanners of d-dimensional posets. It shows that the best-known construction, due to De Santis et al., cannot be improved significantly.     

Viability for Differential Inclusions on Graphs

Let X be a Banach space, I a nonempty, bounded interval and let $K:I\leadsto X$ be a given multi-valued function. We rephrase the concept of tangent set introduced by Cârj? et al. (Trans Amer Math Soc, 2008; Viability, Invariance and Applications. North-Holland Mathematics Studies, vol. 207. Elsevier, 2007) by saying that a bounded set $E\subseteq X$ is right tangent to at if $\liminf_{h\downarrow0}{1}/{h}\,\text{\rm dist}(\xi+hE;K(\tau+h))=0$ . Next, by using a tangency condition expressed in the terms of this concept, we establish several necessary and sufficient conditions for viability referring to differential inclusions on graphs.     

A robust metal-organic framework constructed from alkoxo-bridged binuclear nodes and hexamethylenetetramine spacers: crystal structure and sorption studies

A neutral 3D metal-organic framework, (3)(∞)[Cu(2)(mand)(2)(hmt)]·H(2)O (1), was constructed from binuclear Cu(2)O(2) alkoxo-bridged nodes, generated by the doubly deprotonated mandelic acid. The nodes are connected by hexamethylenetetramine (hmt) spacers, which act as biconnective bridging ligands, and by carboxylato groups. Channels are observed along the crystallographic c axis. The water molecules from the channels can be easily removed, preserving the architecture of the crystal, which is stable up to 280 °C. The Langmuir surface area was found to be 610 m(2) g(-1). The sorption ability of 1 was investigated using H(2) and CO(2).     

Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ₁₂) − S(γ₁) is restricted to states of the form . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L ₁ → L _p for L _p spaces defined by the Schatten p-norm on matrices, and give another proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L ₁ → L _p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.