Basic mechanisms for graded persistent activity: discrete attractors, continuous attractors, and dynamic representations
Abstract
Persistent neural activity is observed in many systems, and is thought to be a neural substrate for holding memories over time delays of a few seconds. Recent work has addressed two issues. First, how can networks of neurons robustly hold such an active memory? Computer systems obtain significant robustness to noise by approximating analogue quantities with discrete digital representations. In a similar manner, theoretical models of persistent activity in spiking neurons have shown that the most robust and stable way to store the short-term memory of a continuous parameter is to approximate it with a discrete representation. This general idea applies very broadly to mechanisms that range from biochemical networks to single cells and to large circuits of neurons. Second, why is it commonly observed that persistent activity in the cortex can be strongly time-varying? This observation is almost ubiquitous, and therefore must be taken into account in our models and our understanding of how short-term memories are held in the cortex.
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Some state variables may exert graded effects on wakefulness rather than triggering discrete state transitions.
“Furthermore, some state variables may exert a graded effect on the character of wakefulness, rather than triggering transitions between discrete states”
From Waking state: rapid variations modulate neural and behavioral responses (2015) · cites this paper as Brody et al., 2003
Cites
Hopfield, J. J. (1984) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.81.10.3088 · Cited by 6,918 · see citing works
Mnemonic coding of visual space in the monkey's dorsolateral prefrontal cortex
Funahashi, S., Bruce, C. J., & Goldman-Rakic, P. S. (1989) · Journal of Neurophysiology · doi:10.1152/jn.1989.61.2.331 · Cited by 2,685 · see citing works
Cellular basis of working memory
Goldman-Rakic, P. S. (1995) · Neuron · doi:10.1016/0896-6273(95)90304-6 · Cited by 2,663 · see citing works
The Prefrontal Cortex—An Update
Fuster, J. M. (2001) · Neuron · doi:10.1016/s0896-6273(01)00285-9 · Cited by 1,760 · see citing works
Neural Mechanisms of Visual Working Memory in Prefrontal Cortex of the Macaque
Miller, E. K., Erickson, C. A., & Desimone, R. (1996) · Journal of Neuroscience · doi:10.1523/jneurosci.16-16-05154.1996 · Cited by 1,441 · see citing works
Compte, A. (2000) · Cerebral Cortex · doi:10.1093/cercor/10.9.910 · Cited by 1,143 · see citing works
Theory of orientation tuning in visual cortex.
Ben-Yishai, R., Bar‐Or, R. L., & Sompolinsky, H. (1995) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.92.9.3844 · Cited by 1,091 · see citing works
Amit, D. (1997) · Cerebral Cortex · doi:10.1093/cercor/7.3.237 · Cited by 1,061 · see citing works
Temporal structure in neuronal activity during working memory in macaque parietal cortex
Pesaran, B., Pezaris, J. S., Sahani, M., Mitra, P. P., & Andersen, R. A. (2002) · Nature Neuroscience · doi:10.1038/nn890 · Cited by 1,029 · see citing works
Zhang, K. (1996) · The Journal of Neuroscience · doi:10.1523/jneurosci.16-06-02112.1996 · Cited by 1,001 · see citing works
Memory related motor planning activity in posterior parietal cortex of macaque
Gnadt, J. W., & Andersen, R. A. (1988) · Experimental Brain Research · doi:10.1007/bf00271862 · Cited by 998 · see citing works
Fuster, J. M. (1973) · Journal of Neurophysiology · doi:10.1152/jn.1973.36.1.61 · Cited by 995 · see citing works
Neural correlates of a decision in the dorsolateral prefrontal cortex of the macaque
Kim, J.-N., & Shadlen, M. N. (1999) · Nature Neuroscience · doi:10.1038/5739 · Cited by 950 · see citing works
Regional and cellular fractionation of working memory
Goldman‐Rakic, P. S. (1996) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.93.24.13473 · Cited by 810 · see citing works
Graded persistent activity in entorhinal cortex neurons
Egorov, A. V., Hamam, B. N., Fransén, E., Hasselmo, M. E., & Alonso, A. A. (2002) · Nature · doi:10.1038/nature01171 · Cited by 769 · see citing works
Activity of neurons in anterior inferior temporal cortex during a short- term memory task
Miller, E. K., Li, L., & Desimone, R. (1993) · Journal of Neuroscience · doi:10.1523/jneurosci.13-04-01460.1993 · Cited by 732 · see citing works
Prefrontal cortical unit activity and delayed alternation performance in monkeys.
