Reduction of a model for an Onchidium pacemaker neuron |
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Authors: | Yoshinobu Maeda K Pakdaman Taishin Nomura Shinji Doi Shunsuke Sato |
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Institution: | (1) Division of Biophysical Engineering, Department of Systems and Human Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan, JP |
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Abstract: | The eight-variable model for the giant neuron localized in the esophageal ganglia of the marine pulmonate mollusk Onchidium verruculatum is reduced to four-and-three-dimensional systems by regrouping variables with similar time scales. These reduced models replicate
the complex behavior including beating, periodic bursting and aperiodic bursting displayed by the original full model when
the parameter I
ext
representing the intensity of the constant DC current stimulation is varied across a wide range. The complex behavior of
the full model arises from the interaction of fast and slow dynamics, and depends on the time scale C
s
of the slow dynamics. The four-variable reduced model is constructed independently from the parameter C
s
so that it reproduces the two-dimensional bifurcation structure of the full model for the two parameters I
ext
and C
s
. The three-variable reduced model is derived for a specific value of C
s
. The parameters of this model are tuned so that its one-parameter bifurcation diagram for I
ext
closely matches that of the full model. Correspondence between bifurcation structures ensures that both reduced models reproduce
the various discharge patterns of the full model. Similarity between the full and reduced models is also confirmed by comparing
mean firing frequencies and membrane potential waveforms in various regimes. The reduction exposes the factors essential for
reproducing the dynamics of the full model; indeed, it shows that the eight variables representing the membrane potential
and seven gating variables of six ionic currents in the full model account, in fact, for three basic processes responsible
for excitability, post-discharge refractoriness and slow membrane modulation.
Received: 7 May 1996 / Accepted 4 December 1997 |
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Keywords: | |
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