Critical transport properties of random metals in large magnetic fields

The threshold behavior of the transport properties of a random metal in the critical region near a metal–insulator transition is strongly affected by the measuring electromagnetic fields. In spite of the randomness, the electrical conductivity exhibits striking phase-coherent effects due to broken symmetry, which greatly sharpen the transition compared with the predictions of effective medium theories, as previously explained for electrical conductivities. Here broken symmetry explains the sign reversal of the T → 0 magnetoconductance of the metal–insulator transition in Si(B,P), also previously not understood by effective medium theories. Finally, the symmetry-breaking features of quantum percolation theory explain the unexpectedly very small electrical conductivity temperature exponent α = 0.22(2) recently observed in Ni(S,Se)2 alloys at the antiferromagnetic metal–insulator transition below T = 0.8 K.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Multicomponent diffusion in polymeric liquids.

It is shown how the phase-space kinetic theory of polymeric liquid mixtures leads to a set of extended Maxwell-Stefan equations describing multicomponent diffusion. This expression reduces to standard results for dilute solutions and for undiluted polymers. The polymer molecules are modeled as flexible bead-spring structures. To obtain the Maxwell-Stefan equations, the usual expression for the hydrodynamic drag force on a bead, used in previous kinetic theories, must be replaced by a new expression that accounts explicitly for bead-bead interactions between different molecules.

The vibrational energy flow transition in organic molecules: Theory meets experiment

Most large dynamical systems are thought to have ergodic dynamics, whereas small systems may not have free interchange of energy between degrees of freedom. This assumption is made in many areas of chemistry and physics, ranging from nuclei to reacting molecules and on to quantum dots. We examine the transition to facile vibrational energy flow in a large set of organic molecules as molecular size is increased. Both analytical and computational results based on local random matrix models describe the transition to unrestricted vibrational energy flow in these molecules. In particular, the models connect the number of states participating in intramolecular energy flow to simple molecular properties such as the molecular size and the distribution of vibrational frequencies. The transition itself is governed by a local anharmonic coupling strength and a local state density. The theoretical results for the transition characteristics compare well with those implied by experimental measurements using IR fluorescence spectroscopy of dilution factors reported by Stewart and McDonald [Stewart, G. M. & McDonald, J. D. (1983) J. Chem. Phys. 78, 3907–3915].

Toward a quantum-mechanical description of metal-assisted phosphoryl transfer in pyrophosphatase

The wealth of kinetic and structural information makes inorganic pyrophosphatases (PPases) a good model system to study the details of enzymatic phosphoryl transfer. The enzyme accelerates metal-complexed phosphoryl transfer 1010-fold: but how? Our structures of the yeast PPase product complex at 1.15 Å and fluoride-inhibited complex at 1.9 Å visualize the active site in three different states: substrate-bound, immediate product bound, and relaxed product bound. These span the steps around chemical catalysis and provide strong evidence that a water molecule (Onu) directly attacks PPi with a pKa vastly lowered by coordination to two metal ions and D117. They also suggest that a low-barrier hydrogen bond (LBHB) forms between D117 and Onu, in part because of steric crowding by W100 and N116. Direct visualization of the double bonds on the phosphates appears possible. The flexible side chains at the top of the active site absorb the motion involved in the reaction, which may help accelerate catalysis. Relaxation of the product allows a new nucleophile to be generated and creates symmetry in the elementary catalytic steps on the enzyme. We are thus moving closer to understanding phosphoryl transfer in PPases at the quantum mechanical level. Ultra-high resolution structures can thus tease out overlapping complexes and so are as relevant to discussion of enzyme mechanism as structures produced by time-resolved crystallography.

