Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Spontaneous transitions in the coordination of a whole body task

This paper describes an example of spontaneous transitions between qualitatively different coordination patterns during a cyclic lifting and lowering task. Eleven participants performed 12 trials of repetitive lifting and lowering in a ramp protocol in which the height of the lower shelf was raised or lowered 1 cm per cycle between 10 and 50 cm. Two distinct patterns of coordination were evident: a squat technique in which moderate range of hip, knee and ankle movement was utilised and ankle plantar-flexion occurred simultaneously with knee and hip extension; and a stoop technique in which the range of knee movement was reduced and knee and hip extension was accompanied by simultaneous ankle dorsi-flexion. Abrupt transitions from stoop to squat techniques were observed during descending trials, and from squat to stoop during ascending trials. Indications of hysteresis was observed in that transitions were more frequently observed during descending trials, and the average shelf height at the transition was 5 cm higher during ascending trials. The transitions may be a consequence of a trade-off between the biomechanical advantages of each technique and the influence of the lift height on this trade-off.

Gauge fields, geometric phases, and quantum adiabatic pumps

Quantum adiabatic pumping of charge and spin between two reservoirs (leads) has recently been demonstrated in nanoscale electronic devices. Pumping occurs when system parameters are varied in a cyclic manner and sufficiently slowly that the quantum system always remains in its ground state. We show that quantum pumping has a natural geometric representation in terms of gauge fields (both Abelian and non-Abelian) defined on the space of system parameters. Tunneling from a scanning tunneling microscope tip through a magnetic atom could be used to demonstrate the non-Abelian character of the gauge field.

Sigmosceptrins A-C: New norditerpenes from a southern Australian marine sponge, Sigmosceptrella sp.

A Sigmosceptrella sp. of sponge collected during trawling operations in the Great Australian Eight, Australia, has yielded a series of new norterpenes. These include a new bisnorditerpene, sigmosceptrin-A (5); two new norditerpenes, sigmosceptrin-B (14) and sigmosceptrin-C (15), isolated as their methyl esters (6) and (7) respectively; and an ethylated artefact, sigmosceptrin-B ethyl ester (8). Complete stereostructures were assigned to the sigmosceptrins by spectroscopic analysis, chemical degradation, derivatization, and by a single-crystal X-ray structural analysis. A biosynthetic pathway is proposed that requires a common biosynthetic precursor to both the sigmosceptrins and norterpene cyclic peroxides.

Mycaperoxides F and G and a related norterpene ketone from southern Australian marine sponges, Mycale species

Investigation of two southern Australian marine sponges, Mycale spp., resulted in isolation of the known norsesterterpene mycaperoxide F methyl ester (5) together with a new norsesterterpene mycaperoxide G methyl ester (10) and a new norterpene ketone 11. All structures were secured by spectroscopic analysis and chemical derivatization. The absolute stereochemistry previously assigned to 5 by application of the Horeau procedure has been revised by application of the Mosher procedure.

Modification of the in vivo four-point loading model for studying mechanically induced bone adaptation

We modified the noninvasive, in vivo technique for strain application in the tibiae of rats (Turner et al,, Bone 12:73-79, 1991), The original model applies four-point bending to right tibiae via an open-loop, stepper-motor-driven spring linkage, Depending on the magnitude of applied load, the model produces new bone formation at periosteal (Ps) or endocortical surfaces (Ec.S). Due to the spring linkage, however, the range of frequencies at which loads can be applied is limited. The modified system replaces this design with an electromagnetic vibrator. A load transducer in series with the loading points allows calibration, the loaders' position to be adjusted, and cyclic loading completed under load central as a closed servo-loop. Two experiments were conducted to validate the modified system: (1) a strain gauge was applied to the lateral surface of the right tibia of 5 adult female rats and strains measured at applied loads from 10 to 60 N; and (2) the bone formation response was determined in 28 adult female Sprague-Dawley rats. Loading was applied as a haversine wave with a frequency of 2 Hz for 18 sec, every second day for 10 days. Peak bending loads mere applied at 33, 40, 52, and 64 N, and a sham-loading group tr as included at 64 N, Strains in the tibiae were linear between 10 and 60 N, and the average peak strain at the Ps.S at 60 N was 2664 +/- 250 microstrain, consistent with the results of Turner's group. Lamellar bone formation was stimulated at the Ec.S by applied bending, but not by sham loading. Bending strains above a loading threshold of 40 N increased Ec Lamellar hone formation rate, bone forming surface, and mineral apposition rate with a dose response similar to that reported by Turner et al, (J Bone Miner Res 9:87-97, 1994). We conclude that the modified loading system offers precision for applied loads of between 0 and 70 N, versatility in the selection of loading rates up to 20 Hz, and a reproducible bone formation response in the rat tibia, Adjustment of the loader also enables study of mechanical usage in murine tibia, an advantage with respect to the increasing variety of transgenic strains available in bone and mineral research. (Bone 23:307-310; 1998) (C) 1998 by Elsevier Science Inc. All rights reserved.

