Passive dendrites enable single neurons to compute linearly non-separable functions.
Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2013-01-01
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| Series: | PLoS Computational Biology |
| Online Access: | https://doi.org/10.1371/journal.pcbi.1002867 |
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| author | Romain Daniel Cazé Mark Humphries Boris Gutkin |
| author_facet | Romain Daniel Cazé Mark Humphries Boris Gutkin |
| author_sort | Romain Daniel Cazé |
| collection | DOAJ |
| description | Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions. |
| format | Article |
| id | doaj-art-bbb87a669bf04499aade9e8616c8aec4 |
| institution | OA Journals |
| issn | 1553-734X 1553-7358 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS Computational Biology |
| spelling | doaj-art-bbb87a669bf04499aade9e8616c8aec42025-08-20T02:34:09ZengPublic Library of Science (PLoS)PLoS Computational Biology1553-734X1553-73582013-01-0192e100286710.1371/journal.pcbi.1002867Passive dendrites enable single neurons to compute linearly non-separable functions.Romain Daniel CazéMark HumphriesBoris GutkinLocal supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions.https://doi.org/10.1371/journal.pcbi.1002867 |
| spellingShingle | Romain Daniel Cazé Mark Humphries Boris Gutkin Passive dendrites enable single neurons to compute linearly non-separable functions. PLoS Computational Biology |
| title | Passive dendrites enable single neurons to compute linearly non-separable functions. |
| title_full | Passive dendrites enable single neurons to compute linearly non-separable functions. |
| title_fullStr | Passive dendrites enable single neurons to compute linearly non-separable functions. |
| title_full_unstemmed | Passive dendrites enable single neurons to compute linearly non-separable functions. |
| title_short | Passive dendrites enable single neurons to compute linearly non-separable functions. |
| title_sort | passive dendrites enable single neurons to compute linearly non separable functions |
| url | https://doi.org/10.1371/journal.pcbi.1002867 |
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