Skip to main content
Top
Published in: Journal of Computational Neuroscience 3/2016

01-12-2016

Linking dynamics of the inhibitory network to the input structure

Authors: Maxim Komarov, Maxim Bazhenov

Published in: Journal of Computational Neuroscience | Issue 3/2016

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Networks of inhibitory interneurons are found in many distinct classes of biological systems. Inhibitory interneurons govern the dynamics of principal cells and are likely to be critically involved in the coding of information. In this theoretical study, we describe the dynamics of a generic inhibitory network in terms of low-dimensional, simplified rate models. We study the relationship between the structure of external input applied to the network and the patterns of activity arising in response to that stimulation. We found that even a minimal inhibitory network can generate a great diversity of spatio-temporal patterning including complex bursting regimes with non-trivial ratios of burst firing. Despite the complexity of these dynamics, the network’s response patterns can be predicted from the rankings of the magnitudes of external inputs to the inhibitory neurons. This type of invariant dynamics is robust to noise and stable in densely connected networks with strong inhibitory coupling. Our study predicts that the response dynamics generated by an inhibitory network may provide critical insights about the temporal structure of the sensory input it receives.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
go back to reference Assisi, C., & Bazhenov, M. (2012). Synaptic inhibition controls transient oscillatory synchronization in a model of the insect olfactory system. Frontiers in neuroengineering, 5(7). Assisi, C., & Bazhenov, M. (2012). Synaptic inhibition controls transient oscillatory synchronization in a model of the insect olfactory system. Frontiers in neuroengineering, 5(7).
go back to reference Assisi, C., Stopfer, M., & Bazhenov, M. (2011). Using the structure of inhibitory networks to unravel mechanisms of spatiotemporal patterning. Neuron, 69(2), 373–86.PubMedPubMedCentralCrossRef Assisi, C., Stopfer, M., & Bazhenov, M. (2011). Using the structure of inhibitory networks to unravel mechanisms of spatiotemporal patterning. Neuron, 69(2), 373–86.PubMedPubMedCentralCrossRef
go back to reference Bal, T., & Mccormick, D.A. (1993). Mechanisms of oscillatory activity in guinea-pig nucleus reticular thalami in vitro: a mammalian pacemaker. Journal of Physiology, 468, 669–691.PubMedPubMedCentralCrossRef Bal, T., & Mccormick, D.A. (1993). Mechanisms of oscillatory activity in guinea-pig nucleus reticular thalami in vitro: a mammalian pacemaker. Journal of Physiology, 468, 669–691.PubMedPubMedCentralCrossRef
go back to reference Bazhenov, M., & Stopfer, M. (2010). Forward and back: motifs of inhibition in olfactory processing. Neuron, 67, 357–358.PubMedCrossRef Bazhenov, M., & Stopfer, M. (2010). Forward and back: motifs of inhibition in olfactory processing. Neuron, 67, 357–358.PubMedCrossRef
go back to reference Bazhenov, M., Timofeev, I., Steriade, M., & Sejnowski, T.J. (1999). Self-sustained rhythmic activity in the thalamic reticular nucleus mediated by depolarizing GABAA receptor potentials. Nature neuroscience, 2(2), 168–174.PubMedCrossRef Bazhenov, M., Timofeev, I., Steriade, M., & Sejnowski, T.J. (1999). Self-sustained rhythmic activity in the thalamic reticular nucleus mediated by depolarizing GABAA receptor potentials. Nature neuroscience, 2(2), 168–174.PubMedCrossRef
go back to reference Bazhenov, M., Stopfer, M., Rabinovich, M., Abarbanel, H.D., Sejnowski, T.J., & Laurent, G. (2001). Model of cellular and network mechanisms for odor-evoked temporal patterning in the locust antennal lobe. Neuron, 30(2), 569–81.PubMedPubMedCentralCrossRef Bazhenov, M., Stopfer, M., Rabinovich, M., Abarbanel, H.D., Sejnowski, T.J., & Laurent, G. (2001). Model of cellular and network mechanisms for odor-evoked temporal patterning in the locust antennal lobe. Neuron, 30(2), 569–81.PubMedPubMedCentralCrossRef
go back to reference Beierlein, M., Gibson, J.R., & Connors, B.W. (2003). Two dynamically distinct inhibitory networks in layer 4 of the neocortex. Journal of neurophysiology, 90(2003), 2987–3000.PubMedCrossRef Beierlein, M., Gibson, J.R., & Connors, B.W. (2003). Two dynamically distinct inhibitory networks in layer 4 of the neocortex. Journal of neurophysiology, 90(2003), 2987–3000.PubMedCrossRef