Kubota, K., & Niki, H. (1971) · Journal of Neurophysiology · doi:10.1152/jn.1971.34.3.337 · Cited by 717 · see citing works
Reward expectancy in primate prefrental neurons
Watanabe, M. (1996) · Nature · doi:10.1038/382629a0 · Cited by 684 · cited 1× · see citing works
“Continuous stimulus recoding Some neurons in the PFC are known to code for an expected reward, as well as for the memory of a past stimulus [20,21,22,49].”
BackgroundChafee, M. V., & Goldman, P. S. (1998) · Journal of Neurophysiology · doi:10.1152/jn.1998.79.6.2919 · Cited by 655 · see citing works
How the brain keeps the eyes still
Seung, H. S. (1996) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.93.23.13339 · Cited by 534 · see citing works
Fuster, J. M. (1999) · Cited by 456 · see citing works
Leon, M. I., & Shadlen, M. N. (1999) · Neuron · doi:10.1016/s0896-6273(00)80854-5 · Cited by 449 · see citing works
Head direction cells and the neurophysiological basis for a sense of direction
Taube, J. S. (1998) · Progress in Neurobiology · doi:10.1016/s0301-0082(98)00004-5 · Cited by 447 · see citing works
Visuospatial coding in primate prefrontal neurons revealed by oculomotor paradigms
Funahashi, S., Bruce, C. J., & Goldman‐Rakic, P. S. (1990) · Journal of Neurophysiology · doi:10.1152/jn.1990.63.4.814 · Cited by 443 · see citing works
A role for NMDA-receptor channels in working memory
Lisman, J. E., Fellous, J., & Wang, X. (1998) · Nature Neuroscience · doi:10.1038/1086 · Cited by 438 · see citing works
Prospective coding for objects in primate prefrontal cortex
Rainer, G., Rao, S. C., & Miller, E. K. (1999) · The Journal of Neuroscience · doi:10.1523/jneurosci.19-13-05493.1999 · Cited by 432 · see citing works
Neuronal correlates of decision-making in secondary somatosensory cortex
Romo, R., Hernández, A., Zainos, A., Lemus, L., & Brody, C. D. (2002) · Nature Neuroscience · doi:10.1038/nn950 · Cited by 387 · see citing works
Self-citationTiming and Neural Encoding of Somatosensory Parametric Working Memory in Macaque Prefrontal Cortex
Brody, C. D. (2003) · Cerebral Cortex · doi:10.1093/cercor/bhg100 · Cited by 350 · see citing works
Self-citationHikosaka, K. (2000) · Cerebral Cortex · doi:10.1093/cercor/10.3.263 · Cited by 345 · see citing works
A Spatial-Temporal Model of Cell Activation
Alkon, D. L., & Rasmussen, H. (1988) · Science · doi:10.1126/science.2830669 · Cited by 342 · see citing works
Stability of the memory of eye position in a recurrent network of conductance-based model neurons
Seung, H. S., Lee, D. D., Reis, B. Y., & Tank, D. W. (2000) · Neuron · doi:10.1016/s0896-6273(00)81155-1 · Cited by 339 · see citing works
All-or-none potentiation at CA3-CA1 synapses
Petersen, C. C. H., Malenka, R. C., Nicoll, R. A., & Hopfield, J. J. (1998) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.95.8.4732 · Cited by 330 · see citing works
Camperi, M., & Wang, X. (1998) · Journal of Computational Neuroscience · doi:10.1023/a:1008837311948 · Cited by 323 · see citing works
McFarland, J. L., & Fuchs, A. F. (1992) · Journal of Neurophysiology · doi:10.1152/jn.1992.68.1.319 · Cited by 323 · see citing works
Model for a robust neural integrator
Koulakov, A. A., Raghavachari, S., Kepecs, Á., & Lisman, J. E. (2002) · Nature Neuroscience · doi:10.1038/nn893 · Cited by 308 · see citing works
Stationary Bumps in Networks of Spiking Neurons
Laing, C. R., & Chow, C. C. (2001) · Neural Computation · doi:10.1162/089976601750264974 · Cited by 277 · see citing works
Lisman, J. E., & Goldring, M. A. (1988) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.85.14.5320 · Cited by 257 · see citing works
A spiking network model of short-term active memory
Zipser, D., Kehoe, B., Littlewort, G. C., & Fuster, J. M. (1993) · Journal of Neuroscience · doi:10.1523/jneurosci.13-08-03406.1993 · Cited by 256 · see citing works
Temporal Evolution of a Decision-Making Process in Medial Premotor Cortex
