Skip to main content
SpringerLink
Log in
Book cover

Hippocampal Microcircuits pp 423–457Cite as

Gamma and Theta Rhythms in Biophysical Models of Hippocampal Circuits

  • Chapter

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI,volume 5))

Abstract

The neural circuits of the hippocampus are extremely complex, with many classes of interneurons whose contributions to network dynamics and function are still unknown. Nevertheless, reduced models can provide insight into aspects of the dynamics and associated function. In this chapter, we discuss models at a variety of levels of complexity, all simple enough to probe the reasons for the behavior of the model. The chapter focuses on the main rhythms displayed by the hippocampus, the gamma (30–90 Hz) and theta (4–12 Hz) rhythms. We concentrate on modeling in vitro experiments, but with an eye toward possible in vivo implications.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   219.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Further Reading

  • Acker, C. D., Kopell, N., and White, J. A. 2003. Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics. J Comput Neurosci, 15, 71–90.

    Article  PubMed  Google Scholar 

  • Amaral, D. G., and Witter, M. P. 1989. The three-dimensional organization of the hippocampal formation: a review of anatomical data. Neuroscience, 31(3), 571–591.

    Article  CAS  PubMed  Google Scholar 

  • Andersen, P., Bliss, T. V., Lomo, T., Olsen, L. I., and Skrede, K. K. 1969. Lamellar organization of hippocampal excitatory pathways. Acta Physiol Scand, 76(1), 4A–5A.

    CAS  PubMed  Google Scholar 

  • Andersen, P., Soleng, A. F., and Raastad, M. 2000. The hippocampal lamella hypothesis revisited. Brain Res, 886(1–2), 165–171.

    Article  CAS  PubMed  Google Scholar 

  • Bartos, M., Vida, I., Frotscher, M., Geiger, J. R., and Jonas, P. 2001. Rapid signaling at inhibitory synapses in a dentate gyrus interneuron network. J Neurosci, 21(8), 2687–98.

    CAS  PubMed  Google Scholar 

  • Bartos, M., Vida, I., Frotscher, M., Meyer, A., Monyer, H., Geiger, J. P. R., and Jonas, P. 2002. Fast synaptic inhibition promotes synchronized gamma oscillations in hippocampal interneuron networks. Proc Natl Acad Sci USA, 99(20), 13222–13227.

    Article  CAS  PubMed  Google Scholar 

  • Bathellier, B., Carleton, A., and Gerstner, W. 2008. Gamma oscillations in a nonlinear regime: a minimal model approach using heterogeneous integrate-and-fire networks. Neural Comp, 20(12), 2973–3002.

    Article  Google Scholar 

  • Börgers, C., and Kopell, N. 2003. Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity. Neural Comp, 15(3), 509–539.

    Article  Google Scholar 

  • Börgers, C., and Kopell, N. 2005. Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons. Neural Comp, 17(3), 557–608.

    Article  Google Scholar 

  • Börgers, C., and Kopell, N. 2008. Gamma oscillations and stimulus selection. Neural Comp, 20, 383–414.

    Article  Google Scholar 

  • Börgers, C., Epstein, S., and Kopell, N. 2005. Background gamma rhythmicity and attention in cortical local circuits: a computational study. Proc Natl Acad Sci USA, 102(19), 7002–7007.

    Article  PubMed  Google Scholar 

  • Börgers, C., Epstein, S., and Kopell, N. 2008. Gamma oscillations mediate stimulus competition and attentional selection in a cortical network model. Proc Natl Acad Sci USA, 105(46),18023–8.

    Article  PubMed  Google Scholar 

  • Buhl, E. H., Cobb, S. R., Halasy, K., and Somogyi, P. 1995. Properties of unitary IPSPs evoked by anatomically identified basket cells in the rat hippocampus. Eur J Neurosci, 7(9), 1989–2004.

    Article  CAS  PubMed  Google Scholar 

  • Canolty, R. T., Edwards, E., Dalal, S. S., Soltani, M., Nagarajan, S. S., Kirsch, H. E., Berger, M. S., Barbaro, N. M., and Knight, R. T. 2006. High gamma power is phase-locked to theta oscillations in human neocortex. Science, 313, 1626–1628.

    Article  CAS  PubMed  Google Scholar 

  • Chapman, C. A., and Lacaille, J. C. 1999. Cholinergic induction of theta-frequency oscillations in hippocampal inhibitory interneurons and pacing of pyramidal cell firing. J Neurosci, 19, 8637–8645.