go back to reference Beggs, J.M. (2004). Neuronal Avalanches Are Diverse and Precise Activity Patterns That Are Stable for Many Hours in Cortical Slice Cultures. Journal of Neuroscience, 24(22), 5216–5229.PubMedCrossRef Beggs, J.M. (2004). Neuronal Avalanches Are Diverse and Precise Activity Patterns That Are Stable for Many Hours in Cortical Slice Cultures. Journal of Neuroscience, 24(22), 5216–5229.PubMedCrossRef
go back to reference Beggs, J.M., & Plenz, D. (2003). Neuronal Avalanches in Neocortical Circuits. The Journal of Neuroscience, 23(35), 11167–11177.PubMed Beggs, J.M., & Plenz, D. (2003). Neuronal Avalanches in Neocortical Circuits. The Journal of Neuroscience, 23(35), 11167–11177.PubMed
go back to reference Belykh, I., & Shilnikov, A. (2008). When Weak Inhibition Synchronizes Strongly Desynchronizing Networks of Bursting Neurons. Physical Review Letters, 101(7), 078102.PubMedCrossRef Belykh, I., & Shilnikov, A. (2008). When Weak Inhibition Synchronizes Strongly Desynchronizing Networks of Bursting Neurons. Physical Review Letters, 101(7), 078102.PubMedCrossRef
go back to reference Benda, J., & Herz, A.V.M. (2003). A universal model for spike-frequency adaptation. Neural computation, 15(11), 2523–64.PubMedCrossRef Benda, J., & Herz, A.V.M. (2003). A universal model for spike-frequency adaptation. Neural computation, 15(11), 2523–64.PubMedCrossRef
go back to reference Bonifazi, P., Goldin, M., Picardo, M.A., Jorquera, I., Cattani, A., Bianconi, G., & et al. (2009). GABAergic hub neurons orchestrate synchrony in developing hippocampal network. Science (New York, N.Y.), 326, 1419–1424.CrossRef Bonifazi, P., Goldin, M., Picardo, M.A., Jorquera, I., Cattani, A., Bianconi, G., & et al. (2009). GABAergic hub neurons orchestrate synchrony in developing hippocampal network. Science (New York, N.Y.), 326, 1419–1424.CrossRef
go back to reference Bouyer, J.J., Montaron, M.F., Vahnėe, J M, Albert, M.P., & Rougeul, A. (1987). Anatomical localization of cortical beta rhythms in cat. Neuroscience, 22(3), 863–869.PubMedCrossRef Bouyer, J.J., Montaron, M.F., Vahnėe, J M, Albert, M.P., & Rougeul, A. (1987). Anatomical localization of cortical beta rhythms in cat. Neuroscience, 22(3), 863–869.PubMedCrossRef
go back to reference Buhl, E.H., Tamás, G, & Fisahn, A. (1998). Cholinergic activation and tonic excitation induce persistent gamma oscillations in mouse somatosensory cortex in vitro. The Journal of physiology, 513, 117–126.PubMedPubMedCentralCrossRef Buhl, E.H., Tamás, G, & Fisahn, A. (1998). Cholinergic activation and tonic excitation induce persistent gamma oscillations in mouse somatosensory cortex in vitro. The Journal of physiology, 513, 117–126.PubMedPubMedCentralCrossRef
go back to reference Cinelli, A.R., & Kauer, J.S. (1992). Voltage-sensitive dyes and functional activity in the olfactory pathway. Annual review of neuroscience, 15, 321–351.PubMedCrossRef Cinelli, A.R., & Kauer, J.S. (1992). Voltage-sensitive dyes and functional activity in the olfactory pathway. Annual review of neuroscience, 15, 321–351.PubMedCrossRef
go back to reference Cinelli, A.R., Hamilton, K.A., & Kauer, J.S. (1995). Salamander olfactory bulb neuronal activity observed by video rate, voltage-sensitive dye imaging. III. Spatial and temporal properties of responses evoked by odorant stimulation. Journal of neurophysiology, 73(5), 2053–2071.PubMed Cinelli, A.R., Hamilton, K.A., & Kauer, J.S. (1995). Salamander olfactory bulb neuronal activity observed by video rate, voltage-sensitive dye imaging. III. Spatial and temporal properties of responses evoked by odorant stimulation. Journal of neurophysiology, 73(5), 2053–2071.PubMed
go back to reference Collins, J.J., & bifurcation, Stewart IN Symmetry-breaking (1992). A possible mechanism for 2:1 frequency locking in animal locomotion. J. Math. Biol., 30, 827–838.PubMedCrossRef Collins, J.J., & bifurcation, Stewart IN Symmetry-breaking (1992). A possible mechanism for 2:1 frequency locking in animal locomotion. J. Math. Biol., 30, 827–838.PubMedCrossRef
