Multistability of clustered states in a globally inhibitory network (Chandrasekaran et al. 2009)


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Accession:120227
"We study a network of m identical excitatory cells projecting excitatory synaptic connections onto a single inhibitory interneuron, which is reciprocally coupled to all excitatory cells through inhibitory synapses possessing short-term synaptic depression. We find that such a network with global inhibition possesses multiple stable activity patterns with distinct periods, characterized by the clustering of the excitatory cells into synchronized sub-populations. We prove the existence and stability of n-cluster solutions in a m-cell network. ... Implications for temporal coding and memory storage are discussed."
Reference:
1 . Chandrasekaran L, Matveev V, Bose A (2009) Multistability of clustered states in a globally inhibitory network Physica D: Nonlinear Phenomena 238(3):253-263
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Model Type: Realistic Network;
Brain Region(s)/Organism: Hippocampus;
Cell Type(s):
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: MATLAB (web link to model);
Model Concept(s): Temporal Pattern Generation; Simplified Models; Short-term Synaptic Plasticity; Depression; Attractor Neural Network;
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Chandrasekaran L, Matveev V, Bose A (2009) Multistability of clustered states in a globally inhibitory network Physica D: Nonlinear Phenomena 238(3):253-263

References and models cited by this paper

References and models that cite this paper

Abbott LF, Varela JA, Sen K, Nelson SB (1997) Synaptic depression and cortical gain control. Science 275:220-4 [PubMed]

Bialek W, Rieke F, de Ruyter van Steveninck RR, Warland D (1991) Reading a neural code. Science 252:1854-7 [PubMed]

Bose A, Manor Y, Nadim F (2001) Bistable oscillations arising from synaptic depression. Siam J Appl Math 62:706-727

Cook DL, Schwindt PC, Grande LA, Spain WJ (2003) Synaptic depression in the localization of sound. Nature 421:66-70 [PubMed]

Doiron B, Chacron MJ, Maler L, Longtin A, Bastian J (2003) Inhibitory feedback required for network oscillatory responses to communication but not prey stimuli. Nature 421:539-43 [PubMed]

Ermentrout GB (2002) Simulating, Analyzing, and Animating Dynamical System: A Guide to XPPAUT for Researchers and Students Society for Industrial and Applied Mathematics (SIAM)

Ermentrout GB, Kopell N (1998) Fine structure of neural spiking and synchronization in the presence of conduction delays. Proc Natl Acad Sci U S A 95:1259-64 [PubMed]

Freund TF, Buzsaki G (1996) Interneurons of the hippocampus. Hippocampus 6:347-470 [PubMed]

Grande LA, Spain WJ (2005) Synaptic depression as a timing device. Physiology (Bethesda) 20:201-10 [PubMed]

Horn D, Opher I (1996) Temporal segmentation in a neural dynamic system. Neural Comput 8:373-89

Kunec S, Bose A (2003) High-frequency, depressing inhibition facilitates synchronization in globally inhibitory networks. Network 14:647-72

Lewis TJ, Rinzel J (2003) Dynamics of spiking neurons connected by both inhibitory and electrical coupling. J Comput Neurosci 14:283-309 [Journal] [PubMed]

Manor Y, Bose A, Booth V, Nadim F (2003) The contribution of synaptic depression to phase maintenance in a model rhythmic network. J Neurophysiol : [Journal] [PubMed]

Maran SK, Canavier CC (2008) Using phase resetting to predict 1:1 and 2:2 locking in two neuron networks in which firing order is not always preserved. J Comput Neurosci 24:37-55 [PubMed]

Marder E, Calabrese RL (1996) Principles of rhythmic motor pattern generation. Physiol Rev 76:687-717 [PubMed]

Mishchenko EF, Rozov NK (1980) Differential Equations with Small Parameters and Relaxation Oscillators

O'Keefe J (1976) Place units in the hippocampus of the freely moving rat. Exp Neurol 51:78-109 [PubMed]

Oh M, Matveev V (2009) Loss of phase-locking in non-weakly coupled inhibitory networks of type-I model neurons. J Comput Neurosci 26(2):303-20 [Journal] [PubMed]

  • Loss of phase-locking in non-weakly coupled inhib. networks of type-I neurons (Oh and Matveev 2009) [Model]

Petersen CC (2002) Short-term dynamics of synaptic transmission within the excitatory neuronal network of rat layer 4 barrel cortex. J Neurophysiol 87:2904-14 [Journal] [PubMed]

Pfeuty B, Mato G, Golomb D, Hansel D (2005) The combined effects of inhibitory and electrical synapses in synchrony. Neural Comput 17:633-70 [PubMed]

Rubin J, Terman D (2000) Analysis of clustered firing patterns in synaptically coupled networks of oscillators. J Math Biol 41:513-45 [PubMed]

Silbering AF, Galizia CG (2007) Processing of odor mixtures in the Drosophila antennal lobe reveals both global inhibition and glomerulus-specific interactions. J Neurosci 27:11966-77 [PubMed]

Skinner FK, Kopell N, Marder E (1994) Mechanisms for oscillation and frequency control in reciprocally inhibitory model neural networks. J Comput Neurosci 1:69-87 [Journal] [PubMed]

Skinner FK, Mulloney B (1998) Intersegmental coordination of limb movements during locomotion: mathematical models predict circuits that drive swimmeret beating. J Neurosci 18:3831-42 [PubMed]

Terman D, Kopell N, Bose A (1998) Dynamics of two mutually coupled slow inhibitory neurons. Physica D 117:241-275

Traub RD, Miles R (1991) Neuronal Networks Of The Hippocampus

Van Vreeswijk C, Abbott LF, Ermentrout GB (1994) When inhibition not excitation synchronizes neural firing. J Comput Neurosci 1:313-21 [Journal] [PubMed]

Wang D, Terman D (1995) Locally excitatory globally inhibitory oscillator networks IEEE Transaction On Neural Networks 6:283-286

Wang XJ, Rinzel J (1993) Spindle rhythmicity in the reticularis thalami nucleus: synchronization among mutually inhibitory neurons. Neuroscience 53:899-904 [PubMed]

Williams TL, Sigvardt KA, Kopell N, Ermentrout GB, Remler MP (1990) Forcing of coupled nonlinear oscillators: studies of intersegmental coordination in the lamprey locomotor central pattern generator. J Neurophysiol 64:862-71 [Journal] [PubMed]

Zucker RS, Regehr WG (2002) Short-term synaptic plasticity. Annu Rev Physiol 64:355-405 [PubMed]

(31 refs)