Randomly-connected networks of integrate-and-fire (IF) neurons are known to display asynchronous irregular (AI) activity states, which resemble the discharge activity recorded in the cerebral cortex of awake animals. However, it is not clear whether such activity states are specific to simple IF models, or if they also exist in networks where neurons are endowed with complex intrinsic properties similar to electrophysiological measurements. Here, we investigate the occurrence of AI states in networks of nonlinear IF neurons, such as the adaptive exponential IF (Brette-Gerstner-Izhikevich) model. This model can display intrinsic properties such as low-threshold spike (LTS), regular spiking (RS) or fast-spiking (FS). We successively investigate the oscillatory and AI dynamics of thalamic, cortical and thalamocortical networks using such models. AI states can be found in each case, sometimes with surprisingly small network size of the order of a few tens of neurons. We show that the presence of LTS neurons in cortex or in thalamus, explains the robust emergence of AI states for relatively small network sizes. Finally, we investigate the role of spike-frequency adaptation (SFA). In cortical networks with strong SFA in RS cells, the AI state is transient, but when SFA is reduced, AI states can be self-sustained for long times. In thalamocortical networks, AI states are found when the cortex is itself in an AI state, but with strong SFA, the thalamocortical network displays Up and Down state transitions, similar to intracellular recordings during slow-wave sleep or anesthesia. Self-sustained Up and Down states could also be generated by two-layer cortical networks with LTS cells. These models suggest that intrinsic properties such as adaptation and low-threshold bursting activity are crucial for the genesis and control of AI states in thalamocortical networks.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Avendaño, C., Rausell, E., Perez-Aguilar, D., & Isorna, S. (1988). Organization of the association cortical afferent connections of area 5: A retrograde tracer study in the cat. Journal of Comparative Neurology, 278, 1–33.
Avendaño, C., Rausell, E., & Reinoso-Suarez, F. (1985). Thalamic projections to areas 5a and 5b of the parietal cortex in the cat: A retrograde horseradish peroxidase study. Journal of Neuroscience, 5, 1446–1470.
Baranyi, A., Szente, M. B., & Woody, C. D. (1993a). Electrophysiological characterization of different types of neurons recorded in vivo in the motor cortex of the cat. I. Patterns of firing activity and synaptic responses. Journal of Neurophysiology, 69, 1850–1864.
Baranyi, A., Szente, M. B., & Woody, C. D. (1993b). Electrophysiological characterization of different types of neurons recorded in vivo in the motor cortex of the cat. II. Membrane parameters, action potentials, current-induced voltage responses and electrotonic structures. Journal of Neurophysiology, 69, 1865–1879.
Binzegger, T., Douglas, R. J., & Martin, K. A. C. (2004). A quantitative map of the circuit of cat primary visual cortex. Journal of Neuroscience, 24, 8441–8453.
Borg-Graham, L. J., Monier, C., & Frégnac, Y. (1998). Visual input evokes transient and strong shunting inhibition in visual cortical neurons. Nature, 393, 369–373.
Bourassa, J., & Deschênes, M. (1995). Corticothalamic projections from the primary visual cortex in rats: A single fiber study using biocytin as an anterograde tracer. Neuroscience, 66, 253–263.
Braitenberg, V., & Schüz, A. (1998). Cortex: Statistics and geometry of neuronal connectivity (2nd ed.). Berlin: Springer.
Brette, R., & Gerstner, W. (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of Neurophysiology, 94, 3637–3642.
Brunel, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of Computational Neuroscience, 8, 183–208.
Cessac, B. (2008). A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics. Journal of Mathematical Biology, 56, 311–345.
Cessac, B., & Viéville, T. (2009). On dynamics of integrate-and-fire neural networks with conductance based synapses. Frontiers of Computer Neuroscience, 3, 1.
Compte, A., Sanchez-Vives, M. V., McCormick, D. A., & Wang, X. J. (2003). Cellular and network mechanisms of slow oscillatory activity (<1 Hz) and wave propagations in a cortical network model. Journal of Neurophysiology, 89, 2707–2725.
Connors, B. W., & Gutnick, M. J. (1990). Intrinsic firing patterns of diverse neocortical neurons. Trends in Neurosciences, 13, 99–104.
Contreras, D., & Steriade, M. (1995). Cellular basis of EEG slow rhythms: A study of dynamic corticothalamic relationships. Journal of Neuroscience, 15, 604–622.
Contreras, D., Timofeev, I., & Steriade, M. (1996). Mechanisms of long lasting hyperpolarizations underlying slow sleep oscillations in cat corticothalamic networks. Journal of Physiology, 494, 251–264.
Cossart, R., Aronov, D., & Yuste, R. (2003). Attractor dynamics of network UP states in the neocortex. Nature, 423, 283–238.
Crutchfield, J. P., & Kaneko, K. (1988). Are attractors relevant to turbulence? Physical Review Letters, 60, 2715–2718.
de la Peña, E., & Geijo-Barrientos, E. (1996). Laminar organization, morphology and physiological properties of pyramidal neurons that have the low-threshold calcium current in the guinea-pig frontal cortex. Journal of Neuroscience, 16, 5301–5311.
