Possible dendritic contribution to unimodal numerosity tuning and Weber-Fechner law-dependent numerical cognition

Frontiers in Computational Neuroscience

Volumn 3, Issue AUG, 2009, Pages

  Morita, Kenji ^a  

^a RIKEN BRAIN SCIENCE INSTITUTE   (Japan)

Author keywords

Cooperative plasticity; Dendrite; Numerical competence; Numerosity tuned neurons; Self organizing map; Weber Fechner law

Indexed keywords

DISTRIBUTED PHENOMENA; HYPOTHETICAL MECHANISM; INITIAL CONDITIONS; NUMERICAL COGNITION; NUMERICAL COMPETENCE; NUMERICAL REPRESENTATION; PROMINENT FEATURES; WEBER-FECHNER LAWS;

CONFORMAL MAPPING; DENDRITES (METALLOGRAPHY); OSCILLATORS (ELECTRONIC); PLASTICITY; SELF ORGANIZING MAPS; TUNING;

NEURONS;

EID: 84856523355     PISSN: 16625188     EISSN: None     Source Type: Journal    
DOI: 10.3389/neuro.10.012.2009     Document Type: Article

References (87)

1. Amari, S. (1980). Topographic organization of nerve fields. Bull. Math. Biol. 42, 339-364.
2. Archie, K. A., and Mel, B. W. (2000). A model for intradendritic computation of binocular disparity. Nat. Neurosci. 3, 54-63.
3. Ascoli, G. A. (2002). Computational Neuroanatomy: Principles and Methods. Totowa, Humana Press.
4. Brannon, E. M., and Terrace, H. S. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science 282, 746-749.
5. Brannon, E. M., Wusthoff, C. J., Gallistel, C. R., and Gibbon, J. (2001). Numerical subtraction in the pigeon: evidence for a linear subjective number scale. Psychol. Sci. 12, 238-243.
6. Brody, C. D., Romo, R., and Kepecs, A. (2003). Basic mechanisms for graded persistent activity: discrete attractors, continuous attractors, and dynamic representations. Curr. Opin. Neurobiol. 13, 204-211.
7. Carandini, M., and Heeger, D. J. (1994). Summation and division by neurons in primate visual cortex. Science 264, 1333-1336.
8. Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. New York, Oxford University Press.
9. Dehaene, S. (2001). Subtracting pigeons: logarithmic or linear? Psychol. Sci. 12, 244-246; discussion 247.
10. Dehaene, S. (2003). The neural basis of the Weber-Fechner law: a logarithmic mental number line. Trends Cogn. Sci. 7, 145-147.
11. Dehaene, S., and Changeux, J. P. (1993). Development of elementary numerical abilities-a neuronal model. J. Cogn. Neurosci. 5, 390-407.
12. Dehaene, S., Izard, V., Spelke, E., and Pica, P. (2008). Log or linear? Distinct intuitions of the number scale in Western and Amazonian indigene cultures. Science 320, 1217-1220.
13. Dehaene, S., Molko, N., Cohen, L., and Wilson, A. J. (2004). Arithmetic and the brain. Curr. Opin. Neurobiol. 14, 218-224.
14. Fechner, G. (1860). Elemente der Psychophysik. Leipzig, Breitkopf & Härtel.
15. Gallistel, C. R., and Gelman, R. (1992). Preverbal and verbal counting and computation. Cognition 44, 43-74.
16. Gasparini, S., Migliore, M., and Magee, J. C. (2004). On the initiation and propagation of dendritic spikes in CA1 pyramidal neurons. J. Neurosci. 24, 11046-11056.
17. Golding, N. L., Staff, N. P., and Spruston, N. (2002). Dendritic spikes as a mechanism for cooperative long-term potentiation. Nature 418, 326-331.
18. Goldman, M. S., Levine, J. H., Major, G., Tank, D. W., and Seung, H. S. (2003). Robust persistent neural activity in a model integrator with multiple hysteretic dendrites per neuron. Cereb. Cortex 13, 1185-1195.
19. Govindarajan, A., Kelleher, R. J., and Tonegawa, S. (2006). A clustered plasticity model of long-term memory engrams. Nat. Rev. Neurosci. 7, 575-583.