Hernández, A., Zainos, A., & Romo, R. (2002) · Neuron · doi:10.1016/s0896-6273(02)00613-x · Cited by 253 · see citing works
Self-citationRenart, A., Song, P., & Wang, X. (2003) · Neuron · doi:10.1016/s0896-6273(03)00255-1 · Cited by 243 · see citing works
Primate spinal interneurons show pre-movement instructed delay activity
Prut, Y., & Fetz, E. E. (1999) · Nature · doi:10.1038/44145 · Cited by 242 · see citing works
The anatomical and computational basis of the rat head-direction cell signal
Sharp, P. E., Blair, H. T., & Cho, J. (2001) · Trends in Neurosciences · doi:10.1016/s0166-2236(00)01797-5 · Cited by 236 · see citing works
Influence of Reward Expectation on Visuospatial Processing in Macaque Lateral Prefrontal Cortex
Kobayashi, S., Lauwereyns, J., Koizumi, M., Sakagami, M., & Hikosaka, O. (2002) · Journal of Neurophysiology · doi:10.1152/jn.00472.2001 · Cited by 206 · see citing works
Gutkin, B. S., Laing, C. R., Colby, C. L., Chow, C. C., & Ermentrout, B. (2001) · Journal of Computational Neuroscience · doi:10.1023/a:1012837415096 · Cited by 172 · see citing works
Aksay, E., Baker, R., Seung, H. S., & Tank, D. W. (2000) · Journal of Neurophysiology · doi:10.1152/jn.2000.84.2.1035 · Cited by 119 · see citing works
Redundancy Reduction and Sustained Firing with Stochastic Depressing Synapses
Goldman, M. S., Maldonado, P. E., & Abbott, L. F. (2002) · Journal of Neuroscience · doi:10.1523/jneurosci.22-02-00584.2002 · Cited by 117 · see citing works
Rainer, G., & Miller, E. K. (2002) · European Journal of Neuroscience · doi:10.1046/j.1460-9568.2002.01958.x · Cited by 113 · see citing works
Eye position and eye velocity integrators reside in separate brainstem nuclei.
Pastor, Á. M., de la Cruz, R. R., & Baker, R. G. V. (1994) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.91.2.807 · Cited by 100 · see citing works
Loewenstein, Y., & Sompolinsky, H. (2002) · Society for Neuroscience Abstract Viewer & Itinerary Planner · Cited by 1 · see citing works
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London, M., & Häusser, M. (2005) · Annual Review of Neuroscience · doi:10.1146/annurev.neuro.28.061604.135703 · Cited by 1,149 · see citing works
Waking state: rapid variations modulate neural and behavioral responses
McGinley, M. J., Vinck, M., Reimer, J., Batista-Brito, R., Zagha, E., Cadwell, C. R., Tolias, A. S., Cardin, J. A., & McCormick, D. A. (2015) · Neuron · doi:10.1016/j.neuron.2015.09.012 · Cited by 801 · see citing works
“Furthermore, some state variables may exert a graded effect on the character of wakefulness, rather than triggering transitions between discrete states (Brody et al., 2003; Ecker et al., 2014).”
Slow cortical dynamics and the accumulation of information over long timescales
Honey, C. J., Thesen, T., Donner, T. H., Silbert, L. J., Carlson, C. E., Devinsky, O., Doyle, W. K., Rubin, N., Heeger, D. J., & Hasson, U. (2012) · Neuron · doi:10.1016/j.neuron.2012.08.011 · Cited by 532 · see citing works
Flexible control of mutual inhibition: a neural model of two-interval discrimination
Machens, C. K., Romo, R., & Brody, C. D. (2005) · Science · doi:10.1126/science.1104171 · Cited by 535 · see citing works
Self-citationHulse, B. K., Haberkern, H., Franconville, R., Turner-Evans, D., Takemura, S.-Y., Wolff, T., Noorman, M., Dreher, M., Dan, C., Parekh, R., et al. (2021) · eLife · doi:10.7554/elife.66039 · Cited by 392 · see citing works
Discrete attractor dynamics underlies persistent activity in the frontal cortex
Inagaki, H. K., Fontolan, L., Romani, S., & Svoboda, K. (2019) · Nature · doi:10.1038/s41586-019-0919-7 · Cited by 334 · see citing works
Memory without Feedback in a Neural Network
Goldman, M. S. (2009) · Neuron · doi:10.1016/j.neuron.2008.12.012 · Cited by 342 · see citing works
Mechanism of Graded Persistent Cellular Activity of Entorhinal Cortex Layer V Neurons
Fransén, E., Tahvildari, B., Egorov, A. V., Hasselmo, M. E., & Alonso, A. A. (2006) · Neuron · doi:10.1016/j.neuron.2006.01.036 · Cited by 279 · see citing works
