PMD fundamentals: Polarization mode dispersion in optical fibers

This paper reviews the fundamental concepts and basic theory of polarization mode dispersion (PMD) in optical fibers. It introduces a unified notation and methodology to link the various views and concepts in Jones space and Stokes space. The discussion includes the relation between Jones vectors and Stokes vectors, rotation matrices, the definition and representation of PMD vectors, the laws of infinitesimal rotation, and the rules for PMD vector concatenation.

Subunit rotation in Escherichia coli FoF1–ATP synthase during oxidative phosphorylation

We report evidence for proton-driven subunit rotation in membrane-bound FoF1–ATP synthase during oxidative phosphorylation. A βD380C/γC87 crosslinked hybrid F1 having epitope-tagged βD380C subunits (βflag) exclusively in the two noncrosslinked positions was bound to Fo in F1-depleted membranes. After reduction of the β–γ crosslink, a brief exposure to conditions for ATP synthesis followed by reoxidation resulted in a significant amount of βflag appearing in the β–γ crosslinked product. Such a reorientation of γC87 relative to the three β subunits can only occur through subunit rotation. Rotation was inhibited when proton transport through Fo was blocked or when ADP and Pi were omitted. These results establish FoF1 as the second example in nature where proton transport is coupled to subunit rotation.

Absence of a barrier to backwards rotation of the bacterial flagellar motor demonstrated with optical tweezers

A cell of the bacterium Escherichia coli was tethered covalently to a glass coverslip by a single flagellum, and its rotation was stopped by using optical tweezers. The tweezers acted directly on the cell body or indirectly, via a trapped polystyrene bead. The torque generated by the flagellar motor was determined by measuring the displacement of the laser beam on a quadrant photodiode. The coverslip was mounted on a computer-controlled piezo-electric stage that moved the tether point in a circle around the center of the trap so that the speed of rotation of the motor could be varied. The motor generated ≈4500 pN nm of torque at all angles, regardless of whether it was stalled, allowed to rotate very slowly forwards, or driven very slowly backwards. This argues against models of motor function in which rotation is tightly coupled to proton transit and back-transport of protons is severely limited.

The Yeast GRD20 Gene Is Required for Protein Sorting in the trans-Golgi Network/Endosomal System and for Polarization of the Actin Cytoskeleton

The proper localization of resident membrane proteins to the trans-Golgi network (TGN) involves mechanisms for both TGN retention and retrieval from post-TGN compartments. In this study we report identification of a new gene, GRD20, involved in protein sorting in the TGN/endosomal system of Saccharomyces cerevisiae. A strain carrying a transposon insertion allele of GRD20 exhibited rapid vacuolar degradation of the resident TGN endoprotease Kex2p and aberrantly secreted ∼50% of the soluble vacuolar hydrolase carboxypeptidase Y. The Kex2p mislocalization and carboxypeptidase Y missorting phenotypes were exhibited rapidly after loss of Grd20p function in grd20 temperature-sensitive mutant strains, indicating that Grd20p plays a direct role in these processes. Surprisingly, little if any vacuolar degradation was observed for the TGN membrane proteins A-ALP and Vps10p, underscoring a difference in trafficking patterns for these proteins compared with that of Kex2p. A grd20 null mutant strain exhibited extremely slow growth and a defect in polarization of the actin cytoskeleton, and these two phenotypes were invariably linked in a collection of randomly mutagenized grd20 alleles. GRD20 encodes a hydrophilic protein that partially associates with the TGN. The discovery of GRD20 suggests a link between the cytoskeleton and function of the yeast TGN.

Is polarization important in cation-π interactions?

The importance of cation->aromatic polarization effects on cation-π interactions has been explored. Theoretical calculations demonstrate that polarization is a large contribution to cation-aromatic interactions, and particularly to cation-π interactions. For a series of compounds with a similar aromatic core, polarization is constant and makes small influence in the relative cation-binding energies. However, when the aromatic core changes polarization contributions might be very different. We found that the generalized molecular interaction potential with polarization is a very fast and powerful tool for the prediction of cation binding of aromatic compounds.

