Cited by 481Neural dynamics and brain functionNeuroscience and Neuropharmacology ResearchAdvanced Memory and Neural Computing

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Neuronal arithmetic

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Silver, R. Angus·2010·Nature Reviews Neuroscience

DOI 10.1038/nrn2864PMC PMC4750293

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Abstract

The vast computational power of the brain has traditionally been viewed as arising from the complex connectivity of neural networks, in which an individual neuron acts as a simple linear summation and thresholding device. However, recent studies show that individual neurons utilize a wealth of nonlinear mechanisms to transform synaptic input into output firing. These mechanisms can arise from synaptic plasticity, synaptic noise, and somatic and dendritic conductances. This tool kit of nonlinear mechanisms confers considerable computational power on both morphologically simple and more complex neurons, enabling them to perform a range of arithmetic operations on signals encoded ina variety of different ways.

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A logical calculus of the ideas immanent in nervous activity
McCulloch, W. S., & Pitts, W. (1943) · The Bulletin of Mathematical Biophysics · doi:10.1007/bf02478259 · Cited by 18,566
Neuronal Oscillations in Cortical Networks
Buzsáki, G., & Draguhn, A. (2004) · Science · doi:10.1126/science.1099745 · Cited by 6,576
Magnesium gates glutamate-activated channels in mouse central neurones
Nowak, L. M., Bregestovski, P. D., Ascher, P., Herbet, A., & Prochiantz, A. (1984) · Nature · doi:10.1038/307462a0 · Cited by 4,116
Interplay between Cortical Spreading Depolarization and Seizures
Kramer, D. R., Fujii, T., Ohiorhenuan, I. E., & Liu, C. Y. (2017) · Stereotactic and Functional Neurosurgery · doi:10.1159/000452841 · Cited by 3,721
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Attwell, D., & Laughlin, S. B. (2001) · Journal of Cerebral Blood Flow & Metabolism · doi:10.1097/00004647-200110000-00001 · Cited by 3,543
Dynamic predictions: Oscillations and synchrony in top–down processing
Engel, A. K., Fries, P., & Singer, W. (2001) · Nature Reviews Neuroscience · doi:10.1038/35094565 · Cited by 3,454
The NEURON Simulation Environment
Hines, M. L., & Carnevale, N. T. (1997) · Neural Computation · doi:10.1162/neco.1997.9.6.1179 · Cited by 2,630
Synaptic depression and cortical gain control
Abbott, L. F., Varela, J. A., Sen, K., & Nelson, S. B. (1997) · Science · doi:10.1126/science.275.5297.221 · Cited by 1,690
Pyramidal neurons: dendritic structure and synaptic integration
Spruston, N. (2008) · Nature Reviews Neuroscience · doi:10.1038/nrn2286 · Cited by 1,688
Synaptic computation
Abbott, L. F., & Regehr, W. G. (2004) · Nature · doi:10.1038/nature03010 · Cited by 1,684

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Research works printed but not linked: 5

Rall, W. in Neuronal Theory and Modeling (ed. Reiss, R. F.) 73–97 (Stanford Univ. Press, 1964).
Rice, S. O. in Selected Papers on Noise and Stochastic Processes (ed. Wax, N.) 113–150 (Dover, New York, 1954).
Feng, T. P. The changes in the end-plate potential during and after prolonged stimulation. Chin. J. Physiol. 16, 341–372 (1941).
Mel, B. in Dendrites (eds Stuart, G. J., Spruston, N. & Hausser, M.) 271–284 (Oxford Univ. Press, 2008).
Stuart, G., Spruston, N. & Häusser, M. (eds). Dendrites (Oxford Univ. Press, Oxford, 2008).

