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.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Rent or buy this article
Prices vary by article type
from$1.95
to$39.95
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Tovée, M. J., Rolls, E. T. & Treves, A. Information encoding and the responses of single neurons in the primate temporal visual cortex. J. Neurophysiol. 70, 640–654 ( 1993).
Heller, J., Hertz, J. A., Kjaer, T. W. & Richmond, B. J. Information flow and temporal coding in primate pattern vision. J. Comput. Neurosci. 2, 175–193 (1995).
Baddeley, R. J. & Hancock, P. J. A statistical analysis of natural images matches psychophysically derived orientation tuning curves. Proc. R. Soc. Lond. B Biol. Sci. 246, 219–223 (1991).
Atick, J. J. Could information theory provide an ecological theory of sensory processing? Network 3, 213–251 (1992).
Ruderman, D. L. Statistics of natural images. Network 5, 517–548 (1995).
Laughlin, S. A simple coding procedure enhances a neuron's information capacity. Z. Naturforsch. 36, 910–912 (1981).
Laughlin, S. B., de Ruyter van Stevenick, R. R. & Anderson, J. C. The metabolic cost of neural information. Nat. Neurosci. 1, 36– 41 (1998).
Baddeley, R. et al. Responses of neurons in primary and inferior temporal visual cortices to natural scenes. Proc. R. Soc. Lond. B Biol. Sci. 264, 1775–1783 (1997).
LeMasson, G., Marder, E. & Abbott, L. F. Activity-dependent regulation of conductances in model neurons. Science 259, 1915– 1917 (1993).
Bell, A. J. Self-organisation in real neurons: Anti-Hebb in 'channel space'? Neural Information Processing Systems 4, 59– 67 (1992).
Hebb, D. O. The Organization of Behavior (Wiley, New York, 1949).
Davis, G. W. & Goodman, C. S. Synapse-specific control of synaptic efficacy at the terminals of a single neuron. Nature 392, 82–86 (1998).
Desai, N S., Rutherford, L. C. & Turrigiano, G. G. Plasticity in the intrinsic excitability of cortical pyramidal neurons. Nat. Neurosci. 2, 515 –520 (1999).
Moyer, J. R. Jr., Thompson, L. T. & Disterhoft, J. F. Trace eyeblink conditioning increases CA1 excitability in a transient and learning-specific manner. J. Neurosci. 16, 5546–5546 (1996).
Schreurs, B. G., Gusev, P. A., Tomsic, D., Alkon, D. L. & Shi, T. Intracellular correlates of acquisition and long-term memory of classical conditioning in Purkinje cell dendrites in slices of rabbit cerebellar lobule HVI. J. Neurosci. 18, 5498–5507 (1998).
Turrigiano, G., Abbott, L. F. & Marder, E. Activity-dependent changes in the intrinsic properties of cultured neurons. Science 264, 974– 977 (1994).
Turrigiano, G., LeMasson, G. & Marder, E. Selective regulation of current densities underlies spontaneous changes in the activity of cultured neurons. J. Neurosci. 15, 3640–3652 ( 1995).
Purves, D. Neural Activity and the Growth of the Brain (Cambridge Univ. Press, New York, 1994).
Gu, X. & Spitzer, N. C. Distinct aspects of neuronal differentiation encoded by frequency of spontaneous Ca2+ transients. Nature 375, 784–787 ( 1995).
Koch, C. Biophysics of Computation: Information Processing in Single Neurons (Oxford Univ. Press, 1998).
Tsypkin, Y. Z. Adaptation and Learning in Automatic Systems (Academic, New York, 1971).
Linsker, R. Local synaptic learning rules suffice to maximize mutual information in a linear network. Neural Comput. 4, 691– 702 (1992).
Bell, A. J. & Sejnowski, T. J. An information maximization approach to blind separation and blind deconvolution. Neural Comput. 7, 1129–1159 ( 1995).
Bialek, W., Rieke, F., de Ruyter van Steveninck, R. & Warland, D. Reading a neural code. Science 252, 1854 –1857 (1991).
Gabbiani, F. & Koch, C. Coding of time-varying signals in spike trains of integrate-and-fire neurons. Neural Comput. 8, 44–66 (1996).
Rieke, F., Warland, D., de Ruyter van Steveninck, R. & Bialek, W. Spikes: Exploring the Neural Code (MIT Press, Cambridge, Massachusetts, 1997).
Reif, F. Fundamentals of Statistical and Thermal Physics (McGraw-Hill, 1965).
Smirnakis, S. M. et al. Adaptation of retinal processing to image contrast and spatial scale. Nature 386, 69–73 (1997).
Hoffman, D. A., Magee, J. C., Colbert, C. & Johnston, D. K+ channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons. Nature 387 869–875 (1997).
Deisseroth, K., Heist, E. K. & Tsien, R. W. Translocation of calmodulin to the nucleus supports CREB phosphorylation in hippocampal neurons. Nature 392, 198–202 (1998).
Connor, J. A., Walter, D. & McKown, R. Neural repetitive firing: modifications of the Hodgkin-Huxley axon suggested by experimental results from crustacean axons. Biophys. J. 18, 81–102 ( 1977).
Stein, R. B. The information capacity of nerve cells using a frequency code. Biophys. J. 7, 797–826 ( 1967).
Pinsker, M. S. Information and Information Stability of Random Variables and Processes (Holden-Day, San Francisco, 1964).
Granit, R., Kernell, D. & Shortess, K. S. Quantitative aspects of repetitive firing of mammalian motoneurons, caused by injected currents. J. Physiol. (Lond.) 168, 911–931 (1963).
Mason, A. & Larkman, A. Correlations between morphology and electrophysiology of pyramidal neurons in slices of rat visual cortex. J. Neurosci. 10, 1415– 1428 (1990).
Jagadeesh, B., Gray, C. M. & Ferster, D. Visually evoked oscillations of membrane potential in cells of cat visual cortex. Science 257, 552–554 (1992).
Ahmed, B., Allison, J. D., Douglas, R. J. & Martin, K. A. An intracellular study of the contrast-dependence of neuronal activity in cat visual cortex. Cereb. Cortex 7, 559– 570 (1997).
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/9173
This article is cited by
-
On the Role of Speed in Technological and Biological Information Transfer for Computations
Acta Biotheoretica (2022)
-
Modeling of sustained spontaneous network oscillations of a sexually dimorphic brainstem nucleus: the role of potassium equilibrium potential
Journal of Computational Neuroscience (2021)
-
Optimal neural inference of stimulus intensities
Scientific Reports (2018)
-
Improved lower bound for the mutual information between signal and neural spike count
Biological Cybernetics (2018)
-
Calcium-activated SK channels control firing regularity by modulating sodium channel availability in midbrain dopamine neurons
Scientific Reports (2017)