Photochemically induced nuclear spin polarization in reaction centers of photosystem II observed by 13C-solid-state NMR reveals a strongly asymmetric electronic structure of the P680.+ primary donor chlorophyll

We report 13C magic angle spinning NMR observation of photochemically induced dynamic nuclear spin polarization (photo- CIDNP) in the reaction center (RC) of photosystem II (PS2). The light-enhanced NMR signals of the natural abundance 13C provide information on the electronic structure of the primary electron donor P680 (chlorophyll a molecules absorbing around 680 nm) and on the pz spin density pattern in its oxidized form, P680⨥. Most centerband signals can be attributed to a single chlorophyll a (Chl a) cofactor that has little interaction with other pigments. The chemical shift anisotropy of the most intense signals is characteristic for aromatic carbon atoms. The data reveal a pronounced asymmetry of the electronic spin density distribution within the P680⨥. PS2 shows only a single broad and intense emissive signal, which is assigned to both the C-10 and C-15 methine carbon atoms. The spin density appears shifted toward ring III. This shift is remarkable, because, for monomeric Chl a radical cations in solution, the region of highest spin density is around ring II. It leads to a first hypothesis as to how the planet can provide itself with the chemical potential to split water and generate an oxygen atmosphere using the Chl a macroaromatic cycle. A local electrostatic field close to ring III can polarize the electronic charge and associated spin density and increase the redox potential of P680 by stabilizing the highest occupied molecular orbital, without a major change of color. This field could be produced, e.g., by protonation of the keto group of ring V. Finally, the radical cation electronic structure in PS2 is different from that in the bacterial RC, which shows at least four emissive centerbands, indicating a symmetric spin density distribution over the entire bacteriochlorophyll macrocycle.

Inactivating one hippocampus impairs avoidance of a stable room-defined place during dissociation of arena cues from room cues by rotation of the arena

Unilateral intrahippocampal injections of tetrodotoxin were used to temporarily inactivate one hippocampus during specific phases of training in an active allothetic place avoidance task. The rat was required to use landmarks in the room to avoid a room-defined sector of a slowly rotating circular arena. The continuous rotation dissociated room cues from arena cues and moved the arena surface through a part of the room in which foot-shock was delivered. The rat had to move away from the shock zone to prevent being transported there by the rotation. Unilateral hippocampal inactivations profoundly impaired acquisition and retrieval of the allothetic place avoidance. Posttraining unilateral hippocampal inactivation also impaired performance in subsequent sessions. This allothetic place avoidance task seems more sensitive to hippocampal disruption than the standard water maze task because the same unilateral hippocampal inactivation does not impair performance of the variable-start, fixed hidden goal task after procedural training. The results suggest that the hippocampus not only encodes allothetic relationships amongst landmarks, it also organizes perceived allothetic stimuli into systems of mutually stable coordinates. The latter function apparently requires greater hippocampal integrity.

Na,K-ATPase β-Subunit Is Required for Epithelial Polarization, Suppression of Invasion, and Cell Motility

The cell adhesion molecule E-cadherin has been implicated in maintaining the polarized phenotype of epithelial cells and suppression of invasiveness and motility of carcinoma cells. Na,K-ATPase, consisting of an α- and β-subunit, maintains the sodium gradient across the plasma membrane. A functional relationship between E-cadherin and Na,K-ATPase has not previously been described. We present evidence that the Na,K-ATPase plays a crucial role in E-cadherin–mediated development of epithelial polarity, and suppression of invasiveness and motility of carcinoma cells. Moloney sarcoma virus-transformed Madin-Darby canine kidney cells (MSV-MDCK) have highly reduced levels of E-cadherin and β1-subunit of Na,K-ATPase. Forced expression of E-cadherin in MSV-MDCK cells did not reestablish epithelial polarity or inhibit the invasiveness and motility of these cells. In contrast, expression of E-cadherin and Na,K-ATPase β1-subunit induced epithelial polarization, including the formation of tight junctions and desmosomes, abolished invasiveness, and reduced cell motility in MSV-MDCK cells. Our results suggest that E-cadherin–mediated cell-cell adhesion requires the Na,K-ATPase β-subunit's function to induce epithelial polarization and suppress invasiveness and motility of carcinoma cells. Involvement of the β1-subunit of Na,K-ATPase in the polarized phenotype of epithelial cells reveals a novel link between the structural organization and vectorial ion transport function of epithelial cells.

