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”When spikes do matter: speed and plasticity” Thomas

”When spikes do matter: speed and plasticity” Thomas Trappenberg. Generation of spikes Hodgkin-Huxley equation Beyond HH (Wilson model) Compartmental model Integrate-and-fire model Hebbian (asymmetric) learning

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”When spikes do matter: speed and plasticity” Thomas

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  1. ”When spikes do matter: speed and plasticity” Thomas Trappenberg • Generation of spikes • Hodgkin-Huxley equation • Beyond HH (Wilson model) • Compartmental model • Integrate-and-fire model • Hebbian (asymmetric) learning • Population rate models

  2. Buracas, Zador, DeWeese, Albright, Neuron, 20:959-969 (1998)

  3. Even without much information in spike trains Spikes do matter ! Even if spikes matter Rate models are well motivated !

  4. Generation of a spike Concentration gradient (Nernst equation) Electrical force

  5. Hodgkin-Huxley equations

  6. Wilson model 1 Equilibrium potential Time constants

  7. Wilson model 2 Na+ leakage and voltage dependent channel K+ voltage dependent channel with slow dynamic Ca2+ voltage dependent channel with slow dynamics K+ dynamic voltage dependent channel (Ca2+ mediated) Hugh R. Wilson Simplified Dynamics of Human and Mammalian Neocortical Neurons J. Theoretical Biology 200: 375-388 (1999)

  8. Compartmental modelling Neuron (and network) simulators like NEURON and GENESIS Cable equations + active channels

  9. Integrate-and-fire neuron (see also spike-response model) 1. Sub-threshold leaky-integrator dynamic 2. Summation of PSPs from synaptic input 3. Firing threshold (spike generation) 4. Reset of membrane potential

  10. Average current-frequency curve (activation,gain,transfer) - function I=8 I=12 I=16

  11. Fine-tuning of synaptic weights? Poisson input spike trains

  12. Hebbian (asymmetric) learning 1 The organization of behavior (1949) “When an axon of a cell A is near enough to excite cell B or repeatedly or persistently takes part in firing it, some growth or metabolic change takes place in both cells such that A's efficiency, as one of the cells firing B, is increased.” Donald Hebb (1904-1985) G.-q. Bi and M.-m. Poo, J. of Neuroscience 18:10464-10472 (1998)

  13. Hebbian (asymmetric) learning 2 Adapted from Abbott & Nelson, Nature Neuroscience Oct. 2000

  14. Hebbian (asymmetric) learning 3

  15. Hebbian (asymmetric) learning 4 Variability control Gain control Song & Abbott, Neurocomputing Oct. 2000

  16. Hebbian (asymmetric) learning 5 Additive vs. Multiplicative rules ? Van Rossum, Bi, & Turrigiano, J. Neuroscience, Dec. 2000 (Fokker-Planck equation)

  17. Rate models 1

  18. Rate models 2 1. 2. 3. 4. • Population of similar neurons (e.g. same input, same time constant, …) • Independent (e.g. no locking, synchronization, no sigma-pi, … • Write as integral equation (e.g. use spike response model; see W. Gerstner) • Mean field theory (e.g. averaging) • Adiabatic limit (e.g. slow changes)

  19. Rate models 3

  20. Fast processing Panzeri, Rolls, Battaglia & Lavis, Network: Comput. Neural Syst. 12:423-440 (2001)

  21. Conclusions • Rate models are now well motivated • Spike models are now well developed • Hebbian plasticity is now better explored • Spikes are important for rapid and robust information processing

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