Conjugation of a novel histidine derivative to biomolecules and labelling with [99mTc(OH2)3(CO)3]+

The new histidine derivative 3-[1-[3-(9H-fluoren-9-ylmethoxycarbonylamino)-propyl]-1H-imidazol-4-yl]-2-(3-trimethylsilanyl-ethylcarboxyamino)-propionic acid methyl ester (7) has been prepared via alkylation of the histidine urea derivative (7S)-5,6,7,8-tetrahydro-7-(methoxycarbonyl)-5-oxoimidazo-[1,5-c]-pyrimidine (2) with Fmoc-protected 3-iodopropyl-amine, followed by ring opening with 2-trimethylsilylethanol. After Fmoc cleavage by HNEt2, the histidine amine derivative was coupled to biotin, to the pentapeptide leucine-enkephalin and to Vitamin B12-b-acid by amide formation, employing TBTU as the coupling reagent. In order to make the histidine accessible for labelling, the teoc protecting group was removed by either NBu4F (for the biotin conjugate) or by TFA (for the enkephalin and B12 conjugates). Reaction of a 10(-4) M solution of the bioconjugates with [99mTc(H2O)3(CO)3]+ at 50 degrees C for 30 min led to the formation of one single new peak in the HPLC radiochromatogram in each case, confirming quantitative labelling of the respective biomolecules. To assess the nature of the labelled compounds, the rhenium analogues with Re(CO)3 were also synthesised and similar retention times confirmed the identity with the 99mTc labelled conjugates.     

Strong bias of group generators: an obstacle to the “product replacement algorithm”

Let G be a finite group. Efficient generation of nearly uniformly distributed random elements in G, starting from a given set of generators of G, is a central problem in computational group theory. In this paper we demonstrate a weakness in the popular “product replacement algorithm,” widely used for this purpose. The main results are the following. Let be the set of generating k-tuples of elements of G. Consider the distribution of the first components of the k-tuples in induced by the uniform distribution over  . We show that there exist infinite sequences of groups G such that this distribution is very far from uniform in two different senses: (1) its variation distance from uniform is >1−ε; and (2) there exists a short word (of length (loglog|G|)^O(k)) which separates the two distributions with probability 1−ε. The class of groups we analyze is direct powers of alternating groups. The methods used include statistical analysis of permutation groups, the theory of random walks, the AKS sorting network, and a randomized simulation of monotone Boolean operations by group operations, inspired by Barrington's work on bounded-width branching programs. The problem is motivated by the product replacement algorithm which was introduced in [Comm. Algebra 23 (1995) 4931–4948] and is widely used. Our results show that for certain groups the probability distribution obtained by the product replacement algorithm has a bias which can be detected by a short straight line program.     

Partition identities and geometric bijections

We present a geometric framework for a class of partition identities. We show that there exists a unique bijection proving these identities, which satisfies certain linearity conditions. In particular, we show that Corteel's bijection enumerating partitions with nonnegative -th differences can be obtained by our approach. Other examples and generalizations are presented.

     

A simulation study of electrostatic effects on mixed ionic micelles confined between two parallel charged plates

Confined colloidal systems have been the subject of extensive theoretical and experimental research, and the recent observation of long-range like-charge attraction in such systems has only highlighted their peculiar behavior. On the other hand, surfactant solutions are often used in small confined space, yet their behavior in confinement has received relatively little attention. A distinct feature of confined self-assembling systems is that the aggregates are capable of adjusting their composition, size, and shape in response to their external environment, which may lead to very different phase characteristics compared to bulk solutions. The primary objective of this study is to explore the effects of varying micelle composition on the structural behavior of a confined mixed ionic micellar solution. Mesoscale canonical Monte Carlo simulations were used to probe the structure of the confined solution, while a molecular-thermodynamic model was used to systematically account for the change in micelle size as we varied its composition. Significant micelle ordering was found under certain conditions, which implies that large deviations from the minimum-energy micelle configuration may not be entropically favorable. Accumulation of micelles along the midplane was observed when the confining walls are weakly charged, suggesting that micelle shape transformation should be considered in more detail. On the other hand, with high wall charge density, apparent attraction was found between like-charged micelles and wall. These findings point to the need for a more quantitative theoretical treatment in describing surfactant self-assembly in confined geometries.     

Crystal structure of Cu(I) π-complexes from the system CuBr−HBr-diallylamine

L'vov State University. Institute of Applied Physics, Moldavian Academy of Sciences. Translated from Zhurnal Strukturnoi Khimii, Vol. 33, No. 1, pp. 121–125, January–February, 1992.     

A short proof of rigidity of convex polytopes

We present a much simplified proof of Dehn’s theorem on the infinitesimal rigidity of convex polytopes. Our approach is based on the ideas of Trushkina [1] and Schramm [2].     

The strong coupling constants of excited positive parity heavy mesons in light-cone QCD

We calculate the strong coupling constants g_p^**p^*π, where P^** (D^**, B^**) is the 1⁺ p-wave state, in the framework of the light-cone QCD sum rules, and using these values ofg_p^**p^*π , we compute the hadronic decay widths forD^** → D^* π and B^** → B^* π.     

Chiral solitons and current algebra

We investigate the possibility of a realistic hadrodynamics based solely on observable currents. The basic idea is to exploit the soliton generation in bosonic chiral theories as a mechanism for finding the fermionic representations of current algebra. A prototype realization is Skyrme's O(4) invariant theory of pions and nucleons. A comprehensive reexamination of this model in the context of chiral dynamics suffices to reveal a strikingly self-consistent dynamical picture. First a differential geometric formulation gives the proper framework for a chiral invariant quantum theory of solitons and allows a compact derivation of Skyrme's main results. While no exact analytic solution is found, the solitons are sufficiently localized so that their singularities can be properly isolated out for analysis. Using Witten's ansatz, a determination of the form of the 1-soliton singularity is obtained from the field equations. It is given by Cayley's steoreographic projection from S³ to $\text{R}{}^3\text{? {∞} ≈ S}{}^3$; a most suitable form for the proof of spinor structure. Williams' proof that the quantized 1-soliton sector gives rise to fermionic spin states is recalled. It is argued that the topological dynamics of this sector induce an invariance group K = SU(2)_I ? SU(2)_J and its associated strong coupling isobaric spectrum for the nucleons. The associated current algebra is derived and resolves the main difficulties of the Sugawara-Sommerfield program. The signature of a field theoretical bootstrap is clear: massive nucleons as soliton bound states of Nambu-Goldstone bosons illustrate a dynamical mechanism dual to that of Nambu and Jona-Lasinio.