A Cross-Polarization, Magic-Angle-Spinning, 13C-Nuclear-Magnetic-Resonance Study of Polysaccharides in Sugar Beet Cell Walls1

Solid-state nuclear magnetic resonance relaxation experiments were used to study the rigidity and spatial proximity of polymers in sugar beet (Beta vulgaris) cell walls. Proton T1ρ decay and cross-polarization patterns were consistent with the presence of rigid, crystalline cellulose microfibrils with a diameter of approximately 3 nm, mobile pectic galacturonans, and highly mobile arabinans. A direct-polarization, magic-angle-spinning spectrum recorded under conditions adapted to mobile polymers showed only the arabinans, which had a conformation similar to that of beet arabinans in solution. These cell walls contained very small amounts of hemicellulosic polymers such as xyloglucan, xylan, and mannan, and no arabinan or galacturonan fraction closely associated with cellulose microfibrils, as would be expected of hemicelluloses. Cellulose microfibrils in the beet cell walls were stable in the absence of any polysaccharide coating.

Roles of a Fimbrin and an α-Actinin-like Protein in Fission Yeast Cell Polarization and Cytokinesis

Eukaryotic cells contain many actin-interacting proteins, including the α-actinins and the fimbrins, both of which have actin cross-linking activity in vitro. We report here the identification and characterization of both an α-actinin-like protein (Ain1p) and a fimbrin (Fim1p) in the fission yeast Schizosaccharomyces pombe. Ain1p localizes to the actomyosin-containing medial ring in an F-actin–dependent manner, and the Ain1p ring contracts during cytokinesis. ain1 deletion cells have no obvious defects under normal growth conditions but display severe cytokinesis defects, associated with defects in medial-ring and septum formation, under certain stress conditions. Overexpression of Ain1p also causes cytokinesis defects, and the ain1 deletion shows synthetic effects with other mutations known to affect medial-ring positioning and/or organization. Fim1p localizes both to the cortical actin patches and to the medial ring in an F-actin–dependent manner, and several lines of evidence suggest that Fim1p is involved in polarization of the actin cytoskeleton. Although a fim1 deletion strain has no detectable defect in cytokinesis, overexpression of Fim1p causes a lethal cytokinesis defect associated with a failure to form the medial ring and concentrate actin patches at the cell middle. Moreover, an ain1 fim1 double mutant has a synthetical-lethal defect in medial-ring assembly and cell division. Thus, Ain1p and Fim1p appear to have an overlapping and essential function in fission yeast cytokinesis. In addition, protein-localization and mutant-phenotype data suggest that Fim1p, but not Ain1p, plays important roles in mating and in spore formation.

Energy-driven subunit rotation at the interface between subunit a and the c oligomer in the FO sector of Escherichia coli ATP synthase

Subunit rotation within the F1 catalytic sector of the ATP synthase has been well documented, identifying the synthase as the smallest known rotary motor. In the membrane-embedded FO sector, it is thought that proton transport occurs at a rotor/stator interface between the oligomeric ring of c subunits (rotor) and the single-copy a subunit (stator). Here we report evidence for an energy-dependent rotation at this interface. FOF1 was expressed with a pair of substituted cysteines positioned to allow an intersubunit disulfide crosslink between subunit a and a c subunit [aN214C/cM65C; Jiang, W. & Fillingame, R. H. (1998) Proc. Natl. Acad. Sci. USA 95, 6607–6612]. Membranes were treated with N,N′-dicyclohexyl-[14C]carbodiimide to radiolabel the D61 residue on less than 20% of the c subunits. After oxidation to form an a–c crosslink, the c subunit properly aligned to crosslink to subunit a was found to contain very little 14C label relative to other members of the c ring. However, exposure to MgATP before oxidation significantly increased the radiolabel in the a–c crosslink, indicating that a different c subunit was now aligned with subunit a. This increase was not induced by exposure to MgADP/Pi. Furthermore, preincubation with MgADP and azide to inhibit F1 or with high concentrations of N,N′-dicyclohexylcarbodiimide to label most c subunits prevented the ATP effect. These results provide evidence for an energy-dependent rotation of the c ring relative to subunit a.