    CAS  PubMed  Google Scholar 

  • Crook, S. M., Ermentrout, G. B., and Bower, J. M. 1998. Spike frequency adaptation affects the synchronization properties of networks of cortical oscillators. Neural Comp, 10(4), 837–854.

    Article  CAS  Google Scholar 

  • Cunningham, M. O., Whittington, M. A., Bibbig, A., Roopun, A., LeBeau, F. E. N., Vogt, A., Monyer, H., Buhl, E. H., and Traub, R. D. 2004. A role for fast rhythmic bursting neurons in cortical gamma oscillations in vitro. Proc Natl Acad Sci USA, 101(18), 7152–7157.

    Article  CAS  PubMed  Google Scholar 

  • Dickson, C. T., Magistretti, J., Shalinsky, M. H., Fransen, E., Hasselmo, M. E., and Alonso, A. 2000. Properties and role of I(h) in the pacing of subthreshold oscillations in entorhinal cortex layer II neurons. J Neurophysiol, 83(5), 2562–2579.

    CAS  PubMed  Google Scholar 

  • Diener, F. 1985a. Propriétés asymptotiques des fleuves. C R Acad Sci Paris, 302, 55–58.

    Google Scholar 

  • Diener, M. 1985b. Détermination et existence des fleuves en dimension 2. C R Acad Sci Paris, 301, 899–902.

    Google Scholar 

  • Dorval, A. D., Christini, D. J., and White, J. A. 2001. Real-time linux dynamic clamp: a fast and flexible way to construct virtual ion channels in living cells. Ann Biomed Eng, 29(10), 897–907.

    Article  CAS  PubMed  Google Scholar 

  • Dragoi, G., and Buzsáki, G. 2006. Temporal encoding of place sequences by hippocampal cell assemblies. Neuron, 50, 145–157.

    Article  CAS  PubMed  Google Scholar 

  • Dugladze, T., Vida, I., Tort, A. B., Gross, A., Otahal, J., Heinemann, U., Kopell, N. J., and Gloveli, T. 2007. Impaired hippocampal rhythmogenesis in a mouse model of mesial temporal lobe epilepsy. Proc Natl Acad Sci USA, 104(44), 17530–17535.

    Article  CAS  PubMed  Google Scholar 

  • Ermentrout, G. B. 1996. Type I membranes, phase resetting curves, and synchrony. Neural Comp, 8, 879–1001.

    Article  Google Scholar 

  • Ermentrout, G. B., and Kopell, N. 1998. Fine structure of neural spiking and synchronization in the presence of conduction delay. Proc Natl Acad Sci USA, 95, 1259–1264.

    Article  CAS  PubMed  Google Scholar 

  • Ermentrout, B., Pascal, M., and Gutkin, B. 2001. The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators. Neural Comp, 13, 1285–1310.

    Article  CAS  Google Scholar 

  • Fisahn, A., Pike, F. G., Buhl, E. H., and Paulsen, O. 1998. Cholinergic induction of network oscillations at 40 Hz in the hippocampus in vitro. Nature, 394(6689), 186–189.

    Article  CAS  PubMed  Google Scholar 

  • Galán, R. F., Ermentrout, G. B., and Urban, N. N. 2005. Efficient estimation of phase-resetting curves in real neurons and its significance for neural-network modeling. Phys Rev Lett, 94(15), 158101.

    Article  PubMed  Google Scholar 

  • Gerstner, W., van Hemmen, J. L., and Cowen, J. 1996. What matters in neuronal locking? Neural Comp, 8, 1653–1676.

    Article  CAS  Google Scholar 

  • Gillies, M. J., Traub, R. D., LeBeau, F. E. N., Davies, C. H., Gloveli, T., Buhl, E. H., and Whittington, M. A. 2002. A model of atropine-resistant theta oscillations in rat hippocampal area CA1. J Physiol, 543(Pt 3), 779–793.

    Article  CAS  PubMed  Google Scholar 

  • Gloveli, T., Dugladze, T., Saha, S., Monyer, H., Heinemann, U., Traub, R. D., Whittington, M. A., and Buhl, E. H. 2005a. Differential involvement of oriens/pyramidale interneurones in hippocampal network oscillations in vitro. J Physiol, 562(Pt 1), 131–147.

