Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum

Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with negative constant drift, described by a Fokker-Planck equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process, that has been extensively studied for its applications in physics, biology and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schroedinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a negative constant drift. We conclude with a comparison with other analytical methods and with numerical solutions.Comment: 21 pages, 8 figure

Protein phosphatase 1-dependent bidirectional synaptic plasticity controls ischemic recovery in the adult brain

Protein kinases and phosphatases can alter the impact of excitotoxicity resulting from ischemia by concurrently modulating apoptotic/survival pathways. Here, we show that protein phosphatase 1 (PP1), known to constrain neuronal signaling and synaptic strength (Mansuy et al., 1998; Morishita et al., 2001), critically regulates neuroprotective pathways in the adult brain. When PP1 is inhibited pharmacologically or genetically, recovery from oxygen/glucose deprivation (OGD) in vitro, or ischemia in vivo is impaired. Furthermore, in vitro, inducing LTP shortly before OGD similarly impairs recovery, an effect that correlates with strong PP1 inhibition. Conversely, inducing LTD before OGD elicits full recovery by preserving PP1 activity, an effect that is abolished by PP1 inhibition. The mechanisms of action of PP1 appear to be coupled with several components of apoptotic pathways, in particular ERK1/2 (extracellular signal-regulated kinase 1/2) whose activation is increased by PP1 inhibition both in vitro and in vivo. Together, these results reveal that the mechanisms of recovery in the adult brain critically involve PP1, and highlight a novel physiological function for long-term potentiation and long-term depression in the control of brain damage and repair

Distribution of the time at which the deviation of a Brownian motion is maximum before its first-passage time

We calculate analytically the probability density $P(t_m)$ of the time $t_m$ at which a continuous-time Brownian motion (with and without drift) attains its maximum before passing through the origin for the first time. We also compute the joint probability density $P(M,t_m)$ of the maximum $M$ and $t_m$. In the driftless case, we find that $P(t_m)$ has power-law tails: $P(t_m)\sim t_m^{-3/2}$ for large $t_m$ and $P(t_m)\sim t_m^{-1/2}$ for small $t_m$. In presence of a drift towards the origin, $P(t_m)$ decays exponentially for large $t_m$. The results from numerical simulations are in excellent agreement with our analytical predictions.Comment: 13 pages, 5 figures. Published in Journal of Statistical Mechanics: Theory and Experiment (J. Stat. Mech. (2007) P10008, doi:10.1088/1742-5468/2007/10/P10008

On arbitrages arising from honest times

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly before an honest time, while classical arbitrage opportunities can be realised exactly at an honest time as well as after an honest time. Moreover, stronger arbitrages of the first kind can only be obtained by trading as soon as an honest time occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR.Comment: 25 pages, revised versio

Gold/Silica biochips: applications to Surface Plasmon Resonance and fluorescence quenching

We report Gold/Silica biochips for low cost biosensor devices. Firstly, the study of biochemical interactions on silica by means of Surface Plasmon Resonance (SPR) is presented. Secondly, Gold/Silica biochips are employed to reduce the strong quenching that occurs when a fluorophore is close to the gold surface. Furthermore, the control of the Silica-like thickness allows optimizing the distance between the metallic surface and the fluorophore in order to enhance the fluorescent signal. These results represent the first steps towards highly sensitive, specific and low cost biosensors based, for example, on Surface Plasmon Coupled Emission (SPCE) techniques

Forgetting of long-term memory requires activation of NMDA receptors, L-type voltage-dependent Ca(2+) channels, and calcineurin

