A generalized topological recursion for arbitrary ramification

The Eynard-Orantin topological recursion relies on the geometry of a Riemann surface S and two meromorphic functions x and y on S. To formulate the recursion, one must assume that x has only simple ramification points. In this paper we propose a generalized topological recursion that is valid for x with arbitrary ramification. We justify our proposal by studying degenerations of Riemann surfaces. We check in various examples that our generalized recursion is compatible with invariance of the free energies under the transformation (x,y) -> (y,x), where either x or y (or both) have higher order ramification, and that it satisfies some of the most important properties of the original recursion. Along the way, we show that invariance under (x,y) -> (y,x) is in fact more subtle than expected; we show that there exists a number of counter examples, already in the case of the original Eynard-Orantin recursion, that deserve further study.Comment: 26 pages, 2 figure

Layered Long Term Co-Culture of Hepatocytes and Endothelial Cells on a Transwell Membrane: Toward Engineering the Liver Sinusoid

This paper presents a novel liver model that mimics the liver sinusoid where most liver activities occur. A key aspect of our current liver model is a layered co-culture of primary rat hepatocytes (PRHs) and primary rat liver sinusoidal endothelial cells (LSECs) or bovine aortic endothelial cells (BAECs) on a transwell membrane. When a layered co-culture was attempted with a thin matrigel layer placed between hepatocytes and endothelial cells to mimic the Space of Disse, the cells did not form completely separated monolayers. However, when hepatocytes and endothelial cells were cultured on the opposite sides of a transwell membrane, PRHs co-cultured with LSECs or BAECs maintained their viability and normal morphology for 39 and 57 days, respectively. We assessed the presence of hepatocyte-specific differentiation markers to verify that PRHs remained differentiated in the long-term co-culture and analyzed hepatocyte function by monitoring urea synthesis. We also noted that the expression of cytochrome P-450 remained similar in the cocultured system from Day 13 to Day 48. Thus, our novel liver model system demonstrated that primary hepatocytes can be cultured for extended times and retain their hepatocyte-specific functions when layered with endothelial cells

Nanodiamond landmarks for subcellular multimodal optical and electron imaging.

There is a growing need for biolabels that can be used in both optical and electron microscopies, are non-cytotoxic, and do not photobleach. Such biolabels could enable targeted nanoscale imaging of sub-cellular structures, and help to establish correlations between conjugation-delivered biomolecules and function. Here we demonstrate a sub-cellular multi-modal imaging methodology that enables localization of inert particulate probes, consisting of nanodiamonds having fluorescent nitrogen-vacancy centers. These are functionalized to target specific structures, and are observable by both optical and electron microscopies. Nanodiamonds targeted to the nuclear pore complex are rapidly localized in electron-microscopy diffraction mode to enable "zooming-in" to regions of interest for detailed structural investigations. Optical microscopies reveal nanodiamonds for in-vitro tracking or uptake-confirmation. The approach is general, works down to the single nanodiamond level, and can leverage the unique capabilities of nanodiamonds, such as biocompatibility, sensitive magnetometry, and gene and drug delivery

Targeted Nanodiamonds for Identification of Subcellular Protein Assemblies in Mammalian Cells

Transmission electron microscopy (TEM) can be used to successfully determine the structures of proteins. However, such studies are typically done ex situ after extraction of the protein from the cellular environment. Here we describe an application for nanodiamonds as targeted intensity contrast labels in biological TEM, using the nuclear pore complex (NPC) as a model macroassembly. We demonstrate that delivery of antibody-conjugated nanodiamonds to live mammalian cells using maltotriose-conjugated polypropylenimine dendrimers results in efficient localization of nanodiamonds to the intended cellular target. We further identify signatures of nanodiamonds under TEM that allow for unambiguous identification of individual nanodiamonds from a resin-embedded, OsO4-stained environment. This is the first demonstration of nanodiamonds as labels for nanoscale TEM-based identification of subcellular protein assemblies. These results, combined with the unique fluorescence properties and biocompatibility of nanodiamonds, represent an important step toward the use of nanodiamonds as markers for correlated optical/electron bioimaging.Comment: 38 pages, 6 figures, SI section with 3 figure

A combined NMR and DFT study of Narrow Gap Semiconductors: The case of PbTe

In this study we present an alternative approach to separating contributions to the NMR shift originating from the Knight shift and chemical shielding by a combination of experimental solid-state NMR results and ab initio calculations. The chemical and Knight shifts are normally distinguished through detailed studies of the resonance frequency as function of temperature and carrier concentration, followed by extrapolation of the shift to zero carrier concentration. This approach is time-consuming and requires studies of multiple samples. Here, we analyzed $^{207}$Pb and $^{125}$Te NMR spin-lattice relaxation rates and NMR shifts for bulk and nanoscale PbTe. The shifts are compared with calculations of the $^{207}$Pb and $^{125}$Te chemical shift resonances to determine the chemical shift at zero charge carrier concentration. The results are in good agreement with literature values from carrier concentration-dependent studies. The measurements are also compared to literature reports of the $^{207}$Pb and $^{125}$Te Knight shifts of $n$- and $p$-type PbTe semiconductors. The literature data have been converted to the currently accepted shift scale. We also provide possible evidence for the "self-cleaning effect" property of PbTe nanocrystals whereby defects are removed from the core of the particles, while preserving the crystal structure.Comment: 34 pages, 9 figure