Feedforward networks

Complex Network

Simpler (but still complicated) Network

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

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

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

Simulations with real neurons Real neurons (God, unpublished results) 1000’s

Whole-cell recordings  Rats or mice are 18 days or older  µm slices of somatosensory or auditory cortex  maintained at degrees  recordings were from L5 pyramidal neurons and interneurons

Implementation of feedforward in vitro networks m 1 2 n

individual spikes histogram ms cells ms

Network type: -> sparsely connected (10%)

L2 L3 L5 L4 L6 L7 L8 Quantification of Synchrony ms L

Is synchrony robust ?

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 Various network configurations Synchrony persists

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

cellRnf/I slope A B C D ms 50 mV Network type: -> sparsely connected (10%) -> Poisson input -> heterogeneous Heterogeneous Networks

Time (ms) Layer 2 Layer 6

Excitatory & Inhibitory network membrane voltage I exc I inh net synaptic current = I exc + I inh

I syn ( t ) = g syn ( t )*(V( t )-E syn ) I epsp = g * (V - E) dynamic clamp I c-clamp ( t ) I ipsp = g(t)*(V + 80 )-62 mV 0.5 mV 50 ms -62 mV I epsp =g(t)*(V - 0)

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

excitatory cells 20 mV 200 ms excitatory + inhibitory

layer 5 Network type: -> sparsely connected (10%) -> Poisson input -> heterogeneous -> excitatory + inhibitory EPSP EPSP + IPSP

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

Why does synchrony develop ?

A simple model

counts ms histograms unitary synaptic current * Composite current experiment seconds A simple model

LIF: FPE: where input: ms 0 autocorr: Fokker-Planck Equations

Diesmann et al., Nature 1999

Is it useful for transmitting signals ?

Signal propagation through the network on off F1F1 F1F1 F2F2 F2F2

1 nA layer 6 25 mV 200 ms layer 2 F in = 25 Hz 55 Hz 25 Hz F in

Layer Avg. rate (Hz) k Firing Rate (Hz) Input rate (=N*F pre ) N Firing rate = F pre F layer = k*N*F layer-1 Input rate = N*F pre Frequency

layer avg. firing rate (Hz) K*N < 1 K*N = 1 K*N > 1 F L = k*N*F L-1

F2 F1 F3 F4 F2F1F3 F4 Synchrony is necessary for signal propagation

Is it found in vivo ?

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

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

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. Summary

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

04080 Hz 0250 Hz Hz With inhib pyramidalsinterneuron