Monophasic Action Potential Duration During Programmed Electrical Stimulation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73599/1/j.1540-8159.1991.tb04156.x.pd

One-Dimensional Birth-Death Process and Delbr\"{u}ck-Gillespie Theory of Mesoscopic Nonlinear Chemical Reactions

As a mathematical theory for the stochasstic, nonlinear dynamics of individuals within a population, Delbr\"{u}ck-Gillespie process (DGP) $n(t)\in\mathbb{Z}^N$, is a birth-death system with state-dependent rates which contain the system size $V$ as a natural parameter. For large $V$, it is intimately related to an autonomous, nonlinear ordinary differential equation as well as a diffusion process. For nonlinear dynamical systems with multiple attractors, the quasi-stationary and stationary behavior of such a birth-death process can be underestood in terms of a separation of time scales by a $T^*\sim e^{\alpha V}$ $(\alpha>0)$: a relatively fast, intra-basin diffusion for $t\ll T^*$ and a much slower inter-basin Markov jump process for $t\gg T^*$. In the present paper for one-dimensional systems, we study both stationary behavior ($t=\infty$) in terms of invariant distribution $p_n^{ss}(V)$, and finite time dynamics in terms of the mean first passsage time (MFPT) $T_{n_1\rightarrow n_2}(V)$. We obtain an asymptotic expression of MFPT in terms of the "stochastic potential" $\Phi(x,V)=-(1/V)\ln p^{ss}_{xV}(V)$. We show in general no continuous diffusion process can provide asymptotically accurate representations for both the MFPT and the $p_n^{ss}(V)$ for a DGP. When $n_1$ and $n_2$ belong to two different basins of attraction, the MFPT yields the $T^*(V)$ in terms of $\Phi(x,V)\approx \phi_0(x)+(1/V)\phi_1(x)$. For systems with a saddle-node bifurcation and catastrophe, discontinuous "phase transition" emerges, which can be characterized by $\Phi(x,V)$ in the limit of $V\rightarrow\infty$. In terms of time scale separation, the relation between deterministic, local nonlinear bifurcations and stochastic global phase transition is discussed. The one-dimensional theory is a pedagogic first step toward a general theory of DGP.Comment: 32 pages, 3 figure

Trophic Garnishes: Cat–Rat Interactions in an Urban Environment

BACKGROUND:Community interactions can produce complex dynamics with counterintuitive responses. Synanthropic community members are of increasing practical interest for their effects on biodiversity and public health. Most studies incorporating introduced species have been performed on islands where they may pose a risk to the native fauna. Few have examined their interactions in urban environments where they represent the majority of species. We characterized house cat (Felis catus) predation on wild Norway rats (Rattus norvegicus), and its population effects in an urban area as a model system. Three aspects of predation likely to influence population dynamics were examined; the stratum of the prey population killed by predators, the intensity of the predation, and the size of the predator population. METHODOLOGY/PRINCIPAL FINDINGS:Predation pressure was estimated from the sizes of the rat and cat populations, and the characteristics of rats killed in 20 alleys. Short and long term responses of rat population to perturbations were examined by removal trapping. Perturbations removed an average of 56% of the rats/alley but had no negative long-term impact on the size of the rat population (49.6+/-12.5 rats/alley and 123.8+/-42.2 rats/alley over two years). The sizes of the cat population during two years (3.5 animals/alley and 2.7 animals/alley) also were unaffected by rat population perturbations. Predation by cats occurred in 9/20 alleys. Predated rats were predominantly juveniles and significantly smaller (144.6 g+/-17.8 g) than the trapped rats (385.0 g+/-135.6 g). Cats rarely preyed on the larger, older portion of the rat population. CONCLUSIONS/SIGNIFICANCE:The rat population appears resilient to perturbation from even substantial population reduction using targeted removal. In this area there is a relatively low population density of cats and they only occasionally prey on the rat population. This occasional predation primarily removes the juvenile proportion of the rat population. The top predator in this urban ecosystem appears to have little impact on the size of the prey population, and similarly, reduction in rat populations doesn't impact the size of the cat population. However, the selected targeting of small rats may locally influence the size structure of the population which may have consequences for patterns of pathogen transmission

