Review Article | Published:

The log-dynamic brain: how skewed distributions affect network operations

Nature Reviews Neuroscience volume 15, pages 264278 (2014) | Download Citation

Abstract

We often assume that the variables of functional and structural brain parameters — such as synaptic weights, the firing rates of individual neurons, the synchronous discharge of neural populations, the number of synaptic contacts between neurons and the size of dendritic boutons — have a bell-shaped distribution. However, at many physiological and anatomical levels in the brain, the distribution of numerous parameters is in fact strongly skewed with a heavy tail, suggesting that skewed (typically lognormal) distributions are fundamental to structural and functional brain organization. This insight not only has implications for how we should collect and analyse data, it may also help us to understand how the different levels of skewed distributions — from synapses to cognition — are related to each other.

Key points

  • At many physiological and anatomical levels in the brain, the distribution of numerous parameters is strongly skewed with a heavy tail and typically follows a lognormal distribution.

  • The power and frequency relationship of brain oscillations is typically expressed in a log scale.

  • Network synchrony, measured as a fraction of spiking neurons in a given time window, shows lognormal distribution in all brain states.

  • Firing rates, spike bursts and synaptic weights follow a lognormal distribution. Importantly, these parameters remain correlated across brain states, environments and situations.

  • The log-dynamic patterns of networks may be supported by the lognormal distribution of corticocortical connections strengths and axon diameters.

  • A preconfigured, strongly connected minority of fast-firing neurons form the backbone of brain connectivity and serve as an ever-ready, fast-acting system. However, full performance of the brain also depends on the activity of very large numbers of weakly connected and slow-firing majority of neurons.

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References

  1. 1.

    & Emergence of scaling in random networks. Science 286, 509–512 (1999).

  2. 2.

    Networks of the Brain (MIT Press, 2010).

  3. 3.

    , & Lognormal distributions across the sciences: keys and clues. Bioscience 51, 341–352 (2001).

  4. 4.

    De Pulsa Resorptione Auditu et Tactu. Annotationes Anatomicae et Physiologicae (Koehler, 1834) (in German).

  5. 5.

    Elemente der Psychophysik (Breitkopf und Härtel, 1860) (in German).

  6. 6.

    & Representation of a perceptual decision in developing oculomotor commands. Nature 404, 390–394 (2000).

  7. 7.

    & Decision-making and Weber's law: a neurophysiological model. Eur. J. Neurosci. 24, 901–916 (2006).

  8. 8.

    Selective Studies and the Principle of Relative Frequency in Language (Harvard Univ. Press, 1932).

  9. 9.

    , , & Lognormal distributions of user post lengths in Internet discussions — a consequence of the Weber–Fechner law? EPJ Data Sci. 2, 2 (2013).

  10. 10.

    The Number Sense (Oxford Univ. Press, 1999).

  11. 11.

    , & The origin of extracellular fields and currents — EEG, ECoG, LFP and spikes. Nature Rev. Neurosci. 13, 407–420 (2012).

  12. 12.

    Rhythms of the Brain (Oxford Univ. Press, 2006).

  13. 13.

    , , & Spatial spectral analysis of human electrocorticograms including the alpha and gamma bands. J. Neurosci. Methods 95, 111–121 (2000).

  14. 14.

    et al. Gamma (40–100 Hz) oscillation in the hippocampus of the behaving rat. J. Neurosci. 15, 47–60 (1995).

  15. 15.

    & Low-frequency neuronal oscillations as instruments of sensory selection. Trends Neurosci. 32, 9–18 (2009).

  16. 16.

    & Brain rhythms and neural syntax: implications for efficient coding of cognitive content and neuropsychiatric disease. Dialogues Clin. Neurosci. 14, 345–367 (2012).

  17. 17.

    , & Self-organized criticality and the development of EEG phase reset. Hum. Brain Mapp. 30, 553–574 (2009).

  18. 18.

    , & Cellular bases of hippocampal EEG in the behaving rat. Brain Res. 287, 139–171 (1983).

  19. 19.

