nach oben

Journal of Computational Neuroscience

Erschienen in:

01.06.2009

A kinetic theory approach to capturing interneuronal correlation: the feed-forward case

verfasst von: Chin-Yueh Liu, Duane Q. Nykamp

Erschienen in: Journal of Computational Neuroscience | Ausgabe 3/2009

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

We present an approach for using kinetic theory to capture first and second order statistics of neuronal activity. We coarse grain neuronal networks into populations of neurons and calculate the population average firing rate and output cross-correlation in response to time varying correlated input. We derive coupling equations for the populations based on first and second order statistics of the network connectivity. This coupling scheme is based on the hypothesis that second order statistics of the network connectivity are sufficient to determine second order statistics of neuronal activity. We implement a kinetic theory representation of a simple feed-forward network and demonstrate that the kinetic theory model captures key aspects of the emergence and propagation of correlations in the network, as long as the correlations do not become too strong. By analyzing the correlated activity of feed-forward networks with a variety of connectivity patterns, we provide evidence supporting our hypothesis of the sufficiency of second order connectivity statistics.

Vorheriger Artikel Relationship between temperature and stimulation frequency in conduction block of amphibian myelinated axon

Nächster Artikel Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

Jetzt informieren

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!

Jetzt informieren

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!

Jetzt informieren

Nur mit Berechtigung zugänglich

Abbott, L. F., & van Vreeswijk, C. (1993). Asynchronous states in networks of pulse-coupled oscillators. Physical Review E., 48, 1483–1490.CrossRef

Apfaltrer, F., Ly, C., & Tranchina, D. (2006). 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.CrossRef

Barna, G., Gröbler, T., & Érdi, P. (1998). Statistical model of the hippocampal CA3 region—II. The population framework: Model of rhythmic activity in the CA3 slice. Biological Cybernetics, 79, 309–321.PubMedCrossRef

Binder, M. D., & Powers, R. K. (2001). Relationship between simulated common synaptic input and discharge synchrony in cat spinal motoneurons. Journal of Neurophysiology, 86, 2266–2275.PubMed

Brunel, N., & Hakim, V. (1999). Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Computation, 11(7), 1621–1671.PubMedCrossRef

Cai, D., Tao, L., Rangan, A., & McLaughlin, D. (2006). Kinetic theory for neuronal network dynamics. Communications in Mathematical Sciences, 4, 97–127.

Casti, A. R., Omurtag, A., Sornborger, A., Kaplan, E., Knight, B., Victor, J., et al. (2002). A population study of integrate-and-fire-or-burst neurons. Neural Computation, 14, 957–86.PubMedCrossRef

Câteau, H., & Fukai, F. (2001). Fokker–Planck approach to the pulse packet propagation in synfire chain. Neural Networks, 14, 675–685.PubMedCrossRef

Câteau, H., & Reyes, A. D. (2006). Relation between single neuron and population spiking statistics and effects on network activity. Physical Review Letters, 96, 058, 101.CrossRef

Diesmann, M., Gewaltig, M. O., & Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature, 402, 529–533.PubMedCrossRef

Doiron, B., Rinzel, J., & Reyes, A. (2006). Stochastic synchronization in finite size spiking networks. Physical Review E., 74, 030, 903.CrossRef

Dorn, J. D., & Ringach, D. L. (2003). Estimating membrane voltage correlations from extracellular spike trains. Journal of Neurophysiology, 89, 2271–2278.PubMedCrossRef

Galán, R. F., Fourcaud-Trocmé, N., Ermentrout, G. B., & Urban, N. N. (2006). Correlation-induced synchronization of oscillations in olfactory bulb neurons. Journal of Neuroscience, 26, 3646–3655.PubMedCrossRef

Gardiner, C. W. (2004).Handbook of stochastic methods for physics, chemistry and the natural sciences, 3rd edn. New York: Springer.

