Twists, knots, and rings in proteins: Structural definition of the cyclotide framework

In recent years an increasing number of miniproteins containing an amide-cyclized backbone have been discovered. The cyclotide family is the largest group of such proteins and is characterized by a circular protein backbone and six conserved cysteine residues linked by disulfide bonds in a tight core of the molecule. These form a cystine knot in which an embedded ring formed by two of the disulfide bonds and the connecting backbone segment is threaded by a third disulfide bond. In the current study we have undertaken high resolution structural analysis of two prototypic cyclotides, kalata B1 and cycloviolacin O1, to define the role of the conserved residues in the sequence. We provide the first comprehensive analysis of the topological features in this unique family of proteins, namely rings (a circular backbone), twists (a cis-peptide bond in the Mobius cyclotides) and knots (a knotted arrangement of the disulfide bonds).

Alpha-cellulose δ13C variation in mangrove tree rings correlates well with annual sea level trend between 1982 and 1999

A pilot study of tree rings in a modern mangrove tree (Rhizophora apiculata) from Leizhou Peninsula, northern South China Sea shows that ( 1) the tree-rings are annual; ( 2) the ring widths decrease; and ( 3) their alpha-cellulose delta(13)C values increase from 1982 to 1999 AD, consistent with the trends of annual sea level, salinity and sea surface temperatures in the same period. We propose that such changes were caused by increasingly longer duration of waterlogging in response to sea-level rise. If this is the case, alpha-cellulose delta(13)C in mangrove tree rings can be used as a potential indicator of past sea level fluctuations.

Radiocarbon in tropical tree rings during the Little Ice Age

Cross-dated tree-ring cores (Pinus merkusii) from north-central Thailand, spanning AD 1620-1780, were used to investigate atmospheric C-14 for the tropics during the latter part of the Little Ice Age. In addition, a cross-dated section of Huon pine from western Tasmania, covering the same period of time, was investigated. A total of 16 pairs of decadal samples were extracted to alpha-cellulose for AMS C-14 analysis using the ANTARES facility at ANSTO. The C-14 results from Thailand follow the trend of the southern hemisphere, rather than that of the northern hemisphere. This is a surprising result, and we infer that atmospheric C-14 for north-central Thailand, at 17degrees N, was strongly influenced by the entrainment of southern hemisphere air parcels during the southwest Asian monsoon, when the Inter-Tropical Convergence Zone moves to the north of our sampling site. Such atmospheric transport and mixing are therefore considered to be one of the principal mechanisms for regional C-14 offsets. (C) 2004 Elsevier B.V. All rights reserved.

Knots in rings - The circular knotted protein momordica cochinchinensis trypsin inhibitor-II folds via a stable two-disulfide intermediate

The aim of this work was to elucidate the oxidative folding mechanism of the macrocyclic cystine knot protein MCoTI-II. We aimed to investigate how the six-cysteine residues distributed on the circular backbone of the reduced unfolded peptide recognize their correct partner and join up to form a complex cystine-knotted topology. To answer this question, we studied the oxidative folding of the naturally occurring peptide using a range of spectroscopic methods. For both oxidative folding and reductive unfolding, the same disulfide intermediate species was prevalent and was characterized to be a native-like two-disulfide intermediate in which the Cys(1)-Cys(18) disulfide bond was absent. Overall, the folding pathway of this head-to-tail cyclized protein was found to be similar to that of linear cystine knot proteins from the squash family of trypsin inhibitors. However, the pathway differs in an important way from that of the cyclotide kalata B1, in that the equivalent two-disulfide intermediate in that case is not a direct precursor of the native protein. The size of the embedded ring within the cystine knot motif appears to play a crucial role in the folding pathway. Larger rings contribute to the independence of disulfides and favor an on-pathway native-like intermediate that has a smaller energy barrier to cross to form the native fold. The fact that macrocyclic proteins are readily able to fold to a complex knotted structure in vitro in the absence of chaperones makes them suitable as protein engineering scaffolds that have remarkable stability.

Twisted quantum affine superalgebra Uq[gl(m|n)(2)] and new Uq[osp(m|n)] invariant R-matrices

The minimal irreducible representations of U-q[gl(m|n)], i.e. those irreducible representations that are also irreducible under U-q[osp(m|n)] are investigated and shown to be affinizable to give irreducible representations of the twisted quantum affine superalgebra U-q[gl(m|n)((2))]. The U-q[osp(m|n)] invariant R-matrices corresponding to the tensor product of any two minimal representations are constructed, thus extending our twisted tensor product graph method to the supersymmetric case. These give new solutions to the spectral-dependent graded Yang-Baxter equation arising from U-q[gl(m|n)((2))], which exhibit novel features not previously seen in the untwisted or non-super cases.

Elliptic Gaudin models and elliptic KZ equations

The Gaudin models based on the face-type elliptic quantum groups and the XYZ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding face-type Knizhnik–Zamolodchikov equations and their solutions are given.

On Quasi-Hopf Superalgebras

In this work we investigate several important aspects of the structure theory of the recently introduced quasi-Hopf superalgebras (QHSAs), which play a fundamental role in knot theory and integrable systems. In particular we introduce the opposite structure and prove in detail (for the graded case) Drinfeld's result that the coproduct Delta ' =_ (S circle times S) (.) T (.) Delta (.) S-1 induced on a QHSA is obtained from the coproduct Delta by twisting. The corresponding "Drinfeld twist" F-D is explicitly constructed, as well as its inverse, and we investigate the complete QHSA associated with Delta '. We give a universal proof that the coassociator Phi ' = (S circle times S circle times S) Phi (321) and canonical elements alpha ' = S(beta), beta ' = S(alpha) correspond to twisting, the original coassociator Phi = Phi (123) and canonical elements alpha, beta with the Drinfeld twist F-D. Moreover in the quasi-tri angular case, it is shown algebraically that the R-matrix R ' = (S circle times S)R corresponds to twisting the original R-matrix R with F-D. This has important consequences in knot theory, which will be investigated elsewhere.

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.