    & Preconfigured, skewed distribution of firing rates in the hippocampus and entorhinal cortex. Cell Rep. 4, 1010–1021 (2013).

  20. 20.

    & Theta oscillations decrease spike synchrony in the hippocampus and entorhinal cortex. Phil. Trans. R. Soc. B 369, 20120530 (2013).

  21. 21.

    , , , & Firing rates of hippocampal neurons are preserved during subsequent sleep episodes and modified by novel awake experience. Proc. Natl Acad. Sci. USA 98, 9386–9390 (2001).

  22. 22.

    , , , & Firing rate modulation: a simple statistical view of memory trace reactivation. Neural Netw. 18, 1280–1291 (2005).

  23. 23.

    et al. Variability in neuronal activity in primate cortex during working memory tasks. Neuroscience 146, 1082–1108 (2007).

  24. 24.

    , & Sparse representation of sounds in the unanesthetized auditory cortex. PLoS Biol. 6, e16 (2008).

  25. 25.

    , , & Neural activity in barrel cortex underlying vibrissa-based object localization in mice. Neuron 67, 1048–1061 (2010).

  26. 26.

    et al. Spatiotemporal dynamics of neocortical excitation and inhibition during human sleep. Proc. Natl Acad. Sci. USA 109, 1731–1736 (2012).

  27. 27.

    Large-scale recording of neuronal ensembles. Nature Neurosci. 7, 446–451 (2004).

  28. 28.

    & Dynamics of the hippocampal ensemble code for space. Science 261, 1055–1058 (1993).

  29. 29.

    et al. Characterization of neocortical principal cells and interneurons by network interactions and extracellular features. J. Neurophysiol. 92, 600–608 (2004).

  30. 30.

    , , & Behavior-dependent short-term assembly dynamics in the medial prefrontal cortex. Nature Neurosci. 11, 823–833 (2008).

  31. 31.

    et al. Entrainment of neocortical neurons and gamma oscillations by the hippocampal theta rhythm. Neuron 60, 683–697 (2008).

  32. 32.

    , , & Theta oscillations provide temporal windows for local circuit computation in the entorhinal–hippocampal loop. Neuron 64, 267–280 (2009).

  33. 33.

    et al. A toolbox of Cre-dependent optogenetic transgenic mice for light-induced activation and silencing. Nature Neurosci. 15, 793–802 (2012).

  34. 34.

    et al. Control of timing, rate and bursts of hippocampal place cells by dendritic and somatic inhibition. Nature Neurosci. 15, 769–775 (2012).

  35. 35.

    , , , & Accuracy of tetrode spike separation as determined by simultaneous intracellular and extracellular measurements. J. Neurophysiol. 84, 401–414 (2000).

  36. 36.

    & Experimental evidence for sparse firing in the neocortex. Trends Neurosci. 35, 345–355 (2012).

  37. 37.

    , , , & Oscillatory coupling of hippocampal pyramidal cells and interneurons in the behaving rat. J. Neurosci. 19, 274–287 (1999).

  38. 38.

    , , & Relationships between sleep spindles and theta oscillations in the hippocampus. J. Neurosci. 34, 662–674 (2014).

  39. 39.

    et al. Independent codes for spatial and episodic memory in hippocampal neuronal ensembles. Science 309, 619–623 (2005).

  40. 40.

    & The effects of changes in the environment on the spatial firing of hippocampal complex-spike cells. J. Neurosci. 7, 1951–1968 (1987).

  41. 41.

    , & The contributions of position, direction, and velocity to single unit activity in the hippocampus of freely-moving rats. Exp. Brain Res. 52, 41–49 (1983).

  42. 42.

    , , & Environment-specific expression of the immediate-early gene Arc in hippocampal neuronal ensembles. Nature Neurosci. 2, 1120–1124 (1999).

  43. 43.

    , & Place representation within hippocampal networks is modified by long-term potentiation. Neuron 39, 843–853 (2003).

  44. 44.

    & Experience-dependent structural synaptic plasticity in the mammalian brain. Nature Rev. Neurosci. 10, 647–658 (2009).

  45. 45.

