Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
article

The high-conductance state of cortical networks

Published: 01 January 2008 Publication History

Abstract

We studied the dynamics of large networks of spiking neurons with conductance-based (nonlinear) synapses and compared them to networks with current-based (linear) synapses. For systems with sparse and inhibition-dominated recurrent connectivity, weak external inputs induced asynchronous irregular firing at low rates. Membrane potentials fluctuated a few millivolts below threshold, and membrane conductances were increased by a factor 2 to 5 with respect to the resting state. This combination of parameters characterizes the ongoing spiking activity typically recorded in the cortex in vivo. Many aspects of the asynchronous irregular state in conductance-based networks could be sufficiently well characterized with a simple numerical mean field approach. In particular, it correctly predicted an intriguing property of conductance-based networks that does not appear to be shared by current-based models: they exhibit states of low-rate asynchronous irregular activity that persist for some period of time even in the absence of external inputs and without cortical pacemakers. Simulations of larger networks (up to 350,000 neurons) demonstrated that the survival time of self-sustained activity increases exponentially with network size.

References

[1]
Abeles, M. (1991). Corticonics: neural circuits of the cerebral cortex. Cambridge: Cambridge University Press.
[2]
Abeles, M., Vaadia, E., & Bergman, H. (1990). Firing patterns of single units in the prefrontal cortex and neural network models. Network: Comput. Neural Systems, 1, 13-25.
[3]
Abramowitz, M., & Stegun, I. A. (1964). Handbook of mathematical functions. Washington, DC: National Bureau of Standards.
[4]
Aertsen, A., Erb, M., & Palm, G. (1994). Dynamics of functional coupling in the cerebral cortex: An attempt at a model-based interpretation. Physica D, 75, 103- 128.
[5]
Amit, D. J., & Brunel, N. (1997). Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cereb. Cortex, 7, 237-252.
[6]
Arieli, A., Sterkin, A., Grinvald, A., & Aertsen, A. (1996). Dynamics of ongoing activity: Explanation of the large variability in evoked cortical responses. Science, 273(5283), 1868-1871.
[7]
Bernander, Ö., Douglas, R. J., Martin, K. A. C., & Koch, C. (1991). Synaptic background activity influences spatiotemporal integration in single pyramidal cells. Proc. Natl. Acad. Sci. USA, 88(24), 11569-11573.
[8]
Bohte, S. M., Spekreijse, H., & Roelfsema, P. R. (2000). The effects of pair-wise and higher-order correlations on the firing rate of a postsynaptic neuron. Neural Comput., 12, 153-179.
[9]
Braitenberg, V., & Schüz, A. (1998). Cortex: Statistics and geometry of neuronal connectivity (2nd ed.). Berlin: Springer-Verlag.
[10]
Brecht, M., & Sakmann, B. (2002). Dynamic representation of whisker deflection by synaptic potentials in spiny stellate and pyramidal cells in the barrels and septa of layer 4 rat somatosensory cortex. J. Physiol. (Lond.), 543, 49-70.
[11]
Brunel, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J. Comput. Neurosci., 8(3), 183-208.
[12]
Brunel, N. (2003). Dynamics and plasticity of stimulus-selective persistent activity in cortical network models. Cereb. Cortex, 13(11), 1151-1161.
[13]
Brunel, N., & Wang, X.-J. (2003). What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance. J. Neurophysiol., 90, 415-430.
[14]
Burns, B. D., & Webb, A. C. (1979). The correlation between discharge times of neighbouring neurons in isolated cerebral cortex. Proc. R. Soc. Lond. B., 203(1115), 347-360.
[15]
