Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Proteins unfold in steps

I present results from an experiment on the dynamics of folding of a globular protein (bovine serum albumin). Employing a micro-mechanical technique, I perform the measurements on very few molecules (1–100). I observed a sequence of steps in time for both unfolding and refolding. The overall characteristic time of the process is thus built up of waiting times between successive steps. The pattern of steps is reproducible, demonstrating the existence of deterministic pathways for folding and unfolding. Certain symmetries in the patterns of steps may reflect the architecture of the protein’s structure.

Direct interaction of flagellin termini essential for polymorphic ability of flagellar filament

We report the structures of flagellar filaments reconstituted from various flagellins with small terminal truncations. Flagellins from Salmonella typhimurium strains SJW1103 (wild type), SJW1660, and SJW1655 were used, which form a left-handed supercoil, the L- and R-type straight forms, respectively. Structure analyses were done by electron cryomicroscopy and helical image reconstruction with a help of x-ray fiber diffraction for determining precise helical symmetries. Truncation of either terminal region, irrespective of the original flagellin species, results in a straight filament having a helical symmetry distinct either from the L- or R-type. This filament structure is named Lt-type. Although the local subunit packing is similar in all three types, a close comparison shows that the Lt-type packing is almost identical to the R-type but distinct from the L-type, which demonstrates the strong two-state preference of the subunit interactions. The structure clearly suggests that both termini are located in the inner tube of the concentric double-tubular structure of the filament core, and their proper interaction is responsible for the correct folding of fairly large terminal regions that form the inner tube. The double tubular structure appears to be essential for the polymorphic ability of flagellar filaments, which is required for the swimming–tumbling of bacterial taxis.

Symmetry, stability, and dynamics of multidomain and multicomponent protein systems

Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions.

Molecular Characterization of an Arabidopsis Gene Encoding Hydroperoxide Lyase, a Cytochrome P-450 That Is Wound Inducible1

Hydroperoxide lyase (HPL) cleaves lipid hydroperoxides to produce volatile flavor molecules and also potential signal molecules. We have characterized a gene from Arabidopsis that is homologous to a recently cloned HPL from green pepper (Capsicum annuum). The deduced protein sequence indicates that this gene encodes a cytochrome P-450 with a structure similar to that of allene oxide synthase. The gene was cloned into an expression vector and expressed in Escherichia coli to demonstrate HPL activity. Significant HPL activity was evident when 13S-hydroperoxy-9(Z),11(E),15(Z)-octadecatrienoic acid was used as the substrate, whereas activity with 13S-hydroperoxy-9(Z),11(E)-octadecadienoic acid was approximately 10-fold lower. Analysis of headspace volatiles by gas chromatography-mass spectrometry, after addition of the substrate to E. coli extracts expressing the protein, confirmed enzyme-activity data, since cis-3-hexenal was produced by the enzymatic activity of the encoded protein, whereas hexanal production was limited. Molecular characterization of this gene indicates that it is expressed at high levels in floral tissue and is wound inducible but, unlike allene oxide synthase, it is not induced by treatment with methyl jasmonate.

Origin and evolution of circular waves and spirals in Dictyostelium discoideum territories.

Randomly distributed Dictyostelium discoideum cells form cooperative territories by signaling to each other with cAMP. Cells initiate the process by sending out pulsatile signals, which propagate as waves. With time, circular and spiral patterns form. We show that by adding spatial and temporal noise to the levels of an important regulator of external cAMP levels, the cAMP phosphodiesterase inhibitor, we can explain the natural progression of the system from randomly firing cells to circular waves whose symmetries break to form double- and single- or multi-armed spirals. When phosphodiesterase inhibitor is increased with time, mimicking experimental data, the wavelength of the spirals shortens, and a proportion of them evolve into pairs of connected spirals. We compare these results to recent experiments, finding that the temporal and spatial correspondence between experiment and model is very close.

Cell cycling and patterned cell proliferation in the wing primordium of Drosophila.