20. Haeckel, E. (1866). Generel le Morphologie der Organismen.
21. Berlin, G. Reimer. Hahnloser, R. H., Sarpeshkar, R., Mahowald, M. A., Douglas, R. J., and Seung, H. S. (2000). Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit. Nature 405, 947-951.
22. Harvey, C. D., and Svoboda, K. (2007). Locally dynamic synaptic learning rules in pyramidal neuron dendrites. Nature 450, 1195-1200.
23. Harvey, C. D., Yasuda, R., Zhong, H., and Svoboda, K. (2008). The Spread of Ras Activity Triggered by Activation of a Single Dendritic Spine. Science 321, 136-140.
24. Ibata, K., Sun, Q., and Turrigiano, G. G. (2008). Rapid synaptic scaling induced by changes in postsynaptic firing. Neuron 57, 819-826.
25. Jadi, M., and Mel, B. W. (2007). Synchrony and location dependent effects of inhibition in a pyramidal neuron model. Computational and Systems Neuroscience Meeting Abstract. Poster 11-91.
26. Kapfer, C., Glickfeld, L. L., Atallah, B.V., and Scanziani, M. (2007). Supralinear increase of recurrent inhibition during sparse activity in the somatosensory cortex. Nat. Neurosci. 10, 743-753.
27. Koch, C. (1998). Biophysics of Computation: Information Processing in Single Neurons. New York, Oxford University Press.
28. Koch, C., Poggio, T., and Torre, V. (1982). Retinal ganglion cells: a functional interpretation of dendritic morphology. Philos. Trans. R. Soc. Lond. B Biol. Sci. 298, 227-263.
29. Koch, C., Poggio, T., and Torre, V. (1983). Nonlinear interactions in a dendritic tree: localization, timing, and role in information processing. Proc. Natl. Acad. Sci. U. S. A. 80, 2799-2802.
30. Koch, C., and Segev, I. (2000). The role of single neurons in information processing. Nat. Neurosci. 3(Suppl.), 1171-1177.
31. Kohonen, T. (1982). Self-organized formation of topologically correct feature maps. Biol. Cybern. 43, 59-69.
32. Larkum, M. E., and Nevian, T. (2008). Synaptic clustering by dendritic signalling mechanisms. Curr. Opin. Neurobiol. 18, 1-11.
33. Liu, G. (2004). Local structural balance and functional interaction of excitatory and inhibitory synapses in hippocampal dendrites. Nat. Neurosci. 7, 373-379.
34. Loewenstein, Y., and Sompolinsky, H. (2003). Temporal integration by calcium dynamics in a model neuron. Nat. Neurosci. 6, 961-967.
35. London, M., and Häusser, M. (2005). Dendritic computation. Annu. Rev. Neurosci. 28, 503-532.
36. Losonczy, A., and Magee, J. C. (2006). Integrative properties of radial oblique Dendrites in hippocampal CA1 pyramidal neurons. Neuron 50, 291-307.
37. Losonczy, A., Makara, J. K., and Magee, J. C. (2008). Compartmentalized dendritic plasticity and input feature storage in neurons. Nature 452, 436-441.
38. Machens, C. K., Romo, R., and Brody, C. D. (2005). Flexible control of mutual inhibition: a neural model of twointerval discrimination. Science 307, 1121-1124.
39. Mainen, Z. F., and Sejnowski, T. J. (1996). Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382, 363-366.
40. Major, G., Polsky, A., Denk, W., Schiller, J., and Tank, D. W. (2008). Spatiotemporally graded NMDA spike/plateau potentials in basal dendrites of neocortical pyramidal neurons. J. Neurophysiol. 99, 2584-2601.
41. Mehta, M. R. (2004). Cooperative LTP can map memory sequences on dendritic branches. Trends Neurosci. 27, 69-72.
42. Mel, B. W. (1993). Synaptic integration in an excitable dendritic tree. J. Neurophysiol. 70, 1086-1101.
43. Mel, B. W. (1994). Information processing in dendritic trees. Neural. Comput. 6, 1031-1085.