Chance, F. S., Abbott, L. F., & Reyes, A. D. (2002). Gain modulation from background synaptic input. Neuron, 35, 773-782.
[16]
Chiu, C., & Weliky, M. (2001). Spontaneous activity in developing ferret visual cortex in vivo. J. Neurosci., 21, 8906-8914.
[17]
Compte, A., Brunel, N., Goldman-Rakic, P. S., & Wang, X. J. (2000). Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model. Cereb. Cortex, 10(9), 910-923.
[18]
Connors, B. W., & Gutnick, M. J. (1990). Intrinsic firing patterns of diverse neocortical neurons. TINS, 13(3), 99-104.
[19]
Dayan, P., & Abbott, L. F. (2001). Theoretical neuroscience. Cambridge; MA: MIT Press.
[20]
Denker, M., Timme, M., Diesmann, M., Wolf, F., & Geisel, T. (2004). Breaking synchrony by heterogeneity in complex networks. Phys. Rev. Lett., 92(7), 074103.
[21]
Destexhe, A., Rudolph, M., & Paré, D. (2003). The high-conductance state of neocortical neurons in vivo. Nat. Rev. Neurosci., 4, 739-751.
[22]
Diesmann, M., & Gewaltig, M.-O. (2002). NEST: An environment for neural systems simulations. In T. Plesser & V. Macho (Eds.), Forschung und wisschenschaftliches Rechnen, Beiträge zum Heinz-Billing-Preis 2001 (pp. 43-70). Göttingen: Ges. für Wiss. Datenverarbeitung.
[23]
Diesmann, M., Gewaltig, M.-O., & Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature, 402(6761), 529-533.
[24]
Fetz, E., Toyama, K., & Smith, W. (1991). Synaptic interactions between cortical neurons. In A. Peters (Ed.), Cerebral cortex (pp. 1-47). New York: Plenum Press.
[25]
Fuster, J. M. (1973). Unit activity in prefrontal cortex during delayed-response performance: Neuronal correlates of transient memory. J. Neurophysiol., 36(1), 61-78.
[26]
Fuster, J. M. (1988). The prefrontal cortex. New York: Raven Press.
[27]
Galassi, M., Davies, J., Theiler, J., Gough, B., Jungman, G., Booth, M., & Rossi, F. (2001). GNU scientific library: Reference manual. Bristol: Network Theory Limited.
[28]
Gerstein, G. L., & Mandelbrot, B. (1964). Random walk models for the spike activity of a single neuron. Biophys. J., 4, 41-68.
[29]
Gerstner, W., & Kistler, W. (2002). Spiking neuron models: Single neurons, populations, plasticity. Cambridge: Cambridge University Press.
[30]
Goldman-Rakic, P. S. (1995). Cellular basis of working memory. Neuron, 14, 477-485.
[31]
Golomb, D., & Hansel, D. (2000). The number of synaptic inputs and the synchrony of large, sparse neuronal networks. Neural Comput., 12, 1095-1139.
[32]
Hansel, D., Mato, G., Meunier, C., & Neltner, L. (1998). On numerical simulations of integrate-and-fire neural networks. Neural Comput., 10(2), 467-483.
[33]
Hasenstaub, A., Shu, Y., Haider, B., Kraushaar, U., Duque, A., & McCormick, D. (2005). Inhibitory postsynaptic potentials carry synchronized frequency information in active cortical networks. Neuron, 3(47), 423-435.
[34]
Jack, J. J. B., Noble, D., & Tsien, R. W. (1975). Electric current flow in excitable cells. Oxford: Clarendon Press.
[35]
Knuth, D. E. (1997). The art of computer programming: Seminumerical algorithms (3rd ed.). Reading, MA: Addison-Wesley.
[36]
Koulakov, A. A., Raghavachari, S., Kepecs, A., & Lisman, J. E. (2002). Model for a robust neural integrator. Nat. Neurosci., 5(8), 775-782.
[37]
Kuhn, A., Aertsen, A., & Rotter, S. (2003). Higher-order statistics of input ensembles and the response of simple model neurons. Neural Comput., 15(1), 67- 101.
[38]
Kuhn, A., Aertsen, A., & Rotter, S. (2004). Neuronal integration of synaptic input in the fluctuation-driven regime. J. Neurosci., 24(10), 2345-2356.
[39]
Kumar, A., Rotter, S., & Aertsen, A. (2006). Propagation of synfire activity in locally connected networks with conductance-based synapses. In Computational and Systems Neuroscience (Cosyne) 2006. Available online at http://cosyne.org/wiki/cosyne_06.
