Stimulus-dependent suppression of chaos in recurrent neural networks

Lewis-Sigler Institute for Integrative Genomics, Icahn 262, Princeton University, Princeton, New Jersey 08544, USA.
Physical Review E (Impact Factor: 2.29). 07/2010; 82(1 Pt 1):011903. DOI: 10.1103/PHYSREVE.82.011903
Source: PubMed


Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a "resonant" frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate.

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Available from: Kanaka Rajan
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    • "Randomly connected, globally balanced networks of leaky integrate-and-fire (LIF) neurons exhibit stable background states (van Vreeswijk and Sompolinsky, 1996; Tsodyks et al., 1997; Brunel, 2000; Vogels et al., 2005; Renart et al., 2010) but cannot autonomously produce the substantial yet reliable, spatially patterned departure from background activity observed in the experiments. Networks with strong recurrent pathways can exhibit ongoing, complex rate fluctuations beyond the population mean (Sompolinsky et al., 1988; Sussillo and Abbott, 2009; Rajan et al., 2010; Litwin-Kumar and Doiron, 2012; Ostojic, 2014) but do not capture the transient nature of movementrelated activity. Moreover, such rate dynamics are chaotic, and sensitivity to noise seems improper in a situation in which the initial conditions dictate the subsequent evolution of the system. "
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    • "The network nevertheless shows roughly asynchronous spiking behavior and is a reasonable candidate model for rich spontaneous cortical dynamics. We implemented this spiking network in an effort to test the alternative theory for stimulus induced reduction in spike count variability proposed by Rajan et al. (2010). "
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