Destexhe, A. (2007). High-conductance state. Scholarpedia, 2(11), 1341. http://www.scholarpedia.org/article/High-Conductance_State
Destexhe, A., Contreras, D., & Steriade, M. (1998). Mechanisms underlying the synchronizing action of corticothalamic feedback through inhibition of thalamic relay cells. Journal of Neurophysiology, 79, 999–1016.
Destexhe, A., Contreras, D., & Steriade, M. (2001). LTS cells in cerebral cortex and their role in generating spike-and-wave oscillations. Neurocomputing, 38, 555–563.
Destexhe, A., & Paré, D. (1999). Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. Journal of Neurophysiology, 81, 1531–1547.
Destexhe, A., Rudolph, M., & Paré, D. (2003). The high-conductance state of neocortical neurons in vivo. Nature Reviews Neuroscience, 4, 739–751.
Destexhe, A., & Sejnowski, T. J. (2003). Interactions between membrane conductances underlying thalamocortical slow-wave oscillations. Physiological Reviews, 83, 1401–1453.
El Boustani, S., & Destexhe, A. (2009). A master equation formalism for macroscopic modeling of asynchronous irregular activity states. Neural Computation, 21, 46–100.
El Boustani, S., Pospischil, M., Rudolph-Lilith, M., & Destexhe, A. (2007). Activated cortical states: Experiments, analyses and models. Journal of Physiology (Paris), 101, 99–109.
FitzGibbon, T., Tevah, L. V., & Jervie-Sefton, A. (1995). Connections between the reticular nucleus of the thalamus and pulvinar-lateralis posterior complex: A WGA-HRP study. Journal of Comparative Neurology, 363, 489–504.
Fourcaud-Trocme, N., Hansel, D., van Vreeswijk, C., & Brunel, N. (2003). How spike generation mechanisms determine the neuronal response to fluctuating inputs. Journal of Neuroscience, 23, 11628–11640.
Freund, T. F., Martin, K. A., Soltesz, I., Somogyi, P., & Whitteridge, D. (1989). Arborisation pattern and postsynaptic targets of physiologically identified thalamocortical afferents in striate cortex of the macaque monkey. Journal of Comparative Neurology, 289, 315–336.
Grenier, F., Timofeev, I., & Steriade, M. (1998). Leading role of thalamic over cortical neurons during postinhibitory rebound excitation. Proceedings of the National Academy of Sciences of the United States of America, 95, 13929–13934.
Hines, M. L. & Carnevale, N. T. (1997). The Neuron simulation environment. Neural Computation, 9, 1179–1209.
Izhikevich, E. M. (2004). Which model to use for cortical spiking neurons? IEEE Transactions on Neural Networks, 15, 1063–1070.
Jones, E. G. (1985). The thalamus. New York: Plenum.
Kim, U., Sanches-Vives, M. V., & McCormick, D. A. (1997). Functional dynamics of GABAergic inhibition in the thalamus. Science, 278, 130–134.
Kumar, A., Schrader, S., Aertsen, A., & Rotter, S. (2008). The high-conductance state of cortical networks. Neural Computation, 20, 1–43.
Landry, P., & Deschênes, M. (1981). Intracortical arborizations and receptive fields of identified ventrobasal thalamocortical afferents to the primary somatic sensory cortex in the cat. Journal of Comparative Neurology, 199, 345–371.
Lee, A. K., Manns, I. D., Sakmann, B., & Brecht, M. (2006). Whole-cell recordings in freely moving rats. Neuron, 51, 399–407.
Llinás, R. R. (1988). The intrinsic electrophysiological properties of mammalian neurons: A new insight into CNS function. Science, 242, 1654–1664.
Matsumura, M., Cope, T., & Fetz, E. E. (1988). Sustained excitatory synaptic input to motor cortex neurons in awake animals revealed by intracellular recording of membrane potentials. Experimental Brain Research, 70, 463–469.
McCormick, D. A. (1992). Neurotransmitter actions in the thalamus and cerebral cortex and their role in neuromodulation of thalamocortical activity. Progress in Neurobiology, 39, 337–388.
Minderhoud, J. M. (1971). An anatomical study of the efferent connections of the thalamic reticular nucleus. Experimental Brain Research, 112, 435–446.
Paré, D., Shink, E., Gaudreau, H., Destexhe, A., & Lang, E. J. (1998). Impact of spontaneous synaptic activity on the resting properties of cat neocortical neurons in vivo. Journal of Neurophysiology, 79, 1450–1460.
Parga, N., & Abbott, L. F. (2007). Network model of spontaneous activity exhibiting synchronous transitions between up and down states. Frontiers in Neuroscience, 1, 57–66.
Plenz, D., & Aertsen, A. (1996). Neural dynamics in cortex-striatum co-cultures II—spatiotemporal characteristics of neuronal activity. Neuroscience, 70, 893–924.
Pospischil, M., Toledo-Rodriguez, M., Monier, C., Piwkowska, Z., Bal, T., Frégnac, Y., et al. (2008). Minimal Hodgkin-Huxley type models for different classes of cortical and thalamic neurons. Biological Cybernetics, 99, 427–441.
