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Stable Propagation of Synchronous Spiking in Cortical Neural Networks Markus Diesmann, Marc-Oliver Gewaltig, Ad Aertsen Nature 402:529-533 Flavio Frohlich Computational Neurobiology UCSD La Jolla CA-92093

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Outline Background –Neural Code –Integrate&Fire Neuron Motivation / Research Questions Methods Results Discussion & Conclusions

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The Neural Code Stimulus s(t) Neural System Neural Response (t) StimulusNeural Response CodingGivenTo determine DecodingTo determineGiven

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The Neural Code Independent-spike versus correlation code. Temporal versus rate code. different

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The Neural Code Independent-spike code –Time-dependent firing rate r ( t ). –Probability distribution of spike times can be computed from r ( t ) as inhomogenous Poisson process. –Firing rate r(t) contains all information about stimulus. –Interspike intervals do not carry information.

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The Neural Code Correlation code –Correlation between spike times carry information. –e.g. information about stimulus carried by interspike intervals.

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The Neural Code Rate code –Assumption: independent-spike hypothesis fulfilled. –Firing rate r ( t ) “varies slowly with time”. Temporal code –Assumption: independent-spike hypothesis fulfilled. –Firing rate r ( t ) “varies rapidly”. –“Information is carried by spike timing on a scale shorter than fastest time characterizing variations of stimulus.” –Requires precise spike timing millisecond precision possible for noisy neurons?

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Motivation / Research Questions High temporal accuracy observed in vivo (precisely timed action potentials related to stimuli and behavioral events in awake behaving monkey, e.g. Abeles 1993 ) and in vitro. “Can instances of synchronous spiking be successful transmitted/propagated by subsequent group of neurons?” “Under which conditions?”

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Integrate & Fire Neuron I No biophysical states (channel dynamics). Integrate transmembrane currents. If threshold reached: –Stipulate action potential (AP). –Reset membrane voltage below threshold.

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Integrate & Fire Neuron II Leaky integrate&fire (i&f) neuron: Time constant m Membrane voltage V Steady state membrane voltage E L Input resistance R m Transmembrane current I E Postsynaptic currents: -function: Background firing (uncorrelated stationary Poisson distribution)

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Network Topology Feedforward architecture. Group = layer. Group i Group i+1 Each neuron: 20’000 synaptic inputs (88% excitatory, 12% inhibitory). 100 neurons/group. 10 groups.

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Predictions “Neurons that share a large enough pool of simultaneously discharging input cells tend to align their action potentials.” “A group of neurons can reproduce its synchronous input activity and act as the source of synchronous shared input for the following group.”

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Synchronous spiking sustained or not? sustained dies out

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Input to Model Neuron Pulse packet: spike volley. –Activity a : number of spikes in volley. –Temporal dispersion : standard deviation of underlying pulse time distribution. in a = 20 Pulse packet

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Output = Neuron(Input) Input to model neurons: pulse packets (pooling from many neurons in previous layer). I&F Neuron Output of model neuron: at most one spike. Spike probability Standard deviation out.

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Neural Transmission Function I Input dispersion in # input spikes Spiking probability

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Neural Transmission Function II Input dispersion # input spikes Output dispersion in > out out > in

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State Space Analysis Stable attractor Saddle point State-space analysis of propagating spike synchrony. State variables: Activity a Dispersion Trajectory t = t ( i ) where i denotes ordered group.

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Size of Neuron Groups W W = 80W = 90W = 100W = 110 zero-isocline activity a zero-isocline dispersion region of attraction Increase W Fixpoints move apart. Decrease W Fixpoints merge to saddle point. Minimal group size W for maintaining synchrony.

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Discussion & Conclusions Stable fixpoint = 0.5 ms temporal precision matching cortical recordings. Region of attraction guarantees robustness. Model parameters in congruence with physiological data.

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