Gerstner, W. (2000). Population dynamics of spiking neurons: Fast transients, asynchronous states, and locking. Neural Computation, 12, 43–89.PubMedCrossRef

Hasegawa, H. (2003). Dynamical mean-field theory of spiking neuron ensembles: Response to a single spike with independent noises. Physical Review E., 67, 041, 903.CrossRef

Haskell, E., Nykamp, D. Q., & Tranchina, D. (2001). Population density methods for large-scale modeling of neuronal networks with realistic synaptic kinetics: Cutting the dimension down to size. Network: Computation in Neural Systems, 12(2), 141–174.CrossRef

Hildebrand, E. J., Buice, M. A., & Chow, C. C. (2007). Kinetic theory of coupled oscillators. Physical Review Letters, 98, 054, 101.CrossRef

Hohn, N., & Burkitt, A. N. (2001). Shot noise in the leaky integrate-and-fire neuron. Physical Review E., 63, 031, 902.CrossRef

Huertas, M. A., & Smith, G. (2006). A multivariate population density model of the dlgn/pgn relay. Journal of Computational Neuroscience, 21, 171–89.PubMedCrossRef

Ichimaru, S. (1973) Basic principles of plasma physics: A statistical approach. New York: Benjamin.

Jaynes, E. T. (1957) Information theory and statistical mechanics. Physical Review, 106, 62–79.CrossRef

Knight, B. W. (2000). Dynamics of encoding in neuron populations: Some general mathematical features. Neural Computation, 12, 473–518.PubMedCrossRef

Knight, B. W., Manin, D., & Sirovich, L. (1996). Dynamical models of interacting neuron populations. In E. C., Gerf, (Ed.), Symposium on robotics and cybernetics: Computational engineering in systems applications, cite scientifique Lille, France.

Litvak, V., Sompolinsky, H., Segev, I., & Abeles, M. (2003). On the transmission of rate code in long feedforward networks with excitatory-inhibitory balance. Journal of Neuroscience, 23, 3006–3015.PubMed

Ly, C., & Tranchina, D. (2008). Spike train statistics and dynamics with synaptic input from any renewal process: A population density approach. Neural Computation. doi:10.1162/neco.2008.03-08-743.

Masuda, N., & Aihara, K. (2002). Bridging rate coding and temporal spike coding by effect of noise. Physical Review Letters, 88, 248, 101.CrossRef

Mattia, M., & Del Giudice, P. (2002). Population dynamics of interacting spiking neurons. Physical Review E., 66, 051, 917.CrossRef

McFadden, J. A. (1965) The entropy of a point process. Journal of the Society for Industrial and Applied Mathematics, 13, 988–994CrossRef

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. Journal of Computational Neuroscience, 16, 159–175PubMedCrossRef

Moreno, R., de la Rocha, J., Renart, A., & Parga, N. (2002). Response of spiking neurons to correlated inputs. Physical Review Letters, 89, 288, 101CrossRef

Moreno-Bote, R., & Parga, N. (2006). Auto- and crosscorrelograms for the spike response of leaky integrate-and-fire neurons with slow synapses. Physical Review Letters, 96, 028, 101.CrossRef

Nicholson, D. (1992) Introduction to plasma theory. Malabar, Florida: Krieger.

Nirenberg, S., & Victor, J. (2007). Analyzing the activity of large populations of neurons: How tractable is the problem? Current Opinion in Neurobiology, 17, 397–400.PubMedCrossRef

Nykamp, D. Q. (2005). Revealing pairwise coupling in linear-nonlinear networks. SIAM Journal on Applied Mathematics, 65, 2005–2032.CrossRef

Nykamp, D. Q. (2007a) Exploiting history-dependent effects to infer network connectivity. SIAM Journal on Applied Mathematics, 68, 354–391.CrossRef

Nykamp, D. Q. (2007b) A mathematical framework for inferring connectivity in probabilistic neuronal networks. Mathematical Biosciences, 205, 204–251.PubMedCrossRef

Nykamp, D. Q., & Tranchina, D. (2000). A. population density approach that facilitates large-scale modeling of neural networks: Analysis and an application to orientation tuning. Journal of Computational Neuroscience, 8, 19–50.PubMedCrossRef

Nykamp, D. Q., & Tranchina, D. (2001). A. population density approach that facilitates large-scale modeling of neural networks: Extension to slow inhibitory synapses. Neural Computation, 13, 511–546.PubMedCrossRef

Omurtag, A., Kaplan, E., Knight, B., & Sirovich, L. (2000a) A population approach to cortical dynamics with an application to orientation tuning. Network: Computation in Neural Systems, 11, 247–260.CrossRef

Omurtag, A., Knight, B. W., & Sirovich, L. (2000b) On the simulation of large populations of neurons. Journal of Computational Neuroscience, 8, 51–63.PubMedCrossRef

