The role of symmetry in fundamental physics

The role of symmetry in fundamental physics is reviewed.

Symmetry arguments in chemistry

The use (and misuse) of symmetry arguments in constructing molecular models and in the interpretation of experimental observations bearing on molecular structure (spectroscopy, diffraction, etc.) is discussed. Examples include the development of point groups and space groups for describing the external and internal symmetry of crystals, the derivation of molecular symmetry by counting isomers (the benzene structure), molecular chirality, the connection between macroscopic and molecular chirality, pseudorotation, the symmetry group of nonrigid molecules, and the use of orbital symmetry arguments in discussing aspects of chemical reactivity.

Five-fold symmetry in crystalline quasicrystal lattices

To demonstrate that crystallographic methods can be applied to index and interpret diffraction patterns from well-ordered quasicrystals that display non-crystallographic 5-fold symmetry, we have characterized the properties of a series of periodic two-dimensional lattices built from pentagons, called Fibonacci pentilings, which resemble aperiodic Penrose tilings. The computed diffraction patterns from periodic pentilings with moderate size unit cells show decagonal symmetry and are virtually indistinguishable from that of the infinite aperiodic pentiling. We identify the vertices and centers of the pentagons forming the pentiling with the positions of transition metal atoms projected on the plane perpendicular to the decagonal axis of quasicrystals whose structure is related to crystalline η phase alloys. The characteristic length scale of the pentiling lattices, evident from the Patterson (autocorrelation) function, is ∼τ2 times the pentagon edge length, where τ is the golden ratio. Within this distance there are a finite number of local atomic motifs whose structure can be crystallographically refined against the experimentally measured diffraction data.

From symmetry to asymmetry: Phylogenetic patterns of asymmetry variation in animals and their evolutionary significance

Phylogenetic analyses of asymmetry variation offer a powerful tool for exploring the interplay between ontogeny and evolution because (i) conspicuous asymmetries exist in many higher metazoans with widely varying modes of development, (ii) patterns of bilateral variation within species may identify genetically and environmentally triggered asymmetries, and (iii) asymmetries arising at different times during development may be more sensitive to internal cytoplasmic inhomogeneities compared to external environmental stimuli. Using four broadly comparable asymmetry states (symmetry, antisymmetry, dextral, and sinistral), and two stages at which asymmetry appears developmentally (larval and postlarval), I evaluated relations between ontogenetic and phylogenetic patterns of asymmetry variation. Among 140 inferred phylogenetic transitions between asymmetry states, recorded from 11 classes in five phyla, directional asymmetry (dextral or sinistral) evolved directly from symmetrical ancestors proportionally more frequently among larval asymmetries. In contrast, antisymmetry, either as an end state or as a transitional stage preceding directional asymmetry, was confined primarily to postlarval asymmetries. The ontogenetic origin of asymmetry thus significantly influences its subsequent evolution. Furthermore, because antisymmetry typically signals an environmentally triggered asymmetry, the phylogenetic transition from antisymmetry to directional asymmetry suggests that many cases of laterally fixed asymmetries evolved via genetic assimilation.

Symmetry in chemistry from the hydrogen atom to proteins

The last 2 decades have seen discoveries in highly excited states of atoms and molecules of phenomena that are qualitatively different from the “planetary” model of the atom, and the near-rigid model of molecules, characteristic of these systems in their low-energy states. A unified view is emerging in terms of approximate dynamical symmetry principles. Highly excited states of two-electron atoms display “molecular” behavior of a nonrigid linear structure undergoing collective rotation and vibration. Highly excited states of molecules described in the “standard molecular model” display normal mode couplings, which induce bifurcations on the route to molecular chaos. New approaches such as rigid–nonrigid correlation, vibrons, and quantum groups suggest a unified view of collective electronic motion in atoms and nuclear motion in molecules.

Mirror symmetry breaking at the molecular level.

Reasoning from two basic principles of molecular physics, P invariance of electromagnetic interaction and the second law of thermodynamics, one would conclude that mirror symmetry retained in the world of chiral molecules. This inference is fully consistent with what is observed in inorganic nature. However, in the bioorganic world, the reverse is true. Mirror symmetry there is definitely broken. Is it possible to account for this phenomenon without going beyond conventional concepts of the kinetics of enantioselective processes? This study is an attempt to survey all existing hypotheses containing this phenomenon.

Independent determination of symmetry and polarity in the Drosophila eye.

In each facet of the Drosophila compound eye, a cluster of photoreceptor cells assumes an asymmetric trapezoidal pattern. These clusters have opposite orientations above and below an equator, showing global dorsoventral mirror symmetry. However, in the mutant spiny legs, the polarization of each cluster appears to be random, so that no equator is evident. The apparent lack of an equator suggests that spiny legs+ may be involved in the establishment of global dorsoventral identity that might be essential for proper polarization of the photoreceptor clusters. Alternatively, a global dorsoventral pattern could be present, but spiny legs+ may be required for local polarization of individual clusters. Using an enhancer trap strain in which white+ gene expression is restricted to the dorsal field, we show that white+ expression in spiny legs correctly respects dorsoventral position even in facets with inappropriate polarizations; the dorsoventral boundary is indeed present, whereas the mechanism for polarization is perturbed. It is suggested that the boundary is established before the action of spiny legs+ by an independent mechanism.

Plant histochemistry by correlation peak imaging.