[40]
Kumar, A., Schrader, S., Rotter, S., & Aertsen, A. (2005). Dynamics of random networks of spiking neurons with conductance-based synapses. In Computational and Systems Neuroscience (Cosyne) 2005 (p. 153). Available online at http://cosyne.org/wiki/Cosyne_05.
[41]
Latham, P. E., Richmond, B. J., Nelson, P. G., & Nirenberg, S. (2000). Intrinsic dynamics in neuronal networks. I. Theory. J. Neurophysiol., 83, 808-827.
[42]
Latham, P. E., Richmond, B. J., Nirenberg, S., & Nelson, P. G. (2000). Intrinsic dynamics in neuronal networks. II. Experiment. J. Neurophysiol., 83, 828-835.
[43]
Leger, J., Stern, E., Aertsen, A., & Heck, D. (2005). Synaptic integration in rat frontal cortex shaped by network activity. J. Neurophysiol., 1(93), 281-293.
[44]
Maex, R., & De Schutter, E. (2003). Resonant synchronization in heterogeneous networks of inhibitory neurons. J. Neurosci., 23(33), 10503-10514.
[45]
Markram, H., Toledo-Rodriguez, M., Wang, Y., Gupta, A., Silberberg, G., & Wu, C. (2004) Interneurons of the neocortical inhibitory system. Nat. Rev. Neurosci., 5(10), 793-807.
[46]
Matsumura, M., Chen, D., Sawaguchi, T., Kubota, K., & Fetz, E. E. (1996). Synaptic interactions between primate precentral cortex neurons revealed by spike-triggered averaging of intracellular membrane potentials in vivo. J. Neurosci., 16(23), 7757- 7767.
[47]
McCormick, D. A., Connors, B. W., Lighthall, J. W., & Prince, D. A. (1985). Comparative electrophysiology of pyramidal and sparsely spiny neurons of the neocortex. J. Neurophysiol., 54(4), 782-806.
[48]
McCormick, D. A., Shu, Y., Hasenstaub, A., Sanchez-Vives, M., Badoual, M., & Bal, T. (2003). Persistent cortical activity: Mechanisms of generation and effects on neuronal excitability. Cereb. Cortex, 13(11), 1219-1231.
[49]
Meffin, H., Burkitt, A. N., & Grayden, D. B. (2004). An analytical model for the large, fluctuating synaptic conductance state typical of neocortical neurons in vivo. J. Comput. Neurosci., 16, 159-175.
[50]
Mehring, C., Hehl, U., Kubo, M., Diesmann, M., & Aertsen, A. (2003). Activity dynamics and propagation of synchronous spiking in locally connected random networks. Biol. Cybern., 88(5), 395-408.
[51]
Mirollo, R. E., & Strogatz, S. H. (1990). Synchronization of pulse-coupled biological oscillators. SIAM J. Appl. Math., 50(6), 1645-1662.
[52]
Morrison, A., Hake, J., Straube, S., Plesser, H. E., & Diesmann, M. (2005). Precise spike timing with exact subthreshold integration in discrete time network simulations. In Proceedings of the 30th Göttingen Neurobiology Conference (p. 205B). Available online at http://cosyne.org/wiki/cosyne_05.
[53]
Morrison, A., Mehring, C., Geisel, T., Aertsen, A., & Diesmann, M. (2005). Advancing the boundaries of high connectivity network simulation with distributed computing. Neural Comput., 17(8), 1776-1801.
[54]
Murray, J. D. (2002). Mathematical biology. I: An introduction (3rd ed.). Berlin: Springer.
[55]
Nawrot, M. P., Riehle, A., Aertsen, A., & Rotter, S. (2000). Spike count variability in motor cortical neurons. European Journal of Neuroscience, 12, 506.
[56]
Plenz, D., & Aertsen, A. (1996). Neural dynamics in cortex-striatum co-cultures II-- spatiotemporal characteristics of neuronal activity. Neuroscience, 70(4), 893-924.
[57]
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992). Numerical recipes in C (2nd ed.). Cambridge: Cambridge University Press.
[58]
Rapp, M., Yarom, Y., & Segev, I. (1992). The impact of parallel fiber background activity on the cable properties of cerebellar Purkinje cells. Neural Comput., 4, 518-533.
[59]
Rauch, A., La Camera, G., Lüscher, H., Senn, W., & Fusi, S. (2003). Neocortical pyramidal cells respond as integrate-and-fire neurons to in vivo like input currents. J. Neurophysiol., 90, 1598-1612.
