A mathematical model of the metabolic and perfusion effects on cortical spreading depression

Cortical spreading depression (CSD) is a slow-moving ionic and metabolic disturbance that propagates in cortical brain tissue. In addition to massive cellular depolarizations, CSD also involves significant changes in perfusion and metabolism-aspects of CSD that had not been modeled and are important to traumatic brain injury, subarachnoid hemorrhage, stroke, and migraine. In this study, we develop a mathematical model for CSD where we focus on modeling the features essential to understanding the implications of neurovascular coupling during CSD. In our model, the sodium-potassium-ATPase, mainly responsible for ionic homeostasis and active during CSD, operates at a rate that is dependent on the supply of oxygen. The supply of oxygen is determined by modeling blood flow through a lumped vascular tree with an effective local vessel radius that is controlled by the extracellular potassium concentration. We show that during CSD, the metabolic demands of the cortex exceed the physiological limits placed on oxygen delivery, regardless of vascular constriction or dilation. However, vasoconstriction and vasodilation play important roles in the propagation of CSD and its recovery. Our model replicates the qualitative and quantitative behavior of CSD-vasoconstriction, oxygen depletion, extracellular potassium elevation, prolonged depolarization-found in experimental studies. We predict faster, longer duration CSD in vivo than in vitro due to the contribution of the vasculature. Our results also help explain some of the variability of CSD between species and even within the same animal. These results have clinical and translational implications, as they allow for more precise in vitro, in vivo, and in silico exploration of a phenomenon broadly relevant to neurological disease. © 2013 Chang et al

Grassmannian flows and applications to nonlinear partial differential equations

We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary matrix Riccati equations can be generated by projecting linear evolutionary flows on a Stiefel manifold onto a coordinate chart of the underlying Grassmann manifold. Our method relies on extending this idea to the infinite dimensional case. The key is an integral equation analogous to the Marchenko equation in integrable systems, that represents the coodinate chart map. We show explicitly how to generate such solutions to scalar partial differential equations of arbitrary order with nonlocal quadratic nonlinearities using our approach. We provide numerical simulations that demonstrate the generation of solutions to Fisher--Kolmogorov--Petrovskii--Piskunov equations with nonlocal nonlinearities. We also indicate how the method might extend to more general classes of nonlinear partial differential systems.Comment: 26 pages, 2 figure

Domestic horses (Equus caballus) prefer to approach humans displaying a submissive body posture rather than a dominant body posture

Signals of dominance and submissiveness are central to conspecific communication in many species. For domestic animals, sensitivities to these signals in humans may also be beneficial. We presented domestic horses with a free choice between two unfamiliar humans, one adopting a submissive and the other a dominant body posture, with vocal and facial cues absent. Horses had previously been given food rewards by both human demonstrators, adopting neutral postures, to encourage approach behaviour. Across four counterbalanced test trials, horses showed a significant preference for approaching the submissive posture in both the first trial and across subsequent trials, and no individual subject showed an overall preference for dominant postures. There was no significant difference in latency to approach the two postures. This study provides novel evidence that domestic horses may spontaneously discriminate between, and attribute communicative significance to, human body postures of dominance; and further, that familiarity with the signaller is not a requirement for this response. These findings raise interesting questions about the plasticity of social signal perception across the species barrier

CLICK:One-step generation of conditional knockout mice

Abstract Background CRISPR/Cas9 enables the targeting of genes in zygotes; however, efficient approaches to create loxP-flanked (floxed) alleles remain elusive. Results Here, we show that the electroporation of Cas9, two gRNAs, and long single-stranded DNA (lssDNA) into zygotes, termed CLICK (CRISPR with lssDNA inducing conditional knockout alleles), enables the quick generation of floxed alleles in mice and rats. Conclusions The high efficiency of CLICK provides homozygous knock-ins in oocytes carrying tissue-specific Cre, which allows the one-step generation of conditional knockouts in founder (F0) mice

Overexpression of IL-1ra gene up-regulates interleukin-1β converting enzyme (ICE) gene expression: possible mechanism underlying IL-1β-resistance of cancer cells

We investigated the interaction of endogenous interleukin (IL)-1β, IL-1ra, and interleukin-1β converting enzyme (ICE) in four human urological cancer cell lines, KU-19-19, KU-1, KU-2 and KU-19-20. Northern blot analysis showed that IL-1β gene was expressed in all cell lines. On the other hand, in KU-19-19 and KU-19-20, the gene expressions of both IL-1ra and ICE were suppressed. MTT assay revealed that IL-1β (10 ng ml−1) promoted cell growth in KU-19-19 and KU-19-20, while it inhibited in KU-1 and KU-2. An ICE inhibitor, Acetyl-Tyr-Val-Ala-Asp-CHO (YVAD-CHO) blocked IL-1β-induced growth inhibition in KU-1 and KU-2. Overexpression of the secretory type IL-1ra with adenovirus vector (AxIL-1ra) enhanced ICE gene expression, while exogenous IL-1ra (100 ng ml–1) did not enhance it. Furthermore, AxIL-1ra treatment promoted endogenous IL-1β secretion and induced significant growth inhibition and apoptotic cell death on KU-19-19 and KU-19-20. Treatment with either IL-1ra (100 ng ml−1), IL-1β antibody (100 μg ml−1), or YVAD-CHO blocked AxIL-1ra-induced cell death in KU-19-19 and KU-19-20. These results suggest that IL-1β-sensitivity depends on the level of ICE gene expression, which is regulated by the level of endogenous sIL-1ra expression. This is a first report on the intracellular function of sIL-1ra and these findings may provide key insights into the mechanism underlying the viability of cancer cells. © 1999 Cancer Research Campaig