Small molecular probes for G-protein-coupled C5a receptors: Conformationally constrained antagonists derived from the C terminus of the human plasma protein C5a

Activation of the human complement system of plasma proteins in response to infection or injury produces a 4-helix bundle glycoprotein (74 amino acids) known as C5a. C5a binds to G-protein-coupled receptors on cell surfaces triggering receptor-ligand internalization, signal transduction, and powerful inflammatory responses. Since excessive levels of C5a are associated with autoimmune and chronic inflammatory disorders, inhibitors of receptor activation may have therapeutic potential. We now report solution structures and receptor-binding and antagonist activities for some of the first small molecule antagonists of C5a derived from its hexapeptide C terminus. The antagonist NMe-Phe-Lys-Pro-D-Cha-Trp-D-Arg-CO2H (1) surprisingly shows an unusually well-defined solution structure as determined by H-1 NMR spectroscopy. This is one of the smallest acyclic peptides found to possess a defined solution conformation, which can be explained by the constraining role of intramolecular hydrogen bonding. NOE and coupling constant data, slow deuterium exchange, and a low dependence on temperature for the chemical shift of the D-Cha-NH strongly indicate an inverse gamma turn stabilized by a D-Cha-NH ... OC-Lys hydrogen bond. Smaller conformational populations are associated with a hydrogen bond between Trp-NH ... OC-Lys, defining a type II beta turn distorted by the inverse gamma turn incorporated within it. An excellent correlation between receptor-affinity and antagonist activity is indicated for a limited set of synthetic peptides. Conversion of the C-terminal carboxylate of 1 to an amide decreases antagonist potency 5-fold, but potency is increased up to 10-fold over 1 if the amide bond is made between the C-terminal carboxylate and a Lys/Orn side chain to form a cyclic analogue. The solution structure of cycle 6 also shows gamma and beta turns; however, the latter occurs in a different position, and there are clear conformational changes in 6 vs 1 that result in enhanced activity. These results indicate that potent C5a antagonists can be developed by targeting site 2 alone of the C5a receptor and define a novel pharmacophore for developing powerful receptor probes or drug candidates.

Activation of beta(2)-adrenergic receptors hastens relaxation and mediates phosphorylation of phospholamban, troponin I, and C-protein in ventricular myocardium from patients with terminal heart failure

Background-Catecholamines hasten cardiac relaxation through beta-adrenergic receptors, presumably by phosphorylation of several proteins, but it is unknown which receptor subtypes are involved in human ventricle. We assessed the role of beta(1)- and beta(2)-adrenergic receptors in phosphorylating proteins implicated in ventricular relaxation. Methods and Results-Right ventricular trabeculae, obtained from freshly explanted hearts of patients with dilated cardiomyopathy (n=5) or ischemic cardiomyopathy (n=5), were paced at 60 bpm. After measurement of the contractile and relaxant effects of epinephrine (10 mu mol/L) or zinterol (10 mu mol/L), mediated through beta(2)-adrenergic receptors, and of norepinephrine (10 mu mol/L), mediated through beta(1)-adrenergic receptors, tissues were freeze clamped. We assessed phosphorylation of phospholamban, troponin I, and C-protein, as well as specific phosphorylation of phospholamban at serine 16 and threonine 17, Data did not differ between the 2 disease groups and were therefore pooled. Epinephrine, zinterol, and norepinephrine increased contractile force to approximately the same extent, hastened the onset of relaxation by 15+/-3%, 5+/-2%, and 20+/-3%, respectively, and reduced the time to half-relaxation by 26+/-3%, 21+/-3%, and 37+/-3%. These effects of epinephrine, zinterol, and norepinephrine were associated with phosphorylation (pmol phosphate/mg protein) of phospholamban 14+/-3, 12+/-4, and 12+/-3, troponin I 40+/-7, 33+/-7, and 31+/-6; and C-protein 7.2+/-1.9, 9.3 +/- 1.4, and 7.5 +/- 2.0. Phosphorylation of phospholamban occurred at both Ser16 and Thr17 residues through both beta(1)- and beta(2)-adrenergic receptors. Conclusions-Norepinephrine and epinephrine hasten human ventricular relaxation and promote phosphorylation of implicated proteins through both beta(1)- and beta(2)-adrenergic receptors, thereby potentially improving diastolic function.

