Differential control of active and silent phases in relaxation models of neuronal rhythms

Journal of Computational Neuroscience

Volumn 21, Issue 3, 2006, Pages 307-328

  Tabak, Joël ^a,c   O'Donovan, Michael J ^a   Rinzel, John ^b  

^a NATIONAL INSTITUTE OF NEUROLOGICAL DISORDERS AND STROKE   (United States)

^b NEW YORK UNIVERSITY   (United States)

^c FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Cellular adaptation; Episodic activity; Excitatory network; Mean field model; Synaptic depression

Indexed keywords

BIOLOGICAL SYSTEMS; CELLULAR NEURAL NETWORKS; MEAN FIELD THEORY; TIME SWITCHES;

ACTIVE PHASIS; CELLULAR ADAPTATION; CELLULARS; DIFFERENTIAL CONTROL; EPISODIC ACTIVITY; EXCITATORY NETWORK; INPUT/OUTPUT FUNCTION; MEAN FIELD MODELS; SILENT PHASE; SYNAPTIC DEPRESSION;

FEEDBACK;

ADAPTATION; ANALYTICAL PARAMETERS; ARTICLE; COMPUTER PROGRAM; COMPUTER SIMULATION; CONTROLLED STUDY; INTERMETHOD COMPARISON; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NEGATIVE FEEDBACK; NERVE CELL EXCITABILITY; NERVE CELL MEMBRANE STEADY POTENTIAL; NERVE CELL NETWORK; PACEMAKER NERVE CELL; POSITIVE FEEDBACK; PRIORITY JOURNAL; SENSITIVITY ANALYSIS; SYNAPTIC TRANSMISSION; TIME;

EID: 33749531532     PISSN: 09295313     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10827-006-8862-7     Document Type: Article

References (41)

