Deger, Moritz

Gerstner, Wulfram

Setareh, Hesam

Infoscience - École polytechnique fédérale de Lausanne

An alternative model of stable activity propagation in cortical networksNCLBidirectional chain of bistable assembliesPopular models of activity propagation (synre chain [1] and propa-gation of ring rates [2]) suer from problems:  Feed-forward structures (unidirectional fashion): have                  not been found experimentaly so far.  High propagation speed of the activity: unable to model              slow behavioral functions like the control of arm movements.Inside assembly: 100 excitatory neurons, dense con-nectivity, strong synapses, short-term depression [3] Inter-assembly synaptic weights control the propagation speedActivation time of assembly: minimum time after which all neurons have red at least once.Grid of bistable assemblies 1. School of Computer and Communication Sciences & School of Life Sciences, Brain Mind Institute, EPFL, SwitzerlandReproducing activity propagation in the barrel cortex after a brief whisker stimulus [6]:  Synaptic ecacy tunes speed of activity propagation through chains of bistable neural assembliesHesam Setareh1, Moritz Deger1, and Wulfram Gerstner1ReferencesFundingResearch was supported by the European Research Council (grant agreement no. 268 689, H.S.), the European Community’s Seventh Framework Program (Grant Agreement no. 269921, BrainScaleS, H.S and M.D.) and the Swiss National Science Foundation (grant agreement no. 200020_147200, M.D.). 1. Diesmann M, Gewaltig M O,  Aertsen A (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature.2. van Rossum M C, Turrigiano G G, Nelson S B (2002). Fast propagation of ring rates through layered networks of noisy neurons. J. Neurosci. 3. Tsodyks M V,  Markram H (1997). The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proc. Natl. Acad. Sci. USA4. Perin R, Berger T K,  Markram H (2011). A synaptic organizing principle for cortical neuronal groups. Proc. Natl Acad. Sci., USA5. Fourcaud N, Brunel N (2002). Dynamics of the ring probability of noisy integrate-and-re neurons. Neural Comput.6. Petersen C, Grinvald A, Sakmann B (2003). Spatiotemporal dynamics of sensory responses in layer 2/3 of rat barrel cortex measured in vivo by voltage-sensitive dye imaging combined with whole-cell voltage recordings and neuron reconstructions. J.  Neurosci.7. Petersen C, Hahn T T, Mehta M, Grinvald A, Sakmann B (2003). Interaction of sensory re-sponses with spontaneous depolarization in layer 2/3 barrel cortex. Proc. Natl. Acad. Sci. USA8. Goodman D, Brette R (2009): The brian simulator. Front. Neurosci. uuWe propose a bidirectional chain of bistable neuronal assemblies:  No need for feed-forward structure  Propagates activity forwards, backwards, or in both directions  Regulation of propagation speed through synaptic weightsuuuAssembly 1 Assembly 2 Assembly 10. . .Based on the place of initial stimulation (transient external Poisson noise), the chain propagates the activity forwards, backwards, or in both directions simultaneously. Weakening inter-assembly synapses è reduction of speedAnalysis of bistable assembly dynamics A common mean-eld method is used for analyzing the dynamics. Two relations between ring rate and synaptic current form an iterative map: 1. Noisy gain function [5]: 2. Synaptic input (mean eld):Driving the assembly with small but sucient input brings it to the “high-point”.During the high-point state, synapses depress è assembly switches to depressed mode and con-verges to the “low-point”. r = g(〈Isyn〉, σ) = (τref+τm√pi∫ythyrex2(1+erf(x))dx)−1Isyn =∑iwi(∫ +∞−∞α(s)Si(t− s)ds) 〈Isyn〉 = Npqw¯rr =〈Isyn〉Npqw¯èè  Assembly       (1,1). . .  Assembly       (1,2)  Assembly       (1,n)  Assembly       (2,1)  Assembly       (2,2)  Assembly       (2,n). . .. . .  Assembly       (n,1)  Assembly       (n,2)  Assembly       (n,n). . .. . .. . .. . .1-dimensional chain of assemblies can be extended to a 2-dimensional topology (grid).inter assembly connections: Weak synapses, low connection probabiliyintra-assembly connections: Strong synapses, high connection probability, short-term depressionweight=1 mV, connection probability=50%weight=0.15mV, connection probability=15%weight=1mV, connection probability=50%weight=0.2mV, connection probability=25%Can be used for modeling columnar organization of cortex (e.g. barrel cortex): Sparse and weak inter-column synaptic connections versus relativey strong intra-column synapses.Dierent patterns of activity propagation in the gridDynamics of intra-assembly synapses are described by a depression variable x [3]. A high (low) value of x denotes recovered  (depressed) synapses.  Using dierent initial values of x for dierent assemblies, we can evoke dierent patterns of activity propagation on the grid. Each cortical column contains ~10K neurons, while each assembly contains 100 neurons!The model is still valid: A few hub neurons (neurons that receive stronger and more synapses) inside each column may govern its dynamics. Each assembly of the grid can be considered as a population of hub neurons in the column. Voltage sensitive dye recording in the cortexSimulation: temporally smoothed spike trains of neurons, arranged in a square per assembly stimulusReproducing activity circulation in the anaesthetised barrel cortex [7] by setting the  initial values of x: The activity can circulate forever or stop after several rounds based on inter-assembly synaptic weights.Relatively strong synapses guarantee enough excitation for the next assem-blies in the trajectory, while very weak synapses cause activity to vanish. 10ms 20ms 50ms 100ms 200ms  0ms  50ms 100ms 150ms200ms 250ms 300ms 350msBetween assemblies: sparse connectivity, weak syn-apsesClustered connectivity is supported by experimental data observed in the cortex [4].(Recovered)(Depressed)

Synaptic efficacy tunes speed of activity propagation through chains of bistable neural assemblies

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Synaptic efficacy tunes speed of activity propagation through chains of bistable neural assemblies

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