Molecular recognition of macrocyclic peptidomimetic inhibitors by HIV-1 protease

High-resolution crystal structures are described for seven macrocycles complexed with HIV-1 protease (HIVPR). The macrocycles possess two amides and an aromatic group within 15-17 membered rings designed to replace N- or C-terminal tripeptides from peptidic inhibitors of HIVPR. Appended to each macrocycle is a transition state isostere and either an acyclic peptide, nonpeptide, or another macrocycle. These cyclic analogues are potent inhibitors of HIVPR, and the crystal structures show them to be structural mimics of acyclic peptides, binding in the active site of HIVPR via the same interactions. Each macrocycle is restrained to adopt a P-strand conformation which is preorganized for protease binding. An unusual feature of the binding of C-terminal macrocyclic inhibitors is the interaction between a positively charged secondary amine and a catalytic aspartate of HIVPR. A bicyclic inhibitor binds similarly through its secondary amine that lies between its component N-terminal and C-terminal macrocycles. In contrast, the corresponding tertiary amine of the N-terminal macrocycles does not interact with the catalytic aspartates. The amine-aspartate interaction induces a 1.5 Angstrom N-terminal translation of the inhibitors in the active site and is accompanied by weakened interactions with a water molecule that bridges the ligand to the enzyme, as well as static disorder in enzyme flap residues. This flexibility may facilitate peptide cleavage and product dissociation during catalysis. Proteases [Aba(67,95)]HIVPR and [Lys(7),Ile(33),Aba(67,95)]- HIVPR used in this work were shown to have very similar crystal structures.

Evolution of the genetic covariance between male and female components of mate recognition: An experimental test

The evolution of a positive genetic correlation between male and female components of mate recognition systems will result as a consequence of assortative mating and, in particular, is central to a number of theories of sexual selection. Although the existence of such genetic correlations has been investigated in a number of taxa, it has yet to be shown that such correlations evolve and whether they may evolve as rapidly as suggested by sexual selection models. In this study, I used a hybridization experiment to disrupt natural mate recognition systems and then observed the subsequent evolutionary dynamics of the genetic correlation between male and female components for 56 generations in hybrids between Drosophila serrata and Drosophila birchii. The genetic correlation between male and female components evolved from 0.388 at generation 5 to 1.017 at generation 37 and then declined to -0.040 after a further 19 generations. These results indicated that the genetic basis of the mate recognition system in the hybrid populations evolved rapidly. The initial rapid increase in the genetic correlation was consistent with the classic assumption that male and female components will coevolve under sexual selection. The subsequent decline in genetic correlation may be attributable to the fixation of major genes or, alternatively, may be a result of a cyclic evolutionary change in mate recognition.

Putative beta(4)-adrenoceptors in rat ventricle mediate increases in contractile force and cell Ca2+: comparison with atrial receptors and relationship to (-)-[H-3]-CGP 12177 binding

1 We identified putative beta(4)-adrenoceptors by radioligand binding, measured increases in ventricular contractile force by (-)-CGP 12177 and (+/-)-cyanopindolol and demonstrated increased Ca2+ transients by (-)-CGP 12177 in rat cardiomyocytes. 2 (-)-[H-3]-CGP 12177 labelled 13-22 fmol mg(-1) protein ventricular beta(1), beta(2)-adrenoceptors (pK(D) similar to 9.0) and 50-90 fmol mg(-1) protein putative beta(4)-adrenoceptors (pK(D) similar to 7.3). The affinity values (PKi) for (beta(1),beta(2)-) and putative beta(4)-adrenoceptors, estimated from binding inhibition, were (-)-propranolol 8.4, 5.7; (-)-bupranolol 9.7, 5.8; (+/-)-cyanopindolol 10.0,7.4. 3 In left ventricular papillary muscle, in the presence of 30 mu M 3-isobutyl-1-methylxanthine, (-)CGP 12177 and (+/-)-cyanopindolol caused positive inotropic effects, (pEC(50) (-)-CGP 12177, 7.6; (+/-)-cyanopindolol, 7.0) which were antagonized by (-)-bupranolol (pK(B) 6.7-7.0) and (-)-CGP 20712A (pK(B) 6.3-6.6). The cardiostimulant effects of(-)-CGP 12177 in papillary muscle, left and right atrium were antagonized by (+/-)-cyanopindolol (pK(i), 7.0-7.4). 4 (-)-CGP 12177 (1 mu M) in the presence of 200 nM (-)-propranolol increased Ca2+ transient amplitude by 56% in atrial myocytes, but only caused a marginal increase in ventricular myocytes. In the presence of 1 mu M 3-isobutyl-1-methylxanthine and 200 nM (-)-propranolol, 1 mu M (-)-CGP 12177 caused a 73% increase in Ca2+ transient amplitude in ventricular myocytes. (-)-CGP 12177 elicited arrhythmic transients in some atrial and ventricular myocytes. 5 Probably by preventing cyclic AMP hydrolysis, 3-isobutyl-1-methylxanthine facilitates the inotropic function of ventricular putative beta(4)-adrenoceptors. suggesting coupling to G(s) protein-adenylyl cyclase. The receptor-mediated increases in contractile force are related to increases of Ca2+ in atrial and ventricular myocytes. The agreement of binding affinities of agonists with cardiostimulant potencies is consistent with mediation through putative beta(4)-adrenoceptors labelled with (-)-[H-3]-CGP 12177.

