We review the principal assumptions underlying the application of phase-response curves (PRCs) to synchronization in neuronal networks. The PRC measures how much a given synaptic input perturbs spike timing in a neural oscillator. Among other applications, PRCs make explicit predictions about whether a given network of interconnected neurons will synchronize, as is often observed in cortical structures. Regarding the assumptions of the PRC theory, we conclude: (i) The assumption of noise-tolerant cellular oscillations at or near the network frequency holds in some but not all cases.

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Central nervous system infection can induce epilepsy that is often refractory to established antiseizure drugs. Previous studies in the Theiler’s murine encephalomyelitis virus (TMEV)-induced mouse model of limbic epilepsy have demonstrated the importance of inflammation, especially that mediated by tumor necrosis factor-α (TNFα), in the development of acute seizures. TNFα modulates glutamate receptor trafficking via TNF receptor 1 (TNFR1) to cause increased excitatory synaptic transmission. Therefore, we hypothesized that an increase in TNFα signaling after TMEV infection might contribute to acute seizures. We found a significant increase in both mRNA and protein levels of TNFα and the protein expression ratio of TNF receptors (TNFR1:TNFR2) in the hippocampus, a brain region most likely involved in seizure initiation, after TMEV infection, which suggests that TNFα signaling, predominantly through TNFR1, may contribute to limbic hyperexcitability. An increase in hippocampal cell-surface glutamate receptor expression was also observed during acute seizures. Although pharmacological inhibition of TNFR1-mediated signaling had no effect on acute seizures, several lines of genetically modified animals deficient in either TNFα or TNFRs had robust changes in seizure incidence and severity after TMEV infection. TNFR2–/– mice were highly susceptible to developing acute seizures, suggesting that TNFR2-mediated signaling may provide beneficial effects during the acute seizure period. Taken together, the present results suggest that inflammation in the hippocampus, caused predominantly by TNFα signaling, contributes to hyperexcitability and acute seizures after TMEV infection. Pharmacotherapies designed to suppress TNFR1-mediated or augment TNFR2-mediated effects of TNFα may provide antiseizure and disease-modifying effects after central nervous system infection.

Nerve outgrowth in the developing nervous system utilizes a variety of attractive and repulsive molecules found in the extracellular environment. In addition, physical cues may play an important regulatory role in determining directional outgrowth of nervous tissue. Here, by culturing nerve cells on filamentous surfaces and measuring directional growth, we tested the hypothesis that substrate curvature is sufficient to influence the directional outgrowth of nerve cells. We found that the mean direction of neurite outgrowth aligned with the direction of minimum principle curvature, and the spatial variance in outgrowth direction was directly related to the maximum principle curvature. As substrate size approached the size of an axon, adherent neurons extended processes that followed the direction of the long axis of the substrate similar to what occurs during development along pioneering axons and radial glial fibers. A simple Boltzmann model describing the interplay between adhesion and bending stiffness of the nerve process was found to be in close agreement with the data suggesting that cell stiffness and substrate curvature can act together in a manner that is sufficient to direct nerve outgrowth in the absence of contrasting molecular cues. The study highlights the potential importance of cellular level geometry as a fidelity-enhancing cue in the developing and regenerating nervous system.

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