[60]
Rotter, S., & Diesmann, M. (1999). Exact digital simulation of time-invariant linear systems with applications to neuronal modeling. Biol. Cybern., 81(5/6), 381-402.
[61]
Roxin, A., Brunel, N., & Hansel, D. (2005). The role of delays in shaping spatio-temporal dynamics of neuronal activity in large networks. Phys. Rev. Lett., 94(23), 238103.
[62]
Salinas, E. (2003). Background synaptic activity as a switch between dynamic states in network. Neural Comput., 15, 1439-1475.
[63]
Schrader, S., Kumar, A., Rotter, S., & Aertsen, A. (2005). Dynamics of self-sustained activity. In Proceedings of the 30th Göttingen Neurobiology Conference. Available at http://www.neuro.uni-goettingen.de/nbc.php?sel=archiv.
[64]
Shadlen, M. N., & Newsome, W. T. (1998). The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding. J. Neurosci., 18(10), 3870-3896.
[65]
Shelley, M., McLaughlin, D., Shapley, R., & Wielaard, J. (2002). States of high conductance in a large-scale model of the visual cortex. J. Comput. Neurosci., 13(2), 93-109.
[66]
Shu, Y., Hasenstaub, A., & McCormick, D. A. (2003). Turning on and off recurrent balanced cortical activity. Nature, 423(6937), 288-293.
[67]
Softky, W. R., & Koch, C. (1993). The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. J. Neurosci., 13(1), 334-350.
[68]
Stroeve, S., & Gielen, S. (2001). Correlation between uncoupled conductance-based integrate-and-fire neurons due to common and synchronous presynaptic firing. Neural Comput., 13(9), 2005-2029.
[69]
Tarczy-Hornoch, K., Martin, K. A. C., Jack, J. J. B., & Stratford, K. J. (1998). Synaptic interactions bewteen smooth and spiny neurones in layer 4 of cat visual cortex in vitro. J. Physiol. (Lond.), 508(2), 351-363.
[70]
Tetzlaff, T., Morrison, A., Timme, M., & Diesmann, M. (2005). Heterogeneity breaks global synchrony in large networks. In Proceedings of the 30th Göttingen Neurobiology Conference. Available online at http://www.neuro.unigoettingen.de/ nbc.php?sel=archiv.
[71]
Tetzlaff, T., Rotter, S., Stark, E., Abeles, M., Aertsen, A., & Diesmann, M. (2007). Time scale dependence of neuronal connections. Manuscript submitted for publication.
[72]
Timofeev, I., Grenier, F., Bazhenov, M., Sejnowski, T. J., & Steriade, M. (2000). Origin of slow cortical oscillations in deafferented cortical slabs. Cereb. Cortex, 10(12), 1185-1199.
[73]
Tuckwell, H. C. (1988a). Introduction to theoretical neurobiology (Vol. 1). Cambridge: Cambridge University Press.
[74]
Tuckwell, H. C. (1988b). Introduction to theoretical neurobiology (Vol. 2). Cambridge: Cambridge University Press.
[75]
Vaadia, E., & Aertsen, A. (1992). Coding and computation in the cortex: Single-neuron activity and cooperative phenomena. In A. Aertsen & V. Braitenberg (Eds.), Information processing in the cortex: Experiments and theory (pp. 81-121). Berlin: Springer-Verlag.
[76]
van Vreeswijk, C., & Sompolinsky, H. (1998). Chaotic balanced state in a model of cortical circuits. Neural Comput., 10, 1321-1371.
[77]
Vogels, T. P., & Abbott, L. F. (2005). Signal propagation and logic gating in networks of integrate-and-fire neurons. J. Neurosci., 25(46), 10786-10795.
[78]
Vogels, T. P., Rajan, K., & Abbott, L. F. (2005). Neural network dynamics. Annu. Rev. Neurosci., 28, 357-376.
[79]
Williams, S. R., & Stuart, G. J. (2002). Dependence of EPSP efficacy on synaptic location in neocortical pyramidal neurons. Science, 295, 1907-1910.
[80]
Williams, S. R., & Stuart, G. J. (2003). Voltage- and site-dependent control of the somatic impact of dendritic IPSPs. J. Neurosci., 23(19), 7358-7367.
[81]
Wilson, H. R., & Cowan, J. D. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik, 13, 55-80.

