Generalized spin Sutherland systems revisited

We present generalizations of the spin Sutherland systems obtained earlier by Blom and Langmann and by Polychronakos in two different ways: from SU(n) Yang--Mills theory on the cylinder and by constraining geodesic motion on the N-fold direct product of SU(n) with itself, for any N>1. Our systems are in correspondence with the Dynkin diagram automorphisms of arbitrary connected and simply connected compact simple Lie groups. We give a finite-dimensional as well as an infinite-dimensional derivation and shed light on the mechanism whereby they lead to the same classical integrable systems. The infinite-dimensional approach, based on twisted current algebras (alias Yang--Mills with twisted boundary conditions), was inspired by the derivation of the spinless Sutherland model due to Gorsky and Nekrasov. The finite-dimensional method relies on Hamiltonian reduction under twisted conjugations of N-fold direct product groups, linking the quantum mechanics of the reduced systems to representation theory similarly as was explored previously in the N=1 case.Comment: 21 page

Derivations of the trigonometric BC(n) Sutherland model by quantum Hamiltonian reduction

The BC(n) Sutherland Hamiltonian with coupling constants parametrized by three arbitrary integers is derived by reductions of the Laplace operator of the group U(N). The reductions are obtained by applying the Laplace operator on spaces of certain vector valued functions equivariant under suitable symmetric subgroups of U(N)\times U(N). Three different reduction schemes are considered, the simplest one being the compact real form of the reduction of the Laplacian of GL(2n,C) to the complex BC(n) Sutherland Hamiltonian previously studied by Oblomkov.Comment: 30 pages, LateX; v2: final version with minor stylistic modification

The Bacterial Photosynthetic Reaction Center as a Model for Membrane Proteins

Membrane proteins participate in many fundamental cellular processes. Until recently, an understanding of the function and properties of membrane proteins was hampered by an absence of structural information at the atomic level. A landmark achievement toward understanding the structure of membrane proteins was the crystallization (1) and structure determination (2-5) the photosynthetic reaction center (RC) from the purple bacteria Rhodopseudomonas viridis, followed by that of the RC from Rhodobacter sphaeroides (6-17). The RC is an integral membrane protein-pigment complex, which carries out the initial steps of photosynthesis (reviewed in 18). RCs from the purple bacteria Rps. viridis and Rb. sphaeroides are composed of three membrane-associated protein subunits (designated L, M, and H), and the following cofactors: four bacteriochlorophylls (Bchl or B), two bacteriopheophytins (Bphe or [phi]), two quinones, and a nonheme iron. The cofactors are organized into two symmetrical branches that are approximately related by a twofold rotation axis (2, 8). A central feature of the structural organization of the RC is the presence of 11 hydrophobic [alpha]-helixes, approximately 20-30 residues long, which are believed to represent the membrane-spanning portion of the RC (3, 9). Five membrane-spanning helixes are present in both the L and M subunits, while a single helix is in the H subunit. The folding of the L and M subunits is similar, consistent with significant sequence similarity between the two chains (19-25). The L and M subunits are approximately related by the same twofold rotation axis that relates the two cofactor branches. RCs are the first membrane proteins to be described at atomic resolution; consequently they provide an important model for discussing the folding of membrane proteins. The structure demonstrates that [alpha]-helical structures may be adopted by integral membrane proteins, and provides confirmation of the utility of hydropathy plots in identifying nonpolar membrane-spanning regions from sequence data. An important distinction between the folding environments of water-soluble proteins and membrane proteins is the large difference in water concentration surrounding the proteins. As a result, hydrophobic interactions (26) play very different roles in stabilizing the tertiary structures of these two classes of proteins; this has important structural consequences. There is a striking difference in surface polarity of membrane and water-soluble proteins. However, the characteristic atomic packing and surface area appear quite similar. A computational method is described for defining the position of the RC in the membrane (10). After localization of the RC structure in the membrane, surface residues in contact with the lipid bilayer were identified. As has been found for soluble globular proteins, surface residues are less well conserved in homologous membrane proteins than the buried, interior residues. Methods based on the variability of residues between homologous proteins are described (13); they are useful (a) in defining surface helical regions of membrane and water-soluble proteins and (b) in assigning the side of these helixes that are exposed to the solvent. A unifying view of protein structure suggests that water-soluble proteins may be considered as modified membrane proteins with covalently attached polar groups that solubilize the proteins in aqueous solution

Proton transfer pathways and mechanism in bacterial reaction centers

AbstractThe focus of this minireview is to discuss the state of knowledge of the pathways and rates of proton transfer in the bacterial reaction center (RC) from Rhodobacter sphaeroides. Protons involved in the light driven catalytic reduction of a quinone molecule QB to quinol QBH2 travel from the aqueous solution through well defined proton transfer pathways to the oxygen atoms of the quinone. Three main topics are discussed: (1) the pathways for proton transfer involving the residues: His-H126, His-H128, Asp-L210, Asp-M17, Asp-L213, Ser-L223 and Glu-L212, which were determined by a variety of methods including the use of proton uptake inhibiting metal ions (e.g. Zn2+ and Cd2+); (2) the rate constants for proton transfer, obtained from a ‘chemical rescue’ study was determined to be 2×105 s−1 and 2×104 s−1 for the proton uptake to Glu-L212 and QB−, respectively; (3) structural studies of altered proton transfer pathways in revertant RCs that lack the key amino acid Asp-L213 show a series of structural changes that propagate toward L213 potentially allowing Glu-H173 to participate in the proton transfer processes

Sine-Gordon multisoliton form factors in finite volume

Multi-soliton form factors in sine-Gordon theory from the bootstrap are compared to finite volume matrix elements computed using the truncated conformal space approach. We find convincing agreement, and resolve most of the issues raised in a previous work.Comment: 24 pages, LaTeX2e file, 8 eps figures. v2: notations improved, some explanatory text and references adde

Optical Detection of a Single Nuclear Spin

We propose a method to optically detect the spin state of a 31-P nucleus embedded in a 28-Si matrix. The nuclear-electron hyperfine splitting of the 31-P neutral-donor ground state can be resolved via a direct frequency discrimination measurement of the 31-P bound exciton photoluminescence using single photon detectors. The measurement time is expected to be shorter than the lifetime of the nuclear spin at 4 K and 10 T.Comment: 4 pages, 3 figure