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Decorrelation of Neural-Network Activity by Inhibitory Feedback

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  • Tom Tetzlaff
  • Moritz Helias
  • Gaute T Einevoll
  • Markus Diesmann

Abstract

Correlations in spike-train ensembles can seriously impair the encoding of information by their spatio-temporal structure. An inevitable source of correlation in finite neural networks is common presynaptic input to pairs of neurons. Recent studies demonstrate that spike correlations in recurrent neural networks are considerably smaller than expected based on the amount of shared presynaptic input. Here, we explain this observation by means of a linear network model and simulations of networks of leaky integrate-and-fire neurons. We show that inhibitory feedback efficiently suppresses pairwise correlations and, hence, population-rate fluctuations, thereby assigning inhibitory neurons the new role of active decorrelation. We quantify this decorrelation by comparing the responses of the intact recurrent network (feedback system) and systems where the statistics of the feedback channel is perturbed (feedforward system). Manipulations of the feedback statistics can lead to a significant increase in the power and coherence of the population response. In particular, neglecting correlations within the ensemble of feedback channels or between the external stimulus and the feedback amplifies population-rate fluctuations by orders of magnitude. The fluctuation suppression in homogeneous inhibitory networks is explained by a negative feedback loop in the one-dimensional dynamics of the compound activity. Similarly, a change of coordinates exposes an effective negative feedback loop in the compound dynamics of stable excitatory-inhibitory networks. The suppression of input correlations in finite networks is explained by the population averaged correlations in the linear network model: In purely inhibitory networks, shared-input correlations are canceled by negative spike-train correlations. In excitatory-inhibitory networks, spike-train correlations are typically positive. Here, the suppression of input correlations is not a result of the mere existence of correlations between excitatory (E) and inhibitory (I) neurons, but a consequence of a particular structure of correlations among the three possible pairings (EE, EI, II). Author Summary: The spatio-temporal activity pattern generated by a recurrent neuronal network can provide a rich dynamical basis which allows readout neurons to generate a variety of responses by tuning the synaptic weights of their inputs. The repertoire of possible responses and the response reliability become maximal if the spike trains of individual neurons are uncorrelated. Spike-train correlations in cortical networks can indeed be very small, even for neighboring neurons. This seems to be at odds with the finding that neighboring neurons receive a considerable fraction of inputs from identical presynaptic sources constituting an inevitable source of correlation. In this article, we show that inhibitory feedback, abundant in biological neuronal networks, actively suppresses correlations. The mechanism is generic: It does not depend on the details of the network nodes and decorrelates networks composed of excitatory and inhibitory neurons as well as purely inhibitory networks. For the case of the leaky integrate-and-fire model, we derive the correlation structure analytically. The new toolbox of formal linearization and a basis transformation exposing the feedback component is applicable to a range of biological systems. We confirm our analytical results by direct simulations.

Suggested Citation

  • Tom Tetzlaff & Moritz Helias & Gaute T Einevoll & Markus Diesmann, 2012. "Decorrelation of Neural-Network Activity by Inhibitory Feedback," PLOS Computational Biology, Public Library of Science, vol. 8(8), pages 1-29, August.
  • Handle: RePEc:plo:pcbi00:1002596
    DOI: 10.1371/journal.pcbi.1002596
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    References listed on IDEAS

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    6. Moritz Helias & Moritz Deger & Stefan Rotter & Markus Diesmann, 2010. "Instantaneous Non-Linear Processing by Pulse-Coupled Threshold Units," PLOS Computational Biology, Public Library of Science, vol. 6(9), pages 1-10, September.
    7. Patrick Blomquist & Anna Devor & Ulf G Indahl & Istvan Ulbert & Gaute T Einevoll & Anders M Dale, 2009. "Estimation of Thalamocortical and Intracortical Network Models from Joint Thalamic Single-Electrode and Cortical Laminar-Electrode Recordings in the Rat Barrel System," PLOS Computational Biology, Public Library of Science, vol. 5(3), pages 1-24, March.
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    Cited by:

    1. Vicente Reyes-Puerta & Suam Kim & Jyh-Jang Sun & Barbara Imbrosci & Werner Kilb & Heiko J Luhmann, 2015. "High Stimulus-Related Information in Barrel Cortex Inhibitory Interneurons," PLOS Computational Biology, Public Library of Science, vol. 11(6), pages 1-32, June.
    2. Hannah Bos & Markus Diesmann & Moritz Helias, 2016. "Identifying Anatomical Origins of Coexisting Oscillations in the Cortical Microcircuit," PLOS Computational Biology, Public Library of Science, vol. 12(10), pages 1-34, October.
    3. Moritz Helias & Tom Tetzlaff & Markus Diesmann, 2014. "The Correlation Structure of Local Neuronal Networks Intrinsically Results from Recurrent Dynamics," PLOS Computational Biology, Public Library of Science, vol. 10(1), pages 1-21, January.
    4. Volker Pernice & Rava Azeredo da Silveira, 2018. "Interpretation of correlated neural variability from models of feed-forward and recurrent circuits," PLOS Computational Biology, Public Library of Science, vol. 14(2), pages 1-26, February.
    5. Sadra Sadeh & Stefan Rotter, 2015. "Orientation Selectivity in Inhibition-Dominated Networks of Spiking Neurons: Effect of Single Neuron Properties and Network Dynamics," PLOS Computational Biology, Public Library of Science, vol. 11(1), pages 1-17, January.
    6. Sacha Jennifer van Albada & Moritz Helias & Markus Diesmann, 2015. "Scalability of Asynchronous Networks Is Limited by One-to-One Mapping between Effective Connectivity and Correlations," PLOS Computational Biology, Public Library of Science, vol. 11(9), pages 1-37, September.
    7. Andrea K Barreiro & Shree Hari Gautam & Woodrow L Shew & Cheng Ly, 2017. "A theoretical framework for analyzing coupled neuronal networks: Application to the olfactory system," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-37, October.
    8. Matthias Schultze-Kraft & Markus Diesmann & Sonja Grün & Moritz Helias, 2013. "Noise Suppression and Surplus Synchrony by Coincidence Detection," PLOS Computational Biology, Public Library of Science, vol. 9(4), pages 1-15, April.
    9. Klas H Pettersen & Henrik Lindén & Tom Tetzlaff & Gaute T Einevoll, 2014. "Power Laws from Linear Neuronal Cable Theory: Power Spectral Densities of the Soma Potential, Soma Membrane Current and Single-Neuron Contribution to the EEG," PLOS Computational Biology, Public Library of Science, vol. 10(11), pages 1-26, November.
    10. Takuya Ito & Scott L Brincat & Markus Siegel & Ravi D Mill & Biyu J He & Earl K Miller & Horacio G Rotstein & Michael W Cole, 2020. "Task-evoked activity quenches neural correlations and variability across cortical areas," PLOS Computational Biology, Public Library of Science, vol. 16(8), pages 1-39, August.

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