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Examining the limits of cellular adaptation bursting mechanisms in biologically-based excitatory networks of the hippocampus. (English) Zbl 1382.92052
Summary: Determining the biological details and mechanisms that are essential for the generation of population rhythms in the mammalian brain is a challenging problem. This problem cannot be addressed either by experimental or computational studies in isolation. Here we show that computational models that are carefully linked with experiment provide insight into this problem. Using the experimental context of a whole hippocampus preparation in vitro that spontaneously expresses theta frequency (\(3-12\) Hz) population bursts in the CA1 region, we create excitatory network models to examine whether cellular adaptation bursting mechanisms could critically contribute to the generation of this rhythm. We use biologically-based cellular models of CA1 pyramidal cells and network sizes and connectivities that correspond to the experimental context. By expanding our mean field analyses to networks with heterogeneity and non all-to-all coupling, we allow closer correspondence with experiment, and use these analyses to greatly extend the range of parameter values that are explored. We find that our model excitatory networks can produce theta frequency population bursts in a robust fashion.Thus, even though our networks are limited by not including inhibition at present, our results indicate that cellular adaptation in pyramidal cells could be an important aspect for the occurrence of theta frequency population bursting in the hippocampus. These models serve as a starting framework for the inclusion of inhibitory cells and for the consideration of additional experimental features not captured in our present network models.

MSC:
92C20 Neural biology
Software:
Brian
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[1] Abbott, LF; van Vreeswijk, C, Asynchronous states in networks of pulse-coupled oscillators, Physical Review E, 48, 1483-1490, (1993)
[2] Amilhon, B; Huh, CL; Manseau, F; Ducharme, G; Nichol, H; Adamantidis, A; Williams, S, Parvalbumin interneurons of hippocampus tune population activity at theta frequency, Neuron, 86, 1277-1289, (2015)
[3] Apfaltrer, F; Ly, C; Tranchina, D, Population density methods for stochastic neurons with realistic synaptic kinetics: firing rate dynamics and fast computational methods, Network: Computation in Neural Systems, 17, 373-418, (2006)
[4] Augustin, M; Ladenbauer, J; Obermayer, K, How adaptation shapes spike rate oscillations in recurrent neuronal networks, Frontiers in Computational Neuroscience, 7, 9, (2013)
[5] Battaglia, FP; Benchenane, K; Sirota, A; Pennartz, CM; Wiener, SI, The hippocampus: hub of brain network communication for memory, Trends in Cognitive Sciences, 15, 310-318, (2011)
[6] Bezaire, MJ; Soltesz, I, Quantitative assessment of CA1 local circuits: knowledge base for interneuron-pyramidal cell connectivity, Hippocampus, 23, 751-785, (2013)
[7] Brette, R; Gerstner, W, Adaptive exponential integrate-and-fire model as an effective description of neuronal activity, Journal of Neurophysiology, 94, 3637-3642, (2005)
[8] Butera, R., Rinzel, J., & Smith, J. (1999a). Models of respiratory rhythm generation in pre-Bötzinger complex. I. Bursting pacemaker neurons. Journal of Neurophysiology, 81, 382-397.
[9] Butera, R., Rinzel, J., & Smith, J. (1999b). Models of respiratory rhythm generation in pre-Bötzinger complex. II. Populations of coupled pacemaker neurons. Journal of Neurophysiology, 81, 398-415.
[10] Buzsaki, G, Hippocampus, Scholarpedia, 6, 1468, (2011)
[11] Destexhe, A; Mainen, Z; Sejnowski, T, An efficient method for computing synaptic conductances based on a kinetic model of receptor binding, Neural Computation, 6, 14-18, (1994)
[12] Deuchars, J; Thomson, A, CA1 pyramid-pyramid connections in rat hippocampus in vitro: dual intracellular recordings with biocytin filling, Neuroscience, 74, 1009-1018, (1996)
[13] Dur-E-Ahmad, M; Nicola, W; Campbell, SA; Skinner, FK, Network bursting using experimentally constrained single compartment CA3 hippocampal neuron models with adaptation, Journal of Computational Neuroscience, 33, 21-40, (2012)
[14] Ermentrout, G.B., & Terman, D.H. (2010). Mathematical foundations of neuroscience. New York: Springer. · Zbl 1320.92002
[15] Ferguson, K., Huh, C., Amilhon, B., Williams, S., & Skinner F. (2014). Parvalbumin-positive interneurons play a key role in determining the frequency and power of CA1 theta oscillations in experimentally constrained network models, program No. 303.22. 2014. In Neuroscience Meeting Planner. Washington, DC Society for Neuroscience.