go back to reference Daun, S., Rubin, J.E., & Rybak, I.A (2009). Control of oscillation periods and phase durations in half-center central pattern generators: A comparative mechanistic analysis. Journal of Computational Neuroscience, 27, 3–36.PubMedPubMedCentralCrossRef Daun, S., Rubin, J.E., & Rybak, I.A (2009). Control of oscillation periods and phase durations in half-center central pattern generators: A comparative mechanistic analysis. Journal of Computational Neuroscience, 27, 3–36.PubMedPubMedCentralCrossRef
go back to reference Diekelmann, S., & Born, J. (2010). The memory function of sleep. Nature reviews Neuroscience, 11(2), 114–126.PubMed Diekelmann, S., & Born, J. (2010). The memory function of sleep. Nature reviews Neuroscience, 11(2), 114–126.PubMed
go back to reference Diesmann, M., Gewaltig, M.O., & Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature, 402(6761), 529–533.PubMedCrossRef Diesmann, M., Gewaltig, M.O., & Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature, 402(6761), 529–533.PubMedCrossRef
go back to reference Ermentrout, B. (1992). Complex dynamics in winner-take-all neural nets with slow inhibition. Neural Networks, 5(1), 415–431.CrossRef Ermentrout, B. (1992). Complex dynamics in winner-take-all neural nets with slow inhibition. Neural Networks, 5(1), 415–431.CrossRef
go back to reference Ermentrout, G.B., & Kopell, N. (1994). Inhibition-Produced Patterning in Chains of Coupled Nonlinear Oscillators. SIAM Journal on Applied Mathematics, 54, 478–507.CrossRef Ermentrout, G.B., & Kopell, N. (1994). Inhibition-Produced Patterning in Chains of Coupled Nonlinear Oscillators. SIAM Journal on Applied Mathematics, 54, 478–507.CrossRef
go back to reference Friedrich, R.W., & Stopfer, M. (2001). Recent dynamics in olfactory population coding. Current Opinion in Neurobiology, 11, 468–474.PubMedCrossRef Friedrich, R.W., & Stopfer, M. (2001). Recent dynamics in olfactory population coding. Current Opinion in Neurobiology, 11, 468–474.PubMedCrossRef
go back to reference Friedrich, R.W., & Laurent, G. (2004). Dynamics of olfactory bulb input and output activity during odor stimulation in zebrafish. Journal of neurophysiology, 91(6), 2658–69.PubMedCrossRef Friedrich, R.W., & Laurent, G. (2004). Dynamics of olfactory bulb input and output activity during odor stimulation in zebrafish. Journal of neurophysiology, 91(6), 2658–69.PubMedCrossRef
go back to reference Foster, D.J., & Ma, W. (2006). Reverse replay of behavioural sequences in hippocampal place cells during the awake state. Nature, 440(7084), 680–683.PubMedCrossRef Foster, D.J., & Ma, W. (2006). Reverse replay of behavioural sequences in hippocampal place cells during the awake state. Nature, 440(7084), 680–683.PubMedCrossRef
go back to reference Gabriel, A., & Eckhorn, R. (2003). A multi-channel correlation method detects traveling γ-waves in monkey visual cortex. Journal of Neuroscience Methods, 131(1-2), 171–184.PubMedCrossRef Gabriel, A., & Eckhorn, R. (2003). A multi-channel correlation method detects traveling γ-waves in monkey visual cortex. Journal of Neuroscience Methods, 131(1-2), 171–184.PubMedCrossRef
go back to reference Grillner, S. (2003). The motor infrastructure: from ion channels to neuronal networks. Nature Reviews Neuroscience, 4(7), 573–586.PubMedCrossRef Grillner, S. (2003). The motor infrastructure: from ion channels to neuronal networks. Nature Reviews Neuroscience, 4(7), 573–586.PubMedCrossRef
go back to reference Golomb, D., & Ermentrout, G.B. (2001). Bistability in pulse propagation in networks of excitatory and inhibitory populations. Physical Review Letters, 86(18), 4179–4182.PubMedCrossRef Golomb, D., & Ermentrout, G.B. (2001). Bistability in pulse propagation in networks of excitatory and inhibitory populations. Physical Review Letters, 86(18), 4179–4182.PubMedCrossRef
go back to reference Golomb, D., Wang, X.J., & Rinzel, J. (1994). Synchronization Properties of Spindle Oscillations in a Thalamic Reticular Nucleus Model. Journal of neurophysiology, 72(3), 1109–1126.PubMed Golomb, D., Wang, X.J., & Rinzel, J. (1994). Synchronization Properties of Spindle Oscillations in a Thalamic Reticular Nucleus Model. Journal of neurophysiology, 72(3), 1109–1126.PubMed
go back to reference Golubitsky, M. (1985). Stewart I Hopf bifurcation in the presence of symmetry Archive for Rational Mechanics and Analysis, (Vol. 87. Golubitsky, M. (1985). Stewart I Hopf bifurcation in the presence of symmetry Archive for Rational Mechanics and Analysis, (Vol. 87.