    CAS  Google Scholar 

  • Gloveli, T., Dugladze, T., Rotstein, H. G., Traub, R. D., Monyer, H., Heinemann, U., Whittington, M. A., and Kopell, N. J. 2005b. Orthogonal arrangement of rhythm-generating microcircuits in the hippocampus. Proc Natl Acad Sci USA, 102(37), 13295–13300.

    Article  CAS  Google Scholar 

  • Goldin, M., Epsztein, J., Jorquera, I., Represa, A., Ben-Ari, Y., Crépel, V., and Cossart, R. 2007. Synaptic kainate receptors tune oriens-lacunosum moleculare interneurons to operate at theta frequency. J Neurosci, 27(36), 9560–9572.

    Article  CAS  PubMed  Google Scholar 

  • Golomb, D., and Hansel, D. 2000. The number of synaptic inputs and the synchrony of large sparse neuronal networks. Neural Comp, 12, 1095–1139.

    Article  CAS  Google Scholar 

  • Gray, C. M. 1999. The temporal correlation hypothesis of visual feature integration: still alive and well. Neuron, 24(1), 31–47.

    Article  CAS  PubMed  Google Scholar 

  • Gutkin, B. S., Ermentrout, G. B., and Reyes, A. D. 2005. Phase-response curves give the responses of neurons to transient inputs. J Neurophysiol, 94, 1623–1635.

    Article  PubMed  Google Scholar 

  • Haas, J. S., and White, J. A. 2002. Frequency selectivity of layer II stellate cells in the medial entorhinal cortex. J Neurophysiol, 88(5), 2422–2429.

    Article  PubMed  Google Scholar 

  • Hamzei-Sichani, F., Kamasawa, N., Janssen, W. G. M., Yasumura, T., Davidson, K. G. V., Hof, P. R., Wearne, S. L., Stewart, M. G., Young, S. R., Whittington, M. A., Rash, J. E., and Traub, R. D. 2007. Gap junctions on hippocampal mossy fiber axons demonstrated by thin-section electron microscopy and freeze-fracture replica immunogold labeling. Proc Natl Acad Sci USA, 104(30), 12548–12553.

    Article  PubMed  Google Scholar 

  • Harris, K. D., Csicsvari, J., Hirase, H., Dragoi, G., and Buzsaki, G. 2003. Organization of cell assemblies in the hippocampus. Nature, 424(6948), 552–556.

    Article  CAS  PubMed  Google Scholar 

  • Hebb, D. O. 1949. The Organization of Behavior: A Neuropsychological Theory. New York: Wiley.

    Google Scholar 

  • Hines, M. L., and Carnevale, N. T. 1997. The NEURON simulation environment. Neural Comp, 9(6), 1179–1209.

    Article  CAS  Google Scholar 

  • Hu, H., Vervaeke, K., and Storm, J. F. 2002. Two forms of electrical resonance at theta frequencies, generated by M-current, h-current and persistent Na+ current in rat hippocampal pyramidal cells. J Physiol, 545(Pt 3), 783–805.

    Article  CAS  PubMed  Google Scholar 

  • Itskov, V., Pastalkova, E., Mizuseki, K., Buzsaki, G., and Harris, K. D. 2008. Theta-mediated dynamics of spatial information in hippocampus. J Neurosci, 28, 5959–5964.

    Article  CAS  PubMed  Google Scholar 

  • Katona, I., Acsády, L., and Freund, T. F. 1999. Postsynaptic targets of somatostain-immunoreactive interneurons in the rat hippocampus. Neuroscience 88(1), 37–55.

    Article  CAS  PubMed  Google Scholar 

  • Kay, L. M. 2003. Two species of gamma oscillations in the olfactory bulb: dependence on behavioral state and synaptic interactions. J Integr Neurosci, 2(1), 31–44.

    Article  PubMed  Google Scholar 

  • Klausberger, T., Magill, P. J., Márton, L. F., Roberts, J. D. B., Cobden, P. M., Buzsáki, G., and Somogyi, P. 2003. Brain-state- and cell-type-specific firing of hippocampal interneurons in vivo. Nature, 421, 844–848.

    Article  CAS  PubMed  Google Scholar 

  • Kopell, N., and Ermentrout, G. B. 2002. Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators. In Handbook on Dynamical Systems: Toward Applications. Ed. B. Fiedler, Vol. 2, Elsevier, Amsterdam, 3–54.

