Twist fields, the elliptic genus, and hidden symmetry

We combine infinite dimensional analysis (in particular a priori estimates and twist positivity) with classical geometric structures, supersymmetry, and noncommutative geometry. We establish the existence of a family of examples of two-dimensional, twist quantum fields. We evaluate the elliptic genus in these examples. We demonstrate a hidden SL(2,ℤ) symmetry of the elliptic genus, as suggested by Witten.

The two-dimensional IR nonlinear spectroscopy of a cyclic penta-peptide in relation to its three-dimensional structure

A form of two-dimensional (2D) vibrational spectroscopy, which uses two ultrafast IR laser pulses, is used to examine the structure of a cyclic penta-peptide in solution. Spectrally resolved cross peaks occur in the off-diagonal region of the 2D IR spectrum of the amide I region, analogous to those in 2D NMR spectroscopy. These cross peaks measure the coupling between the different amide groups in the structure. Their intensities and polarizations relate directly to the three-dimensional structure of the peptide. With the help of a model coupling Hamiltonian, supplemented by density functional calculations, the spectra of this penta-peptide can be regenerated from the known solution phase structure. This 2D-IR measurement, with an intrinsic time resolution of less than 1 ps, could be used in all time regimes of interest in biology.

Abscisic acid-induced stomatal closure mediated by cyclic ADP-ribose

Abscisic acid (ABA) is a plant hormone involved in the response of plants to reduced water availability. Reduction of guard cell turgor by ABA diminishes the aperture of the stomatal pore and thereby contributes to the ability of the plant to conserve water during periods of drought. Previous work has demonstrated that cytosolic Ca2+ is involved in the signal transduction pathway that mediates the reduction in guard cell turgor elicited by ABA. Here we report that ABA uses a Ca2+-mobilization pathway that involves cyclic adenosine 5′-diphosphoribose (cADPR). Microinjection of cADPR into guard cells caused reductions in turgor that were preceded by increases in the concentration of free Ca2+ in the cytosol. Patch clamp measurements of isolated guard cell vacuoles revealed the presence of a cADPR-elicited Ca2+-selective current that was inhibited at cytosolic Ca2+ ≥ 600 nM. Furthermore, microinjection of the cADPR antagonist 8-NH2-cADPR caused a reduction in the rate of turgor loss in response to ABA in 54% of cells tested, and nicotinamide, an antagonist of cADPR production, elicited a dose-dependent block of ABA-induced stomatal closure. Our data provide definitive evidence for a physiological role for cADPR and illustrate one mechanism of stimulus-specific Ca2+ mobilization in higher plants. Taken together with other recent data [Wu, Y., Kuzma, J., Marechal, E., Graeff, R., Lee, H. C., Foster, R. & Chua, N.-H. (1997) Science 278, 2126–2130], these results establish cADPR as a key player in ABA signal transduction pathways in plants.

Nanohedra: Using symmetry to design self assembling protein cages, layers, crystals, and filaments

A general strategy is described for designing proteins that self assemble into large symmetrical nanomaterials, including molecular cages, filaments, layers, and porous materials. In this strategy, one molecule of protein A, which naturally forms a self-assembling oligomer, An, is fused rigidly to one molecule of protein B, which forms another self-assembling oligomer, Bm. The result is a fusion protein, A-B, which self assembles with other identical copies of itself into a designed nanohedral particle or material, (A-B)p. The strategy is demonstrated through the design, production, and characterization of two fusion proteins: a 49-kDa protein designed to assemble into a cage approximately 15 nm across, and a 44-kDa protein designed to assemble into long filaments approximately 4 nm wide. The strategy opens a way to create a wide variety of potentially useful protein-based materials, some of which share similar features with natural biological assemblies.

