A master equation formalism for macroscopic modeling of asynchronous irregular activity states

Neural Computation

Volumn 21, Issue 1, 2009, Pages 46-100

  Boustani, Sami El ^a   Destexhe, Alain ^a  

^a Unite de Neurosciences Integratives et Computationnelles   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ANIMAL; ARTICLE; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; BRAIN CORTEX; CLASSIFICATION; COMPUTER SIMULATION; CYTOLOGY; NERVE CELL; NERVE CELL INHIBITION; PHYSIOLOGY; STATISTICAL MODEL; TIME; WAKEFULNESS;

ACTION POTENTIALS; ANIMALS; CEREBRAL CORTEX; COMPUTER SIMULATION; LINEAR MODELS; MODELS, NEUROLOGICAL; NEURAL INHIBITION; NEURAL NETWORKS (COMPUTER); NEURONS; TIME FACTORS; WAKEFULNESS;

EID: 59149102161     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/neco.2009.02-08-710     Document Type: Article

References (31)

1. Amit, D. J., & Brunei, N. (1997). Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cereb. Cortex, 7, 237-252.
2. Braitenberg, V., & Schüz, A. (1998). Cortex: Statistics and geometry of neuronal connectivity (2nd ed.). Berlin: Springer-Verlag.
3. Brette, R., Rudolph, M., Carnevale, T., Hines, M., Beeman, D., Bower, J. M., et al. (2007). Simulation of networks of spiking neurons: A review of tools and strategies. J. Comput. Neurosci., 23, 349-398.
4. Brunei, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J. Comput. Neurosci., 8, 183-208.
5. Brunei, N., & Hakim, V. (1999). Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Cornput., 11, 1621-1671.
6. Brunei, N., & Sergi, S. (1998). Firing frequency of leaky integrate-and-fire neurons with synaptic currents dynamics. J. Theor. Biol., 195, 87-95.
7. Crutchfield, J. R, & Kaneko, K. (1988). Are attractors relevant to turbulence? Phys. Rev. Lett., 60, 2715-2718.
8. DeFelipe, J., Alonso-Nanclares, L., & Arellano, J.I. (2002). Microstructure of the neocortex: Comparative aspects, J. Neurocytology, 39, 299-316.
9. Destexhe, A., & Contreras, D. (2006). Neuronal computations with stochastic network states. Science, 314, 85-90.
10. Destexhe, A., Rudolph, M., & Paré, D. (2003). The high-conductance state of neocortical neurons in vivo. Nature Reviews Neurosci., 4, 739-751.
11. El Boustani, S. (2006). Information transport in networks during irregular activity states (in French). Master's thesis, Ecole Normale Supérieure, France.
12. El Boustani, S., & Destexhe, A. (2007). Mesoscopic model of balanced neuron networks using a master equation formalism. (abstract) In Computation and Neural Systems 2007 Conference. Available online at http://www.cnsorg. org.
13. El Boustani, S., Pospischil, M., Rudolph-Lilith, M., & Destexhe, A. (2007). Activated cortical states: Experiments, analyses and models. J. Physiol. Paris 101, 99-109.
14. Fourcaud, N., & Brunei, N. (2002). Dynamics of the firing probability of noisy integrate-and-fire neurons. Neural Comput., 14, 2057-2110.
15. Gerstner, W. (2000). Population dynamics of spiking neurons: Fast transients, asynchronous states, and locking. Neural Comput., 12, 43-89.
16. Ginzburg, I., & Sompolinsky, H. (1994). Theory of correlations in stochastic neural networks. Phys. Rev., 50, 3171-3191.
17. Hertz, J., Lerchner, A., & Ahmadi, M. (2004). Mean field methods for cortical network dynamics. Comput. Neurosci., 3146, 71-89.
18. Kuhn, A., Aertsen, A., & Rotter, S. (2004). Neuronal integration of synaptic input in the fluctuation-driven regime. J. Neurosci., 24, 2345-2356.
19. Kumar, A., Schrader, S., Aertsen, A., & Rotter, S. (2008). The high-conductance state of cortical networks. Comput. Neurosci., 20, 1-43.
20. Latham, P. E., Richmond, B. J., Nelson, P. G, & Nirenberg, S. (2000). Intrinsic dynamics in neuronal networks. I. Theory. J. Neurophysiol., 83, 808-827.
21. Matsumura, M., Cope, T., & Fetz, E. E. (1988). Sustained excitatory synaptic input to motor cortex neurons in awake animals revealed by intracellular recording of membrane potentials. Exp. Brain Res., 70, 463-469.
22. 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, 395-408.
23. Ohira, T., & Cowan, J. D. (1993). Master-equation approach to stochastic neurodynamics. Phys. Rev. E, 48, 2259-2266.
24. Plesser, H. E., & Gerstner, W. (2000). Noise in integrate-and-fire neurons: From stochastic input to escape rates. Neural Commit., 12, 367-384.
25. Soula, H., & Chow, C. C. (2007). Stochastic dynamics of a finite-size spiking neural network. Neural Comput., 19, 3262-3292.
26. Steriade, M., Timofeev, I., & Grenier, F. (2001). Natural waking and sleep states: A view from inside neocortical neurons. J. Neurophysiol., 85, 1969-1985.
27. Tuckwell, H. C. (1988). Introduction to theoretical neurobiology. Cambridge: Cambridge University Press.
28. van Kampen, N. G. (2003). Stochastic processes in physics and chemistry. Amsterdam: North-Holland Personal Library.
29. van Vreeswijk, C., & Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science, 274, 1724-1726.
30. van Vreeswijk, C., & Sompolinsky, H. (1998). Chaotic balanced state in a model of cortical circuits. Neural Comput., 10, 1321-1371.
31. Vogels, T. P., & Abbott, L. F. (2005). Signal propagation and logic gating in networks of integrate-and-fire neurons, J. Neurosci., 25, 10786-10795.