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Wu HY, Baer SM (1998) Analysis of an excitable dendritic spine with an activity-dependent stem conductance. J Math Biol 36:569-92 [PubMed]

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References and models that cite this paper

Auto E (1981) AUTO: A program for the automatic bifurcation analysis of autonomous systems. Cong Num 30:265
Baer SM, Erneux T (1986) Singular Hopf bifurcation to relaxation oscillations. Siam J Appl Math 46:721-739
Baer SM, Erneux T (1992) Singular Hopf bifurcation to relaxation oscillations II Siam J Appl Math 52:1651-1664
Baer SM, Erneux T, Rinzel J (1989) The slow passage through Hopf bifurcation: delay, memory ecects, and resonance. J Appl Math 49:55-71
Baer SM, Rinzel J (1991) Propagation of dendritic spikes mediated by excitable spines: a continuum theory. J Neurophysiol 65:874-90 [Journal] [PubMed]
Baer SM, Rinzel J, Carrillo H (1995) Analysis of an autonomous phase model for neuronal parabolic bursting. J Math Biol 33:309-33 [PubMed]
Baer SM, Tier C (1986) An analysis of a dendritic neuron model with an active membrane site. J Math Biol 23:137-61 [PubMed]
Barinaga M (1995) Dendrites shed their dull image. Science 268:200-1 [PubMed]
Colonnier M (1968) Synaptic patterns on different cell types in the different laminae of the cat visual cortex. An electron microscope study. Brain Res 9:268-87 [PubMed]
Coss RG, Perkel DH (1985) The function of dendritic spines: a review of theoretical issues. Behav Neural Biol 44:151-85 [PubMed]
Diamond J, Gray EG, Yasargil EN (1970) The function of a dendritic spine: an hypothesis. Excitatory Synaptic Mechanisms.,  Anderse, P, Jansen JKS, ed. pp.213
Ermentrout GB, Kopell N (1986) Parabolic bursting in an excitable system coupled with a slow oscillation. Siam J Appl Math 46:233-253
Fifková E (1985) A possible mechanism of morphometric changes in dendritic spines induced by stimulation. Cell Mol Neurobiol 5:47-63 [PubMed]
Fifková E, Van Harreveld A (1977) Long-lasting morphological changes in dendritic spines of dentate granular cells following stimulation of the entorhinal area. J Neurocytol 6:211-30 [PubMed]
Fitzhugh R (1969) Mathematical models for excitation and propagation in nerve Biological Engineering, Schwan HP, ed.
Garthwaite J (1991) Glutamate, nitric oxide and cell-cell signalling in the nervous system. Trends Neurosci 14:60-7 [PubMed]
Gear C (1967) The numerical integration of ordinary dicerential equations. Math Comp 21:146-156
Geinisman Y (1993) Perforated axospinous synapses with multiple, completely partitioned transmission zones: probable structural intermediates in synaptic plasticity. Hippocampus 3:417-33 [Journal] [PubMed]
Grasman J (1987) Asymptotic methods for relaxaton oscillations and applications applied Mathematical Sciences
GRAY EG (1959) Axo-somatic and axo-dendritic synapses of the cerebral cortex: an electron microscope study. J Anat 93:420-33 [PubMed]
Greenough WT (1975) Experiential modification of the developing brain. Am Sci 63:37-46 [PubMed]
Hadeler KP, der Heiden U, Schumacher K (1976) Generation of the nervous impulse and periodic oscillations. Biol Cybern 23:211-8 [PubMed]
Harris KM, Kater SB (1994) Dendritic spines: cellular specializations imparting both stability and flexibility to synaptic function. Annu Rev Neurosci 17:341-71 [Journal] [PubMed]
Harris KM, Stevens JK (1988) Dendritic spines of rat cerebellar Purkinje cells: serial electron microscopy with reference to their biophysical characteristics. J Neurosci 8:4455-69 [PubMed]
Hille B (1992) Potassium channels and chloride channels Ionic Channels of Excitable Membrane, Hille B, ed. pp.115
Holden L, Erneux T (1993) Slow passage through a Hopf bifurcation: from oscillatory to steady state solutions. Siam J Appl Math 53:1045-1058
Holden L, Erneux T (1993) Understanding bursting oscillations as periodic slow passages through bifurcation and limit points. J Math Biol 31:351-365
Hosokawa T, Bliss TV, Fine A (1992) Persistence of individual dendritic spines in living brain slices. Neuroreport 3:477-80 [PubMed]
Hsu I, Kazarinoc NK (1976) An applicable Hopf bifurcation formula and stability of small periodic solutions of the Field-Noyes Model. J Math Anal Appl 55:61-89
Jack JJB, Noble D, Tsien RW (1983) Linear cable theory Electrical Current Flow in Excitable Cells, Jack JJB:Noble D:Tsien RW, ed. pp.25
Kawato M, Tsukahara N (1984) Electrical properties of dendritic spines with bulbous end terminals. Biophys J 46:155-66 [Journal] [PubMed]