    Google Scholar 

  • Kopell, N., and Ermentrout, B. 2004. Chemical and electrical synapses perform complementary roles in the synchronization of interneuronal networks. Proc Natl Acad Sci USA, 101(43), 15482–15487.

    Article  CAS  PubMed  Google Scholar 

  • Kopell, N. 2005. Does it have to be this complicated? Focus on ‘Single-column thalamocortical network model exhibiting gamma oscillations, spindles, and epileptogenic bursts’. J Neurophysiol, 93(4), 1829–1830.

    Article  PubMed  Google Scholar 

  • Lawrence, J. J., Saraga, F., Churchill, J. F., Statland, J. M., Travis, K. E., Skinner, F. K., and McBain, C. J. 2006. Somatodendritic Kv7/KCNQ/M channels control interspike interval in hippocampal interneurons. J Neurosci, 26(47), 12325–12338.

    Article  CAS  PubMed  Google Scholar 

  • Lewis, T. J., and Rinzel, J. 2000. Self-organized synchronous oscillations in a network of excitable cells coupled by gap junctions. Network Comput Neural Syst, 11, 299–320.

    Article  CAS  Google Scholar 

  • Lewis, T. J., and Rinzel, J. 2001. Topological target patterns and population oscillations in a network with random gap junctional coupling. Neurocomputing, 763–768.

    Google Scholar 

  • Middleton, S., Jalics, J., Kispersky, T., Lebeau, F. E. N., Roopun, A. K., Kopell, N. J., Whittington, M. A., and Cunningham, M. O. 2008. NMDA receptor-dependent switching between different gamma rhythm-generating microcircuits in entorhinal cortex. Proc Natl Acad Sci USA, 105(47), 18572–18577.

    Article  CAS  PubMed  Google Scholar 

  • Munro, E. C. 2008. The axonal plexus: a description of the behavior of a network of axons connected by gap junctions. Ph.D. thesis, Tufts University.

    Google Scholar 

  • Netoff, T. I., Acker, C. D., Bettencourt, J. C., and White, J. A. 2005a. Beyond two-cell networks: experimental measurement of neuronal responses to multiple synaptic inputs. J Comput Neurosci, 18(3), 287–295.

    Article  Google Scholar 

  • Netoff, T. I., Banks, M. I., Dorval, A. D., Acker, C. D., Haas, J. S., Kopell, N., and White, J. A. 2005b. Synchronization in hybrid neuronal networks of the hippocampal formation. J Neurophysiol, 93(3), 1197–1208.

    Article  Google Scholar 

  • Olufsen, M., Whittington, M., Camperi, M., and Kopell, N. 2003. New functions for the gamma rhythm: population tuning and preprocessing for the beta rhythm. J Comput Neurosci, 14,33–54.

    Article  PubMed  Google Scholar 

  • Oprisan, S. A., Prinz, A. A., and Canavier, C. C. 2004. Phase resetting and phase locking in hybrid circuits of one model and one biological neuron. Biophys J, 87, 2283–2298.

    Article  CAS  PubMed  Google Scholar 

  • Orban, G., Kiss, T., and Erdi, P. 2006. Intrinsic and synaptic mechanisms determining the timing of neuron population activity during hippocampal theta oscillation. J Neurophysiol, 96(6),2889–2904.

    Article  PubMed  Google Scholar 

  • Oren, I., Nissen, W., Kullmann, D. M., Somogyi, P., and Lamsa, K. P. 2009. Role of ionotropic glutamate receptors in long-term potentiation in rat hippocampal CA1 oriens-lacunosum moleculare interneurons. J Neurosci, 29(4), 939–950.

    Article  CAS  PubMed  Google Scholar 

  • Pastalkova, E., Itskov, V., Amarasingham, A., and Buzsáki, G. 2008. Internally generated cell assembly sequences in the rat hippocampus. Science, 321, 1322–1327.

    Article  CAS  PubMed  Google Scholar 

  • Pervouchine, D. D., Netoff, T. I., Rotstein, H. G., White, J. A., Cunningham, M. O., Whittington, M. A., and Kopell, N. J. 2006. Low-dimensional maps encoding dynamics in entorhinal cortex and hippocampus. Neural Comp, 18(11), 2617–2650.

    Article  Google Scholar 

  • Reinker, S., Li, Y.-X., and Kuske, R. 2006. Noise-induced coherence and network oscillations in a reduced bursting model. Bull Math Biol, 68(6), 1401–1427.

