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J Math Biol
2006 Jul 01;531:179-213. doi: 10.1007/s00285-006-0381-7.
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The asymptotic behavior of solutions of the buffered bistable system.
Guo JS
,
Tsai JC
.
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In this paper, we study a model for calcium buffering with bistable nonlinearity. We present some results on the stability of equilibrium states and show that there exists a threshold phenomenon in our model. In comparing with the model without buffers, we see that stationary buffers cannot destroy the asymptotic stability of the associated equilibrium states and the threshold phenomenon. Moreover, we also investigate the propagation property of solutions with initial data being a disturbance of one of the stable states which is confined to a half-line. We show that the more stable state will eventually dominate the whole dynamics and that the speed of this propagation (or invading process) is positive.
Allbritton,
Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate.
1992, Pubmed,
Xenbase
Allbritton,
Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate.
1992,
Pubmed
,
Xenbase
Atri,
A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte.
1993,
Pubmed
,
Xenbase
Berridge,
Inositol trisphosphate and calcium signalling.
1993,
Pubmed
Bers,
A practical guide to the preparation of Ca2+ buffers.
1994,
Pubmed
Bezprozvanny,
Bell-shaped calcium-response curves of Ins(1,4,5)P3- and calcium-gated channels from endoplasmic reticulum of cerebellum.
1991,
Pubmed
De Young,
A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration.
1992,
Pubmed
Dupont,
Properties of intracellular Ca2+ waves generated by a model based on Ca(2+)-induced Ca2+ release.
1994,
Pubmed
,
Xenbase
Evans,
Solutions to axon equations.
1970,
Pubmed
Falcke,
Buffers and oscillations in intracellular Ca2+ dynamics.
2003,
Pubmed
Finch,
Calcium as a coagonist of inositol 1,4,5-trisphosphate-induced calcium release.
1991,
Pubmed
Fontanilla,
Characterization of the sperm-induced calcium wave in Xenopus eggs using confocal microscopy.
1998,
Pubmed
,
Xenbase
Fulton,
Activation of mammalian oocytes by intracellular injection of calcium.
1978,
Pubmed
Girard,
Two-dimensional model of calcium waves reproduces the patterns observed in Xenopus oocytes.
1992,
Pubmed
,
Xenbase
Igusa,
Effects of altered extracellular and intracellular calcium concentration on hyperpolarizing responses of the hamster egg.
1983,
Pubmed
Iino,
Biphasic Ca2+ dependence of inositol 1,4,5-trisphosphate-induced Ca release in smooth muscle cells of the guinea pig taenia caeci.
1990,
Pubmed
Jaffe,
Classes and mechanisms of calcium waves.
1993,
Pubmed
Jafri,
On the roles of Ca2+ diffusion, Ca2+ buffers, and the endoplasmic reticulum in IP3-induced Ca2+ waves.
1995,
Pubmed
Kaftan,
Inositol 1,4,5-trisphosphate (InsP3) and calcium interact to increase the dynamic range of InsP3 receptor-dependent calcium signaling.
1997,
Pubmed
Kline,
Regulation of intracellular calcium in the mouse egg: evidence for inositol trisphosphate-induced calcium release, but not calcium-induced calcium release.
1994,
Pubmed
Lechleiter,
Molecular mechanisms of intracellular calcium excitability in X. laevis oocytes.
1992,
Pubmed
,
Xenbase
Li,
Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism.
1994,
Pubmed
Marshall,
Regulation of inositol 1,4,5-trisphosphate receptors.
1993,
Pubmed
Miyazaki,
Block of Ca2+ wave and Ca2+ oscillation by antibody to the inositol 1,4,5-trisphosphate receptor in fertilized hamster eggs.
1992,
Pubmed
Naraghi,
Linearized buffered Ca2+ diffusion in microdomains and its implications for calculation of [Ca2+] at the mouth of a calcium channel.
1997,
Pubmed
Naraghi,
Two-dimensional determination of the cellular Ca2+ binding in bovine chromaffin cells.
1998,
Pubmed
Neher,
Usefulness and limitations of linear approximations to the understanding of Ca++ signals.
1998,
Pubmed
Neher,
Calcium gradients and buffers in bovine chromaffin cells.
1992,
Pubmed
Nowycky,
Time courses of calcium and calcium-bound buffers following calcium influx in a model cell.
1993,
Pubmed
Nuccitelli,
How do sperm activate eggs?
1991,
Pubmed
Nuccitelli,
The sperm-induced Ca2+ wave following fertilization of the Xenopus egg requires the production of Ins(1, 4, 5)P3.
1993,
Pubmed
,
Xenbase
Parker,
Inhibition by Ca2+ of inositol trisphosphate-mediated Ca2+ liberation: a possible mechanism for oscillatory release of Ca2+.
1990,
Pubmed
,
Xenbase
Peres,
InsP3- and Ca2(+)-induced Ca2+ release in single mouse oocytes.
1990,
Pubmed
Ridgway,
Free calcium increases explosively in activating medaka eggs.
1977,
Pubmed
Sala,
Calcium diffusion modeling in a spherical neuron. Relevance of buffering properties.
1990,
Pubmed
Smith,
Analytical steady-state solution to the rapid buffering approximation near an open Ca2+ channel.
1996,
Pubmed
Sneyd,
Mechanisms of calcium oscillations and waves: a quantitative analysis.
1995,
Pubmed
Terasaki,
Continuous network of endoplasmic reticulum in cerebellar Purkinje neurons.
1994,
Pubmed
Wagner,
Effects of rapid buffers on Ca2+ diffusion and Ca2+ oscillations.
1994,
Pubmed
Wagner,
Simulation of the fertilization Ca2+ wave in Xenopus laevis eggs.
1998,
Pubmed
,
Xenbase
Watras,
Inositol 1,4,5-trisphosphate-gated channels in cerebellum: presence of multiple conductance states.
1991,
Pubmed