Phase Splitting for Periodic Lie Systems

In the context of the Floquet theory, using a variation of parameter argument, we show that the logarithm of the monodromy of a real periodic Lie system with appropriate properties admits a splitting into two parts, called dynamic and geometric phases. The dynamic phase is intrinsic and linked to the Hamiltonian of a periodic linear Euler system on the co-algebra. The geometric phase is represented as a surface integral of the symplectic form of a co-adjoint orbit.Comment: (v1) 15 pages. (v2) 16 pages. Some typos corrected. References and further comments added. Final version to appear in J. Phys. A

Continuous dielectric permittivity II: An Iterative Method for Calculating the Polar Component of the Molecular Solvation Gibbs Energy Under a Smooth Change in the Dielectric Permittivity of a Solution

An iterative method for calculating the polar component of the solvation Gibbs energy under a smooth change in dielectric permittivity, both between a substrate and a solvent and in a solvent is formulated on the basis of a previously developed model. The method is developed in the approximation of the local relationship D = \eps (r) E between the displacement vectors D and the electric field intensity E.Comment: 36 pages,3 Figures, in English and in Russia

Spin sensitive bleaching and monopolar spin orientation in quantum wells

Spin sensitive bleaching of the absorption of far-infrared radiation has been observed in $p$-type GaAs/AlGaAs quantum well structures. The absorption of circularly polarized radiation saturates at lower intensities than that of linearly polarized light due to monopolar spin orientation in the first heavy hole subband. Spin relaxation times of holes in $p$-type material in the range of tens of ps were derived from the intensity dependence of the absorption.Comment: Figures have been updated due to technical printing problems (Postscript mismatch

CSAP localizes to polyglutamylated microtubules and promotes proper cilia function and zebrafish development

The diverse populations of microtubule polymers in cells are functionally distinguished by different posttranslational modifications, including polyglutamylation. Polyglutamylation is enriched on subsets of microtubules including those found in the centrioles, mitotic spindle, and cilia. However, whether this modification alters intrinsic microtubule dynamics or affects extrinsic associations with specific interacting partners remains to be determined. Here we identify the microtubule-binding protein centriole and spindle–associated protein (CSAP), which colocalizes with polyglutamylated tubulin to centrioles, spindle microtubules, and cilia in human tissue culture cells. Reducing tubulin polyglutamylation prevents CSAP localization to both spindle and cilia microtubules. In zebrafish, CSAP is required for normal brain development and proper left–right asymmetry, defects that are qualitatively similar to those reported previously for depletion of polyglutamylation-conjugating enzymes. We also find that CSAP is required for proper cilia beating. Our work supports a model in which polyglutamylation can target selected microtubule-associated proteins, such as CSAP, to microtubule subpopulations, providing specific functional capabilities to these populations.National Institutes of Health (U.S.) (Grant no. GM074746)American Cancer Society. Research Scholar Grant (121776)National Institute of General Medical Sciences (U.S.) (GM088313

Investigations of the auroral luminosity distribution and the dynamics of discrete auroral forms in a historical retrospective

Abstract. Research results about planetary-scale auroral distributions are presented in a historical retrospective, beginning with the first "maps of isochasms" – lines of equal visibility of auroras in the firmament (Fig. 2) – up to "isoaurora maps" – lines of equal occurrence frequency of auroras in the zenith (Fig. 4). The exploration of auroras in Russia from Lomonosov in the 18th century (Fig. 1) until the start of the International Geophysical Year (IGY) in 1957 is shortly summed up. A generalised pattern of discrete auroral forms along the auroral oval during geomagnetically very quiet intervals is presented in Fig. 5. The changes of discrete auroral forms versus local time exhibit a fixed pattern with respect to the sun. The auroral forms comprise rays near noon, homogeneous arcs during the evening, and rayed arcs and bands during the night and in the morning. This fixed auroral pattern is unsettled during disturbances, which occur sometimes even during very quiet intervals. The azimuths of extended auroral forms vary with local time. Such variations in the orientation of extended forms above stations in the auroral zone have been used by various investigators to determine the position of the auroral oval (Fig. 9). Auroral luminosity of the daytime and nighttime sectors differ owing to different luminosity forms, directions of motion of the discrete forms, the height of the luminescent layers, and the spectral composition (predominant red emissions during daytime and green emissions during the night). Schemes that summarise principal peculiarities of daytime luminosity, its structure in MLT (magnetic local time) and MLat (magnetic latitude) coordinates, and the spectral composition of the luminosity are presented in Figs. 15 and 19. We discuss in detail the daytime sector dynamics of individual discrete forms for both quiet conditions and auroral substorms. The most important auroral changes during substorms occur in the nighttime sector. We present the evolution of conceptions about the succession of discrete auroral forms and their dynamics during disturbance intervals. This ranges from Birkeland's polar elementary storms, over the prospect of a fixed auroral pattern up to the auroral substorm model. The classic schemes of the spatial distribution and motion of discrete auroral forms during single substorms are shown in Fig. 20 (expansive and recovery phases) and Fig. 21 (creation, expansive and recovery phases). In this review we discuss various models of bulge formation, in particular as a result of new formation of arcs about 50–100 km poleward of previously existing auroral structures (Fig. 24). Discrete steps in the development of an expanding bulge are separated by 1–3 min from each other. The model of successive activations confines only to a ~40° longitudinal portion of the magnetotail (Fig. 28). We consider differences in the development of single substorms and substorms during magnetic storms. The structure and dynamics of auroras during steady magnetospheric convection (SMC) periods are dealt with in Sect. 8. A generalised scheme of the auroral distribution during SMC periods is shown in Fig. 34. Separate sections describe discrete auroras in the polar cap (Sect. 5), and the diffuse luminosity equatorward of the auroral oval (Sect. 9). Visual observations of diffuse auroral forms at midlatitudes suggest that the whole latitudinal interval between the auroral oval and the stable auroral red (SAR) arc is filled up with diffuse luminosity. SAR arcs with intensities of several tens of Rayleigh enclose systematically the region of diffuse luminosity; they are positioned at the border of the plasmasphere.</jats:p