Spatiotemporal dynamics of guanosine 3′,5′-cyclic monophosphate revealed by a genetically encoded, fluorescent indicator

To investigate the dynamics of guanosine 3′,5′-cyclic monophosphate (cGMP) in single living cells, we constructed genetically encoded, fluorescent cGMP indicators by bracketing cGMP-dependent protein kinase (cGPK), minus residues 1–77, between cyan and yellow mutants of green fluorescent protein. cGMP decreased fluorescence resonance energy transfer (FRET) and increased the ratio of cyan to yellow emissions by up to 1.5-fold with apparent dissociation constants of ≈2 μM and >100:1 selectivity for cGMP over cAMP. To eliminate constitutive kinase activity, Thr516 of cGPK was mutated to Ala. Emission ratio imaging of the indicators transfected into rat fetal lung fibroblast (RFL)-6 showed cGMP transients resulting from activation of soluble and particulate guanylyl cyclase, respectively, by nitric oxide (NO) and C-type natriuretic peptide (CNP). Whereas all naive cells tested responded to CNP, only 68% responded to NO. Both sets of signals showed large and variable (0.5–4 min) latencies. The phosphodiesterase (PDE) inhibitor 3-isobutyl-1-methylxanthine (IBMX) did not elevate cGMP on its own but consistently amplified responses to NO or CNP, suggesting that basal activity of guanylate cyclase is very low and emphasizing the importance of PDEs in cGMP recycling. A fraction of RFL cells showed slowly propagating tides of cGMP spreading across the cell in response to delocalized application of NO. Biolistically transfected Purkinje neurons showed cGMP responses to parallel fiber activity and NO donors, confirming that single-cell increases in cGMP occur under conditions appropriate to cause synaptic plasticity.

Cyclic AMP Increases Cell Surface Expression of Functional Na,K-ATPase Units in Mammalian Cortical Collecting Duct Principal Cells

Cyclic AMP (cAMP) stimulates the transport of Na+ and Na,K-ATPase activity in the renal cortical collecting duct (CCD). The aim of this study was to investigate the mechanism whereby cAMP stimulates the Na,K-ATPase activity in microdissected rat CCDs and cultured mouse mpkCCDc14 collecting duct cells. db-cAMP (10−3 M) stimulated by 2-fold the activity of Na,K-ATPase from rat CCDs as well as the ouabain-sensitive component of 86Rb+ uptake by rat CCDs (1.7-fold) and cultured mouse CCD cells (1.5-fold). Pretreatment of rat CCDs with saponin increased the total Na,K-ATPase activity without further stimulation by db-cAMP. Western blotting performed after a biotinylation procedure revealed that db-cAMP increased the amount of Na,K-ATPase at the cell surface in both intact rat CCDs (1.7-fold) and cultured cells (1.3-fold), and that this increase was not related to changes in Na,K-ATPase internalization. Brefeldin A and low temperature (20°C) prevented both the db-cAMP-dependent increase in cell surface expression and activity of Na,K-ATPase in both intact rat CCDs and cultured cells. Pretreatment with the intracellular Ca2+ chelator bis-(o-aminophenoxy)-N,N,N′,N′-tetraacetic acid also blunted the increment in cell surface expression and activity of Na,K-ATPase caused by db-cAMP. In conclusion, these results strongly suggest that the cAMP-dependent stimulation of Na,K-ATPase activity in CCD results from the translocation of active pump units from an intracellular compartment to the plasma membrane.

Further Studies of the Role of Cyclic β-Glucans in Symbiosis. An ndvC Mutant of Bradyrhizobium japonicum Synthesizes Cyclodecakis-(1→3)-β-Glucosyl1

The cyclic β-(1→3),β-(1→6)-d-glucan synthesis locus of Bradyrhizobium japonicum is composed of at least two genes, ndvB and ndvC. Mutation in either gene affects glucan synthesis, as well as the ability of the bacterium to establish a successful symbiotic interaction with the legume host soybean (Glycine max). B. japonicum strain AB-14 (ndvB::Tn5) does not synthesize β-glucans, and strain AB-1 (ndvC::Tn5) synthesizes a cyclic β-glucan lacking β-(1→6)-glycosidic bonds. We determined that the structure of the glucan synthesized by strain AB-1 is cyclodecakis-(1→3)-β-d-glucosyl, a cyclic β-(1→3)-linked decasaccharide in which one of the residues is substituted in the 6 position with β-laminaribiose. Cyclodecakis-(1→3)-β-d-glucosyl did not suppress the fungal β-glucan-induced plant defense response in soybean cotyledons and had much lower affinity for the putative membrane receptor protein than cyclic β-(1→3),β-(1→6)-glucans produced by wild-type B. japonicum. This is consistent with the hypothesis presented previously that the wild-type cyclic β-glucans may function as suppressors of a host defense response.

