Neuron Circuits & Communication

Bo DengUniversity of Nebraska-LincolnSept. 2004

Rinzel & Wang (1997)Rinzel & Wang (1997)

Gated Currents by ElectrodiffissionGated Currents by Electrodiffission

Ionic Pumps by Chemical Energy Ionic Pumps by Chemical Energy

Circuit Model Circuit Model

• Kandel, E.R., J.H. Schwartz, and T.M. Jessell Principles of Neural Science, 3rd ed., Elsevier, 1991.• Zigmond, M.J., F.E. Bloom, S.C. Landis, J.L. Roberts, and L.R. Squire Fundamental Neuroscience, Academic Press, 1999.

• Kandel, E.R., J.H. Schwartz, and T.M. Jessell Principles of Neural Science, 3rd ed., Elsevier, 1991.• Zigmond, M.J., F.E. Bloom, S.C. Landis, J.L. Roberts, and L.R. Squire Fundamental Neuroscience, Academic Press, 1999.

Hodgkin, A.L. and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117(1952), pp.500--544.

Hodgkin, A.L. and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117(1952), pp.500--544.

Alan Lloyd Hodgkin Andrew Fielding Huxley

Kirchhoff LawsKirchhoff Laws - I (t)

-I (t)

Mahowald, M. and Douglas, R. A silicon neuron. Nature, 354(1991), pp.515-518.

ElectrophysiologicalModel

ElectrophysiologicalModel

Equivalent Circuit

Equivalent Circuit

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Chua, L.O., Introduction to Nonlinear Circuit Theory, McGraw-Hill, New York, 1969.Chua, L.O., Introduction to Nonlinear Circuit Theory, McGraw-Hill, New York, 1969.

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( , ) 0mg V E I ( , ) 0mg V E I van der Pol Oscillator (R = 0) and FitzHugh-Nagumo Oscillator

van der Pol Oscillator (R = 0) and FitzHugh-Nagumo Oscillator

van der Pol (1928), FitzHugh(1961), Nagumo(1964)Keener(1982)

van der Pol (1928), FitzHugh(1961), Nagumo(1964)Keener(1982)

Balthazar van der Pol (1889-1959)

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• Morris, C. and H. Lecar, Voltage oscillations in the barnacle giant muscle fiber, Biophysical J., 35(1981), pp.193--213.

• Hindmarsh, J.L. and R.M. Rose, A model of neuronal bursting using three coupled first order differential equations, Proc. R. Soc. Lond. B. 221(1984), pp.87--102.

• Chay, T.R., Y.S. Fan, and Y.S. Lee Bursting, spiking, chaos, fractals, and universality in biological rhythms, Int. J. Bif. & Chaos, 5(1995), pp.595--635.

• Izhikevich, E.M Neural excitability, spiking, and bursting, Int. J. Bif. & Chaos, 10(2000), pp.1171--1266. (also see his article in SIAM Review)

(Non-circuit) Models for Square Burster and Other Bursters

Deng(1991)Deng(1991)

Disclaimer: With the exception of the square burster and SEED simulation, all artworks are found from the internet.