Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?

We present a bifurcation analysis of a normal form for travelling waves in one-dimensional excitable media. The normal form which has been recently proposed on phenomenological grounds is given in form of a differential delay equation. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf bifurcation for the propagation of a single pulse in a ring by means of a center manifold reduction, and for a wave train by means of a multiscale analysis leading to a real Ginzburg-Landau equation as the corresponding amplitude equation. Both, the center manifold reduction and the multiscale analysis show that the Hopf bifurcation is always subcritical independent of the parameters. This may have links to cardiac alternans which have so far been believed to be stable oscillations emanating from a supercritical bifurcation. We discuss the implications for cardiac alternans and revisit the instability in some excitable media where the oscillations had been believed to be stable. In particular, we show that our condition for the onset of the Hopf bifurcation coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao

Instability and Spatiotemporal Dynamics of Alternans in Paced Cardiac Tissue

We derive an equation that governs the spatiotemporal dynamics of small amplitude alternans in paced cardiac tissue. We show that a pattern-forming linear instability leads to the spontaneous formation of stationary or traveling waves whose nodes divide the tissue into regions with opposite phase of oscillation of action potential duration. This instability is important because it creates dynamically an heterogeneous electrical substrate for inducing fibrillation if the tissue size exceeds a fraction of the pattern wavelength. We compute this wavelength analytically as a function of three basic length scales characterizing dispersion and inter-cellular electrical coupling.Comment: 4 pages, 3 figures, submitted to PR

Cultures of caste and rural development in the social network of a south Indian village

Cultures of caste in much of rural India have become entangled with institutions of rural development. In community-driven development, emphasis on “local resource persons” and “community spokespersons” has created new opportunities for brokerage and patronage within some villages, which interact with existing forms of authority and community afforded by caste identity and intra-caste headmanship. In this article, we study how these entangled cultures of caste and development translate into social network structures using data on friendship ties from a south Indian village. We find that although caste continues to be important in shaping community structures and leadership in the village’s network, its influence varies across different communities. This fluidity of caste’s influence on community network structures is argued to be the result of multiple distinct yet partially overlapping cultural-political forces, which include sharedness afforded by caste identity and new forms of difference and inequality effected through rural development

Experimental Study on the Low-velocity Impact Behavior of Foam-core Sandwich Panels

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97064/1/AIAA2012-1701.pd

Reorganization Energy for Internal Electron Transfer in Multicopper Oxidases.

We have calculated the reorganization energy for the intramolecular electron transfer between the reduced type 1 copper site and the peroxy intermediate of the trinuclear cluster in the multicopper oxidase CueO. The calculations are performed at the combined quantum mechanics and molecular mechanics (QM/MM) level, based on molecular dynamics simulations with tailored potentials for the two copper sites. We obtain a reorganization energy of 91-133 kJ/mol, depending on the theoretical treatment. The two Cu sites contribute by 12 and 22 kJ/mol to this energy, whereas the solvent contribution is 34 kJ/mol. The rest comes from the protein, involving small contributions from many residues. We have also estimated the energy difference between the two electron-transfer states and show that the reduction of the peroxy intermediate is exergonic by 43-87 kJ/mol, depending on the theoretical method. Both the solvent and the protein contribute to this energy difference, especially charged residues close to the two Cu sites. We compare these estimates with energies obtained from QM/MM optimizations and QM calculations in a vacuum and discuss differences between the results obtained at various levels of theory

Ubiquitination of CXCR7 Controls Receptor Trafficking

The chemokine receptor CXCR7 binds CXCL11 and CXCL12 with high affinity, chemokines that were previously thought to bind exclusively to CXCR4 and CXCR3, respectively. Expression of CXCR7 has been associated with cardiac development as well as with tumor growth and progression. Despite having all the canonical features of G protein-coupled receptors (GPCRs), the signalling pathways following CXCR7 activation remain controversial, since unlike typical chemokine receptors, CXCR7 fails to activate Gαi-proteins. CXCR7 has recently been shown to interact with β-arrestins and such interaction has been suggested to be responsible for G protein-independent signals through ERK-1/2 phosphorylation. Signal transduction by CXCR7 is controlled at the membrane by the process of GPCR trafficking. In the present study we investigated the regulatory processes triggered by CXCR7 activation as well as the molecular interactions that participate in such processes. We show that, CXCR7 internalizes and recycles back to the cell surface after agonist exposure, and that internalization is not only β-arrestin-mediated but also dependent on the Serine/Threonine residues at the C-terminus of the receptor. Furthermore we describe, for the first time, the constitutive ubiquitination of CXCR7. Such ubiquitination is a key modification responsible for the correct trafficking of CXCR7 from and to the plasma membrane. Moreover, we found that CXCR7 is reversibly de-ubiquitinated upon treatment with CXCL12. Finally, we have also identified the Lysine residues at the C-terminus of CXCR7 to be essential for receptor cell surface delivery. Together these data demonstrate the differential regulation of CXCR7 compared to the related CXCR3 and CXCR4 receptors, and highlight the importance of understanding the molecular determinants responsible for this process

Being Tamil, being Hindu:Tamil migrants’ negotiations of the absence of Tamil Hindu spaces in the West Midlands and South West of England

This paper considers the religious practices of Tamil Hindus who have settled in the West Midlands and South West of England in order to explore how devotees of a specific ethno-regional Hindu tradition with a well-established UK infrastructure in the site of its adherents’ population density adapt their religious practices in settlement areas which lack this infrastructure. Unlike the majority of the UK Tamil population who live in the London area, the participants in this study did not have ready access to an ethno-religious infrastructure of Tamil-orientated temples and public rituals. The paper examines two means by which this absence was addressed as well as the intersections and negotiations of religion and ethnicity these entailed: firstly, Tamil Hindus’ attendance of temples in their local area which are orientated towards a broadly imagined Hindu constituency or which cater to a non-Tamil ethno-linguistic or sectarian community; and, secondly, through the ‘DIY’ performance of ethnicised Hindu ritual in non-institutional settings