Reyes, A. D. (2003). Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nature Neuroscience, 6, 593–599.PubMedCrossRef

de la Rocha, J., Doiron, B., Shea-Brown, E., Josić, K., & Reyes, A. (2007). Correlation between neural spike trains increases with firing rate. Nature, 448, 802–806.PubMedCrossRef

de la Rocha, J., Moreno-Bote, R., & Câteau, H. (2008). Propagation of temporally correlated spike trains: A Fokker-Planck analysis (in preparation).

van Rossum, M. C. W., Turrigiano, G. G., & Nelson, S. B. (2002). Fast propagation of firing rates through layered networks of noisy neurons. Journal of Neuroscience, 22, 1956–1966.PubMed

Saad, Y., & Schultz, M. H. (1986) GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing, 7, 856–869.CrossRef

Salinas, E., & Sejnowski, T. (2002). Integrate-and-fire neurons driven by correlated stochastic input. Neural Computation, 14, 2111–2155.PubMedCrossRef

Schneidman, E., Berry, M. J. II, Segev, R., & Bialek, W. (2006). Weak pairwise correlations imply strongly correlated network states in a neural population. Nature, 440, 1007–1012.PubMedCrossRef

Shadlen, M. N., & Newsome, W. T. (2001). Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. Journal of Neurophysiology, 86, 1916–1936.PubMed

Shea-Brown, E., Josić, K., de la Rocha, J., & Doiron, B. (2008). Correlation and synchrony transfer in integrate-and-fire neurons: Basic properties and consequences for coding. Physical Review Letters, 100, 108, 102.CrossRef

Shinomoto, S., Shima, K., & Tanji, J. (2003). Differences in spiking patterns among cortical neurons. Neural Computation, 15, 2823–2842.PubMedCrossRef

Shlens, J., Field, G. D., Gauthier, J. L., Grivich, M. I., Petrusca, D., Sher, A., et al. (2006). The structure of multi-neuron firing patterns in primate retina. Journal of Neuroscience, 26, 8254–8266.PubMedCrossRef

Sirovich, L. (2008). Populations of tightly coupled neurons: The RGC/LGN system. Neural Computation, 20, 1179–1210.PubMedCrossRef

Sirovich, L., Knight, B., & Omurtag, A. (2000). Dynamics of neuronal populations: The equilibrium solution. SIAM Journal on Applied Mathematics, 60, 2009–2028.CrossRef

Sirovich, L., Omurtag, A., & Lubliner, K. (2006). Dynamics of neural populations: Stability and synchrony. Network: Computation in Neural Systems, 17, 3–29.CrossRef

Stevens, C., & Zador, A. (1998). Input synchrony and the irregular firing of cortical neurons. Nature Neuroscience, 1, 210–207.CrossRef

Svirskis, G., & Hounsgaard, J. (2003). Influence of membrane properties on spike synchronization in neurons: theory and experiments. Network: Computation in Neural Systems 14, 747–763.CrossRef

Tang, A., Jackson, D., Hobbs, J., Chen, W., Smith, J. L., Patel, H., et al. (2008). A maximum entropy model applied to spatial and temporal correlations from cortical networks in vitro. Journal of Neuroscience, 28, 505–518.PubMedCrossRef

Wang, S., Wang, W., & Liu, F. (2006). Propagation of firing rate in a feed-forward neuronal network. Physical Review Letters, 96, 018, 103.

Yu, S., Huang, D., Singer, W., & Nikolic, D. (2008). A small world of neuronal synchrony. Cereb Cortex. doi:10.1093/cercor/bhn047.

Titel: A kinetic theory approach to capturing interneuronal correlation: the feed-forward case
verfasst von: Chin-Yueh Liu
Duane Q. Nykamp
Publikationsdatum: 01.06.2009
Verlag: Springer US
Erschienen in: Journal of Computational Neuroscience / Ausgabe 3/2009
Print ISSN: 0929-5313
Elektronische ISSN: 1573-6873
DOI: https://doi.org/10.1007/s10827-008-0116-4

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 3/2009

A finite volume method for stochastic integrate-and-fire models

A kinetic model unifying presynaptic short-term facilitation and depression

Voltage-stepping schemes for the simulation of spiking neural networks

Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities

Superposition of masking releases

Slow and fast pulses in 1-D cultures of excitatory neurons