[16] Ferguson, KA; Huh, CYL; Amilhon, B; Williams, S; Skinner, FK, Experimentally constrained CA1 fast-firing parvalbumin-positive interneuron network models exhibit sharp transitions into coherent high frequency rhythms, Frontiers in Computational Neuroscience, 7, 144, (2013)
[17] Ferguson, KA; Huh, CYL; Amilhon, B; Williams, S; Skinner, FK, Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context, F1000Research, 3, 104, (2015)
[18] Gerstner, W; Brette, R, Adaptive exponential integrate-and-fire model, Scholarpedia, 4, 8427, (2009)
[19] Goodman, DFM; Brette, R, The Brian simulator, Frontiers in Neuroscience, 3, 192-197, (2009)
[20] Goutagny, R; Jackson, J; Williams, S, Self-generated theta oscillations in the hippocampus, Nature Neuroscience, 12, 1491-1493, (2009)
[21] Gutkin, B; Zeldenrust, F, Spike frequency adaptation, Scholarpedia, 9, 30643, (2014)
[22] Hansel, D; Mato, G, Existence and stability of persistent states in large neuronal networks, Physical Review Letters, 86, 4175, (2001) · Zbl 1031.68098
[23] Hansel, D; Mato, G, Asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons, Neural Computation, 15, 1-56, (2003) · Zbl 1031.68098
[24] Hasselmo, M, Models of hippocampus, Scholarpedia, 6, 1371, (2011)
[25] Hemond, P; Epstein, D; Boley, A; Migliore, M; Ascoli, GA; Jaffe, DB, Distinct classes of pyramidal cells exhibit mutually exclusive firing patterns in hippocampal area CA3b, Hippocampus, 18, 411-424, (2008)
[26] Ho, ECY; Zhang, L; Skinner, FK, Inhibition dominates in shaping spontaneous CA3 hippocampal network activities in vitro, Hippocampus, 19, 152-165, (2009)
[27] Ho, ECY; Strüber, M; Bartos, M; Zhang, L; Skinner, FK, Inhibitory networks of fast-spiking interneurons generate slow population activities due to excitatory fluctuations and network multistability, The Journal of Neuroscience, 32, 9931-9946, (2012)
[28] Ho, ECY; Eubanks, JH; Zhang, L; Skinner, FK, Network models predict that reduced excitatory fluctuations can give rise to hippocampal network hyper-excitability in mecp2-null mice, PLoS ONE, 9, e91148, (2014)
[29] Huh, C., Amilhon, B., Ferguson, K., Torres-Platas, S., Manseau, F., Peach, J., Scodras, S., Mechawar, N., Skinner, F., & Williams, S. (2015). Excitatory inputs determine phase-locking strength and spike-timing of CA1 stratum oriens/alveus parvalbumin and somatostatin interneurons during intrinsically generated hippocampal theta rhythm. In Revision.