44. Mel, B. W. (2007). Why have dendrites? A computational perspective. In Dendrites, 2nd edn, G. Stuart et al., eds (New York, Oxford University Press), pp. 421-440.
45. Mel, B. W., Ruderman, D. L., and Archie, K. A. (1998). Translationinvariant orientation tuning in visual "complex" cells could derive from intradendritic computations. J. Neurosci. 18, 4325-4334.
46. Merten, K., and Nieder, A. (2009). Compressed scaling of abstract numerosity representations in adult humans and monkeys. J. Cogn. Neurosci. 21, 333-346.
47. Miller, J. A., and Kenyon, G. T. (2007). Extracting number-selective responses from coherent oscillations in a computer model. Neural. Comput. 19, 1766-1797.
48. Miller, P., Brody, C. D., Romo, R., and Wang, X.-J. (2003). A recurrent network model of somatosensory parametric working memory in the prefrontal cortex. Cereb. Cortex 13, 1208-1218.
49. Milojkovic, B. A., Radojicic, M. S., and Antic, S. D. (2005). A strict correlation between dendritic and somatic plateau depolarizations in the rat prefrontal cortex pyramidal neurons. J. Neurosci. 25, 3940-3951.
50. Minsky, M., and Papert, S. (1969). Perceptrons: An Introduction to Computational Geometry. Cambridge, MA, The MIT Press.
51. Morita, K. (2008). Possible role of dendritic compartmentalization in the spatial working memory circuit. J. Neurosci. 28, 7699-7724.
52. Morita, K. (2009). Computational implications of cooperative plasticity induction at nearby dendritic sites. Sci. Signal. 2, pe2.
53. Nevian, T., Larkum, M. E., Polsky, A., and Schiller, J. (2007). Properties of basal dendrites of layer 5 pyramidal neurons: a direct patch-clamp recording study. Nat. Neurosci. 10, 206-214.
54. Nieder, A. (2005). Counting on neurons: the neurobiology of numerical competence. Nat. Rev. Neurosci. 6, 177-190.
55. Nieder, A., and Dehaene, S. (2009). The representation of number in the brain. Annu. Rev. Neurosci. 32, 185-208.
56. Nieder, A., Freedman, D. J., and Miller, E. K. (2002). Representation of the quantity of visual items in the primate prefrontal cortex. Science 297, 1708-1711.
57. Nieder, A., and Merten, K. (2007). A labeled-line code for small and large numerosities in the monkey prefrontal cortex. J. Neurosci. 27, 5986-5993.
58. Nieder, A., and Miller, E. K. (2003). Coding of cognitive magnitude: compressed scaling of numerical information in the primate prefrontal cortex. Neuron 37, 149-157.
59. Nieder, A., and Miller, E. K. (2004). A parieto-frontal network for visual numerical information in the monkey. Proc. Natl. Acad. Sci. U. S. A. 101, 7457-7462.
60. Poirazi, P., Brannon, T., and Mel, B. W. (2003a). Arithmetic of subthreshold synaptic summation in a model CA1 pyramidal cell. Neuron 37, 977-987.
61. Poirazi, P., Brannon, T., and Mel, B. W. (2003b). Pyramidal neuron as two-layer neural network. Neuron 37, 989-999.
62. Poirazi, P., and Mel, B. W. (2001). Impact of active dendrites and structural plasticity on the memory capacity of neural tissue. Neuron 29, 779-796.
63. Polsky, A., Mel, B. W., and Schiller, J. (2004). Computational subunits in thin dendrites of pyramidal cells. Nat. Neurosci. 7, 621-627.
64. Rabinowitch, I., and Segev, I. (2006a). The endurance and selectivity of spatial patterns of long-term potentiation/ depression in dendrites under homeostatic synaptic plasticity. J. Neurosci. 26, 13474-13484.
65. Rabinowitch, I., and Segev, I. (2006b). The interplay between homeostatic synaptic plasticity and functional dendritic compartments. J. Neurophysiol. 96, 276-283.
