Response Characteristics of a Low-Dimensional Model Neuron

It is shown that a low-dimensional model neuron with a response time constant smaller than the membrane time constant closely reproduces the activity and excitability behavior of a detailed conductance-based model of Hodgkin-Huxley type. The fast response of the activity variable also makes it possible to reduce the model to a one-dimensional model, in particular for typical conditions. As an example, the reduction to a single-variable model from a multivariable conductance-based model of a neocortical pyramidal cell with somatic input is demonstrated. The conditions for avoiding a spurious damped oscillatory response to a constant input are derived, and it is shown that a limit-cycle response cannot occur. The capability of the low-dimensional model to approximate higher-dimensional models accurately makes it useful for describing complex dynamics of nets of interconnected neurons. The simplicity of the model facilitates analytic studies, elucidation of neurocomputational mechanisms, and applications to large-scale systems.

[1]  Bo Cartling.  Control Of The Complexity Of Associative Memory Dynamics By Neuronal Adaptation , 1993, Int. J. Neural Syst..

[2]  B. Cartling,et al.  Autonomous neuromodulatory control of associative processes , 1995 .

[3]  久保 亮五,et al.  H. Haken: Synergetics; An Introduction Non-equilibrium Phase Transitions and Self-Organization in Physics, Chemistry and Biology, Springer-Verlag, Berlin and Heidelberg, 1977, viii+325ページ, 251×17.5cm, 11,520円. , 1978 .

[4]  R. Palmer,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[5]  J. Hindmarsh,et al.  The assembly of ionic currents in a thalamic neuron I. The three-dimensional model , 1989, Proceedings of the Royal Society of London. B. Biological Sciences.

[6]  J. Hindmarsh,et al.  The assembly of ionic currents in a thalamic neuron III. The seven-dimensional model , 1989, Proceedings of the Royal Society of London. B. Biological Sciences.

[7]  C. Koch,et al.  Multiple channels and calcium dynamics , 1989 .

[8]  Bo Cartling.  Generation of Associative Processes in a Neural Network with Realistic Features of Architecture and Units , 1994, Int. J. Neural Syst..

[9]  A. Lansner,et al.  Low spiking rates in a population of mutually exciting pyramidal cells , 1995 .

[10]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[11]  Bo Cartling,et al.  Dynamics control of semantic processes in a hierarchical associative memory , 1996, Biological Cybernetics.

[12]  B. Hille.  Ionic channels of excitable membranes , 2001 .

[13]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[14]  B. Cartling,et al.  A generalized neuronal activation function derived from ion-channel characteristics , 1995 .

[15]  L. Abbott,et al.  Model neurons: From Hodgkin-Huxley to hopfield , 1990 .

[16]  L. Abbott.  A network of oscillators , 1990 .

[17]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[18]  H. Haken.  Synergetics: an Introduction, Nonequilibrium Phase Transitions and Self-organization in Physics, Chemistry, and Biology , 1977 .

[19]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[20]  John Rinzel,et al.  Activity Patterns of a Slow Synapse Network Predicted by Explicitly Averaging Spike Dynamics , 1992, Neural Computation.

[21]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Kenji Doya,et al.  Dimension Reduction of Biological Neuron Models by Artificial Neural Networks , 1994, Neural Computation.

[23]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[24]  Bard Ermentrout,et al.  Reduction of Conductance-Based Models with Slow Synapses to Neural Nets , 1994, Neural Computation.