Embedding optimization reveals long-lasting history dependence in neural spiking activity

PLoS Comput Biol. 2021 Jun 1;17(6):e1008927. doi: 10.1371/journal.pcbi.1008927. eCollection 2021 Jun.

Abstract

Information processing can leave distinct footprints on the statistics of neural spiking. For example, efficient coding minimizes the statistical dependencies on the spiking history, while temporal integration of information may require the maintenance of information over different timescales. To investigate these footprints, we developed a novel approach to quantify history dependence within the spiking of a single neuron, using the mutual information between the entire past and current spiking. This measure captures how much past information is necessary to predict current spiking. In contrast, classical time-lagged measures of temporal dependence like the autocorrelation capture how long-potentially redundant-past information can still be read out. Strikingly, we find for model neurons that our method disentangles the strength and timescale of history dependence, whereas the two are mixed in classical approaches. When applying the method to experimental data, which are necessarily of limited size, a reliable estimation of mutual information is only possible for a coarse temporal binning of past spiking, a so-called past embedding. To still account for the vastly different spiking statistics and potentially long history dependence of living neurons, we developed an embedding-optimization approach that does not only vary the number and size, but also an exponential stretching of past bins. For extra-cellular spike recordings, we found that the strength and timescale of history dependence indeed can vary independently across experimental preparations. While hippocampus indicated strong and long history dependence, in visual cortex it was weak and short, while in vitro the history dependence was strong but short. This work enables an information-theoretic characterization of history dependence in recorded spike trains, which captures a footprint of information processing that is beyond time-lagged measures of temporal dependence. To facilitate the application of the method, we provide practical guidelines and a toolbox.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Action Potentials / physiology*
  • Computer Simulation
  • Hippocampus / cytology
  • Hippocampus / physiology*
  • Humans
  • Models, Neurological
  • Neurons / physiology
  • Visual Cortex / cytology
  • Visual Cortex / physiology*

Grants and funding

All authors received support from the Max-Planck-Society, https://www.mpg.de/de. L.R. was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) as part of the SPP 2205 - project number 430157073. L.R. acknowledges funding by SMARTSTART, the joint training program in computational neuroscience by the VolkswagenStiftung and the Bernstein Network, https://www.smartstart-compneuro.de/. M. W. is employed at the Campus Institute for Dynamics of Biological Networks funded by the VolkswagenStiftung, https://www.volkswagenstiftung.de. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.