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From integrative biology to the nerve impulse: Rethinking neural information and semiotics in functional systems perspective
Kurismaa, A. (2022) · Adaptive Behavior · doi:10.1177/10597123221089557 · Cited by 2
“…problem has been hardly resolved or even recognized in subsequent work (for reviews cf. Drukarch et al., 2019; Haider & McCormick, 2009; Payeur et al., 2019; Silver, 2010) indicates the potentially broad horizon of new problems that functional systems analysis can still open in respective areas.”
Background
Neural Information Processing and Computations of Two-Input Synapses
Kim, S. H., Woo, J., Choi, K., Choi, M. Y., & Han, K. (2022) · Neural Computation · doi:10.1162/neco_a_01534 · Cited by 2
“…partly in the lack of nonlinear synaptic integration mechanisms for multiple synaptic inputs via homo-and heterosynaptic transmissions (Mel, 1994; London & H˘ausser, 2005; Bailey, Giustetto, Huang, Hawkins, & Kandel, 2000; Koch & Segev, 2000; Sjostrom, Rancz, Roth, & Hausser, 2008; Silver, 2010).”
Background
Somatic Integration of Incoherent Dendritic Inputs in the Gerbil Medial Superior Olive
Mackenbach, Y., & Borst, J. G. G. (2023) · Journal of Neuroscience · doi:10.1523/jneurosci.2215-22.2023 · Cited by 2
Overcoming the limitations of motion sensor models by considering dendritic computations
Luna, R., Serrano‐Pedraza, I., & Bertalmı́o, M. (2025) · Scientific Reports · doi:10.1038/s41598-025-90095-z · Cited by 2
“…are absent from classical models of single-neuron responses, including the following: (a) for the same neuron, some dendrites may act linearly while others may act nonlinearly [40, 58]; (b) there is feedback from the neuron soma to the dendrites, and it can modify the dendritic nonlinearity [56].”
Emergence of Robust Memory Manifolds
Can, T., & Krishnamurthy, K. (2025) · PRX Life · doi:10.1103/prxlife.3.023006 · Cited by 12
The Mechanism of Orientation Detection Based on Dendritic Neuron
Zhang, X., Todo, Y., Tang, C. C., & Tang, Z. (2021) · IEEE International Conference on Big Data and Artificial Intelligence (BDAI) · doi:10.1109/bdai52447.2021.9515286 · Cited by 2
Parallel Functional Architectures Within a Single Dendritic TreePreprint
Kim, Y. J., Ujfalussy, B., & Lengyel, M. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4047251 · Cited by 2
Serotonergic modulation of the claustrum
Wong, K. L. L. (2021) · DR-NTU (Nanyang Technological University) · doi:10.32657/10356/155926 · Cited by 2
Presynaptic cAMP-PKA-mediated potentiation induces reconfiguration of synaptic vesicle pools and channel-vesicle coupling at hippocampal mossy fiber boutonsPreprint
Kim, O., Okamoto, Y., Brose, N., Shigemoto, R., & Jónás, P. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.12.04.569907 · Cited by 2
Multi-output computation by single neuron biophysics in a visual systemPreprint
Seung, H. S. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.02.02.636137 · Cited by 2
Untangling stability and gain modulation in cortical circuits with multiple interneuron classesPreprint
Bos, H., Miehl, C., Oswald, A.-M. M., & Doiron, B. (2025) · eLife · doi:10.7554/elife.99808.3 · Cited by 2
Neuromorphic Computing Based on Memristor Dynamics
Duan, Q., Xiao, Z., Ke, Y., & Yang, Y. (2022) · Springer eBooks · doi:10.1007/978-3-031-11506-6_1 · Cited by 1
Inhibitory cell type heterogeneity in a spatially structured mean-field model of V1
Kim, S. H., & Choi, H. (2026) · Physical review. E · doi:10.1101/2025.03.13.643046 · Cited by 1
“We define gain modulations as changes in the slope of the visual response curves in excitatory neurons: a decrease in the slope indicates a divisive modulation, while a vertical shift without slope change indicates a purely subtractive modulation [21, 25, 27].”
Reverse correlation of natural statistics for ecologically relevant characterization of human perceptual templates
Landolfi, L., & Neri, P. (2025) · Journal of Neurophysiology · doi:10.1152/jn.00059.2024 · Cited by 1
Heterogeneity of ictal firing during generalized seizures in the awake cortex
Sere, P., Nagy, O., Zsigri, N., Crunelli, V., & Lörincz, M. L. (2026) · Cerebral Cortex · doi:10.1093/cercor/bhag049 · Cited by 1
“Balanced elevations of excitatory and inhibitory conductances can therefore adjust neuronal gain divisively (Silver 2010), enabling neurons to maintain proportional firing across brain states.”
Ultra‐Low‐Power and Reconfigurable Optoelectronic Memtransistor Based on Vertical Nb‐WSe 2 /Te van der Waals Heterostructure
Zhou, Y., Li, Y., Ma, X., Meng, L., Zhang, L., & Zhang, M. (2026) · Small · doi:10.1002/smll.202514918 · Cited by 1
Short-term depression of inhibitory Purkinje cell synapses enhances gain modulation in the cerebellar nuclei
Bampasakis, D., Maex, R., Davey, N., & Steuber, V. (2013) · BMC Neuroscience · doi:10.1186/1471-2202-14-s1-p374 · Cited by 1
Arithmetic computing via rate coding in neural circuits with spike-triggered adaptive synapses
Thorat, S., & Rajendran, B. (2015) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2015.7280822 · Cited by 1
The tune of sensory inputs
Kingwell, K. (2010) · Nature reviews. Neuroscience · doi:10.1038/nrn2872 · Cited by 1
Effects of short-term oral administration of propranolol on tear secretion in clinically normal dogs.
Ghaffari, M. S., Arzani, V., Khorami, N., & Rajaei, S. M. (2011) · PubMed Central · Cited by 1
Impact of Structural Plasticity on Memory Capacity
Bozelos, P., & Poirazi, P. (2017) · Elsevier eBooks · doi:10.1016/b978-0-12-803784-3.00015-9 · Cited by 1
Oxide-Based EDL Transistors for Neuromorphic Computing Applications
Wan, C. (2018) · Springer theses · doi:10.1007/978-981-13-3314-9_4 · Cited by 1
Multi-Band Bathymetry Mapping with Spiking Neuron Anomaly Detection
Lawen, J., Lawen, K., Salman, G. F., & Schuster, A. (2022) · Water · doi:10.3390/w14050810 · Cited by 1
“If the entire processing is supposed to be integrated into one neural net, then the computation of the input for the spiking neurons can be formulated as arithmetic neurons [10] which are fed by neurons which conduct a spline ﬁt.”
Method

