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How voltage-dependent conductances can adapt to maximize the information encoded by neuronal firing rate

Abstract

Information from the senses must be compressed into the limited range of responses that spiking neurons can generate. For optimal compression, the neuron's response should match the statistics of stimuli encountered in nature. Given a maximum firing rate, a nerve cell should learn to use each available firing rate equally often. Given a set mean firing rate, it should self-organize to respond with high firing rates only to comparatively rare events. Here we derive an unsupervised learning rule that continuously adapts membrane conductances of a Hodgkin-Huxley model neuron to optimize the representation of sensory information in the firing rate. Maximizing information transfer between the stimulus and the cell's firing rate can be interpreted as a non-Hebbian developmental mechanism.

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Figure 1: The model neuron.
Figure 2: The first term in the learning rule for changing the peak conductance of voltage-dependent conductances in the dendritic compartment.
Figure 3: Learning the optimal firing rate response with the constraint that the firing rate must lie between 20 and 60 spikes per second.
Figure 4: Learning the optimal firing rate response curve assuming an average firing constraint of 30 Hz.
Figure 5: An experimental prediction.
Figure 6: Mechanism for state-dependent channel modification.

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Acknowledgements

This work was supported by the Alexander v. Humboldt Foundation, the Howard Hughes Medical Institute, the Deutsche Forschungsgemeinschaft, NIMH, ONR, NSF and the NSF-ERC Program at Caltech and was carried out in part at Caltech. We thank V. Lucic, F. Gabbiani, D. Schmitz and R. Stemmler for comments on the manuscript.

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Correspondence to Martin Stemmler.

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Stemmler, M., Koch, C. How voltage-dependent conductances can adapt to maximize the information encoded by neuronal firing rate. Nat Neurosci 2, 521–527 (1999). https://doi.org/10.1038/9173

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