Insect peptides with improved protease-resistance protect mice against bacterial infection

At a time of the emergence of drug-resistant bacterial strains, the development of antimicrobial compounds with novel mechanisms of action is of considerable interest. Perhaps the most promising among these is a family of antibacterial peptides originally isolated from insects. These were shown to act in a stereospecific manner on an as-yet unidentified target bacterial protein. One of these peptides, drosocin, is inactive in vivo due to the rapid decomposition in mammalian sera. However, another family member, pyrrhocoricin, is significantly more stable, has increased in vitro efficacy against Gram-negative bacterial strains, and if administered alone, as we show here, is devoid of in vitro or in vivo toxicity. At low doses, pyrrhocoricin protected mice against Escherichia call infection, but at a higher dose augmented the infection of compromised animals. Analogs of pyrrhocoricin were, therefore, synthesized to further improve protease resistance and reduce toxicity. A linear derivative containing unnatural amino acids at both termini showed high potency and lack of toxicity in vivo and an expanded cyclic analog displayed broad activity spectrum in vitro. The bioactive conformation of native pyrrhocoricin was determined by nuclear magnetic resonance spectroscopy, and similar to drosocin, reverse turns were identified as pharmacologically important elements at the termini, bridged by an extended peptide domain. Knowledge of the primary and secondary structural requirements for in vivo activity of these peptides allows the design of novel antibacterial drug leads.

An Activated O N Acyl Transfer Auxiliary: Efficient Amide-Backbone Substitution of Hindered "Difficult" Peptides

Overcoming the phenomenon known as difficult synthetic sequences has been a major goal in solid-phase peptide synthesis for over 30 years. In this work the advantages of amide backbone-substitution in the solid-phase synthesis of difficult peptides are augmented by developing an activated N-alpha-acyl transfer auxiliary. Apart from disrupting troublesome intermolecular hydrogen-bonding networks, the primary function of the activated N-alpha-auxiliary was to facilitate clean and efficient acyl capture of large or beta-branched amino acids and improve acyl transfer yields to the secondary N-alpha-amine. We found o-hydroxyl-substituted nitrobenzyl (Hnb) groups were suitable N-alpha-auxiliaries for this purpose. The relative acyl transfer efficiency of the Hnb auxiliary was superior to the 2-hydroxy-4-methoxybenzyl (Hmb) auxiliary with protected amino acids of varying size. Significantly, this difference in efficiency was more pronounced between more sterically demanding amino acids. The Hnb auxiliary is readily incorporated at the N-alpha-amine during SPPS by reductive alkylation of its corresponding benzaldehyde derivative and conveniently removed by mild photolysis at 366 nm. The usefulness of the Hnb auxiliary for the improvement of coupling efficiencies in the chain-assembly of difficult peptides was demonstrated by the efficient Hnb-assisted Fmoc solid-phase synthesis of a known hindered difficult peptide sequence, STAT-91. This work suggests the Hnb auxiliary will significantly enhance our ability to synthesize difficult polypeptides and increases the applicability of amide-backbone substitution.

The radiation chemistry of poly(dimethylsiloxane)

The radiation chemistry of poly(dimethyl siloxane) has been investigated with respect to identification of the nature of the small molecule chain scission products. Low molecular weight linear and cyclic products have been identified through the use of Si-29 solution NMR, GPC and MALDI-TOF mass spectrometry. It has been suggested that the low molecular weight cyclic products are formed by back-biting depolymerization reactions.