Using a new NMR correlation-peak imaging technique, we were able to investigate noninvasively the spatial distribution of carbohydrates and amino acids in the hypocotyl of castor bean seedlings. In addition to the expected high sucrose concentration in the phloem area of the vascular bundles, we could also observe high levels of sucrose in the cortex parenchyma, but low levels in the pith parenchyma. In contrast, the glucose concentration was found to be lower in the cortex parenchyma than in the pith parenchyma. Glutamine and/or glutamate was detected in the cortex parenchyma and in the vascular bundles. Lysine and arginine were mainly visible in the vascular bundles, whereas valine was observed in the cortex parenchyma, but not in the vascular bundles. Although the physiological significance of these metabolite distribution patterns is not known, they demonstrate the potential of spectroscopic NMR imaging to study noninvasively the physiology and spatial metabolic heterogeneity of living plants.

Modulation of retinoblastoma gene in normal adult hematopoiesis: peak expression and functional role in advanced erythroid differentiation.

The retinoblastoma (RB) gene specifies a nuclear phosphoprotein (pRb 105), which is a prototype tumor suppressor inactivated in a variety of human tumors. Recent studies suggest that RB is also involved in embryonic development of murine central nervous and hematopoietic systems. We have investigated RB expression and function in human adult hematopoiesis--i.e., in liquid suspension culture of purified quiescent hematopoietic progenitor cells (HPCs) induced by growth factor stimulus to proliferation and unilinage differentiation/maturation through the erythroid or granulocytic lineage. In the initial HPC differentiation stages, the RB gene is gradually induced at the mRNA and protein level in both erythroid and granulopoietic cultures. In late HPC differentiation and then precursor maturation, RB gene expression is sustained in the erythroid lineage, whereas it is sharply downmodulated in the granulocytic series. Functional studies were performed by treatment of HPC differentiation culture with phosphorothioate antisense oligomer targeting Rb mRNA; coherent with the expression pattern, oligomer treatment of late HPCs causes a dose-dependent and selective inhibition of erythroid colony formation. These observations suggest that the RB gene plays an erythroid- and stage-specific functional role in normal adult hematopoiesis, particularly at the level of late erythroid HPCs.

ABT-538 is a potent inhibitor of human immunodeficiency virus protease and has high oral bioavailability in humans.

Examination of the structural basis for antiviral activity, oral pharmacokinetics, and hepatic metabolism among a series of symmetry-based inhibitors of the human immunodeficiency virus (HIV) protease led to the discovery of ABT-538, a promising experimental drug for the therapeutic intervention in acquired immunodeficiency syndrome (AIDS). ABT-538 exhibited potent in vitro activity against laboratory and clinical strains of HIV-1 [50% effective concentration (EC50) = 0.022-0.13 microM] and HIV-2 (EC50 = 0.16 microM). Following a single 10-mg/kg oral dose, plasma concentrations in rat, dog, and monkey exceeded the in vitro antiviral EC50 for > 12 h. In human trials, a single 400-mg dose of ABT-538 displayed a prolonged absorption profile and achieved a peak plasma concentration in excess of 5 micrograms/ml. These findings demonstrate that high oral bioavailability can be achieved in humans with peptidomimetic inhibitors of HIV protease.

Thermodynamic glass transition in a spin glass without time-reversal symmetry

Spin glasses are a longstanding model for the sluggish dynamics that appear at the glass transition. However, spin glasses differ from structural glasses in a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behavior of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d < 6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method.

Interplay between sublattice and spin symmetry breaking in graphene

We study the effect of sublattice symmetry breaking on the electronic, magnetic, and transport properties of two-dimensional graphene as well as zigzag terminated one- and zero-dimensional graphene nanostructures. The systems are described with the Hubbard model within the collinear mean field approximation. We prove that for the noninteracting bipartite lattice with an unequal number of atoms in each sublattice, in-gap states still exist in the presence of a staggered on-site potential ±Δ/2. We compute the phase diagram of both 2D and 1D graphene with zigzag edges, at half filling, defined by the normalized interaction strength U/t and Δ/t, where t is the first neighbor hopping. In the case of 2D we find that the system is always insulating, and we find the Uc(Δ) curve above which the system goes antiferromagnetic. In 1D we find that the system undergoes a phase transition from nonmagnetic insulator for U

(Table T2) Integrated intensity (peak area) of matrix minerals of ODP Hole 173-1068A

Mass-wasting deposits characterize the Upper Jurassic(?) to Lower Cretaceous sedimentary record of the Iberia Abyssal Plain. These deposits include olistostromes at Site 897, olistostromes and/or possible rock-fall deposits at Site 899, a breccia succession at Site 1068, slumped and fractured deposits at Site 1069, and a breccia succession at Site 1070. Whereas the exact origin of these deposits is uncertain, the regional common occurrence of middle to upper Mesozoic mass-wasting deposits suggests that they record the early rifting evolution of the west Iberia margin. This data report presents both qualitative and semiquantitative results from XRD analyses of the breccia matrix at Site 1068. In this study the matrix is defined as the fine-grained particles (as viewed through a binocular microscope) plus cement. Results are based on analytical methods that aimed to isolate the desired matrix from larger clast contamination prior to XRD analyses. In addition, the breccia was sampled at a higher resolution than was conducted aboard ship, producing a more complete description of downcore matrix mineralogical changes. The data presented here may be used to (1) further justify the subunit designation of Unit IV made aboard ship, (2) help determine to what degree the matrix and the larger clasts (studied in thin section aboard ship; Shipboard Scientific Party, 1998, doi:10.2973/odp.proc.ir.173.106.1998) are compositionally distinct, (3) help identify the extent of hydrothermal fluid migration in the breccia, and (4) support the proposed shipboard hypothesis that the Site 1068 breccia succession resulted from multiple mass-wasting.