The pattern of cell proliferation in the Drosophila imaginal wing primordium is spatially and temporally heterogeneous. Direct visualization of cells in S, G2, and mitosis phases of the cell cycle reveals several features invariant throughout development. The fraction of cells in the disc in the different cell cycle stages is constant, the majority remaining in G1. Cells in the different phases of the cell cycle mainly appear in small synchronic clusters that are nonclonally derived but result from changing local cell-cell interactions. Cluster synchronization occurs before S and in the G2/M phases. Rates of cell division are neither constant nor clonal features. Cell cycle progression is linear rather than concentric. Clusters appear throughout the disc but with symmetries related to presumptive wing patterns, compartment boundaries, and vein clonal restrictions.

Quantisation of the bosonic string

In this work we review the basic principles of the theory of the relativistic bosonic string through the study of the action functionals of Nambu-Goto and Polyakov and the techniques required for their canonical, light-cone, and path-integral quantisation. For this purpose, we briefly review the main properties of the gauge symmetries and conformal field theory involved in the techniques studied.

Caroço de algodão integral e vitamina E em dietas para bovinos Nelore, confinados por 83, 104 e 111 dias

O objetivo deste trabalho foi avaliar os efeitos da inclusão de caroço de algodão e vitamina E em dietas para bovinos confinados por 83, 104 e 111 dias sobre as características da carcaça, qualidade da carne e características sensoriais da carne in natura e de hambúrgueres. Foram utilizados 54 bovinos da raça Nelore, machos, não castrados, com média de 350 kg ± 30 kg de peso vivo inicial e 24 meses de idade, divididos em três grupos de acordo com o peso vivo inicial e distribuídos em três dietas: dieta sem inclusão de caroço de algodão (C), dieta contendo 30% MS de caroço de algodão (CA) e dieta contendo 30% MS de caroço de algodão e 500 UI de vitamina E/kg de matéria seca da ração (CAE). As dietas empregadas foram compostas de diferentes concentrados, incluindo milho grão seco, polpa cítrica, bagaço de cana cru e farelo de soja, com relação volumoso:concentrado de 14:86 e média de 16% PB nas três dietas. Os animais abatidos aos 83 dias de confinamento eram correspondentes ao grupo de maior peso vivo, já os animais mais leves foram abatidos aos 111 dias de confinamento. O experimento foi em arranjo fatorial 3 x 3, considerando três dietas e três períodos de confinamento, totalizando 9 tratamentos. Os animais que permaneceram em confinamento por mais tempo apresentaram maior rendimento de carcaça (56,33%) e carnes mais macias (3,02 kg). As dietas CA e CAE resultaram em menor força de cisalhamento (3,15 e 3,31 kg, respectivamente). A inclusão de vitamina E se mostrou indiferente para a cor e TBARS, em relação à dieta CA. A inclusão do caroço de algodão em dietas para bovinos não influenciou no teor de ácidos graxos saturados, porém aumentou os teores de alguns ácidos graxos poli-insaturados (AGPI) nas carnes. Por outro lado, houve um aumento linear nos níveis de ácidos graxos saturados (AGS) à medida que aumentaram os dias de confinamento. Em relação às características sensoriais, no teste descritivo, as carnes in natura dos animais alimentados com CA e CAE foram mais macias e suculentas (P < 0,05), porém apresentaram um sabor mais intenso e os provadores treinados detectaram um sabor estranho nestas carnes (P < 0,05). No entanto, para o teste afetivo, apenas foi detectado sabor estranho para os hambúrgueres provenientes da dieta CA, os atributos aroma e aroma estranho não foram influenciados pelas dietas (P > 0,05). Por meio do teste discriminativo, foi observado que os hambúrgueres provenientes de animais alimentados com CA e CAE por 104 e 111 dias de confinamento apresentaram diferença em relação ao sabor quando comparados aos hambúrgueres de animais do grupo C destes mesmos períodos, e que os hambúrgueres da dieta CA não apresentaram diferença de sabor quanto aos dias de confinamento. A inclusão de 30% MS de caroço de algodão mostrou ser uma boa alternativa para melhorar as características físico-químicas da carne e seu perfil de ácidos graxos, entretanto atribui um sabor estranho ao produto final, independente do período de confinamento, sendo perceptível ao consumidor e reduzindo aceitabilidade. Ao longo dos dias de confinamento, a carne dos animais se torna menos saudável, do ponto de vista de composição lipídica, ao consumo humano. A adição de 500 UI de vitamina E em dietas contendo caroço de algodão mostrou-se desnecessária