    & Preplay of future place cell sequences by hippocampal cellular assemblies. Nature 469, 397–401 (2011).

  46. 46.

    , , , & Sequential structure of neocortical spontaneous activity in vivo. Proc. Natl Acad. Sci. USA 104, 347–352 (2007).

  47. 47.

    , & Spontaneous events outline the realm of possible sensory responses in neocortical populations. Neuron 62, 413–425 (2009).

  48. 48.

    et al. Formation and reverberation of sequential neural activity patterns evoked by sensory stimulation are enhanced during cortical desynchronization. Neuron 79, 555–566 (2013).

  49. 49.

    & Differences in hippocampal neuronal population responses to modifications of an environmental context: evidence for distinct, yet complementary, functions of CA3 and CA1 ensembles. J. Neurosci. 24, 6489–6496 (2004).

  50. 50.

    , , , & Distinct ensemble codes in hippocampal areas CA3 and CA1. Science 305, 1295–1298 (2004).

  51. 51.

    , , & Activity dynamics and behavioral correlates of CA3 and CA1 hippocampal pyramidal neurons. Hippocampus 22, 1659–1680 (2012).

  52. 52.

    & Reactivation of hippocampal ensemble memories during sleep. Science 265, 676–679 (1994).

  53. 53.

    , , , & Long-term plasticity in hippocampal place-cell representation of environmental geometry. Nature 416, 90–94 (2002).

  54. 54.

    , , & Experience-dependent compartmentalized dendritic plasticity in rat hippocampal CA1 pyramidal neurons. Nature Neurosci. 12, 1485–1487 (2009).

  55. 55.

    & Genetic analysis of learning behavior-induced structural plasticity. Hippocampus 10, 605–609 (2000).

  56. 56.

    et al. Long-term dynamics of CA1 hippocampal place codes. Nature Neurosci. 16, 264–266 (2013).

  57. 57.

    , , & Spread of dendritic excitation in layer 2/3 pyramidal neurons in rat barrel cortex in vivo. Nature Neurosci. 2, 65–73 (1999).

  58. 58.

    , & Compartmentalized dendritic plasticity and input feature storage in neurons. Nature 452, 436–441 (2008).

  59. 59.

    , & Expression of c-fos protein in brain: metabolic mapping at the cellular level. Science 240, 1328–1331 (1988).

  60. 60.

    et al. An embedded subnetwork of highly active neurons in the neocortex. Neuron 68, 1043–1050 (2010).

  61. 61.

    , , & Hippocampal CA1 pyramidal cells form functionally distinct sublayers. Nature Neurosci. 14, 1174–1181 (2011).

  62. 62.

    , & Adult neurogenesis: integrating theories and separating functions. Trends Cogn. Sci. 14, 325–337 (2010).

  63. 63.

    & Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274, 1724–1726 (1996).

  64. 64.

    & Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cereb. Cortex 7, 237–252 (1997).

  65. 65.

    & Spike-driven synaptic dynamics generating working memory states. Neural Comput. 15, 565–596 (2003).

  66. 66.

    & A balanced memory network. PLoS Comput. Biol. 3, 1679–1700 (2007).

  67. 67.

    , , , , & On the distribution of firing rates in networks of cortical neurons. J. Neurosci. 31, 16217–16226 (2011).

  68. 68.

    et al. Interpyramid spike transmission stabilizes the sparseness of recurrent network activity. Cereb. Cortex 23, 293–304 (2013).

  69. 69.

    , & Postsynaptic contribution to long-term potentiation revealed by the analysis of miniature synaptic currents. Nature 355, 50–55 (1992).

  70. 70.

    , & The time course and amplitude of EPSPs evoked at synapses between pairs of CA3/CA1 neurons in the hippocampal slice. J. Neurosci. 10, 826–836 (1990).

  71. 71.

    , , & Synaptic connections between layer 4 spiny neurone-layer 2/3 pyramidal cell pairs in juvenile rat barrel cortex: physiology and anatomy of interlaminar signalling within a cortical column. J. Physiol. 538, 803–822 (2002).

