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September  2011, 16(2): 529-545. doi: 10.3934/dcdsb.2011.16.529

Firing control of ink gland motor cells in Aplysia californica

Xiangying Meng 1, , Quanbao Ji 2, and  John Rinzel 3,

1. 

Department of Dynamics and Control, Beihang University, Beijing 100191, China
2. 

Mathematical and Computational Department, Anhui Huainan Normal University, Anhui, 232007, China
3. 

Center for Neural Science and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States

Received  April 2010 Revised  November 2010 Published  June 2011

The release of ink in Aplysia californica occurs selectively to long-lasting stimuli. There is a good correspondence between features of the behavior and the firing pattern of the ink gland motor neurons. Indeed, the neurons do not fire for brief inputs and there is a delayed firing for long duration inputs. The biophysical mechanisms for the long delay before firing is due to a transient potassium current which activates rapidly but inactivates more slowly. Based on voltage-clamp experiments, a nine-variable Hodgkin-Huxley-like model for the ink gland motor neurons was developed by Byrne. Here, fast-slow analysis and two-parameter dynamical analysis are used to investigate the contribution of different currents and to predict various firing patterns, including the long latency before firing.
Keywords: transient potassium current, Bifurcation, neuron, oscillation, bistability..
Mathematics Subject Classification: Primary: 34C05, 34C23, 34G20; Secondary: 92C2.
Citation: Xiangying Meng, Quanbao Ji, John Rinzel. Firing control of ink gland motor cells in Aplysia californica. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 529-545. doi: 10.3934/dcdsb.2011.16.529
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show all references

References:
[1]

MIT Press, 2001.  Google Scholar

[2]

Acta Mech. Sin., 24 (2008), 593-628. Google Scholar

[3]

J. Physiol. Lond., 117 (1952), 500-544. Google Scholar

[4]

In "Ordinary and Partial Differential Equations" (B. D. sleeman, R. J. Jarvis eds.), Springer, Berlin (1987), 267-281.  Google Scholar

[5]

J. Neurophysiol., 43 (1980), 630-650. Google Scholar

[6]

J. Neurophysiol., 43 (1980), 651-668. Google Scholar

[7]

Brain Res., 204 (1981), 200-203. Google Scholar

[8]

PLos Comp. Biol., 3 (2007), 1498-1512.  Google Scholar

[9]

Biophys. J., 18 (1977), 81-102. Google Scholar

[10]

Bulletin of Mathematical Biology, 57 (1995), 899-929. Google Scholar

[11]

J. Neurophysiol., 89 (2003), 3097-3113. Google Scholar

[12]

J. Neurophysiol., 85 (2001), 523-538. Google Scholar

[13]

X. Y. Meng, Q. S. Lu and J. Rinzel, Control of firing patterns by two transient potassium currents: leading spike, latency, bistability,, J. Computl. Neurosci., ().   Google Scholar

[14]

Nature, 336 (1988), 379-381. Google Scholar

[15]

J. Neurosci., 10 (1990), 2338-2351. Google Scholar

[16]

J. Comparative Neurol., 213 (1983), 426-447. Google Scholar

[17]

J. Neurophysiol., 40 (1977), 692-707. Google Scholar

[18]

J. Neurophysiol., 42 (1979), 1223-1232. Google Scholar

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