Cited By

View all
  • (2021)A novel density-based neural mass model for simulating neuronal network dynamics with conductance-based synapses and membrane current adaptationNeural Networks10.1016/j.neunet.2021.06.009143:C(183-197)Online publication date: 1-Nov-2021
  • (2020)Machine Learning in Mental HealthACM Transactions on Computer-Human Interaction10.1145/339806927:5(1-53)Online publication date: 17-Aug-2020
  • (2019)Controlling complexity of cerebral cortex simulations-iiNeural Computation10.1162/neco_a_0118831:6(1066-1084)Online publication date: 1-Jun-2019
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image Neural Computation
Neural Computation  Volume 20, Issue 1
January 2008
309 pages

Publisher

MIT Press

Cambridge, MA, United States

Publication History

Published: 01 January 2008

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)0
  • Downloads (Last 6 weeks)0
Reflects downloads up to 25 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2021)A novel density-based neural mass model for simulating neuronal network dynamics with conductance-based synapses and membrane current adaptationNeural Networks10.1016/j.neunet.2021.06.009143:C(183-197)Online publication date: 1-Nov-2021
  • (2020)Machine Learning in Mental HealthACM Transactions on Computer-Human Interaction10.1145/339806927:5(1-53)Online publication date: 17-Aug-2020
  • (2019)Controlling complexity of cerebral cortex simulations-iiNeural Computation10.1162/neco_a_0118831:6(1066-1084)Online publication date: 1-Jun-2019
  • (2019)Stochasticity from function — Why the Bayesian brain may need no noiseNeural Networks10.1016/j.neunet.2019.08.002119:C(200-213)Online publication date: 1-Nov-2019
  • (2018)Dynamics of spontaneous activity in random networks with multiple neuron subtypes and synaptic noiseJournal of Computational Neuroscience10.1007/s10827-018-0688-645:1(1-28)Online publication date: 1-Aug-2018
  • (2018)Modeling mesoscopic cortical dynamics using a mean-field model of conductance-based networks of adaptive exponential integrate-and-fire neuronsJournal of Computational Neuroscience10.1007/s10827-017-0668-244:1(45-61)Online publication date: 1-Feb-2018
  • (2018)How does transient signaling input affect the spike timing of postsynaptic neuron near the threshold regimeJournal of Computational Neuroscience10.1007/s10827-017-0664-644:2(147-171)Online publication date: 1-Apr-2018
  • (2016)Dynamic effective connectivity in cortically embedded systems of recurrently coupled synfire chainsJournal of Computational Neuroscience10.1007/s10827-015-0581-540:1(1-26)Online publication date: 1-Feb-2016
  • (2013)Generation and annihilation of localized persistent-activity states in a two-population neural-field modelNeural Networks10.1016/j.neunet.2013.04.01246(75-90)Online publication date: 1-Oct-2013
  • (2013)A new method to infer higher-order spike correlations from membrane potentialsJournal of Computational Neuroscience10.1007/s10827-013-0446-835:2(169-186)Online publication date: 1-Oct-2013
  • Show More Cited By

View Options

View options

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media