66. Rabinowitch, I., and Segev, I. (2008). Two opposing plasticity mechanisms pulling a single synapse. Trends Neurosci. 31, 377-383.
67. Rall, W. (1964). Theoretical significance of dendritic trees for neuronal input-output relations. In Neural Theory and Modeling, R. F. Reiss, ed. (Stanford, CA, Stanford University Press), pp. 73-97.
68. Rhodes, P. (2006). The properties and implications of NMDA spikes in neocortical pyramidal cells. J. Neurosci. 26, 6704-6715.
69. Rinzel, J. (1975). Voltage transients in neuronal dendritic trees. Fed. Proc. 34, 1350-1356.
70. Roitman, J. D., Brannon, E. M., and Platt, M. L. (2007). Monotonic coding of numerosity in macaque lateral intraparietal area. PLoS Biol. 5, e208. doi: 10.1371/journal.pbio.0050208.
71. Sawamura, H., Shima, K., and Tanji, J. (2002). Numerical representation for action in the parietal cortex of the monkey. Nature 415, 918-922.
72. Schiller, J., Major, G., Koester, H. J., and Schiller, Y. (2000). NMDA spikes in basal dendrites of cortical pyramidal neurons. Nature 404, 285-289.
73. Segev, I. (1995). Dendritic processing. In The Handbook of Brain Theory and Neuronal Networks, M. Arbib, ed. (Cambridge, MA, The MIT Press), pp. 282-289.
74. Segev, I., Rinzel, J., and Shepherd, G. M. (1995). The Theoretical Foundation of Dendritic Function: Selected Papers of Wilfrid Rall with Commentaries. Cambridge, MA, The MIT Press.
75. Shepherd, G. M. (2003). Information processing in complex dendrites. In From Molecules to Networks: An Introduction to Cellular and Molecular Neuroscience, J. Byrne and J. Roberts, eds (San Diego, CA, Academic Press), pp. 479-497.
76. Shepherd, G., Brayton, R., Miller, J., Segev, I., Rinzel, J., and Rall, W. (1985). Signal enhancement in distal cortical dendrites by means of interactions between active dendritic spines. Proc. Natl. Acad. Sci. U. S. A. 82, 2192-2195.
77. Shu, Y., Hasenstaub, A., and McCormick, D. A. (2003). Turning on and off recurrent balanced cortical activity. Nature 423, 288-293.
78. Silberberg, G., Markram, H. (2007). Disynaptic inhibition between neocortical pyramidal cells mediated by Martinotti cells. Neuron 53, 735-746.
79. Sjöström, P. J., Rancz, E. A., Roth, A., and Häusser, M. (2008). Dendritic excitability and synaptic plasticity. Physiol. Rev. 88, 769-840.
80. Tanaka, J., Horiike, Y., Matsuzaki, M., Miyazaki, T., Ellis-Davies, G. C., and Kasai, H. (2008). Protein synthesis and neurotrophin-dependent structural plasticity of single dendritic spines. Science 319, 1683-1687.
81. Turrigiano, G. G., and Nelson, S. B. (2004). Homeostatic plasticity in the developing nervous system. Nat. Rev. Neurosci. 5, 97-107.
82. Verguts, T., and Fias, W. (2004). Representation of number in animals and humans: a neural model. J. Cogn. Neurosci. 16, 1493-1504.
83. von der Malsburg, C. (1973). Self-organization of orientation sensitive cells in the striate cortex. Kybernetik 14, 85-100.
84. Wang, S. S., and Major, G. (2003). Integrating over time with dendritic wave-fronts. Nat. Neurosci. 6, 906-908.
85. Wang, X.-J. (2001). Synaptic reverberation underlying mnemonic persistent activity. Trends Neurosci. 24, 455-463.
86. Weber, E. (1850). Der Tastsinn und das Gemeingefühl. In Handwörterbuch der Physiologie, Vol. 3, Part 2, R. Wagner, ed. BraunschweigVieweg), pp. 481-588.
87. Wei, D. S., Mei, Y. A., Bagal, A., Kao, J. P., Thompson, S. M., and Tang, C. M. (2001). Compartmentalized and binary behavior of terminal dendrites in hippocampal pyramidal neurons. Science 293, 2272-2275.