In the past decades, the cellular and molecular mechanisms underlying memory consolidation, reconsolidation, and extinction have been well characterized. However, the neurobiological underpinnings of forgetting processes remain to be elucidated. Here we used behavioral, pharmacological and electrophysiological approaches to explore mechanisms controlling forgetting. We found that post-acquisition chronic inhibition of the N-methyl-D-aspartate receptor (NMDAR), L-type voltage-dependent Ca2+ channel (LVDCC), and protein phosphatase calcineurin (CaN), maintains long-term object location memory that otherwise would have been forgotten. We further show that NMDAR activation is necessary to induce forgetting of object recognition memory. Studying the role of NMDAR activation in the decay of the early phase of long-term potentiation (E-LTP) in the hippocampus, we found that ifenprodil infused 30min after LTP induction in vivo blocks the decay of CA1-evoked postsynaptic plasticity, suggesting that GluN2B-containing NMDARs activation are critical to promote LTP decay. Taken together, these findings indicate that a well-regulated forgetting process, initiated by Ca2+ influx through LVDCCs and GluN2B-NMDARs followed by CaN activation, controls the maintenance of hippocampal LTP and long-term memories over time

Identification of Protein Targets of Reactive Metabolites of Tienilic Acid in Human Hepatocytes

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Chemical Research in Toxicology, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/tx300103jTienilic acid (TA) is a uricosuric diuretic that was withdrawn from the market only months after its introduction because of reports of serious incidents of drug-induced liver injury including some fatalities. Its hepatotoxicity is considered to be primarily immunoallergic in nature. Like other thiophene compounds, TA undergoes biotransformation to a S-oxide metabolite which then reacts covalently with cellular proteins. To identify protein targets of TA metabolites, we incubated [14C]-TA with human hepatocytes, separated cellular proteins by 2D gel electrophoresis, and analyzed proteins in 36 radioactive spots by tryptic digestion followed by LC-MS/MS. Thirty one spots contained at least one identifiable protein. Sixteen spots contained only one of 14 non-redundant proteins which were thus considered to be targets of TA metabolites. Six of the 14 were also found in other radioactive spots that contained from 1 to 3 additional proteins. Eight of the 14 had not been reported to be targets for any reactive metabolite other than TA. The other 15 spots each contained from 2–4 identifiable proteins, many of which are known targets of other chemically reactive metabolites, but since adducted peptides were not observed, the identity of the adducted protein(s) in these spots is ambiguous. Interestingly, all the radioactive spots corresponded to proteins of low abundance, while many highly abundant proteins in the mixture showed no radioactivity. Furthermore, of approximately 16 previously reported protein targets of TA in rat liver (Methogo, R., Dansette, P. and Klarskov, K. (2007) Int. J. Mass Spectrom., 268, 284–295), only one (fumarylacetoacetase) is among the 14 targets identified in this work. One reason for this difference may be statistical, given that each study identified a small number of targets from among thousands present in hepatocytes. Another may be the species difference (i.e. rat vs. human), and still another may be the method of detection of adducted proteins (i.e. Western blot vs. C-14). Knowledge of human target proteins is very limited. Of more than 350 known protein targets of reactive metabolites, only 42 are known from human and only 21 of these are known to be targets for more than one chemical. Nevertheless, the demonstration that human target proteins can be identified using isolated hepatocytes in vitro should enable the question of species differences to be addressed more fully in the future

Inducible Transgenic Rat Model for Diabetes Mellitus Based on shRNA-Mediated Gene Knockdown

The rat is an important animal model in biomedical research, but gene targeting technology is not established for this species. Therefore, we aimed to produce transgenic knockdown rats using shRNA technology and pronuclear microinjection. To this purpose, we employed a tetracycline-inducible shRNA expression system targeting the insulin receptor (IR). Doxycycline (DOX) treatment of the resulting transgenic rats led to a dose-dependent and reversible increase in blood glucose caused by ubiquitous inhibition of IR expression and signalling. We could neither detect an interferon response nor disturbances in microRNA processing after DOX treatment excluding toxic effects of shRNA expression. Low dose DOX treatment induced a chronic state of diabetes mellitus. In conclusion, we have developed a technology which allows the specific, inducible, and reversible suppression of any gene of interest in the rat. Our first transgenic rat line generated with this method represents an inducible model for diabetes mellitus