  72. 72.

    , , , & Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol. 3, e68 (2005).

  73. 73.

    , , & Ultrastructure of dendritic spines: correlation between synaptic and spine morphologies. Front. Neurosci. 1, 131–143 (2007).

  74. 74.

    , , & The excitatory neuronal network of the C2 barrel column in mouse primary somatosensory cortex. Neuron 61, 301–316 (2009).

  75. 75.

    , & Heterogeneous reallocation of presynaptic efficacy in recurrent excitatory circuits adapting to inactivity. Nature Neurosci. 15, 250–257 (2012).

  76. 76.

    , & Correlated connectivity and the distribution of firing rates in the neocortex. J. Neurosci. 29, 3685–3694 (2009).

  77. 77.

    , , & Reliability and state dependence of pyramidal cell-interneuron synapses in the hippocampus: an ensemble approach in the behaving rat. Neuron 21, 179–189 (1998).

  78. 78.

    , , & Reactivation of the same synapses during spontaneous up states and sensory stimuli. Cell Rep. 4, 31–39 (2013).

  79. 79.

    , , & Internal dynamics determine the cortical response to thalamic stimulation. Neuron 48, 811–823 (2005).

  80. 80.

    , , , & Spontaneously emerging cortical representations of visual attributes. Nature 425, 954–956 (2003).

  81. 81.

    , & Reverberation of recent visual experience in spontaneous cortical waves. Neuron 60, 321–327 (2008).

  82. 82.

    , & Equilibrium properties of temporally asymmetric Hebbian plasticity. Phys. Rev. Lett. 86, 364–367 (2001).

  83. 83.

    & Stability versus neuronal specialization for STDP: long-tail weight distributions solve the dilemma. PLoS ONE. 6, e25339 (2011).

  84. 84.

    et al. Dendritic spine geometry is critical for AMPA receptor expression in hippocampal CA1 pyramidal neurons. Nature Neurosci. 4, 1086–1092 (2001).

  85. 85.

    , , , & Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. J. Physiol. 500, 409–440 (1997).

  86. 86.

    , , & Three-dimensional reconstruction of the axon arbor of a CA3 pyramidal cell recorded and filled in vivo. Brain Struct. Funct. 212, 75–83 (2007).

  87. 87.

    & Quantal analysis and synaptic anatomy—integrating two views of hippocampal plasticity. Trends Neurosci. 16, 141–147 (1993).

  88. 88.

    & Dendritic spines of CA 1 pyramidal cells in the rat hippocampus: serial electron microscopy with reference to their biophysical characteristics. J. Neurosci. 9, 2982–2997 (1989).

  89. 89.

    , & Synaptic strength of individual spines correlates with bound Ca2+-calmodulin-dependent kinase II. J. Neurosci. 27, 14007–14011 (2007).

  90. 90.

    , & Dendritic spine dynamics. Annu. Rev. Physiol. 71, 261–282 (2009).

  91. 91.

    , & Multiplicative dynamics underlie the emergence of the log-normal distribution of spine sizes in the neocortex in vivo. J. Neurosci. 31, 9481–9488 (2011).

  92. 92.

    , , , & Principles of long-term dynamics of dendritic spines. J. Neurosci. 28, 13592–13608 (2008).

  93. 93.

    , & The size of motor units during post-natal development of rat lumbrical muscle. J. Physiol. 297, 463–478 (1979).

  94. 94.

    & Interneurons of the hippocampus. Hippocampus 6, 347–470 (1996).

  95. 95.

    & Neuronal diversity and temporal dynamics: the unity of hippocampal circuit operations. Science 321, 53–57 (2008).

  96. 96.

    , , & On the origin of the extracellular action potential waveform: a modeling study. J. Neurophysiol. 95, 3113–3128 (2006).

  97. 97.

    & Functional maps within a single neuron. J. Neurophysiol. 108, 2343–2351 (2012).

  98. 98.

    , , , & Temporal interaction between single spikes and complex spike bursts in hippocampal pyramidal cells. Neuron 32, 141–149 (2001).

  99. 99.