go back to reference Golubitsky, M., Stewart, I., Buono, P.-L., & Collins, J.J. (1998). A modular network for legged locomotion Physica D, (Vol. 115. Golubitsky, M., Stewart, I., Buono, P.-L., & Collins, J.J. (1998). A modular network for legged locomotion Physica D, (Vol. 115.
go back to reference Hebb, D.O. (1949). The organization of behavior. New York: Wiley. Hebb, D.O. (1949). The organization of behavior. New York: Wiley.
go back to reference Hosler, J.S., Buxton, K.L., & Smith, B.H. (2000). Impairment of olfactory discrimination by blockade of GABA and nitric oxide activity in the honey bee antennal lobes. Behavioral Neuroscience, 114, 514–525.PubMedCrossRef Hosler, J.S., Buxton, K.L., & Smith, B.H. (2000). Impairment of olfactory discrimination by blockade of GABA and nitric oxide activity in the honey bee antennal lobes. Behavioral Neuroscience, 114, 514–525.PubMedCrossRef
go back to reference Ito, I., Bazhenov, M., Ong, R.C.Y., Raman, B., & Stopfer, M. (2009). Frequency Transitions in Odor-Evoked Neural Oscillations. Neuron, 64(5), 692–706.PubMedPubMedCentralCrossRef Ito, I., Bazhenov, M., Ong, R.C.Y., Raman, B., & Stopfer, M. (2009). Frequency Transitions in Odor-Evoked Neural Oscillations. Neuron, 64(5), 692–706.PubMedPubMedCentralCrossRef
go back to reference Jensen, O., Goel, P., Kopell, N., Pohja, M., Hari, R., & Ermentrout, B. (2005). On the human sensorimotor-cortex beta rhythm: Sources and modeling. NeuroImage, 26(2), 347–355.PubMedCrossRef Jensen, O., Goel, P., Kopell, N., Pohja, M., Hari, R., & Ermentrout, B. (2005). On the human sensorimotor-cortex beta rhythm: Sources and modeling. NeuroImage, 26(2), 347–355.PubMedCrossRef
go back to reference Ji, D., & Wilson, M.A. (2007). Coordinated memory replay in the visual cortex and hippocampus during sleep. Nature neuroscience, 10(1), 100–107.PubMedCrossRef Ji, D., & Wilson, M.A. (2007). Coordinated memory replay in the visual cortex and hippocampus during sleep. Nature neuroscience, 10(1), 100–107.PubMedCrossRef
go back to reference Jones, L.M., Fontanini, A., Sadacca, B.F., Miller, P., & Katz, D.B. (2007). Natural stimuli evoke dynamic sequences of states in sensory cortical ensembles. PNAS, 104(47), 18772–7.PubMedPubMedCentralCrossRef Jones, L.M., Fontanini, A., Sadacca, B.F., Miller, P., & Katz, D.B. (2007). Natural stimuli evoke dynamic sequences of states in sensory cortical ensembles. PNAS, 104(47), 18772–7.PubMedPubMedCentralCrossRef
go back to reference Joseph, J., Dunn, F.A., & Stopfer, M. (2012). Spontaneous Olfactory Receptor Neuron Activity Determines Cell Response Properties. The Journal of neuroscience, 32(8), 2900–2910.PubMedPubMedCentralCrossRef Joseph, J., Dunn, F.A., & Stopfer, M. (2012). Spontaneous Olfactory Receptor Neuron Activity Determines Cell Response Properties. The Journal of neuroscience, 32(8), 2900–2910.PubMedPubMedCentralCrossRef
go back to reference Kawaguchi, Y., & Kubota, Y. (1993). Correlation of physiological subgroupings of nonpyramidal cells with parvalbumin- and calbindinD28k-immunoreactive neurons in layer V of rat frontal cortex. Journal of neurophysiology, 70(1), 387–396.PubMed Kawaguchi, Y., & Kubota, Y. (1993). Correlation of physiological subgroupings of nonpyramidal cells with parvalbumin- and calbindinD28k-immunoreactive neurons in layer V of rat frontal cortex. Journal of neurophysiology, 70(1), 387–396.PubMed
go back to reference Kawaguchi, Y., & Kubota, Y. (1997). GABAergic cell subtypes and their synaptic connections in rat frontal cortex. Cerebral Cortex, 7(6), 476–486.PubMedCrossRef Kawaguchi, Y., & Kubota, Y. (1997). GABAergic cell subtypes and their synaptic connections in rat frontal cortex. Cerebral Cortex, 7(6), 476–486.PubMedCrossRef