Valence bond solid formalism for d-level one-way quantum computation

The d-level or qudit one-way quantum computer (d1WQC) is described using the valence bond solid formalism and the generalised Pauli group. This formalism provides a transparent means of deriving measurement patterns for the implementation of quantum gates in the computational model. We introduce a new universal set of qudit gates and use it to give a constructive proof of the universality of d1WQC. We characterise the set of gates that can be performed in one parallel time step in this model.Comment: 26 pages, 9 figures. Published in Journal of Physics A: Mathematical and Genera

Quantum algebra in the mixed light pseudoscalar meson states

In this paper, we investigate the entanglement degrees of pseudoscalar meson states via quantum algebra Y(su(3)). By making use of transition effect of generators J of Y(su(3)), we construct various transition operators in terms of J of Y(su(3)), and act them on eta-pion-eta mixing meson state. The entanglement degrees of both the initial state and final state are calculated with the help of entropy theory. The diagrams of entanglement degrees are presented. Our result shows that a state with desired entanglement degree can be achieved by acting proper chosen transition operator on an initial state. This sheds new light on the connect among quantum information, particle physics and Yangian algebra.Comment: 9 pages, 3 figure

Microglia-synapse engulfment via PtdSer-TREM2 ameliorates neuronal hyperactivity in Alzheimer's disease models

Neuronal hyperactivity is a key feature of early stages of Alzheimer's disease (AD). Genetic studies in AD support that microglia act as potential cellular drivers of disease risk, but the molecular determinants of microglia-synapse engulfment associated with neuronal hyperactivity in AD are unclear. Here, using super-resolution microscopy, 3D-live imaging of co-cultures, and in vivo imaging of lipids in genetic models, we found that spines become hyperactive upon Aβ oligomer stimulation and externalize phosphatidylserine (ePtdSer), a canonical "eat-me" signal. These apoptotic-like spines are targeted by microglia for engulfment via TREM2 leading to amelioration of Aβ oligomer-induced synaptic hyperactivity. We also show the in vivo relevance of ePtdSer-TREM2 signaling in microglia-synapse engulfment in the hAPP NL-F knock-in mouse model of AD. Higher levels of apoptotic-like synapses in mice as well as humans that carry TREM2 loss-of-function variants were also observed. Our work supports that microglia remove hyperactive ePtdSer+ synapses in Aβ-relevant context and suggest a potential beneficial role for microglia in the earliest stages of AD

Perivascular cells induce microglial phagocytic states and synaptic engulfment via SPP1 in mouse models of Alzheimer's disease

Alzheimer's disease (AD) is characterized by synaptic loss, which can result from dysfunctional microglial phagocytosis and complement activation. However, what signals drive aberrant microglia-mediated engulfment of synapses in AD is unclear. Here we report that secreted phosphoprotein 1 (SPP1/osteopontin) is upregulated predominantly by perivascular macrophages and, to a lesser extent, by perivascular fibroblasts. Perivascular SPP1 is required for microglia to engulf synapses and upregulate phagocytic markers including C1qa, Grn and Ctsb in presence of amyloid-β oligomers. Absence of Spp1 expression in AD mouse models results in prevention of synaptic loss. Furthermore, single-cell RNA sequencing and putative cell-cell interaction analyses reveal that perivascular SPP1 induces microglial phagocytic states in the hippocampus of a mouse model of AD. Altogether, we suggest a functional role for SPP1 in perivascular cells-to-microglia crosstalk, whereby SPP1 modulates microglia-mediated synaptic engulfment in mouse models of AD

Perivascular cells induce microglial phagocytic states and synaptic engulfment via SPP1 in mouse models of Alzheimer\u27s disease.

Alzheimer\u27s disease (AD) is characterized by synaptic loss, which can result from dysfunctional microglial phagocytosis and complement activation. However, what signals drive aberrant microglia-mediated engulfment of synapses in AD is unclear. Here we report that secreted phosphoprotein 1 (SPP1/osteopontin) is upregulated predominantly by perivascular macrophages and, to a lesser extent, by perivascular fibroblasts. Perivascular SPP1 is required for microglia to engulf synapses and upregulate phagocytic markers including C1qa, Grn and Ctsb in presence of amyloid-β oligomers. Absence of Spp1 expression in AD mouse models results in prevention of synaptic loss. Furthermore, single-cell RNA sequencing and putative cell-cell interaction analyses reveal that perivascular SPP1 induces microglial phagocytic states in the hippocampus of a mouse model of AD. Altogether, we suggest a functional role for SPP1 in perivascular cells-to-microglia crosstalk, whereby SPP1 modulates microglia-mediated synaptic engulfment in mouse models of AD