    , , & Distribution of bursting neurons in the CA1 region and the subiculum of the rat hippocampus. J. Comp. Neurol. 506, 535–547 (2008).

  100. 100.

    et al. A weighted and directed interareal connectivity matrix for macaque cerebral cortex. Cereb. Cortex 24, 17–36 (2014).

  101. 101.

    , & Network analysis of corticocortical connections reveals ventral and dorsal processing streams in mouse visual cortex. J. Neurosci. 32, 4386–4399 (2012).

  102. 102.

    et al. A mesoscale connectome of the mouse brain. Nature (in the press).

  103. 103.

    et al. A predictive network model of cerebral cortical connectivity based on a distance rule. Neuron 80, 184–197 (2013).

  104. 104.

    , , & Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci. 27, 186–193 (2004).

  105. 105.

    , & A computational perspective on the neural basis of multisensory spatial representations. Nature Rev. Neurosci. 3, 741–747 (2002).

  106. 106.

    Conduction velocity and diameter of nerve fibers. Am. J. Physiol. 127, 131–139 (1939).

  107. 107.

    The electro-saltatory transmission of the nerve impulse and the effect of narcosis upon the nerve fiber. Am. J. Physiol. 127, 211–227 (1939).

  108. 108.

    in Time and the Brain (ed. Miller, R.) 151–179 (Harwood Academic, 2000).

  109. 109.

    et al. Functional trade-offs in white matter axonal scaling. J. Neurosci. 28, 4047–4056 (2008).

  110. 110.

    , & Long distance communication in the human brain: timing constraints for inter-hemispheric synchrony and the origin of brain lateralization. Biol. Res. 36, 89–99 (2003).

  111. 111.

    , & The diameter of cortical axons depends both on the area of origin and target. Cereb. Cortex (2013).

  112. 112.

    , , , & How the optic nerve allocates space, energy capacity, and information. J. Neurosci. 29, 7917–7928 (2009).

  113. 113.

    & Discharges of pyramidal tract and other motor cortical neurones during locomotion in the cat. J. Physiol. 346, 471–495 (1984).

  114. 114.

    et al. Age-related changes in Arc transcription and DNA methylation within the hippocampus. Neurobiol. Aging 32, 2198–2210 (2011).

  115. 115.

    & Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177 (2003).

  116. 116.

    & Rich-club organization of the human connectome. J. Neurosci. 31, 15775–15786 (2011). This work discusses the importance of strong connections among 'hubs' in the brain. Hubs are connected not only to a large number of other nodes but even more so to each other; they thus form a rich-club organization in which hub members share the bulk of the critical information.

  117. 117.

    & Consciousness and complexity. Science 282, 1846–1851 (1998).

  118. 118.

    , & A neuronal model of a global workspace in effortful cognitive tasks. Proc. Natl Acad. Sci. USA 95, 14529–14534 (1998).

  119. 119.

    & Path integration and cognitive mapping in a continuous attractor neural network model. J. Neurosci. 17, 5900–5920 (1997).

  120. 120.

    Neural syntax: cell assemblies, synapsembles, and readers. Neuron 68, 362–385 (2010).

  121. 121.

    , , & Internally generated cell assembly sequences in the rat hippocampus. Science 321, 1322–1327 (2008).

  122. 122.

    , , , & Invariant visual representation by single neurons in the human brain. Nature 435, 1102–1107 (2005).

  123. 123.

    & Olfactory pattern classification by discrete neuronal network states. Nature 465, 47–52 (2010).

  124. 124.

    et al. Learning to control a brain-machine interface for reaching and grasping by primates. PLoS Biol. 1, E42 (2003).

  125. 125.

    et al. Neuronal ensemble control of prosthetic devices by a human with tetraplegia. Nature 442, 164–171 (2006).

  126. 126.

    , & Optimal spike-based communication in excitable networks with strong-sparse and weak-dense links. Sci. Rep. 2, 485 (2012).

  127. 127.

    Globally networked risks and how to respond. Nature 497, 51–59 (2013).

  128. 128.