go back to reference Kawaguchi, Y., & Kubota, Y. (1998). Neurochemical features and synaptic connections of large physiologically-identified GABAergic cells in the rat frontal cortex. Neuroscience, 85(3), 677–701.PubMedCrossRef Kawaguchi, Y., & Kubota, Y. (1998). Neurochemical features and synaptic connections of large physiologically-identified GABAergic cells in the rat frontal cortex. Neuroscience, 85(3), 677–701.PubMedCrossRef
go back to reference Kilpatrick, ZP, & Ermentrout, B (2011). Sparse gamma rhythms arising through clustering in adapting neuronal networks. PLoS Computational Biology, 7(11), e1002281.PubMedPubMedCentralCrossRef Kilpatrick, ZP, & Ermentrout, B (2011). Sparse gamma rhythms arising through clustering in adapting neuronal networks. PLoS Computational Biology, 7(11), e1002281.PubMedPubMedCentralCrossRef
go back to reference Kisvarday, Z.F., Beaulieu, C., & Eysel, U.T. (1993). Network of GABAergic large basket cells in cat visual cortex (area 18): Implication for lateral disinhibition. Journal of Comparative Neurology, 327, 398–415.PubMedCrossRef Kisvarday, Z.F., Beaulieu, C., & Eysel, U.T. (1993). Network of GABAergic large basket cells in cat visual cortex (area 18): Implication for lateral disinhibition. Journal of Comparative Neurology, 327, 398–415.PubMedCrossRef
go back to reference Komarov, M.A., Osipov, G.V., & Suykens, J.A.K. (2009). Sequentially activated groups in neural networks. EPL (Europhysics Letters), 86(6), 60006.CrossRef Komarov, M.A., Osipov, G.V., & Suykens, J.A.K. (2009). Sequentially activated groups in neural networks. EPL (Europhysics Letters), 86(6), 60006.CrossRef
go back to reference Komarov, M.A., Osipov, G.V., Suykens, J.A.K., & Rabinovich, M.I. (2009). Numerical studies of slow rhythms emergence in neural microcircuits: Bifurcations and stability. Chaos, 19, 015107.PubMedCrossRef Komarov, M.A., Osipov, G.V., Suykens, J.A.K., & Rabinovich, M.I. (2009). Numerical studies of slow rhythms emergence in neural microcircuits: Bifurcations and stability. Chaos, 19, 015107.PubMedCrossRef
go back to reference Lam, Y.W., Cohen, L.B., Wachowiak, M., & Zochowski, M.R. (2000). Odors elicit three different oscillations in the turtle olfactory bulb. The Journal of neuroscience : the official journal of the Society for Neuroscience, 20(2), 749–762. Lam, Y.W., Cohen, L.B., Wachowiak, M., & Zochowski, M.R. (2000). Odors elicit three different oscillations in the turtle olfactory bulb. The Journal of neuroscience : the official journal of the Society for Neuroscience, 20(2), 749–762.
go back to reference Laurent, G. (2002). Olfactory network dynamics and the coding of multidimensional signals. Nature reviews Neuroscience, 3(11), 884–95.PubMedCrossRef Laurent, G. (2002). Olfactory network dynamics and the coding of multidimensional signals. Nature reviews Neuroscience, 3(11), 884–95.PubMedCrossRef
go back to reference Laurent, G., & Davidowitz, H. (1994). Encoding of olfactory information with oscillating neural assemblies. Science, 265(5180), 1872–5.PubMedCrossRef Laurent, G., & Davidowitz, H. (1994). Encoding of olfactory information with oscillating neural assemblies. Science, 265(5180), 1872–5.PubMedCrossRef
go back to reference Laurent, G., Wehr, M., & Davidowitz, H. (1996). Temporal Representations of Odors in an Olfactory. The Journal of Neuroscuence, 16(12), 3837–3847. Laurent, G., Wehr, M., & Davidowitz, H. (1996). Temporal Representations of Odors in an Olfactory. The Journal of Neuroscuence, 16(12), 3837–3847.