[30] Izhikevich, EM, Simple model of spiking neurons, IEEE transactions on neural networks, 14, 1569-1572, (2003)
[31] Kilpatrick, ZP; Ermentrout, B, Sparse gamma rhythms arising through clustering in adapting neuronal networks, PLoS Comput Biol, 7, e1002281, (2011)
[32] Knight, BW, Dynamics of encoding in neuron populations: some general mathematical features, Neural Computation, 12, 473-518, (2000)
[33] Krupa, M., Gielen, S., & Gutkin, B. (2014). Adaptation and shunting inhibition leads to pyramidal/interneuron gamma with sparse firing of pyramidal cells. Journal of Computational Neuroscience, 37(2), 357-376. doi:10.1007/s10827-014-0508-6. · Zbl 1409.92044
[34] Latham, PE; Richmond, BJ; Nelson, PG; Nirenberg, S, Intrinsic dynamics in neuronal networks. I. theory., Journal of Neurophysiology, 83, 808-827, (2000)
[35] Lisman, JE, Bursts as a unit of neural information: making unreliable synapses reliable, Trends in Neurosciences, 20, 38-43, (1997)
[36] Loken, C; Gruner, D; Groer, L; Peltier, R; Bunn, N; Craig, M; Henriques, T; Dempsey, J; Yu, CH; Chen, J; Dursi, J; Chong, J; Northrup, S; Pinto, J; Knecht, N; Van Zon, R, Scinet: lessons learned from building a power-efficient top-20 system and data centre, Journal of Physics: Conference Series, 256, 012026, (2010)
[37] Ly, C; Tranchina, D, Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling, Neural Computation, 19, 2032-2092, (2007) · Zbl 1131.92016
[38] Nesse, WH; Borisyuk, A; Bressloff, P, Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation, Journal of Computational Neuroscience, 25, 317-333, (2008)
[39] Nicola, W., & Campbell, S.A. (2013a). Bifurcations of large networks of two-dimensional integrate and fire neurons. Journal of Computational Neuroscience, 35(1), 87-108. doi:10.1007/s10827-013-0442-z. · Zbl 1276.92018
[40] Nicola, W., & Campbell, S.A. (2013b). Mean-field models for heterogeneous networks of two-dimensional integrate and fire neurons. Frontiers in Computational Neuroscience, \(7\), 184. doi:10.3389/fncom.2013.00184. · Zbl 1004.92011
[41] Nicola, W., Ly, C., & Campbell, S.A. (2014). One-dimensional population density approaches to recurrently coupled networks of neurons with noise. arXiv:1408.4767. · Zbl 1352.37199
[42] Skinner, FK, Cellular-based modeling of oscillatory dynamics in brain networks, Current opinion in neurobiology, 22, 660-669, (2012)
[43] Skinner, FK; Ferguson, KA, Modeling oscillatory dynamics in brain microcircuits as a way to help uncover neurological disease mechanisms: A proposal, Chaos: An Interdisciplinary Journal of Nonlinear Science, 23, 046108, (2013)
[44] Spruston, N; Jonas, P; Sakmann, B, Dendritic glutamate receptor channels in rat hippocampal CA3 and CA1 pyramidal neurons, The Journal of Physiology, 482, 325-352, (1995)
[45] Tabak, J; Senn, W; O’Donovan, MJ; Rinzel, J, Modeling of spontaneous activity in developing spinal cord using activity-dependent depression in an excitatory network, The Journal of Neuroscience, 20, 3041-3056, (2000)
[46] Tóth, K. (2010) In Cutsuridis, V, Graham, B., Cobb, S., & Vida, I. (Eds.), Glutamatergic neurotransmission in the hippocampus, (pp. 99-128). New York: Springer. · Zbl 1149.34027
[47] Touboul, J, Bifurcation analysis of a general class of nonlinear integrate-and-fire neurons, SIAM Journal on Applied Mathematics, 68, 1045-1079, (2008) · Zbl 1149.34027
[48] Vladimirski, B; Tabak, J; O’Donovan, M; Rinzel, J, Episodic activity in a heterogeneous excitatory network, from spiking neurons to Mean field, Journal of Computational Neuroscience, 25, 39-63, (2008) · Zbl 1412.92005
[49] van Vreeswijk, C; Hansel, D, Patterns of synchrony in neural networks with spike adaptation, Neural Computation, 13, 959-992, (2001) · Zbl 1004.92011
[50] Wu, C; Asl, MN; Gillis, J; Skinner, FK; Zhang, L, An in vitro model of hippocampal sharp waves: regional initiation and intracellular correlates, Journal of Neurophysiology, 94, 741-753, (2005)
[51] Yoder, N. (2014). Peak Finder: Noise tolerant fast peak finding algorithm. http://www.mathworks.com/matlabcentral/fileexchange/25500-peakfinder.
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