    Ultra Low Power Bioelectronics: Fundamentals, Biomedical Applications, and Bio-inspired Systems (Cambridge Univ. Press, 2010).

  129. 129.

    , , & Synthetic analog computation in living cells. Nature 497, 619–623 (2013).

  130. 130.

    Feed-forward inhibition in the hippocampal formation. Prog. Neurobiol. 22, 131–153 (1984).

  131. 131.

    & in Single Neuron Computation (eds McKenna, T. M., Davis, J. L. & Zornetzer, S. F.) 315–345 (Academic, 1992).

  132. 132.

    & Auditory spatial receptive fields created by multiplication. Science 292, 249–252 (2001).

  133. 133.

    , , & Multiplicative computation in a visual neuron sensitive to looming. Nature 420, 320–324 (2002). Along with reference 131, this work is among the first to show that neural circuits can use multiplication and division computation.

  134. 134.

    Neuronal arithmetic. Nature Rev. Neurosci. 11, 474–489 (2010).

  135. 135.

    , , & Division and subtraction by distinct cortical inhibitory networks in vivo. Nature 488, 343–348 (2012).

  136. 136.

    et al. Activation of specific interneurons improves V1 feature selectivity and visual perception. Nature 488, 379–383 (2012).

  137. 137.

    I of the Vortex: From Neurons to Self (Bradford Books, 2002).

  138. 138.

    , , & Linking spontaneous activity of single cortical neurons and the underlying functional architecture. Science 286, 1943–1946 (1999).

  139. 139.

    , , & Spontaneous cortical activity reveals hallmarks of an optimal internal model of the environment. Science 331, 83–87 (2011). This work suggests that neural activity in the visual system is the result of the interaction between an internal model of the environment (the prior) and the input from the environment (the posterior), and that the interaction follows a Bayesian rule.

  140. 140.

    Neural networks and physical systems with emergent collective computational abilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982).

  141. 141.

    et al. Dynamical coding of sensory information with competitive networks. J. Physiol. Paris 94, 465–471 (2000).

  142. 142.

    , , , & Categorical representation of facial expressions in the infant brain. Infancy 14, 346–362 (2009).

  143. 143.

    , , & Development of the hippocampal cognitive map in preweanling rats. Science 328, 1573–1576 (2010).

  144. 144.

    et al. Development of the spatial representation system in the rat. Science 328, 1576–1580 (2010).

  145. 145.

    & Psychophysical and physiological evidence for viewer-centered object representations in the primate. Cereb. Cortex 5, 270–288 (1995).

  146. 146.

    et al. Early motor activity drives spindle bursts in the developing somatosensory cortex. Nature 432, 758–761 (2004).

  147. 147.

    , & Methodological considerations on the use of template matching to study long-lasting memory trace replay. J. Neurosci. 26, 10727–10742 (2006).

  148. 148.

    & Neuronal oscillations in cortical networks. Science 304, 1926–1929 (2004).

  149. 149.

    The logarithm in biology. 1. Mechanisms generating the log-normal distribution exactly. J. Theor. Biol. 12, 276–290 (1966).

  150. 150.

    A brief history of generative models for power law and lognormal distributions. Internet Math. 1, 226–251 (2003). An excellent discussion about the similarities and differences between lognormal, power law and double Pareto distributions and how these distributions may be linked naturally despite different appearances. It also demonstrates that ideas mature slowly over time and that nearly all discoveries have a history.

  151. 151.

    , , & Communication between neocortex and hippocampus during sleep in rodents. Proc. Natl Acad. Sci. USA 100, 2065–2069 (2003).

  152. 152.

    , , & in Advances in Neural Information Processing Systems Vol. 5 (eds Hanson, S. J., Cowan, J. D. & Giles, C. L.) 1030–1037 (Morgan Kaufmann, 1993).