    Article  PubMed  Google Scholar 

  • Rotstein, H. G., Pervouchine, D. D., Acker, C. D., Gillies, M. J., White, J. A., Buhl, E. H., Whittington, M. A., and Kopell, N. 2005. Slow and fast inhibition and an H-current interact to create a theta rhythm in a model of CA1 interneuron network. J Neurophysiol, 94(2), 1509–1518.

    Article  PubMed  Google Scholar 

  • Rotstein, H. G., Oppermann, T., White, J. A., and Kopell, N. 2006. The dynamic structure underlying subthreshold oscillatory activity and the onset of spikes in a model of medial entorhinal cortex stellate cells. J Comput Neurosci, 21(3), 271–292.

    Article  PubMed  Google Scholar 

  • Saraga, F., Wu, C. P., Zhang, L., and Skinner, F. K. 2003. Active dendrites and spike propagation in multi-compartment models of oriens-lacunosum/moleculare hippocampal interneurons. J Physiol, 552(3), 502–509.

    Article  Google Scholar 

  • Senior, T. J., Huxter, J. R., Allen, K., O’Neill, J., and Csicsvari, J. 2008. Gamma oscillatory firing reveals distinct populations of pyramidal cells in the CA1 region of the hippocampus. J Neurosci, 28(9), 2274–2286.

    Article  CAS  PubMed  Google Scholar 

  • Serenevy, A. 2007. Dynamic mechanisms in networks of interneurons with periodic drives. Ph.D. thesis, Boston University.

    Google Scholar 

  • Sharp, A. A., O’Neil, M. B., Abbott, L. F., and Marder, E. 1993. Dynamic clamp: computer-generated conductances in real neurons. J Neurophysiol, 69(3), 992–995.

    CAS  PubMed  Google Scholar 

  • Singer, W., and Gray, C. M. 1995. Visual feature integration and the temporal correlation hypothesis. Annu Rev Neurosci, 18, 555–586.

    Article  CAS  PubMed  Google Scholar 

  • Tort, A. B. L., Rotstein, H. G., Dugladze, T., Gloveli, T., and Kopell, N. J. 2007. On the formation of gamma-coherent cell assemblies by oriens lacunosum-moleculare interneurons in the hippocampus. Proc Natl Acad Sci USA, 104(33), 13490–13495.

    Article  CAS  PubMed  Google Scholar 

  • Tort, A. B. L., Kramer, M. A., Thorn, C., Gibson, D. J., Kubota, Y., Graybiel, A. M., and Kopell, N. 2008. Dynamic cross-frequency couplings of local field potential oscillations in rat striatum and hippocampus during performance of a T-maze task. Proc Natl Acad Sci USA, 105(51), 20517–20522.

    Article  CAS  PubMed  Google Scholar 

  • Traub, R. D., and Miles, R. 1991. Neuronal Networks of the Hippocampus. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  • Traub, R. D., Jefferys, J. G. R., and Whittington, M. 1997. Simulation of gamma rhythms in networks of interneurons and pyramidal cells. J Comput Neurosci, 4, 141–150.

    Article  CAS  PubMed  Google Scholar 

  • Traub, R. D., Bibbig, A., Fisahn, A., LeBeau, F. E. N., Whittington, M. A., and Buhl, E. H. 2000. A model of gamma-frequency network oscillations induced in the rat CA3 region by carbachol in vitro. Eur J Neurosci, 12, 4093–4106.

    Article  CAS  PubMed  Google Scholar 

  • Traub, R. D., Kopell, N., Bibbig, A., Buhl, E. H., Lebeau, F. E. N., and Whittington, M. A. 2001. Gap junctions between interneuron dendrites can enhance long-range synchrony of gamma oscillations. J Neurosci, 21, 9478–9486.

    CAS  PubMed  Google Scholar 

  • Traub, R. D., Bibbig, A., LeBeau, F. E. N., Buhl, E. H., and Whittington, M. A. 2004. Cellular mechanisms of neuronal population oscillations in the hippocampus in vitro. Annu Rev Neurosci, 27, 247–278.

    Article  CAS  PubMed  Google Scholar 

  • Traub, R. D., Contreras, D., Cunningham, M. O., Murray, H., LeBeau, F. E. N., Roopun, A., Bibbig, A., Wilent, W. B., Higley, M. J., and Whittington, M. A. 2005. Single-column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts. J Neurophysiol, 93(4), 2194–2232.

