Quantification of coarse-graining error in Langevin and overdamped Langevin dynamics

In molecular dynamics and sampling of high dimensional Gibbs measures coarse-graining is an important technique to reduce the dimensionality of the problem. We will study and quantify the coarse-graining error between the coarse-grained dynamics and an effective dynamics. The effective dynamics is a Markov process on the coarse-grained state space obtained by a closure procedure from the coarse-grained coefficients. We obtain error estimates both in relative entropy and Wasserstein distance, for both Langevin and overdamped Langevin dynamics. The approach allows for vectorial coarse-graining maps. Hereby, the quality of the chosen coarse-graining is measured by certain functional inequalities encoding the scale separation of the Gibbs measure. The method is based on error estimates between solutions of (kinetic) Fokker-Planck equations in terms of large-deviation rate functionals

Homogenization of the one-dimensional wave equation

We present a method for two-scale model derivation of the periodic homogenization of the one-dimensional wave equation in a bounded domain. It allows for analyzing the oscillations occurring on both microscopic and macroscopic scales. The novelty reported here is on the asymptotic behavior of high frequency waves and especially on the boundary conditions of the homogenized equation. Numerical simulations are reported

Pathogenesis of peroxisomal deficiency disorders (Zellweger syndrome) may be mediated by misregulation of the GABAergic system via the diazepam binding inhibitor

BACKGROUND: Zellweger syndrome (ZS) is a fatal inherited disease caused by peroxisome biogenesis deficiency. Patients are characterized by multiple disturbances of lipid metabolism, profound hypotonia and neonatal seizures, and distinct craniofacial malformations. Median live expectancy of ZS patients is less than one year. While the molecular basis of peroxisome biogenesis and metabolism is known in considerable detail, it is unclear how peroxisome deficiency leads to the most severe neurological symptoms. Recent analysis of ZS mouse models has all but invalidated previous hypotheses. HYPOTHESIS: We suggest that a regulatory rather than a metabolic defect is responsible for the drastic impairment of brain function in ZS patients. TESTING THE HYPOTHESIS: Using microarray analysis we identify diazepam binding inhibitor/acyl-CoA binding protein (DBI) as a candidate protein that might be involved in the pathogenic mechanism of ZS. DBI has a dual role as a neuropeptide antagonist of GABA(A) receptor signaling in the brain and as a regulator of lipid metabolism. Repression of DBI in ZS patients could result in an overactivation of GABAergic signaling, thus eventually leading to the characteristic hypotonia and seizures. The most important argument for a misregulation of GABA(A) in ZS is, however, provided by the striking similarity between ZS and "benzodiazepine embryofetopathy", a malformation syndrome observed after the abuse of GABA(A) agonists during pregnancy. IMPLICATIONS OF THE HYPOTHESIS: We present a tentative mechanistic model of the effect of DBI misregulation on neuronal function that could explain some of the aspects of the pathology of Zellweger syndrome

The Endozepine Odn Stimulates Polyphosphoinositide Metabolism in Rat Astrocytes

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