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Rhythm-induced spike-timing patterns characterized by 1D firing maps

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Abstract

We explore patterns in the spike timing of neurons receiving periodic inputs, with an emphasis on stable characteristics which are realized in both models and in-vitro whole-cell recordings. We report on whole-cell recordings of pyramidal CA1 cells from rat hippocampus and entorhinal cortex and compare this data to model simulations. Cells were injected with a constant current to induce a steady firing rate and then a modest rhythm was added which altered the spike times and their corresponding phases relative to the rhythm. For both experiment and theory the relationship between consecutive spike phases is characterized by a probability distribution with peaks concentrated near a one-dimensional firing map. As is well-known, stable fixed points of this map correspond to the neuron phase-locking to the rhythm. We show that the interaction between noise and sufficiently steep maps can also cause a new kind of spike-time organization, in which consecutive spike time pairs organize into discrete clusters, with transitions between these clusters proceeding in a fixed sequence. This structure is not just a vestige of the noise-free dynamics. This slow dynamics and temporal organization in the relationship between consecutive spike phases is not evident in either the neuron’s voltage traces or single phase or interspike interval histograms. Furthermore, the consecutive spike relationship is also evident in consecutive ISIs, and hence this ordering can be observed without detailed knowledge of the rhythm (e.g. without concurrent LFP recordings).

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Notes

  1. This complements the analysis of a transient pulse on spike timing; in that case the neuron resumes firing at the same rate but with a shift in phase which can be described by a phase-resetting curve (PRC) (Ermentrout and Terman 2010). However a PRC-based analysis cannot fully describe the firing patterns that occur when a neuron is subjected to a continuously varying rhythmic input, since its firing pattern and average rate may be permanently altered (Izhikevich 2007).

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Acknowledgements

We thank Chuck Stevens and Vitaly Klyachko for very useful interactions. We also thank both referees for providing many constructive comments and suggestions. This work was supported in part by ICAM, the Institute for Complex Adaptive Matter, grant NIMH R01 MH61492; MH60013 and the Japan Society for the Promotion of Science.

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Correspondence to Jan R. Engelbrecht.

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Engelbrecht, J.R., Loncich, K., Mirollo, R. et al. Rhythm-induced spike-timing patterns characterized by 1D firing maps. J Comput Neurosci 34, 59–71 (2013). https://doi.org/10.1007/s10827-012-0406-8

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  • DOI: https://doi.org/10.1007/s10827-012-0406-8

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