Growth factors regulate phototransduction in retinal rods by modulating cyclic nucleotide-gated channels through dephosphorylation of a specific tyrosine residue

Illumination of vertebrate rod photoreceptors leads to a decrease in the cytoplasmic cGMP concentration and closure of cyclic nucleotide-gated (CNG) channels. Except for Ca2+, which plays a negative feedback role in adaptation, and 11-cis-retinal, supplied by the retinal pigment epithelium, all of the biochemical machinery of phototransduction is thought to be contained within rod outer segments without involvement of extrinsic regulatory molecules. Here we show that insulin-like growth factor-I (IGF-I), a paracrine factor released from the retinal pigment epithelium, alters phototransduction by rapidly increasing the cGMP sensitivity of CNG channels. The IGF-I-signaling pathway ultimately involves a protein tyrosine phosphatase that catalyzes dephosphorylation of a specific residue in the α-subunit of the rod CNG channel protein. IGF-I conjointly accelerates the kinetics and increases the amplitude of the light response, distinct from events that accompany adaptation. These effects of IGF-I could result from the enhancement of the cGMP sensitivity of CNG channels. Hence, in addition to long-term control of development and survival of rods, growth factors regulate phototransduction in the short term by modulating CNG channels.

T cell activation up-regulates cyclic nucleotide phosphodiesterases 8A1 and 7A3

Agents that increase intracellular cAMP inhibit the activation and function of T cells and can lead to cell death. Recently, it has been postulated that cAMP inhibits T cell function in large part by acting as a brake on the T cell receptor and costimulatory receptor pathways. Therefore, for full activation of the T cell to occur, this inhibitory influence must be removed. One likely mechanism for accomplishing this is by up-regulation and/or activation of specific cyclic nucleotide phosphodiesterases (PDEs), and such a mechanism for one phosphodiesterase, PDE7A1, has been reported. In this paper, we extend this mechanism to another isozyme variant of the same PDE family, PDE7A3. We also report the full-length sequence of human PDE8A1 and show that it also is induced in response to a combination of T cell receptor and costimulatory receptor pathway activation. However, the time course for induction of PDE8A1 is slower than that of PDE7A1. The basal level measured and, therefore, the apparent fold induction of PDE7A1 mRNA and protein depend in large part on the method of isolation of the T cells. On the other hand, regardless of the isolation method, the basal levels of PDE7A3 and PDE8A1 are very low and fold activation is much higher. Constitutively expressed PDE8A1 and PDE7A3 also have been isolated from a human T cell line, Hut78.

Symmetries in bacterial motility

Descriptions are given of three kinds of symmetries encountered in studies of bacterial locomotion, and of the ways in which they are circumvented or broken. A bacterium swims at very low Reynolds number: it cannot propel itself using reciprocal motion (by moving through a sequence of shapes, first forward and then in reverse); cyclic motion is required. A common solution is rotation of a helical filament, either right- or left-handed. The flagellar rotary motor that drives each filament generates the same torque whether spinning clockwise or counterclockwise. This symmetry is broken by coupling to the filament. Finally, bacterial populations, grown in a nutrient medium from an inoculum placed at a single point, usually move outward in symmetric circular rings. Under certain conditions, the cells excrete a chemoattractant, and the rings break up into discrete aggregates that can display remarkable geometric order.

A brief survey of symmetry in mathematics

This paper presents a brief survey of the idea of symmetry in mathematics, as exemplified by some particular developments in algebra, differential equations, topology, and number theory.

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.

Symmetry and the energy landscapes of biomolecules

The role of symmetry in the folding of proteins is discussed using energy landscape theory. An analytical argument shows it is much easier to find sequences with funneled energy landscape capable of fast folding if the structure is symmetric. The analogy with phase transitions of small clusters with magic numbers is discussed.

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.