Koch C, Poggio T (1983) A theoretical analysis of electrical properties of spines. Proc R Soc Lond B Biol Sci 218:455-77 [Journal] [PubMed]
Koch C, Zador A, Brown TH (1992) Dendritic spines: convergence of theory and experiment. Science 256:973-4 [PubMed]
LeMasson G, Marder E, Abbott LF (1993) Activity-dependent regulation of conductances in model neurons. Science 259:1915-7 [PubMed]
Miller JP, Rall W, Rinzel J (1985) Synaptic amplification by active membrane in dendritic spines. Brain Res 325:325-30 [PubMed]
Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35:193-213 [Journal] [PubMed]
   Morris-Lecar model of the barnacle giant muscle fiber (Morris, Lecar 1981) [Model]
Perkel DH, Perkel DJ (1985) Dendritic spines: role of active membrane in modulating synaptic efficacy. Brain Res 325:331-5 [PubMed]
Peters A, Kaiserman-Abramof IR (1970) The small pyramidal neuron of the rat cerebral cortex. The perikaryon, dendrites and spines. Am J Anat 127:321-55 [Journal] [PubMed]
Rall W (1978) Dendritic spines and synaptic potency. Studies in Neurophysiology., Porter R, ed. pp.203
Rall W, Rinzel J (1971) Dendritic spines and synaptic potency explored theoretically. Progc Int Union Physiol Sci (xxv Int Congr ) Ix
Rall W, Rinzel J (1971) Dendritic spine function and synaptic attenuation calculations. Prog Abstr Soc Neurosci 1:64
Rall W, Segev I (1987) Functional possibilities for synapses on dendrites and on dendritic spines. Synaptic Function. Edelman G, Gall W, and Cowan W eds., Edelman GM:Gall WE:Cowan WM, ed. pp.605
Rinzel J (1982) Neuronal plasticity (learning) Some Mathematical Questions in Biology-Neurobiology. Lectures on Mathematics in the Life Sciences., Miura RM, ed. pp.7
Rinzel J, Baer SM (1988) Threshold for repetitive activity for a slow stimulus ramp: a memory effect and its dependence on fluctuations. Biophys J 54:551-5 [Journal] [PubMed]
Rinzel J, Ermentrout GB (1989) Analysis of neuronal excitability and oscillations Methods In Neuronal Modeling: From Synapses To Networks, Koch C:Segev I, ed. pp.135
Rinzel J, Lee YS (1987) Dissection of a model for neuronal parabolic bursting. J Math Biol 25:653-75 [PubMed]
Rinzel JA (1987) A formal classification of bursting mechanisms in excitable systems Proc Intl Congress Mathematicians, Gleason AM, ed. pp.1578
Segev I, Rall W (1988) Computational study of an excitable dendritic spine. J Neurophysiol 60:499-523 [Journal] [PubMed]
Shepherd GM (1990) The Synaptic Organization Of The Brain
Shepherd GM (1996) The dendritic spine: a multifunctional integrative unit. J Neurophysiol 75:2197-210 [Journal] [PubMed]
Shepherd GM, Brayton RK, Miller JP, Segev I, Rinzel J, Rall W (1985) Signal enhancement in distal cortical dendrites by means of interactions between active dendritic spines. Proc Natl Acad Sci U S A 82:2192-5 [PubMed]
Shepherd GM, Greer CA (1988) The dendritic spine: adaptations of structure and function for dicerent types of synaptic integration. Intrinsic Determinants Of Neuronal Form And Function, Lasek R:BLACK MM, ed.
Troy WC (1978) The bifurcation of periodic solutions in the Hodgkin-Huxley equations. Quart Appl Math 36:73-83
Turner PJ (1994) XMGR: A plotting tool for workstations. Version 3.01
Van Harreveld A, Fifkova E (1975) Swelling of dendritic spines in the fascia dentata after stimulation of the perforant fibers as a mechanism of post-tetanic potentiation. Exp Neurol 49:736-49 [PubMed]
Wang XJ, Rinzel J (1995) Oscillatory and bursting properties of neurons The Handbook Of Brain Theory And Neural Networks, Arbib MA, ed. pp.686
Wilson CJ (1984) Passive cable properties of dendritic spines and spiny neurons. J Neurosci 4:281-97 [PubMed]
Wilson CJ, Groves PM, Kitai ST, Linder JC (1983) Three-dimensional structure of dendritic spines in the rat neostriatum. J Neurosci 3:383-8 [PubMed]
Yuste R, Denk W (1995) Dendritic spines as basic functional units of neuronal integration. Nature 375:682-4 [Journal] [PubMed]
Crook SM, Dur-E-Ahmad M, Baer SM (2007) A model of activity-dependent changes in dendritic spine density and spine structure. Math Biosci Eng 4:617-31 [Journal] [PubMed]
   Activity dependent changes in dendritic spine density and spine structure (Crook et al. 2007) [Model]
Tsay D, Yuste R (2002) Role of dendritic spines in action potential backpropagation: a numerical simulation study. J Neurophysiol 88:2834-45 [Journal] [PubMed]
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