Authors: Silver, R. A.
Affiliations: University College London (GB)
Corresponding author: Silver, R. Angus
ORCID: Silver, R. Angus
Venue: Nature Reviews Neuroscience
Publisher: Springer Science and Business Media LLC
Published: 2010-06-09
Volume: 11
Issue: 7
Pages: 474-489
ISSN: 1471-003X (ISSN-L)
1471-0048
DOI: 10.1038/nrn2864
PMC: PMC4750293
OpenAlex: W4233766477
Cited by: 481
References: 177
Citations by year: 2026: 23 · 2025: 32 · 2024: 26 · 2023: 22 · 2022: 39 · 2021: 35 · 2020: 35 · 2019: 34 · 2018: 34 · 2017: 23 · 2016: 38 · 2015: 48 · 2014: 30 · 2013: 23 · 2012: 25
FWCI: 1.44
Type: journal article
Language: en
Open access: green
www.ncbi.nlm.nih.gov
Licence: www.springer.com/tdm (tdm)
Locations: Nature reviews. Neuroscience (publishedVersion)
PubMed (publishedVersion)
PubMed Central (acceptedVersion)
UCL Discovery (University College London) (submittedVersion)
Funders: Wellcome Trust (064413)
Biotechnology and Biological Sciences Research Council (BB/F005490/1)
Topics: Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
Life Sciences › Neuroscience › Cellular and Molecular Neuroscience › Neuroscience and Neuropharmacology Research
Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Memory and Neural Computing
Keywords: neural computation, synaptic plasticity, synaptic noise, neuronal morphology, neural coding, dendritic integration
MeSH terms: Animals, Dendrites, Humans, Mathematics, Nerve Net, Synaptic Transmission, Neurons, Synapses

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