zbMATH — the first resource for mathematics

Adaptation and shunting inhibition leads to pyramidal/interneuron gamma with sparse firing of pyramidal cells. (English) Zbl 1409.92044
Summary: Gamma oscillations are a prominent phenomenon related to a number of brain functions. Data show that individual pyramidal neurons can fire at rate below gamma with the population showing clear gamma oscillations and synchrony. In one kind of idealized model of such weak gamma, pyramidal neurons fire in clusters. Here we provide a theory for clustered gamma PING rhythms with strong inhibition and weaker excitation. Our simulations of biophysical models show that the adaptation of pyramidal neurons coupled with their low firing rate leads to cluster formation. A partially analytic study of a canonical model shows that the phase response curves with a near zero flat region, caused by the presence of the slow adaptive current, are the key to the formation of clusters. Furthermore we examine shunting inhibition and show that clusters become robust and generic.

92C20 Neural biology
Full Text: DOI
[1] Bartos, M; Vida, I; Jonas, P, Synaptic mechanisms of synchronized gamma oscillations in inhibitory interneuron networks, Nature Reviews Neuroscience, 8, 45-56, (2007)
[2] Börgers, C; Kopell, N, Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity, Neural Computation, 15, 509-539, (2003) · Zbl 1085.68615
[3] Börgers, C; Kopell, N, Effects of noisy drive on rhythms in networks of excitatory and inhibitory neurons, Neural Computation, 17, 557-608, (2005) · Zbl 1059.92008
[4] Börgers, C; Epstein, S; Kopell, N, Background gamma rhythmicity and attention in cortical local circuits: a computational study, Proceedings of the National Academy of Science USA, 102, 7002-7007, (2005)
[5] Cunningham, MO; Whittington, MA; Bibbig, A; Roopun, A; LeBeau, FEN; Vogt, A; Monyer, H; Buhl, EH; Traub, R, A role for fast rhythmic bursting neurons in cortical gamma oscillations in vitro, PNAS, 101, 7152-7157, (2004)
[6] Engel, A; Fries, P; Singer, W, Dynamic predictions: oscillations and synchrony in top-down processing, Nature Reviews Neuroscience, 2, 704-716, (2001)
[7] Ermentrout, GB; Pascal, M; Gutkin, BS, The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators, Neural Computation, 13, 1285-1310, (2001) · Zbl 0963.68647
[8] Ermentrout, GB; Kopell, N, No article title, Journal of Mathematical Biology, 29, 195-217, (1991) · Zbl 0718.92004
[9] Ermentrout, GB; Kopell, N, Oscillator death in systems of coupled neural oscillators, SIAM Journal on Applied Mathematics, 50, 125-146, (1990) · Zbl 0686.34033
[10] Fenichel, N, Geometric singular perturbation theory for ordinary differential equations, Journal Differential Equations, 31, 53-98, (1979) · Zbl 0476.34034
[11] Fries, P; Reynolds, J; Rorie, A; Desimone, R, Modulation of oscillatory neuronal synchronization by selective visual attention, Science, 291, 1560-1563, (2001)
[12] Golomb, D; Rinzel, J, Clustering in globally coupled inhibitory neurons, Physica D, 72, 259-282, (1994) · Zbl 0809.92003
[13] Gray, CM, The temporal correlation hypothesis of visual feature integration: still alive and well, Neuron, 24, 31-47, (1999)
[14] Jeong, HY; Gutkin, BS, Synchrony of neuronal oscillations controlled by gabaergic reversal potentials, Neural Computation, 19, 706-729, (2007) · Zbl 1117.92006
[15] Gutkin, BS; Ermentrout, GB; Reyes, A, Phase-response curves give the responses of neurons to transient inputs, Journal of Neurophysiology, 94, 1623-1635, (2005)
[16] Jia, X; Smith, MA; Kohn, A, Stimulus selectivity and spatial coherence of gamma components of the local field potential, Journal of Neuroscience, 31, 9390-9403, (2011)
[17] Kilpatrick, Z., & Ermentrout, B. E. (2011). Sparse gamma rhythms arising through clustering in adapting neuronal networks. PLOS Computational Biology, to appear.
[18] Krupa, M; Szmolyan, P, Extending singular perturbation theory to nonhyperbolic points - fold and canard points in two dimensions, SIAM Journal on Mathematical Analysis, 33, 286-314, (2001) · Zbl 1002.34046
[19] von Stein, A; Sarnthein, J, Different frequencies for different scales of cortical integration: from local gamma to long range alpha/theta synchronization, International Journal of Psychophysiology, 38, 301-13, (2000)
[20] Stiefel, KM; Gutkin, BS; Sejnowski, TE, The effects of cholinergic neuromodulation on neuronal phase-response curves of modeled cortical neurons, Journal Computational Neuroscience, 29, 289-301, (2009)
[21] Tallon-Baudry, C., Bertrand, O., Peronnet, F., Pernier, J. (1998). Induced gamma- band activity during the delay of a visual short-term memory task in humans. Journal of Neuroscience,18, 4244-4254.
[22] Vida, I; Bartos, M; Jonas, P, Shunting inhibition improves robustness of gamma oscillations in hippocampal interneuron networks by homogenizing firing rates, Neuron, 49, 107-117, (2006)
[23] Wang, XJ, Neurophysiological and computational principles of cortical rhythms in cognition, Physiology Review, 90, 1195-1268, (2010)
[24] Whittington, MA; Stanford, IM; Colling, SB; Jefferys, JRG; Traub, RD, Spatiotemporal patterns of gamma frequency oscillations tetanically induced in the rat hippocampal slice, Journal Physiology, 502, 591-607, (1997)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.