dorsal/arxiv
View SchemaComputation in a single neuron: Hodgkin and Huxley revisited
| Authors | Blaise Aguera y Arcas, Adrienne L. Fairhall, William Bialek |
|---|---|
| Categories | |
| ArXiv ID | physics/0212113 |
| URL | https://arxiv.org/abs/physics/0212113 |
Abstract
A spiking neuron ``computes'' by transforming a complex dynamical input into a train of action potentials, or spikes. The computation performed by the neuron can be formulated as dimensional reduction, or feature detection, followed by a nonlinear decision function over the low dimensional space. Generalizations of the reverse correlation technique with white noise input provide a numerical strategy for extracting the relevant low dimensional features from experimental data, and information theory can be used to evaluate the quality of the low--dimensional approximation. We apply these methods to analyze the simplest biophysically realistic model neuron, the Hodgkin--Huxley model, using this system to illustrate the general methodological issues. We focus on the features in the stimulus that trigger a spike, explicitly eliminating the effects of interactions between spikes. One can approximate this triggering ``feature space'' as a two dimensional linear subspace in the high--dimensional space of input histories, capturing in this way a substantial fraction of the mutual information between inputs and spike time. We find that an even better approximation, however, is to describe the relevant subspace as two dimensional, but curved; in this way we can capture 90% of the mutual information even at high time resolution. Our analysis provides a new understanding of the computational properties of the Hodgkin--Huxley model. While it is common to approximate neural behavior as ``integrate and fire,'' the HH model is not an integrator nor is it well described by a single threshold.
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"abstract": "A spiking neuron ``computes\u0027\u0027 by transforming a complex dynamical input into\na train of action potentials, or spikes. The computation performed by the\nneuron can be formulated as dimensional reduction, or feature detection,\nfollowed by a nonlinear decision function over the low dimensional space.\nGeneralizations of the reverse correlation technique with white noise input\nprovide a numerical strategy for extracting the relevant low dimensional\nfeatures from experimental data, and information theory can be used to evaluate\nthe quality of the low--dimensional approximation. We apply these methods to\nanalyze the simplest biophysically realistic model neuron, the Hodgkin--Huxley\nmodel, using this system to illustrate the general methodological issues. We\nfocus on the features in the stimulus that trigger a spike, explicitly\neliminating the effects of interactions between spikes. One can approximate\nthis triggering ``feature space\u0027\u0027 as a two dimensional linear subspace in the\nhigh--dimensional space of input histories, capturing in this way a substantial\nfraction of the mutual information between inputs and spike time. We find that\nan even better approximation, however, is to describe the relevant subspace as\ntwo dimensional, but curved; in this way we can capture 90% of the mutual\ninformation even at high time resolution. Our analysis provides a new\nunderstanding of the computational properties of the Hodgkin--Huxley model.\nWhile it is common to approximate neural behavior as ``integrate and fire,\u0027\u0027\nthe HH model is not an integrator nor is it well described by a single\nthreshold.",
"arxiv_id": "physics/0212113",
"authors": [
"Blaise Aguera y Arcas",
"Adrienne L. Fairhall",
"William Bialek"
],
"categories": [
"physics.bio-ph",
"physics.data-an",
"q-bio.NC"
],
"title": "Computation in a single neuron: Hodgkin and Huxley revisited",
"url": "https://arxiv.org/abs/physics/0212113"
},
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