On the absorbance changes in the photocycle of the photoactive yellow protein: A quantum-chemical analysis

Spectral changes in the photocycle of the photoactive yellow protein (PYP) are investigated by using ab initio multiconfigurational second-order perturbation theory at the available structures experimentally determined. Using the dark ground-state crystal structure [Genick, U. K., Soltis, S. M., Kuhn, P., Canestrelli, I. L. & Getzoff, E. D. (1998) Nature (London) 392, 206–209], the ππ* transition to the lowest excited state is related to the typical blue-light absorption observed at 446 nm. The different nature of the second excited state (nπ*) is consistent with the alternative route detected at 395-nm excitation. The results suggest the low-temperature photoproduct PYPHL as the most plausible candidate for the assignment of the cryogenically trapped early intermediate (Genick et al.). We cannot establish, however, a successful correspondence between the theoretical spectrum for the nanosecond time-resolved x-ray structure [Perman, B., Šrajer, V., Ren, Z., Teng, T., Pradervand, C., et al. (1998) Science 279, 1946–1950] and any of the spectroscopic photoproducts known up to date. It is fully confirmed that the colorless light-activated intermediate recorded by millisecond time-resolved crystallography [Genick, U. K., Borgstahl, G. E. O., Ng, K., Ren, Z., Pradervand, C., et al. (1997) Science 275, 1471–1475] is protonated, nicely matching the spectroscopic features of the photoproduct PYPM. The overall contribution demonstrates that a combined analysis of high-level theoretical results and experimental data can be of great value to perform assignments of detected intermediates in a photocycle.

Quantum groups with invariant integrals

Quantum groups have been studied intensively for the last two decades from various points of view. The underlying mathematical structure is that of an algebra with a coproduct. Compact quantum groups admit Haar measures. However, if we want to have a Haar measure also in the noncompact case, we are forced to work with algebras without identity, and the notion of a coproduct has to be adapted. These considerations lead to the theory of multiplier Hopf algebras, which provides the mathematical tool for studying noncompact quantum groups with Haar measures. I will concentrate on the *-algebra case and assume positivity of the invariant integral. Doing so, I create an algebraic framework that serves as a model for the operator algebra approach to quantum groups. Indeed, the theory of locally compact quantum groups can be seen as the topological version of the theory of quantum groups as they are developed here in a purely algebraic context.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

Increase in the Quantum Yield of Photoinhibition Contributes to Copper Toxicity in Vivo1

The effect of copper on photoinhibition of photosystem II in vivo was studied in bean (Phaseolus vulgaris L. cv Dufrix). The plants were grown hydroponically in the presence of various concentrations of Cu2+ ranging from the optimum 0.3 μm (control) to 15 μm. The copper concentration of leaves varied according to the nutrient medium from a control value of 13 mg kg−1 dry weight to 76 mg kg−1 dry weight. Leaf samples were illuminated in the presence and absence of lincomycin at different light intensities (500–1500 μmol photons m−2 s−1). Lincomycin prevents the concurrent repair of photoinhibitory damage by blocking chloroplast protein synthesis. The photoinhibitory decrease in the light-saturated rate of O2 evolution measured from thylakoids isolated from treated leaves correlated well with the decrease in the ratio of variable to maximum fluorescence measured from the leaf discs; therefore, the fluorescence ratio was used as a routine measurement of photoinhibition in vivo. Excess copper was found to affect the equilibrium between photoinhibition and repair, resulting in a decrease in the steady-state concentration of active photosystem II centers of illuminated leaves. This shift in equilibrium apparently resulted from an increase in the quantum yield of photoinhibition (ΦPI) induced by excess copper. The kinetic pattern of photoinhibition and the independence of ΦPI on photon flux density were not affected by excess copper. An increase in ΦPI may contribute substantially to Cu2+ toxicity in certain plant species.

Force and kinetic barriers to unzipping of the DNA double helix

A theory of the unzipping of double-stranded DNA is presented and is compared to recent micromanipulation experiments. It is shown that the interactions that stabilize the double helix and the elastic rigidity of single strands simply determine the sequence-dependent ≈12-pN force threshold for DNA strand separation. Using a semimicroscopic model of the binding between nucleotide strands, we show that the greater rigidity of the strands when formed into double-stranded DNA, relative to that of isolated strands, gives rise to a potential barrier to unzipping. The effects of this barrier are derived analytically. The force to keep the extremities of the molecule at a fixed distance, the kinetic rates for strand unpairing at fixed applied force, and the rupture force as a function of loading rate are calculated. The dependence of the kinetics and of the rupture force on molecule length is also analyzed.