1. Bertam R, Previte J, Sherman A, Kinard TA, Satin LS (2000) The phantom burster model for pancreatic β-cells. Biophys J 79: 2880-2892.
2. Borodinsky LN, Root CM, Cronin JA, Sann SB, Gu X, Spitzer NC (2004) Activity-dependent homeostatic specification of transmitter expression in embryonic neurons. Nature 429: 523-530.
3. Bracci E, Ballerini L, Nistri A (1996) Spontaneous bursts induced by pharmacological block of inhibition in lumbar motoneurons of the neonatal rat spinal cord. J Neurophysiol 75: 640-647.
4. Butera RJ, Rinzel J, Smith JC (1999) Models of respiratory rhythm generation in the pre-Bötzinger complex: I. Bursting pacemaker neurons. J Neurophysiol 82: 382-397.
5. Butts DA, Feller MB, Shatz CJ, Rokhsar DS (1999) Retinal waves are governed by collective network properties. J Neurosci 19: 3580-3593.
6. Compte A, Sanchez-Vives MV, McCormick DA, Wang X-J (2003) Cellular and network mechanisms of slow oscillatory activity (<1 Hz) and wave propagations in a cortical network model. J Neurophysiol 89: 2707-2725.
7. Coombes S, Bressloff PC (eds.) (2005) Bursting: The genesis of rhythm in the nervous system. World Scientific.
8. Ermentrout B (1998) Linearization of f-i curves by adaptation. Neural Comput 10: 1721-1729.
9. Ermentrout B (2002) Simulating, analyzing, and animating dynamical systems. SIAM.
10. Ermentrout G, Chow CC (2002) Modeling neural oscillations. Physiol and Behav 77: 629-633.
11. Friesen WO, Block GD (1984) What is a biological oscillator? Am J Physiol 246: R847-853.
12. Giugliano M, Darbon P, Arsiero M, Lüscher H-R, Streit J (2004) Single-neuron discharge properties and network activity in dissociated cultures of neocortex. J Neurophysiol 92: 977-996.
13. 2+ transients. Nature 375: 784-787.
14. Hanson MG, Landmesser LT (2004) Normal patterns of spontaneous activity are required for correct motor axon guidance and the expression of specific guidance molecules. Neuron 43: 687-701.
15. Heeger DJ (1993) Modeling simple-cell direction selectivity with normalized, half-squared, linear operators. J Neurophysiol 70: 1885-1898.
16. Holt GR, Koch C (1997) Shunting inhibition does not have a divisive effect on firing rates. Neural Comput 9: 1001-1013.
17. Latham PE, Richmond BJ, Nelson PG, Nirenberg S (2000) Intrinsic dynamics in neuronal networks. I. Theory. J Neurophysiol 83: 808-827.
18. Marchetti C, Tabak J, Chub N, O'Donovan MJ, Rinzel J (2005) Modeling spontaneous activity in the developing spinal cord using activity-dependent variations of intracellular chloride. J Neurosci 25: 3601-3612.
19. Marder E, Calabrese R (1996) Principles of rhythmic motor pattern generation. Physiol Rev 76: 687-717.
20. Netoff TI, Clewley R, Arno S, Keck T, White JA (2004) Epilepsy in small-world networks. J Neurosci 24: 8075-8083.
21. O'Donovan MJ (1999) The origin of spontaneous activity in developing networks of the vertebrate nervous system. Curr Opin Neurobiol 9: 94-104.
22. Pena F, Parkis MA, Tryba AK, Ramirez J-M (2004) Differential contribution of pacemaker properties to the generation of respiratory rhythms during normoxia and hypoxia. Neuron 43: 105-117.
23. Pinto DJ, Brumberg JC, Simons DJ, Ermentrout GB (1996) A quantitative population model of whisker barrels: Re-examining the wilson-cowan equations. J Comput Neurosci 3: 247-264.
24. Rinzel J, Ermentrout GB (1998) Analysis of neural excitability and oscillations. In Methods in Neuronal Modeling. MIT Press.
25. Rinzel J (1985) Excitation dynamics: Insights from simplified membrane models. Fed Proc 44: 2944-2946.
26. + pump and synaptic inhibition in the rat spinal cord. J Neurophysiol 88: 676-691.
27. Sanchez-Vives MV, Nowak LG, McCormick DA (2000) Cellular mechanisms of long lasting adaptation in visual cortical neurons in vitro. J Neurosci 20: 4286-4299.
28. Skinner FK, Turrigiano GG, Marder E (1993) Frequency and burst duration in oscillating neurons and two-cell networks. Biol Cybern 69: 375-383.
29. Smolen P, Sherman A (1994) Phase independent resetting in relaxation and bursting oscillators. J theor Biol 169: 339-348.
30. Staley KJ, Longacher M, Bains JS, Yee A (1998) Presynaptic modulation of CA3 network activity. Nature Neurosci 1: 201-209.
31. Stellwagen D, Shatz CJ (2002) An instructive role for retinal waves in the development of retinogeniculate connectivity. Neuron 33: 357-367.
32. Tabak J, Latham PE (2003) Analysis of spontaneous bursting activity in random neural networks. Neuroreport 14: 1445-1449.
33. Tabak J, Rinzel J, O'Donovan MJ (2001) The role of activity-dependent network depression in the expression and self-regulation of spontaneous activity in the developing spinal cord. J Neurosci 21: 8966-8978.
34. Tabak J, Rinzel J (2005) Bursting in excitatory neural networks. In Coombes S, Bressloff, P (eds.) Bursting: The Genesis of Rhythm in the Nervous System, World Scientific, pp. 273-301.
35. Tabak J, Senn W, O'Donovan MJ, Rinzel J (2000) Modeling of spontaneous activity in the developing spinal cord using activity-dependent depression in an excitatory network. J Neurosci 20: 3041-3056.
36. Tsodyks M, Uziel A, Markram H (2000) Synchrony generation in recurrent networks with frequency-dependent synapses. J Neurosci 20: RC50.
37. Viemari J-C, Ramirez J-M (2004) Role of norepinephrine in respiratory rhythm generation. Soc Neurosci Abs 755.1.
38. Wiedemann UA, Lüthi A (2003) Timing of network synchronization by refractory mechanisms. J Neurophysiol 90: 3902-3911.
39. Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12: 1-24.
40. Wilson HR (2003) Computational evidence for a rivalry hierarchy in vision. Proc Natl Acad Sci 100: 14499-14503.
41. Yee AS, Longacher M, Staley KJ (2003) Convulsant and anticonvulsant effects on spontaneous CA3 population bursts. J Neurophysiol 89: 427-441.