Natural abundance solid-state carbon NMR studies of photosynthetic reaction centers with photoinduced polarization.

Solid-state NMR spectra of natural abundance 13C in reaction centers from photosynthetic bacteria Rhodobacter sphaeroides R-26 was measured. When the quinone acceptors were removed and continuous visible illumination of the sample was provided, exceptionally strong nuclear spin polarization was observed in NMR lines with chemical shifts resembling those of the aromatic carbons in bacteriochlorophyll and bacteriopheophytin. The observation of spin polarized 15N nuclei in bacteriochlorophyll and bacteriopheophytin was previously demonstrated with nonspecifically 15N-labeled reaction centers. Both the carbon and the nitrogen NMR studies indicate that the polarization is developed on species that carry unpaired electrons in the early electron transfer steps, including the bacteriochlorophyll dimer donor P860 and probably the bacteriopheophytin acceptor. I. Both enhanced-absorptive and emissive polarization were seen in the carbon spectrum; most lines were absorptive but the methine carbons of the porphyrin ring (alpha, beta, gamma, ) exhibited emissive polarization. The change in the sign of the hyperfine coupling at these sites indicates the existence of nodes in the spin density distribution on the tetrapyrrole cofactors flanking each methine carbon bridge.

Compact steep-spectrum sources and the unified scheme.

The compact steep-spectrum sources (CSSs) are an interesting class of objects which are of subgalactic dimensions; they occur more frequently in high-frequency surveys because their spectra often turn over at lower frequencies. We have estimated the symmetry parameters of a well-defined sample of CSSs and compared these with the larger 3CR sources of similar luminosity to understand the evolution and the consistency of CSSs with the unified scheme. We suggest that the majority of CSSs are likely to be young sources advancing outward through an asymmetric, inhomogeneous environment to form the larger ones. The radio properties of the CSSs are consistent with the unified scheme, where the axes of the quasars are seen closer to the line of sight while the radio galaxies lie closer to the plane of the sky. We discuss how radio polarization observations may be used to probe whether the physical conditions in the central regions of the CSSs are different from the larger ones. We present a simple scenario where the depolarization and high rotation measures seen in many CSSs can be consistent with the low rotation measures of cores in the more extended quasars and suggest further observations to test this scenario.

Rotation of subunits during catalysis by Escherichia coli F1-ATPase.

During oxidative and photo-phosphorylation, F0F1-ATP synthases couple the movement of protons down an electrochemical gradient to the synthesis of ATP. One proposed mechanistic feature that has remained speculative is that this coupling process requires the rotation of subunits within F0F1. Guided by a recent, high-resolution structure for bovine F1 [Abrahams, J. P., Leslie, A. G., Lutter, R. & Walker, J. E. (1994) Nature (London) 370, 621-628], we have developed a critical test for rotation of the central gamma subunit relative to the three catalytic beta subunits in soluble F1 from Escherichia coli. In the bovine F1 structure, a specific point of contact between the gamma subunit and one of the three catalytic beta subunits includes positioning of the homolog of E. coli gamma-subunit C87 (gamma C87) close to the beta-subunit 380DELSEED386 sequence. A beta D380C mutation allowed us to induce formation of a specific disulfide bond between beta and gamma C87 in soluble E. coli F1. Formation of the crosslink inactivated beta D380C-F1, and reduction restored full activity. Using a dissociation/reassembly approach with crosslinked beta D380C-F1, we incorporated radiolabeled beta subunits into the two noncrosslinked beta-subunit positions of F1. After reduction of the initial nonradioactive beta-gamma crosslink, only exposure to conditions for catalytic turnover results in similar reactivities of unlabeled and radiolabeled beta subunits with gamma C87 upon reoxidation. The results demonstrate that gamma subunit rotates relative to the beta subunits during catalysis.