Unique "cradled barbell" complex between a secondary diammonium ion and bis(m-phenylene)-32-crown-10

[formula: see text] The complexation between N,N'-dibenzyl(m-xylylene)diammonium bis(hexafluorophosphate) (2) and bis(m-phenylene)-32-crown-10 (5) was shown to occur in solution by nuclear magnetic resonance with 1:1 stoichiometry and a Ka value of 189 +/- 19 M-1. A crystal structure of 2:5 revealed a unique 1:1 "exo" or "cradled barbell" complex, instead of the expected pseudorotaxane. This unexpected result illustrates that caution be used in interpreting the results from these types of complexes in the solution and "gas" phases on the basis of crystal structures.     

The combinatorics and extreme value statistics of protein threading

In protein threading, one is given a protein sequence, together with a database of protein core structures that may contain the natural structure of the sequence. The object of protein threading is to correctly identify the structure(s) corresponding to the sequence. Since the core structures are already associated with specific biological functions, threading has the potential to provide biologists with useful insights about the function of a newly discovered protein sequence. Statistical tests for threading results based on the theory of extreme values suggest several combinatorial problems. For example, what is the number of waysm′=# _t {L _i >x _i } _i ⁼⁰ⁿ of choosing a sequence {X _i } _i ⁼¹ⁿ from the set {1, 2, ...,t}, subject to the difference constraints {L _i =X _i+1?X _i >x _i } _i ⁼⁰ⁿ , whereX ₀=0,X _n+1=t+1, and {x _i } _i ⁼⁰ⁿ is an arbitrary sequence of integers? The quantitym′ has many attractive combinatorial interpretations and reduces in special continuous limits to a probabilistic formula discovered by the Finetti. Just as many important probabilities can be derived from de Finetti's formula, many interesting combinatorial quantities can be derived fromm′. Empirical results presented here show that the combinatorial approach to threading statistics appears promising, but that structural periodicities in proteins and energetically unimportant structure elements probably introduce statistical correlations that must be better understood.     

Radiation damage and decay characteristics of zinc selenide emission bands and their equivalence to zinc sulphide emission bands

Irradiation of zinc selenide at ～ 20°K with electrons capable of displacing zinc atoms results in the production of cathodoluminescence emission bands at 610 and 630 nm. Enhancement of the 630 nm emission band by electron damage requires the presence of copper in the samples. These emissions have been shown to give a peak energy shift to lower energies after excitation, as is characteristic of donor-acceptor pair recombination. It is concluded that the 610 and 630 nm emission bands of zinc selenide are equivalent to the self-activated and copper green emission bands of zinc sulphide. The 530 nm emission band of zinc selenide is not sensitive to electron damage, shows no time shift and is thought to be equivalent to the copper blue emission of zinc sulphide.     

Nuclear magnetic resonance and spin relaxation in biological systems

Proton nuclear spin-lattice relaxation in biological systems is generally distinguished from that in inorganic systems such as rocks by the presence of locally disordered macromolecular environments. Rapid exchange of readily observed labile small molecules among differently oriented macromolecular sites generally nearly averages the spectral anisotropies in the small molecule resonances. The biological tissue is generally distinguished from the inorganic matrix by the presence of a significant population of protons in the solid components that are well connected by dipolar spin couplings. Magnetic coupling between the solid and the liquid components generally dominates the magnetic field dependence of the spin-lattice relaxation rates observed in the small molecule components which is generally described by a power law in the Larmor frequency. Recent theory involving a modification of the spin-phonon class of relaxation mechanism provides a quantitative understanding of these data in terms of the dynamics of the chain molecules generally present in the solid spin systems, folded proteins for example.     

End-to-end correlation for a C-12 hydrocarbon chain

The 19F nuclear spin-lattice relaxation rate constants were measured as a function of magnetic field strength for 1,12-diaminododecane labeled at one end with a nitroxide radical and at the other with a trifluoromethyl group. The magnetic relaxation dispersion profile (MRD) reports the spectral density function appropriate to the end-to-end correlation function for the doubly labeled molecule. After extrapolation to zero concentration to eliminate the intermolecular relaxation contribution to relaxation, the resulting intramolecular MRD profile was compared with several model approaches. The rotational model for the spectral density functions as included in the Solomon-Bloembergen-Morgan equations does not describe the data well. The earlier model of Freed for nuclear spin relaxation induced by a freely diffusing paramagnetic co-solute is not rigorous for this case because the paramagnet is tethered to the observed nuclear spin and only a restricted space in the immediate vicinity of the nuclear spin is accessible for pseudo-translational diffusion of one end of the molecule with respect to the other. A generalization of the Torrey model for magnetic relaxation by translational diffusion developed by Nevzorov and Freed, which includes the effect of restrictions imposed by the finite length of the chain, describes the experiment within experimental errors. A simple modification of the Hwang-Freed model that does not specifically include the dynamical effects of the finite tether also provides a good approximation to the data when the tether chain is sufficiently long.     

Factorizations of the Complete Graph into C 5-Factors and 1-Factors

In this paper, we show that K_10n can be factored into C₅-factors and 1-factors for all non-negative integers and satisfying 2+=10n–1.Research partially supported by an NSF-AWM Mentoring Travel Grant     

Embeddings in generalized manifolds

We prove that a ()-connected map from a compact PL -manifold to a generalized -manifold with the disjoint disks property, , is homotopic to a tame embedding. There is also a controlled version of this result, as well as a version for noncompact and proper maps that are properly ()-connected. The techniques developed lead to a general position result for arbitrary maps , , and a Whitney trick for separating submanifolds of that have intersection number 0, analogous to the well-known results when is a manifold.

     

27Al field-swept and frequency-stepped NMR for sites with large quadrupole coupling constants

Spectra of nonspinning samples with large quadrupole coupling constants, 16-32 MHz, are acquired by frequency-stepping. A series of spin-echoes are acquired at arbitrary frequency increments, frequency-shifted in the time domain, and co-added as magnitude spectra. This procedure is derived from a method in use for field-swept NMR. The two methods are compared.