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Feedforward networks

Feedforward networks. Complex Network. Simpler (but still complicated) Network. Feedforward Network. 3d. 2a. 2a. 2c. 1a. 1a. 3a. 3a. 3a. 2b. 2b. 1b. 1b. 3b. 3b. 3c. 3e. 1b. 1a. 2c. 2c. 3c. 3c. 1c. 1c. 2a. 1c. 2d. 2d. 1d. 1d. 3d. 3d. 2e. 3b. 2e. 2e. 1e.

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Feedforward networks

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  1. Feedforward networks

  2. Complex Network

  3. Simpler (but still complicated) Network

  4. Feedforward Network 3d 2a 2a 2c 1a 1a 3a 3a 3a 2b 2b 1b 1b 3b 3b 3c 3e 1b 1a 2c 2c 3c 3c 1c 1c 2a 1c 2d 2d 1d 1d 3d 3d 2e 3b 2e 2e 1e 1e 3e 3e 1e 2d 1d 2b 2a 1a 3a 2b 1b 3b 2c 1c 3c 2d 1d 3d 2e 1e 3e

  5. Signal propagation through the network off on Hz Hz ms ms “rate mode” Shadlen & Newsome, 1998 Van Rossum et al., 2002 “synchrony mode” Abeles, corticonics, 1991 Diesmann et al.,1999

  6. Questions Is synchrony robust ? Why does synchrony develop ? Is it useful for transmitting signals ? Is it found in vivo?

  7. 1000’s Real neurons (God, unpublished results) Simulations with real neurons

  8. Whole-cell recordings • Rats or mice are 18 days or older • 300-500 µm slices of somatosensory or auditory cortex • maintained at 32-34 degrees • recordings were from L5 pyramidal neurons and interneurons

  9. Implementation of feedforward in vitro networks m 3 2 1 1 2 n

  10. cells 0 0 200 200 400 400 600 600 800 800 1000 1000 1200 1200 1400 1400 ms ms individual spikes histogram

  11. Network type: -> sparsely connected (10%)

  12. L1 L2 L3 2.5 L4 2.0 L5 1.5 Normalized CCH area L6 1.0 0.5 10% connection L7 0.0 2 4 6 8 10 Layer L8 -300 -200 -100 0 100 200 300 ms Quantification of Synchrony

  13. Is synchrony robust ?

  14. Various network configurations 1. sparsely connected networks 2. Poisson input 3. heterogeneous networks 4. excitatory & inhibitory networks 5. extremely noisy 6. sinusoidally-modulated inputs 7. NMDA-like EPSPs 8. different initial conditions 9. facilitating/depressing synapses Synchrony persists

  15. Network type: -> sparsely connected (10%) -> Poisson input Poisson Periodic

  16. Heterogeneous Networks Network type: -> sparsely connected (10%) -> Poisson input -> heterogeneous 50 mV 200 ms cell Rn f/I slope A 49 164 B 54 227 C 28 134 D 121 303

  17. Layer 2 Layer 6 Time (ms) Time (ms)

  18. Excitatory & Inhibitory network net synaptic current = Iexc + Iinh Iexc membrane voltage Iinh

  19. Ic-clamp(t) dynamic clamp Iepsp = g * (V - E) 0.5 mV 50 ms Iepsp =g(t)*(V - 0) -62 mV Iipsp = g(t)*(V + 80 ) -62 mV Isyn(t) = gsyn(t)*(V(t)-Esyn)

  20. Effects of conductance noise on membrane potential threshold EPSP rate: 7000 Hz IPSP rate: 3000 Hz -58 mV 2 mV 200 ms EPSP rate: 28,000 Hz IPSP rate: 12,000 Hz -58 mV Chance, Abbott, Reyes 2002 (V = I/g)

  21. excitatory + inhibitory 20 mV 200 ms excitatory cells

  22. layer 5 EPSP EPSP + IPSP 2 3 5 1 4 6 Network type: -> sparsely connected (10%) -> Poisson input -> heterogeneous -> excitatory + inhibitory

  23. Network type: -> sparsely connected (10%) -> Poisson input -> heterogeneous -> epsp + ipsp -> ‘unphysiologically’ noisy layer 2 CCH area layer 1 2 3 4 5 6 6 layer 6

  24. Why does synchrony develop ?

  25. A simple model

  26. experiment A simple model counts counts 0.0 0.4 0.8 1.0 100 80 20 60 0 40 50 40 10 30 0 20 seconds ms ms Composite current unitary synaptic current histograms 1 * 2 3 4

  27. input: autocorr: <G(t)G(0)> <G(t)G(0)> 0 0 10 20 30 40 50 60 70 ms Fokker-Planck Equations LIF: FPE: where

  28. Diesmann et al., Nature 1999

  29. Is it useful for transmitting signals ?

  30. Signal propagation through the network off on F1 F1 F2 F2

  31. Fin 25 Hz 55 Hz layer 6 layer 2 Fin = 25 Hz 25 mV 1 nA 200 ms 55 Hz

  32. Frequency Frequency Firing rate = Fpre 1 2 3 N 20 k 15 Firing Rate (Hz) 10 5 0 0 800 1600 Input rate (=N*Fpre) 2 5 2 0 Avg. rate (Hz) 1 5 Input rate = N*Fpre 1 0 5 0 1 3 5 7 9 11 L a y e r Flayer = k*N*Flayer-1

  33. K*N > 1 K*N = 1 K*N < 1 0 1 2 3 4 5 6 layer 30 20 avg. firing rate (Hz) 10 FL = k*N*FL-1

  34. Is it found in vivo ?

  35. layer 6 (synchronous) layer 2 (asynchronous) 25 mV 1 nA 200 ms What to look for in vivo

  36. In vivo intracellular recordings 0.5 mV 25 ms Reyes & Sakmann, 1999 10 mV 50 ms Azouz & Gray, 1999 Ikegaya et al., 2004 Lampl et al.,1999 10 mV Brecht & Sakmann, 2002 25 ms wD4

  37. Summary Is synchrony robust ? yes, for a wide range of physiological conditions Why does synchrony develop ? Neurons become correlated at stimulus onset Is it useful for transmitting signals ? Yes. In fact, it’s necessary! In vivo evidence? Yes. Quite strong.

  38. Feedforward Network 2a 2a 1a 1a 3a 3a 2b 2b 1b 1b 3b 3b 2c 2c 3c 3c 1c 1c 2d 2d 1d 1d 3d 3d 2e 2e 1e 1e 3e 3e 2a 1a 3a 2b 1b 3b 2c 1c 3c 2d 1d 3d 2e 1e 3e

  39. pyramidals interneuron With inhib 0 250 0 40 80 0 40 80 Hz Hz Hz

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