    Article  PubMed  Google Scholar 

  • Tukker, J., Fuentealba, P., Hartwich, K., Somogyi, P., and Klausberger, T. 2007. Cell type-specific tuning of hippocampal interneuron firing during gamma oscillations in vivo. J Neurosci, 27(31), 8184–8189.

    Article  CAS  PubMed  Google Scholar 

  • van Vreeswijk, C., Abbott, L. F., and Ermentrout, G. B. 1994. When inhibition not excitation synchronizes neural firing. J Comput Neurosci, 1, 313–322.

    Article  PubMed  Google Scholar 

  • Wang, X.-J., and Buzsáki, G. 1996. Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J Neurosci, 16, 6402–6413.

    CAS  PubMed  Google Scholar 

  • White, J., Chow, C., Ritt, J., Soto-Trevino, C., and Kopell, N. 1998a. Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons. J Comput Neurosci, 5, 5–16.

    Article  CAS  Google Scholar 

  • White, J. A., Klink, R., Alonso, A., and Kay, A. R. 1998b. Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex. J Neurophysiol, 80, 262–269.

    CAS  Google Scholar 

  • White, J. A., Banks, M. I., Pearce, R. A., and Kopell, N. J. 2000. Networks of interneurons with fast and slow gamma-aminobutyric acid type A (GABAA) kinetics provide substrate for mixed gammatheta rhythm. Proc Natl Acad Sci USA, 97(14), 8128–8133.

    Article  CAS  PubMed  Google Scholar 

  • Whittington, M. A., Jefferys, J. G., and Traub, R. D. 1996. Effects of intravenous anaesthetic agents on fast inhibitory oscillations in the rat hippocampus in vitro. Br J Pharmacol, 118(8), 1977–1986.

    CAS  PubMed  Google Scholar 

  • Whittington, M. A., Traub, R. D., Kopell, N., Ermentrout, B., and Buhl, E. H. 2000. Inhibitionbased rhythms: experimental and mathematical observations on network dynamics. Int J Psychophysiol, 38, 315–336.

    Article  CAS  PubMed  Google Scholar 

  • Wittner, L., Henze, D. A., Zaborszky, L., and Buzsaki, G. 2007. Three-dimensional reconstruction of the axon arbor of a CA3 pyramidal cell recorded and filled in vivo. Brain Struct Funct, 212(1), 75–83.

    Article  PubMed  Google Scholar 

  • Wulff, P., Ponomarenko, A. A., Bartos, M., Korotkova, T. M., Fuchs, E. C., Bähner, F., Both, M., Tort, A. B. L., Kopell, N., Wisden, W., and Monyer, H. 2009. Hippocampal theta rhythm and its coupling with gamma oscillations require fast inhibition onto parvalbumin-positive interneurons. Proc Natl Acad Sci USA, 106(9), 3561–3566.

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Center for BioDynamics, Boston University, Boston, MA, 02215, USA

    N. Kopell

  2. Department of Mathematics, Tufts University, Medford, MA, USA

    C. Börgers

  3. Faculty of Bioengineering and Bioinformatics, Moscow State University, 1-73, GSP-2 Leninskie Gory, 119992, Moscow, Russia

    D. Pervouchine

  4. Center for BioDynamics and Department of Mathematics, Boston University, Boston, MA, 02215, USA

    P. Malerba

  5. Edmond and Lily Safra International Institute of Neuroscience of Natal, Federal University of Rio Grande do Norte, Natal, RN, 59066, Brazil

    A. Tort

Authors
  1. N. Kopell
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Börgers
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. Pervouchine
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. P. Malerba
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Tort
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK

    Vassilis Cutsuridis  & Bruce Graham  & 

  2. Neuroscience & Molecular Pharmacology, Faculty of Biomedical and Life Sciences, University of Glasgow, Glasgow, G12 8QQ, UK

    Stuart Cobb  & Imre Vida  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Kopell, N., Börgers, C., Pervouchine, D., Malerba, P., Tort, A. (2010). Gamma and Theta Rhythms in Biophysical Models of Hippocampal Circuits. In: Cutsuridis, V., Graham, B., Cobb, S., Vida, I. (eds) Hippocampal Microcircuits. Springer Series in Computational Neuroscience, vol 5. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0996-1_15

Download citation

Publish with us

Policies and ethics

Search

Navigation