Attractor Dynamics of Spatially Correlated Neural Activity in the Limbic System
Knierim, J. J., & Zhang, K. (2012) · Annual Review of Neuroscience · doi:10.1146/annurev-neuro-062111-150351 · Cited by 222 · see citing works
Variability in neuronal activity in primate cortex during working memory tasks
Shafi, M., Zhou, Y., Quintana, J., Chow, C., Fuster, J., & Bodner, M. (2007) · Neuroscience · doi:10.1016/j.neuroscience.2006.12.072 · Cited by 215 · see citing works
Chen, J., Honey, C. J., Simony, E., Arcaro, M. J., Norman, K. A., & Hasson, U. (2016) · Cerebral Cortex · doi:10.1093/cercor/bhv155 · Cited by 135 · see citing works
Stimulus-specific hypothalamic encoding of a persistent defensive state
Kennedy, A., Kunwar, P. S., Li, L.-Y., Stagkourakis, S., Wagenaar, D. A., & Anderson, D. J. (2020) · Nature · doi:10.1038/s41586-020-2728-4 · Cited by 144 · see citing works
The head direction circuit of two insect species
Pisokas, I., Heinze, S., & Webb, B. (2020) · eLife · doi:10.7554/elife.53985 · Cited by 84 · see citing works
Fisher, D., Olasagasti, I., Tank, D. W., Aksay, E. R. F., & Goldman, M. S. (2013) · Neuron · doi:10.1016/j.neuron.2013.06.041 · Cited by 75 · see citing works
Arsiero, M., Lüscher, H.-R., Lundstrom, B. N., & Giugliano, M. (2007) · The Journal of Neuroscience · doi:10.1523/jneurosci.4937-06.2007 · Cited by 75 · see citing works
Hulse, B. K., Haberkern, H., Franconville, R., Turner-Evans, D. B., Takemura, S., Wolff, T., Noorman, M., Dreher, M., Dan, C., Parekh, R., et al. (2020) · doi:10.1101/2020.12.08.413955 · Cited by 392 · see citing works
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BackgroundSpatial Patterns of Persistent Neural Activity Vary with the Behavioral Context of Short-Term Memory
Daie, K., Goldman, M. S., & Aksay, E. R. F. (2015) · Neuron · doi:10.1016/j.neuron.2015.01.006 · Cited by 42 · see citing works
Optogenetic perturbations reveal the dynamics of an oculomotor integrator
Gonçalves, P. J., Arrenberg, A. B., Hablitzel, B., Baier, H., & Machens, C. K. (2014) · Frontiers in Neural Circuits · doi:10.3389/fncir.2014.00010 · Cited by 28 · see citing works
Encoding certainty in bump attractors
Carroll, S., Josić, K., & Kilpatrick, Z. P. (2014) · Journal of Computational Neuroscience · doi:10.1007/s10827-013-0486-0 · Cited by 23 · see citing works
Functional alterations of the prefrontal circuit underlying cognitive aging in mice
Chong, H. R., Ranjbar-Slamloo, Y., Ho, M. Z. H., Ouyang, X., & Kamigaki, T. (2023) · Nature Communications · doi:10.1038/s41467-023-43142-0 · Cited by 19 · see citing works
- Authors
- Brody, C. D., Romo, R., & Kepecs, A.
- Affiliations
- Cold Spring Harbor Laboratory (US)
- Universidad Nacional Autónoma de México (MX)
- Corresponding author
- Brody, Carlos D
- Venue
- Current Opinion in Neurobiology
- Publisher
- Elsevier BV
- Published
- 2003-04
- Volume
- 13
- Issue
- 2
- Pages
- 204-211
- ISSN
- 0959-4388 (ISSN-L)
- OpenAlex
- W1974408180
- Cited by
- 284
- References
- 49
- Citations by year
- 2026: 10 · 2025: 11 · 2024: 15 · 2023: 14 · 2022: 11 · 2021: 20 · 2020: 16 · 2019: 16 · 2018: 12 · 2017: 10 · 2016: 11 · 2015: 10 · 2014: 13 · 2013: 16 · 2012: 13
- FWCI
- 1.18
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Current Opinion in Neurobiology (publishedVersion)
- PubMed (publishedVersion)
- Cold Spring Harbor Laboratory Institutional Repository (Cold Spring Harbor Laboratory) (acceptedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Life Sciences › Neuroscience › Cognitive Neuroscience › Memory and Neural Mechanisms
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Memory and Neural Computing
- Keywords
- persistent activity, short-term memory, continuous attractors, dynamic representations, spiking neural networks
- MeSH terms
- Animals, Brain, Humans, Memory, Short-Term, Models, Neurological, Nerve Net, Neurons
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