Loss of neuronal network resilience precedes seizures and determines the ictogenic nature of interictal synaptic perturbations

The mechanisms of seizure emergence, and the role of brief interictal epileptiform discharges (IEDs) in seizure generation are two of the most important unresolved issues in modern epilepsy research. Our study shows that the transition to seizure is not a sudden phenomenon,but a slow process characterized by the progressive loss of neuronal network resilience. From a dynamical perspective, the slow transition is governed by the principles of critical slowing, a robust natural phenomenon observable in systems characterized by transitions between dynamical regimes. In epilepsy, this process is modulated by the synchronous synaptic input from IEDs. IEDs are external perturbations that produce phasic changes in the slow transition process and exert opposing effects on the dynamics of a seizure-generating network, causing either anti-seizure or pro-seizure effects. We show that the multifaceted nature of IEDs is defined by the dynamical state of the network at the moment of the discharge occurrence

Relation between hepatic expression of ATP-binding cassette transporters G5 and G8 and biliary cholesterol secretion in mice

Background/Aims: Mutations in genes encoding the ATP-binding cassette (ABC)-transporters ABCG5 and ABCG8 underlie sitosterolemia, which is characterized by elevated plasma levels of phytosterols due to increased intestinal absorption and impaired biliary secretion of sterols. The aim of our study was to correlate the expression levels of Abcg5 and Abcg8 to biliary cholesterol secretion in various (genetically-modified) mouse models. Methods: Bile was collected from genetically-modified mice fed a chow diet, or from mice fed either a chow diet, or chow supplemented with either 1% diosgenin, 0.1% simvastatin, or a synthetic liver X receptor agonist, for determination of biliary lipids. Livers and small intestines were harvested and expression levels of Abcg5, Abcg8 and Abcb4 were determined by real-time polymerase chain reaction. Results: Intestinal expression of Abcg5 and Abcg8 did not show much variation between the various models. In contrast, a linear correlation between hepatic expression levels of Abcg5 and Abcg8 and biliary cholesterol secretion rates was found. This relation was independent of Abcb4-mediated phospholipid secretion. However, in diosgenin-fed mice showing cholesterol hypersecretion, hepatic Abcg5 and Abcg8 expression levels remained unchanged. Conclusions: Our results strongly support a role for Abcg5 and Abcg8 in regulation of biliary cholesterol secretion, but also indicate the existence of a largely independent route of cholesterol secretion. (C) 2003 European Association for the Study of the Liver. Published by Elsevier Science B.V. All rights reserve

Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection

Matrix functions are a central topic of linear algebra, and problems of their numerical approximation appear increasingly often in scientific computing. We review various rational Krylov methods for the computation of large-scale matrix functions. Emphasis is put on the rational Arnoldi method and variants thereof, namely, the extended Krylov subspace method and the shift-and-invert Arnoldi method, but we also discuss the nonorthogonal generalized Leja point (or PAIN) method. The issue of optimal pole selection for rational Krylov methods applied for approximating the resolvent and exponential function, and functions of Markov type, is treated in some detail