Pigmentation Chemistry and Radical‐Based Collagen Degradation in Alkaptonuria and Osteoarthritic Cartilage

Alkaptonuria (AKU) is a rare disease characterized by high levels of homogentisic acid (HGA); patients suffer from tissue ochronosis: dark brown pigmentation, especially of joint cartilage, leading to severe early osteoarthropathy. No molecular mechanism links elevated HGA to ochronosis; the pigment's chemical identity is still not known, nor how it induces joint cartilage degradation. Here we give key insight on HGA‐derived pigment composition and collagen disruption in AKU cartilage. Synthetic pigment and pigmented human cartilage tissue both showed hydroquinone‐resembling NMR signals. EPR spectroscopy showed that the synthetic pigment contains radicals. Moreover, we observed intrastrand disruption of collagen triple helix in pigmented AKU human cartilage, and in cartilage from patients with osteoarthritis. We propose that collagen degradation can occur via transient glycyl radicals, the formation of which is enhanced in AKU due to the redox environment generated by pigmentation.     

Synthesis of mesocyclic and macrocyclic polythioethers using the cesium dithiolate technique

The mesocyclic trithioethers, 1,4,7-trithiacyclodecane, 1,4,7-trithiacycloundecane, 1,4,8-trithiacycloundecane, and 1,5,9-trithiacyclododecane; the mesocyclic trithioether ketones, 1,4,7-trithiacyclodecan-9-one; 1,4,8-trithiacycloundecan-6-one, and 1,5,9-trithiacyclododecan-3-one; and the mesocyclic trithioether alcohols, 1,4,7-trithiacyclodecan-9-ol, 1,4,8-trithiacycloundecan-6-ol, and 1,5,9-trithiacyclododecan-3-ol, have been synthesized using the cesium dithiolate technique. In some cases, the corresponding macrocyclic hexathioether was isolated from the reaction mixture in addition to the mesocyclic trithioether; 1,4,7,11,14,17-hexathiacycloeicosane, 1,4,7,11,14,17-hexathiacycloeicosan-9,19-dione, 1,4,7,12,15,18-hexathiacyclodocosane, and 1,5,9,13,17,21-hexathiacyclotetracosane. Single-crystal X-ray structures have been determined for 1,5,9-trithiacyclododecan-3-ol and 1,4,7,12,15,18-hexathiacyclodocosane. For 1,5,9-trithiacyclododecane-3-ol, the compound crystallizes in the monoclinic space group, C2/c, with a = 10.5926( 9 ) Å, b = 15.582(2) Å, c = 13.6015(8) Å, β = 98.186(6)⁰, Z = 8, and R = 0.038. The macrocycle, 1,4,7,12,15,18-hexathiacyclodocosane, crystallizes in the orthorhombic space group, Pbca, with a = 21.406(5) Å, b = 9.810(2) Å, c = 10.225(2) Å, Z = 4, and R = 0.020.     

Gas hydrate single-crystal structure analyses

The first single-crystal diffraction studies on methane, propane, methane/propane, and adamantane gas hydrates SI, SII, and SH have been performed. To circumvent the problem of very slow crystal growth, a novel technique of in situ cocrystallization of gases and liquids resulting in oligocrystalline material in a capillary has been developed. With special data treatment, termed oligo diffractometry, structural data of the gas hydrates of methane, acetylene, propane, a propane/ethanol/methane-mixture and an adamantane/methane-mixture were obtained. Cell parameters are in accord with reported values. Host network and guest are subject to extensive disorder, reducing the reliability of structural information. It was found that most cages are fully occupied by a guest molecule with the exception of the dodecahedral cage in the acetylene hydrate which is only filled to 60%. For adamantane in the icosahedral cage a disordered model is proposed.     

Frequency down-conversion using cascading arrays of coupled nonlinear oscillators

A novel coupling scheme using M≥2 arrays of coupled nonlinear elements arranged in a specific configuration can produce multifrequency patterns or a frequency down-converting effect on an external (input) signal. In such a configuration, each array contains N≥3 nonlinear elements with similar dynamics and each element is coupled unidirectionally within the array. The subsequent arrays in the cascade are coupled in a similar fashion except that the coupling direction is arranged in the opposite direction with respect to that of the preceding array. Previous theoretical work and numerical results have already been reported in [P. Longhini, A. Palacios, V. In, J. Neff, A. Kho, A. Bulsara, Exploiting dynamical symmetry in coupled nonlinear elements for efficient frequency down-conversion, Phys. Rev. E 76 (2007) 026201]. This paper is focused on results of experiments implemented on two distinct systems: the first system is fabricated using discrete component circuits to approximate an overdamped bistable Duffing oscillator described by a quartic potential system, and the second system is built in a microcircuit, where the nonlinearity is described by a hyperbolic tangent function, with the option of applying an external signal to investigate resonant effects. In particular, the circuit implementations for each case use M=2 arrays, but their voltage oscillations already demonstrate that the frequency relations between each of the successive arrays decrease by a rational factor, conforming to earlier theoretical and numerical results for the general case containing M arrays. This behavior is important for efficient frequency down-converting applications which are essential in many communication systems where heterodyning is typically used and it involves multi-step processes with complicated circuitry.     

Commutativity of operators on the lattice of existence varieties

In a previous paper the authors introduced seven complete congruences on the lattice _ev(I of e-varieties of regular semigroups of the form _P :U _P VPU=PV, whereP is drawn from a small set of e-varieties: left zero, right zero, rectangular bands, groups, left groups, right groups and completely simple semigroups. Four new complete congruences are introduced here of the form _P :U _P VPU=PV, whereP is one of the following classes of regular semigroups: left monoids, right monoids, monoids, idempotent generated semigroups. For each complete congruence on _ev(I) and eachU_ev(I), the -class ofU is an interval [U ,U ] so that there is associated with each such congruence an idempotent operatorUU on _ev(I). This paper establishes numerous results concerning the commutativity of operators of this form.This work was supported in part by NSERC Grant 4044.     

Operational Research and Decision-Making

This paper was originally presented under the title "Decision" at the Third Operational Research Conference of the Universities of Lancaster and Sussex held at Windermere in April 1968. In it, the question of what is meant by "improved decision-making" is examined and the ways in which operational research can and does contribute to this are discussed. In the course of this the "American School" of Decision Analysis is reviewed. The paper concludes with some suggestions on computational procedures. This paper was written as a vehicle for discussion. In order to stimulate this, the authors have been deliberately provocative and presented an extreme point of view. The paper which follows this is a condensed version of some of the discussion which took place at the Conference. The authors would welcome further contributions.