Challenges for brain repair: insights from adult neurogenesis in birds and mammals

Adult neurogenesis is a widespread phenomenon occurring in many species, including humans. The functional and therapeutic implications of this form of brain plasticity are now beginning to be realized. Comparative approaches to adult neurogenesis will yield important clues about brain repair. Here, we compare adult neurogenesis in birds and mammals. We review recent studies on the glial identity of stem cells that generate new neurons, the different modes of migration used by the newly generated neurons to reach their destinations, and how these systems respond to experimentally induced cell death. We integrate these findings to address how comparative analysis at the molecular level might be used for brain repair

Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy

Spatial non-locality of space-fractional viscoelastic equations of motion is studied. Relaxation effects are accounted for by replacing second-order time derivatives by lower-order fractional derivatives and their generalizations. It is shown that space-fractional equations of motion of an order strictly less than 2 allow for a new kind anisotropy, associated with angular dependence of non-local interactions between stress and strain at different material points. Constitutive equations of such viscoelastic media are determined. Explicit fundamental solutions of the Cauchy problem are constructed for some cases isotropic and anisotropic non-locality

A fluorescent perilipin 2 knock-in mouse model visualizes lipid droplets in the developing and adult brain

Lipid droplets (LDs) are dynamic lipid storage organelles. They are tightly linked to metabolism and can exert protective functions, making them important players in health and disease. Most LD studies in vivo rely on staining methods, providing only a snapshot. We therefore developed a LD-reporter mouse by endogenously labelling the LD coat protein perilipin 2 (PLIN2) with tdTomato, enabling staining-free fluorescent LD visualisation in living and fixed tissues and cells. Here we validate this model under standard and high-fat diet conditions and demonstrate that LDs are present in various cells in the healthy brain, including neurons, astrocytes, ependymal cells, neural stem/progenitor cells and microglia. Furthermore, we show that LDs are abundant during brain development and can be visualized using live-imaging of embryonic slices. Taken together, our tdTom-Plin2 mouse serves as a novel tool to study LDs and their dynamics under both physiological and diseased conditions in all tissues expressing Plin2

Fractional diffusion modeling of ion channel gating

An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe non-exponential, power-law like distributions of residence time intervals in several types of ion channels. Our method presents a generalization of the discrete diffusion model by Millhauser, Salpeter and Oswald [Proc. Natl. Acad. Sci. USA 85, 1503 (1988)] to the case of a continuous, anomalous slow conformational diffusion. The corresponding generalization is derived from a continuous time random walk composed of nearest neighbor jumps which in the scaling limit results in a fractional diffusion equation. The studied model contains three parameters only: the mean residence time, a characteristic time of conformational diffusion, and the index of subdiffusion. A tractable analytical expression for the characteristic function of the residence time distribution is obtained. In the limiting case of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. USA 99, 3552 (2002)] are reproduced. Depending on the chosen parameters, the fractional diffusion model exhibits a very rich behavior of the residence time distribution with different characteristic time-regimes. Moreover, the corresponding autocorrelation function of conductance fluctuations displays nontrivial features. Our theoretical model is in good agreement with experimental data for large conductance potassium ion channels

Inducible Cre recombinase activity in mouse mature astrocytes and adult neural precursor cells

Two transgenic mouse lines expressing an inducible form of the Cre recombinase (CreERTM) under the control of the human GFAP promoter have been generated and characterized. In adult mice, expression of the fusion protein is largely confined to astrocytes in all regions of the central nervous system. Minimal spontaneous Cre activity was detected and recombination was efficiently induced by intraperitoneal administration of tamoxifen in adult mice. The pattern of recombination closely mirrored that of transgene expression. The percentage of astrocytes undergoing recombination varied from region to region ranging from 35% to 70% while a much smaller portion (<1%) of oligodendrocytes and neural precursor cells showed evidence of Cre activity. These mouse lines will provide important tools to dissect gene function in glial cells and in gliomagenesis

Analysis of Fourier transform valuation formulas and applications

The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ

Lattice Kinetics of Diffusion-Limited Coalescence and Annihilation with Sources

We study the 1D kinetics of diffusion-limited coalescence and annihilation with back reactions and different kinds of particle input. By considering the changes in occupation and parity of a given interval, we derive sets of hierarchical equations from which exact expressions for the lattice coverage and the particle concentration can be obtained. We compare the mean-field approximation and the continuum approximation to the exact solutions and we discuss their regime of validity.Comment: 24 pages and 3 eps figures, Revtex, accepted for publication in J. Phys.

Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State

As Charles Goodyear discovered in 1839, when he first vulcanised rubber, a macromolecular liquid is transformed into a solid when a sufficient density of permanent crosslinks is introduced at random. At this continuous equi- librium phase transition, the liquid state, in which all macromolecules are delocalised, is transformed into a solid state, in which a nonzero fraction of macromolecules have spontaneously become localised. This solid state is a most unusual one: localisation occurs about mean positions that are distributed homogeneously and randomly, and to an extent that varies randomly from monomer to monomer. Thus, the solid state emerging at the vulcanisation transition is an equilibrium amorphous solid state: it is properly viewed as a solid state that bears the same relationship to the liquid and crystalline states as the spin glass state of certain magnetic systems bears to the paramagnetic and ferromagnetic states, in the sense that, like the spin glass state, it is diagnosed by a subtle order parameter. In this review we give a detailed exposition of a theoretical approach to the physical properties of systems of randomly, permanently crosslinked macromolecules. Our primary focus is on the equilibrium properties of such systems, especially in the regime of Goodyear's vulcanisation transition.Comment: Review Article, REVTEX, 58 pages, 3 PostScript figure

Tripotential Differentiation of Adherently Expandable Neural Stem (NS) Cells

BACKGROUND: A recent study has shown that pure neural stem cells can be derived from embryonic stem (ES) cells and primary brain tissue. In the presence of fibroblast growth factor 2 (FGF2) and epidermal growth factor (EGF), this population can be continuously expanded in adherent conditions. In analogy to continuously self-renewing ES cells, these cells were termed ‘NS’ cells (Conti et al., PLoS Biol 3: e283, 2005). While NS cells have been shown to readily generate neurons and astrocytes, their differentiation into oligodendrocytes has remained enigmatic, raising concerns as to whether they truly represent tripotential neural stem cells. METHODOLOGY/PRINCIPAL FINDINGS: Here we provide evidence that NS cells are indeed tripotent. Upon proliferation with FGF2, platelet-derived growth factor (PDGF) and forskolin, followed by differentiation in the presence of thyroid hormone (T3) and ascorbic acid NS cells efficiently generate oligodendrocytes (∼20%) alongside astrocytes (∼40%) and neurons (∼10%). Mature oligodendroglial differentiation was confirmed by transplantation data showing that NS cell-derived oligodendrocytes ensheath host axons in the brain of myelin-deficient rats. CONCLUSIONS/SIGNIFICANCE: In addition to delineating NS cells as a potential donor source for myelin repair, our data strongly support the view that these adherently expandable cells represent bona fide tripotential neural stem cells