Circulating microparticles: square the circle

Background: The present review summarizes current knowledge about microparticles (MPs) and provides a systematic overview of last 20 years of research on circulating MPs, with particular focus on their clinical relevance. Results: MPs are a heterogeneous population of cell-derived vesicles, with sizes ranging between 50 and 1000 nm. MPs are capable of transferring peptides, proteins, lipid components, microRNA, mRNA, and DNA from one cell to another without direct cell-to-cell contact. Growing evidence suggests that MPs present in peripheral blood and body fluids contribute to the development and progression of cancer, and are of pathophysiological relevance for autoimmune, inflammatory, infectious, cardiovascular, hematological, and other diseases. MPs have large diagnostic potential as biomarkers; however, due to current technological limitations in purification of MPs and an absence of standardized methods of MP detection, challenges remain in validating the potential of MPs as a non-invasive and early diagnostic platform. Conclusions: Improvements in the effective deciphering of MP molecular signatures will be critical not only for diagnostics, but also for the evaluation of treatment regimens and predicting disease outcomes

Efficiency of Organelle Capture by Microtubules as a Function of Centrosome Nucleation Capacity: General Theory and the Special Case of Polyspermia

Transport of organelles along microtubules is essential for the cell metabolism and morphogenesis. The presented analysis derives the probability that an organelle of a given size comes in contact with the microtubule aster. The question is asked how this measure of functionality of the microtubule aster is controlled by the centrosome. A quantitative model is developed to address this question. It is shown that for the given set of cellular parameters, such as size and total tubulin content, a centrosome nucleation capacity exists that maximizes the probability of the organelle capture. The developed general model is then applied to the capture of the female pronucleus by microtubules assembled on the sperm centrosome, following physiologically polyspermic fertilization. This application highlights an unintuitive reflection of nonlinearity of the nucleated polymerization of the cellular pool of tubulin. The prediction that the sperm centrosome should lower its nucleation capacity in the face of the competition from the other sperm is a stark illustration of the new optimality principle. Overall, the model calls attention to the capabilities of the centrosomal pathway of regulation of the transport-related functionality of the microtubule cytoskeleton. It establishes a quantitative and conceptual framework that can guide experiment design and interpretation

Adenine and guanine recognition of stop codon is mediated by different N domain conformations of translation termination factor eRF1

Positioning of release factor eRF1 toward adenines and the ribose-phosphate backbone of the UAAA stop signal in the ribosomal decoding site was studied using messenger RNA (mRNA) analogs containing stop signal UAA/UAAA and a photoactivatable cross-linker at definite locations. The human eRF1 peptides cross-linked to these analogs were identified. Cross-linkers on the adenines at the 2nd, 3rd or 4th position modified eRF1 near the conserved YxCxxxF loop (positions 125–131 in the N domain), but cross-linker at the 4th position mainly modified the tripeptide 26-AAR-28. This tripeptide cross-linked also with derivatized 3′-phosphate of UAA, while the same cross-linker at the 3′-phosphate of UAAA modified both the 26–28 and 67–73 fragments. A comparison of the results with those obtained earlier with mRNA analogs bearing a similar cross-linker at the guanines indicates that positioning of eRF1 toward adenines and guanines of stop signals in the 80S termination complex is different. Molecular modeling of eRF1 in the 80S termination complex showed that eRF1 fragments neighboring guanines and adenines of stop signals are compatible with different N domain conformations of eRF1. These conformations vary by positioning of stop signal purines toward the universally conserved dipeptide 31-GT-32, which neighbors guanines but is oriented more distantly from adenines

Control of daughter centriole formation by the pericentriolar material

Author Posting. © The Author(s), 2008. This is the author's version of the work. It is posted here by permission of Nature Publishing Group for personal use, not for redistribution. The definitive version was published in Nature Cell Biology 10 (2008): 322-328, doi:10.1038/ncb1694.Controlling the number of its centrioles is vital for the cell as supernumerary centrioles result in multipolar mitosis and genomic instability. Normally, just one daughter centriole forms on each mature (mother) centriole; however, a mother centriole can produce multiple daughters within a single cell cycle. The mechanisms that prevent centriole ‘overduplication’ are poorly understood. Here we use laser microsurgery to test the hypothesis that attachment of the daughter centriole to the wall of the mother inhibits formation of additional daughters. We show that physical removal of the daughter induces reduplication of the mother in Sarrested cells. Under conditions when multiple daughters simultaneously form on a single mother, all of these daughters must be removed to induce reduplication. Intriguingly, the number of daughter centrioles that form during reduplication does not always match the number of ablated daughter centrioles. We also find that exaggeration of the pericentriolar material (PCM) via overexpression of the PCM protein pericentrin in S-arrested CHO cells induces formation of numerous daughter centrioles. We propose that that the size of the PCM cloud associated with the mother centriole restricts the number of daughters that can form simultaneously.This work was supported by grants from the National Institutes of Health (GM GM59363) and the Human Frontiers Science Program (RGP0064). Construction of our laser microsurgery workstation was supported in part by a fellowship from Nikon/Marine Biological Laboratory (A.K.)