Synaptic activity initiates many adaptive responses in neurons. Here we report a novel form of structural plasticity in dissociated hippocampal cultures and slice preparations. Using a recently developed algorithm for three-dimensional image reconstruction and quantitative measurements of cell organelles, we found that many nuclei from hippocampal neurons are highly infolded and form unequally sized nuclear compartments. Nuclear infoldings are dynamic structures, which can radically transform the geometry of the nucleus in response to neuronal activity. Action potential bursting causing synaptic NMDA receptor activation dramatically increases the number of infolded nuclei via a process that requires the ERK-MAP kinase pathway and new protein synthesis. In contrast, deathsignaling pathways triggered by extrasynaptic NMDA receptors cause a rapid loss of nuclear infoldings. Compared with near-spherical nuclei, infolded nuclei have a larger surface and increased nuclear pore complex immunoreactivity. Nuclear calcium signals evoked by cytosolic calcium transients are larger in small nuclear compartments than in the large compartments of the same nucleus; moreover, small compartments are more efficient in temporally resolving calcium signals induced by trains of action potentials in the theta frequency range (5 Hz). Synaptic activity-induced phosphorylation of histone H3 on serine 10 was more robust in neurons with infolded nuclei compared with neurons with near-spherical nuclei, suggesting a functional link between nuclear geometry and transcriptional regulation. The translation of synaptic activity-induced signaling events into changes in nuclear geometry facilitates the relay of calcium signals to the nucleus, may lead to the formation of nuclear signaling microdomains, and could enhance signal-regulated transcription.

A major challenge in computational finance is the pricing of options that depend on a large number of risk factors. Prominent examples are basket or index options where dozens or even hundreds of stocks constitute the underlying asset and determine the dimensionality of the corresponding degenerate parabolic equation. The objective of this article is to show how an efficient discretisation can be achieved by hierarchical approximation as well as asymptotic expansions of the underlying continuous problem. The relation to a number of state-of-the-art methods is highlighted.

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