go back to reference Lee, A.K., & Wilson, M.A. (2002). Memory of sequential experience in the hippocampus during slow wave sleep. Neuron, 36(6), 1183–1194.PubMedCrossRef Lee, A.K., & Wilson, M.A. (2002). Memory of sequential experience in the hippocampus during slow wave sleep. Neuron, 36(6), 1183–1194.PubMedCrossRef
go back to reference Leitch, B., & Laurent, G. (1993). Distribution of GABAergic synaptic terminals on the dendrites of locust spiking local interneurones. J Comp Neurol, 337(3), 461–470.PubMedCrossRef Leitch, B., & Laurent, G. (1993). Distribution of GABAergic synaptic terminals on the dendrites of locust spiking local interneurones. J Comp Neurol, 337(3), 461–470.PubMedCrossRef
go back to reference Leitch, B., & Laurent, G. (1996). GABAergic synapses in the antennal lobe and mushroom body of the locust olfactory system. Journal of Comparative Neurology, 372(4), 487–514.PubMedCrossRef Leitch, B., & Laurent, G. (1996). GABAergic synapses in the antennal lobe and mushroom body of the locust olfactory system. Journal of Comparative Neurology, 372(4), 487–514.PubMedCrossRef
go back to reference Lewis, T.J., & Rinzel, J. (2003). Dynamics of Spiking Neurons Connected by Both Inhibitory and Electrical Coupling. Journal of Computational Neuroscience, 14, 283–309.PubMedCrossRef Lewis, T.J., & Rinzel, J. (2003). Dynamics of Spiking Neurons Connected by Both Inhibitory and Electrical Coupling. Journal of Computational Neuroscience, 14, 283–309.PubMedCrossRef
go back to reference Louie, K., & Wilson, M.A. (2001). Temporally structured replay of awake hippocampal ensemble activity during rapid eye movement sleep. Neuron, 29(1), 145–156.PubMedCrossRef Louie, K., & Wilson, M.A. (2001). Temporally structured replay of awake hippocampal ensemble activity during rapid eye movement sleep. Neuron, 29(1), 145–156.PubMedCrossRef
go back to reference MacLeod, K., Bäcker, A, & Laurent, G. (1998). Who reads temporal information contained across synchronized and oscillatory spike trains Nature, 395(6703), 693–698.PubMedCrossRef MacLeod, K., Bäcker, A, & Laurent, G. (1998). Who reads temporal information contained across synchronized and oscillatory spike trains Nature, 395(6703), 693–698.PubMedCrossRef
go back to reference Marder, E., & Calabrese, R.L. (1996). Principles of rhythmic motor pattern generation. Physiological Reviews, 76(3), 687–717.PubMed Marder, E., & Calabrese, R.L. (1996). Principles of rhythmic motor pattern generation. Physiological Reviews, 76(3), 687–717.PubMed
go back to reference Matveev, V., Bose, A., & Nadim, F. (2007). Capturing the bursting dynamics of a two-cell inhibitory network using a one-dimensional map. Journal of Computational Neuroscience, 23, 169–187.PubMedPubMedCentralCrossRef Matveev, V., Bose, A., & Nadim, F. (2007). Capturing the bursting dynamics of a two-cell inhibitory network using a one-dimensional map. Journal of Computational Neuroscience, 23, 169–187.PubMedPubMedCentralCrossRef
go back to reference Nowotny, T., & Rabinovich, M.I. (2007). Dynamical origin of independent spiking and bursting activity in neural microcircuits. Physical Review Letters, 98(March), 1–4. Nowotny, T., & Rabinovich, M.I. (2007). Dynamical origin of independent spiking and bursting activity in neural microcircuits. Physical Review Letters, 98(March), 1–4.
go back to reference O’Keefe, J., & Dostrovsky, J. (1971). The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. Brain research, 34(1), 171–175.PubMedCrossRef O’Keefe, J., & Dostrovsky, J. (1971). The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. Brain research, 34(1), 171–175.PubMedCrossRef
go back to reference Pinto, D.J., & Ermentrout, G.B. (2001). Spatially Structured Activity in Synaptically Coupled Neuronal Networks: II. Lateral Inhibition and Standing Pulses. SIAM Journal on Applied Mathematics, 62(1), 226–243.CrossRef Pinto, D.J., & Ermentrout, G.B. (2001). Spatially Structured Activity in Synaptically Coupled Neuronal Networks: II. Lateral Inhibition and Standing Pulses. SIAM Journal on Applied Mathematics, 62(1), 226–243.CrossRef
go back to reference Rabinovich, M.I., Huerta, R., Varona, P., & Afraimovich, V.S. (2006). Generation and reshaping of sequences in neural systems. Biological Cybernetics, 95, 519–536.PubMedCrossRef Rabinovich, M.I., Huerta, R., Varona, P., & Afraimovich, V.S. (2006). Generation and reshaping of sequences in neural systems. Biological Cybernetics, 95, 519–536.PubMedCrossRef
go back to reference Rinzel, J., Terman, D., Wang, X., & Ermentrout, B. (1998). Propagating activity patterns in large-scale inhibitory neuronal networks. Science (New York, NY), (Vol. 279. Rinzel, J., Terman, D., Wang, X., & Ermentrout, B. (1998). Propagating activity patterns in large-scale inhibitory neuronal networks. Science (New York, NY), (Vol. 279.