Rausell, E., & Jones, E. G. (1995). Extent of intracortical arborization of thalamocortical axons as a determinant of representational plasticity in monkey somatic sensory cortex. Journal of Neuroscience, 15, 4270–4288.
Robertson, R. T., & Cunningham, T. J. (1981). Organization of corticothalamic projections from parietal cortex in cat. Journal of Comparative Neurology, 199, 569–585.
Rudolph, M., Pelletier, J.-G., Paré, D., & Destexhe, A. (2005). Characterization of synaptic conductances and integrative properties during electrically-induced EEG-activated states in neocortical neurons in vivo. Journal of Neurophysiology, 94, 2805–2821.
Rudolph, M., Pospischil, M., Timofeev, I., & Destexhe, A. (2007). Inhibition determines membrane potential dynamics and controls action potential generation in awake and sleeping cat cortex. Journal of Neuroscience, 27, 5280–5290.
Sanchez-Vives, M. V., & McCormick, D. A. (2000). Cellular and network mechanisms of rhythmic recurrent activity in neocortex. Nature Neuroscience, 10, 1027–1034.
Sherman, S. M., & Guillery, R. W. (2001). Exploring the thalamus. New York: Academic.
Smith, G. D., Cox, C. L., Sherman, M. & Rinzel, J. (2000). Fourier analysis of sinusoidally driven thalamocortical relay neurons and a minimal integrate-and-fire-or-burst model. Journal of Neurophysiology, 83, 588–610.
Steriade, M. (2003). Neuronal substrates of sleep and epilepsy. Cambridge: Cambridge University Press.
Steriade, M., Amzica, F., & Nunez, A. (1993a). Cholinergic and noradrenergic modulation of the slow (~0.3 Hz) oscillation in neocortical cells. Journal of Neurophysiology, 70, 1384–1400.
Steriade, M., Deschênes, M., Domich, L., & Mulle, C. (1985). Abolition of spindle oscillations in thalamic neurons disconnected from nucleus reticularis thalami. Journal of Neurophysiology, 54, 1473–1497.
Steriade, M., Nunez, A., & Amzica, F. (1993b). Intracellular analysis of relations between the slow (< 1 Hz) neocortical oscillation and other sleep rhythms of the electroencephalogram. Journal of Neuroscience, 13, 3266–3283.
Steriade, M., Timofeev, I., & Grenier, F. (2001). Natural waking and sleep states: A view from inside neocortical neurons. Journal of Neurophysiology, 85, 1969–1985.
Tél, T., & Lai, Y.-C. (2008). Chaotic transients in spatially extended systems. Physics Reports, 460, 245–275.
Thomson, A. M., & Bannister, A. P. (2003). Interlaminar connections in the neocortex. Cerebral Cortex, 13, 5–14.
Timofeev, I., Grenier, F., Bazhenov, M., Sejnowski, T. J., & Steriade, M. (2000). Origin of slow cortical oscillations in deafferented cortical slabs. Cerebral Cortex, 10, 1185–1199.
Updyke, B. V. (1981). Projections from visual areas of the middle suprasylvian sulcus onto the lateral posterior complex and adjacent thalamic nuclei in cat. Journal of Comparative Neurology, 201, 477–506.
Vogels, T. P., & Abbott, L. F. (2005). Signal propagation and logic gating in networks of integrate-and-fire neurons. Journal of Neuroscience, 25, 10786–10795.
von Krosigk, M., Bal, T., & McCormick, D. A. (1993). Cellular mechanisms of a synchronized oscillation in the thalamus. Science, 261, 361–364.
White, E. L. (1986). Termination of thalamic afferents in the cerebral cortex. In E. G. Jones & A. Peters (Eds.), Cerebral cortex (Vol. 5, pp. 271–289). New York: Plenum.
White, E. L., & Hersch, S. M. (1982). A quantitative study of thalamocortical and other synapses involving the apical dendrites of corticothalamic cells in mouse SmI cortex. Journal of Neurocytology, 11, 137–157.
Xiang, Z., Huguenard, J. R., & Prince, D. A. (1998). Cholinergic switching within neocortical inhibitory networks. Science, 281, 985–988.
Zillmer, R., Livi, R., Politi, A., & Torcini, A. (2006). Desynchronization in diluted neural networks. Physical Review E, 74, 036203.
Thanks to Sami El Boustani for comments on the manuscript. Research supported by the Centre National de la Recherche Scientifique (CNRS, France), Agence Nationale de la Recherche (ANR, France) and the Future and Emerging Technologies program (FET, European Union; FACETS project). Additional information is available at http://cns.iaf.cnrs-gif.fr.
Action Editor: Barry Richmond
About this article
Cite this article
Destexhe, A. Self-sustained asynchronous irregular states and Up–Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons. J Comput Neurosci 27, 493 (2009). https://doi.org/10.1007/s10827-009-0164-4
- Computational models
- Cerebral cortex
- Thalamocortical system
- Intrinsic neuronal properties
- Network models