Full system bifurcation analysis of endocrine bursting models.
Full system bifurcation analysis of endocrine bursting models.
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DOI：
10.1016/j.jtbi.2010.03.030
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发表时间：
2010-06-21
影响因子：
2
通讯作者：
Sherman A
中科院分区：
文献类型：
--
作者：
Tsaneva-Atanasova K;Osinga HM;Riess T;Sherman A
平台破裂是许多电兴奋细胞的典型特征，例如分泌激素的内分泌细胞和分泌神经递质的某些类型的神经元。虽然在许多这类细胞类型中，突发模式是由电压门控钙通道和钙敏感钾通道之间的相互作用来调节的，但它们可以非常不同。我们研究了在内分泌细胞模型中发现的所谓的方波和伪平台爆发模式，这些模式分别以快子系统中的超临界或亚临界Hopf分叉为特征。通过使用Hindmarsh和Rose(伦敦皇家学会学报B 221(1222)，87-102)的多项式模型，它保留了我们所考虑的生物物理模型的主要性质，我们对两种爆发模式的完整快-慢系统进行了详细的分叉分析。我们发现，这两种情况导致两条路径爆炸的可能性相同，即Hopf分支的临界性与表征路径到爆炸的特征无关。实际的路径取决于全系统的不动点相对于快速子系统的同宿分支的相对位置。我们的全系统分叉分析揭示了标准快慢分析没有捕捉到的内分泌爆发的特性。
Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221(1222), 87–102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system’s fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.
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DOI：
10.1085/jgp.200409206
发表时间：
2004-12
期刊：
The Journal of general physiology
影响因子：
--
作者：
Barg S;Rorsman P
通讯作者：
Rorsman P
DOI：
10.1098/rspb.1984.0024
发表时间：
1984-01-01
期刊：
PROCEEDINGS OF THE ROYAL SOCIETY SERIES B-BIOLOGICAL SCIENCES
影响因子：
--
作者：
HINDMARSH, JL;ROSE, RM
通讯作者：
ROSE, RM
影响因子：
1.9
作者：
BAER, SM;ERNEUX, T;RINZEL, J
通讯作者：
RINZEL, J
影响因子：
3.4
作者：
Bertram, R;Previte, J;Satin, LS
通讯作者：
Satin, LS
影响因子：
5.5
作者：
Beauvois, MC;Merezak, C;Gilon, P
通讯作者：
Gilon, P