go back to reference Schoppa, N.E. (2006). Synchronization of olfactory bulb mitral cells by precisely timed inhibitory inputs. Neuron, 49, 271–283.PubMedCrossRef Schoppa, N.E. (2006). Synchronization of olfactory bulb mitral cells by precisely timed inhibitory inputs. Neuron, 49, 271–283.PubMedCrossRef
go back to reference Schwabedal, J.T.C., Neiman, A.B., & Shilnikov, A.L. (2014). Robust design of polyrhythmic neural circuits. Physical Review E, 90(2), 022715.CrossRef Schwabedal, J.T.C., Neiman, A.B., & Shilnikov, A.L. (2014). Robust design of polyrhythmic neural circuits. Physical Review E, 90(2), 022715.CrossRef
go back to reference Steriade, M., & Deschenes, M. (1984). The thalamus as a neuronal oscillator. Brain Research Reviews, 8, 1–63.CrossRef Steriade, M., & Deschenes, M. (1984). The thalamus as a neuronal oscillator. Brain Research Reviews, 8, 1–63.CrossRef
go back to reference Steriade, M., Jones, E., & McCormick, D. (1997). Thalamus: organization and function. Oxford: Elsevier Science Ltd. Steriade, M., Jones, E., & McCormick, D. (1997). Thalamus: organization and function. Oxford: Elsevier Science Ltd.
go back to reference Stopfer, M., Bhagavan, S., Smith, B.H., & Laurent, G. (1997). Impaired odour discrimination on desynchronization of odour-encoding neural assemblies. Nature, 390(6655), 70–74.PubMedCrossRef Stopfer, M., Bhagavan, S., Smith, B.H., & Laurent, G. (1997). Impaired odour discrimination on desynchronization of odour-encoding neural assemblies. Nature, 390(6655), 70–74.PubMedCrossRef
go back to reference Terman, D., Kopell, N., & Bose, A. (1998). Dynamics of two mutually coupled slow inhibitory neurons. Physica D: Nonlinear Phenomena, 117, 241–275.CrossRef Terman, D., Kopell, N., & Bose, A. (1998). Dynamics of two mutually coupled slow inhibitory neurons. Physica D: Nonlinear Phenomena, 117, 241–275.CrossRef
go back to reference Traub, R.D. (1982). Simulation of intrinsic bursting in CA3. The Journal of Neuroscuence, 7(5), 1233–1242.CrossRef Traub, R.D. (1982). Simulation of intrinsic bursting in CA3. The Journal of Neuroscuence, 7(5), 1233–1242.CrossRef
go back to reference Treves, A. (1993). Mean-field analysis of neuronal spike dynamics. Network: Computation in Neural Systems, 4, 259–284.CrossRef Treves, A. (1993). Mean-field analysis of neuronal spike dynamics. Network: Computation in Neural Systems, 4, 259–284.CrossRef
go back to reference Ulrich, D., & Huguenard, J.R. (1997). GABA(A)-receptor-mediated rebound burst firing and burst shunting in thalamus. Journal of neurophysiology, 78(3), 1748–1751.PubMed Ulrich, D., & Huguenard, J.R. (1997). GABA(A)-receptor-mediated rebound burst firing and burst shunting in thalamus. Journal of neurophysiology, 78(3), 1748–1751.PubMed
go back to reference Van Vreeswijk, C., Abott, L.F., & Ermentrout, G.B. (1994). When Inhibition not Excitation Synchronizes Neural Firing. Journal of Computational Neuroscience, 1, 313.PubMedCrossRef Van Vreeswijk, C., Abott, L.F., & Ermentrout, G.B. (1994). When Inhibition not Excitation Synchronizes Neural Firing. Journal of Computational Neuroscience, 1, 313.PubMedCrossRef
go back to reference Von Krosigk, M., Bal, T., & McCormick, D.A. (1993). Cellular mechanisms of a synchronized oscillations in the thalamus. Science, 261, 361.PubMedCrossRef Von Krosigk, M., Bal, T., & McCormick, D.A. (1993). Cellular mechanisms of a synchronized oscillations in the thalamus. Science, 261, 361.PubMedCrossRef
go back to reference Wang, X.J., & Rinzel, J. (1992). Alternating and Synchronous Rhythms in Reciprocally Inhibitory Model Neurons. Wang, X.J., & Rinzel, J. (1992). Alternating and Synchronous Rhythms in Reciprocally Inhibitory Model Neurons.