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Acknowledgements

The authors thank A. Berardino, S. Burke, T. Fukai, A. Grosmark, K. Harris, Y. Ikegaya, M. Kahana, C. Koch, J. Magee, A. Maurer, A. Peyrache, A. Reyes, E. Schomburg, L. Sjulson, S. Song, R. Tsien and S. Wang for comments and discussions. The authors are supported by the US National Institutes of Health (NS034994, MH54671 and NS074015 (to G.B.)), National Science Foundation (0542013), the J.D. McDonnell Foundation, Human Frontiers Science Program (grant RGP0032/2011 (to G.B.)), Uehara Memorial Foundation (K.M.), Astellas Foundation for Research on Metabolic Disorders (K.M.) and the Japan Society of Promotion for Sciences (K.M.).

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Affiliations

  1. New York University Neuroscience Institute, New York University Langone Medical Center, New York, New York 10016, USA.

    • György Buzsáki
    •  & Kenji Mizuseki
  2. Center for Neural Science, New York University, New York, New York 10003, USA.

    • György Buzsáki
  3. Allen Institute for Brain Science, 551 North 34th Street, Seattle, Washington 98103, USA.

    • Kenji Mizuseki

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The authors declare no competing financial interests.

Corresponding author

Correspondence to György Buzsáki.

Glossary

Spike transfer

The fraction of spikes in the postsynaptic neuron relative to the number of spikes in the presynaptic, driver neuron (or neurons). It is an indirect way of measuring synaptic strength.

Power laws

A term to describe a relationship between two variables, where one varies as a power of the other. The indication of a power law is a distribution of values on a straight line on a double log plot. The right tail of the lognormal distribution often follows a power law distribution.

Scale-free properties

Properties that characterize networks with a degree distribution that follows a power law, characterized by a heavy tail ('Pareto tail').

Cross-frequency phase–amplitude coupling

This is perhaps the most prominent 'law' underlying the hierarchy of the system of brain oscillators. The phase of the slower oscillation modulates the power of the faster rhythm (or rhythms).

Decibel

A logarithmic unit used to express the ratio between two values of a variable. It is often used to describe gain or attenuation: for example, the ratio of input and output.

Sharp-wave ripples

Patterns of activity in the hippocampus, consisting of a sharp wave reflecting the strong depolarization of the apical dendrites of pyramidal cells and a short-lived, fast oscillation ('ripple') as a result of the interaction between bursting pyramidal cells and perisomatic interneurons.

Theta oscillations

A prominent 4–10 Hz collective rhythm of the hippocampus. Other brain regions can also generate oscillations in this band.

Remap

This term refers to the observation that place cell representations can abruptly change.

Immediate-early gene

A gene that is rapidly and transiently activated in response to relevant stimuli.

Fos

A prominent immediate-early gene in the brain; it is often used as an indicator of neuronal activity.

Synaptic weights

A measure of the strength of the synapse, which determines the amplitude of the postsynaptic neuron's response to a presynaptic spike.

Up states

The active phases of the slow oscillation. Intracellularly, an up state corresponds to latching the membrane potential to a more depolarized, near-spiking threshold value.

Spike-timing-dependent plasticity

(STDP). A plasticity-inducing paradigm in which the relative timing of spikes between the pre- and postsynaptic neurons determines the direction and magnitude of the change in synaptic strength.

Wiring economy

The idea that connections among multiple brain regions and neurons are arranged to reduce energy cost and volume demand.

Feedforward inhibition

Excitatory afferents to the various domains of pyramidal cells are matched by parallel sets of inhibitory interneurons to filter, attenuate or route excitation. It can perform division operation.

Redundancy

This term refers to the observation that multiple replicas of input representations exist.

Degeneracy

In biology, this term refers to the idea that different solutions evolved to carry out the same functions.

Preconfigured brain

This term refers to an idea that connections and dynamics in the brain are largely self-generated and that experience matches the pre-existing patterns to the external world, thereby giving rise to 'meaning'.

Attractors

Hypothetical effectors that move elements of a system to more stable states over time. Inhibition-based brain rhythms often show properties of an attractor.

Internal models

A term derived from the hypothesis that the perceived world is not simply a reflection of the objective reality but depends on previous experience and brain state. In this hypothesis, internal models reflect the source of our individual views.

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https://doi.org/10.1038/nrn3687

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