go back to reference Wang, X.J., & Rinzel, J. (1993). Spindle rhythmicity in the reticularis thalami nucleus: synchronization among mutually inhibitory neurons. Neuroscience, 53(4), 899–904.PubMedCrossRef Wang, X.J., & Rinzel, J. (1993). Spindle rhythmicity in the reticularis thalami nucleus: synchronization among mutually inhibitory neurons. Neuroscience, 53(4), 899–904.PubMedCrossRef
go back to reference Wang, X.J., & Buzsáki, G. (1996). Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. The Journal of neuroscience : the official journal of the Society for Neuroscience, 16(20), 6402–6413. Wang, X.J., & Buzsáki, G. (1996). Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. The Journal of neuroscience : the official journal of the Society for Neuroscience, 16(20), 6402–6413.
go back to reference Wang, Y., Toledo-Rodriguez, M., Gupta, A., Wu, C., Silderberg, G., Luo, J., & Markram, H. (2004). Anatomical, physiological and molecular properties of Martinotti cells in the somatosensory cortex of the juvenile rat. Journal of Physiology, 561(1), 65–90.PubMedPubMedCentralCrossRef Wang, Y., Toledo-Rodriguez, M., Gupta, A., Wu, C., Silderberg, G., Luo, J., & Markram, H. (2004). Anatomical, physiological and molecular properties of Martinotti cells in the somatosensory cortex of the juvenile rat. Journal of Physiology, 561(1), 65–90.PubMedPubMedCentralCrossRef
go back to reference Warren, B., & Kloppenburg, P. (2014). Rapid and Slow Chemical Synaptic Interactions of Cholinergic Projection Neurons and GABAergic Local Interneurons in the Insect Antennal Lobe. Journal of Neuroscience, 34 (39), 13039–13046.PubMedCrossRef Warren, B., & Kloppenburg, P. (2014). Rapid and Slow Chemical Synaptic Interactions of Cholinergic Projection Neurons and GABAergic Local Interneurons in the Insect Antennal Lobe. Journal of Neuroscience, 34 (39), 13039–13046.PubMedCrossRef
go back to reference Wehr, M., & Laurent, G. (1996). Odors encoding by temporal sequences of firing in oscillating neural assemblies. Nature, 384, 162–166.PubMedCrossRef Wehr, M., & Laurent, G. (1996). Odors encoding by temporal sequences of firing in oscillating neural assemblies. Nature, 384, 162–166.PubMedCrossRef
go back to reference Wojcik, J., Schwabedal, J., Clewley, R., & Shilnikov, A.L. (2014). Key bifurcations of bursting polyrhythms in 3-cell central pattern generators. PloS one, 9(4), e92918.PubMedPubMedCentralCrossRef Wojcik, J., Schwabedal, J., Clewley, R., & Shilnikov, A.L. (2014). Key bifurcations of bursting polyrhythms in 3-cell central pattern generators. PloS one, 9(4), e92918.PubMedPubMedCentralCrossRef
go back to reference Yoshimura, Y., & Callaway, E.M. (2005). Fine-scale specificity of cortical networks depends on inhibitory cell type and connectivity. Nature neuroscience, 8(11), 1552–1559.PubMedCrossRef Yoshimura, Y., & Callaway, E.M. (2005). Fine-scale specificity of cortical networks depends on inhibitory cell type and connectivity. Nature neuroscience, 8(11), 1552–1559.PubMedCrossRef
Metadata
Title
Linking dynamics of the inhibitory network to the input structure
Authors
Maxim Komarov
Maxim Bazhenov
Publication date
01-12-2016
Publisher
Springer US
Published in
Journal of Computational Neuroscience / Issue 3/2016
Print ISSN: 0929-5313
Electronic ISSN: 1573-6873
DOI
https://doi.org/10.1007/s10827-016-0622-8

Other articles of this Issue 3/2016

Journal of Computational Neuroscience 3/2016 Go to the issue

Premium Partner