Research Article

The Emergence of Up and Down States in Cortical Networks

  • David Holcman mail,

    To whom correspondence should be addressed. E-mail:

    Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel

    ¤ Current address: Departement de Biologie, INSERM 497, Ecole Normale Supérieure, Paris, France

  • Misha Tsodyks

    Affiliations: Department of Neurobiology, Weizmann Institute of Science, Rehovot, Israel, Departement d'etudes cognitives, Ecole Normale Superieure, Paris, France

  • Published: March 24, 2006
  • DOI: 10.1371/journal.pcbi.0020023

Reader Comments (1)

Post a new comment on this article

Comment on The Emergence of Up and Down States in Cortical Networks

Posted by PLoS_CompBiol on 20 Feb 2008 at 10:49 GMT

Originally posted as a Reader Response on 15th September, 2006

With great interest, we have read the recent publication by Holcman and Tsodyks (PLoS Comput Biol. 2006 Mar;2(3):e23). It is very exciting to see how the experimentally observed 'switching' between up and down states can be understood as a consequence of synaptic depression.

We want to mention that in our article published in 2002 (1), we in fact predicted this behaviour, as the consequence of recurrent connectivity and synaptic depression. We studied the parameter space and identified a new phase of rapid switching between two or more attractors in the network, which is the consequence of synaptic depression. The phase space and bifurcation analysis was performed for binary neurons using a mean field analysis and was validated using MC simulations. In addition, it was shown that the curious behaviour of rapid switching was also observed in networks of more realistic integrate-and-fire neurons. We showed that the time that the network spends in the metastable states is affected by synaptic properties, such as tau_rec, and the noise in the network, and that this time can diverge to infinity for critical values of these parameters. We mention the possible importance of the switching behaviour for working memory and attention.

We therefore think that the main message of the Holcman and Tsodyks paper is already in our paper.

In more recent papers, we have extended this analysis in several directions, such as the computation of the storage capacity of networks with depressing synapses (2) and analysis of the consequence of synaptic facilitation on the network behaviour (3).

Best regards,
Joaquin J. Torres, University of Granada, Spain
Hilbert J. Kappen, Radboud University, Nijmegen, the Netherlands

1. Pantic L, Torres JJ, Kappen HJ, Gielen SC (2002) Associative memory with dynamic synapses. Neural Comput Dec;14(12):2903-2923.

2. Torres, JJ, Pantic L, Kappen HJ (2002) Storage capacity of attractor neural networks with depressing synapses. Phys Review E, 66:061910.

3. Torres JJ, Cortes JM, Marro J, Kappen HJ. Competition between synaptic depression and facilitation in attractor neural networks. Neural Comput, In press.

Submitted by: Hilbert Kappen
Occupation: Professor of Physics
Radboud University Nijmegen The Netherlands
Additional authors: Joaquin J. Torres

RE: Comment on The Emergence of Up and Down States in Cortical Networks

PLoS_CompBiol replied to PLoS_CompBiol on 26 Feb 2008 at 14:11 GMT

Originally submitted as a Reader Response on 26th June, 2007

We became aware recently of the comment by Hilbert J. Kappen and Joaquin J. Torres concerning our publication entitled 'The Emergence of Up and Down States in Cortical Networks' (PLoS Comput Biol. 2006 Mar;2(3):e23). In our paper, we presented a novel mechanism for experimentally-observed transitions between Up and Down states in cortical neurons. In the model, Up-Down transitions resulted from synaptic depression in recurrent excitatory connections and intrinsic noise. In their comment, the authors argue that 'the main message of the Holcman and Tsodyks paper is already in our paper' (i.e. Pantic L, Torres JJ, Kappen HJ, Gielen SC (2002) Associative memory with dynamic synapses. Neural Comput Dec;14(12):2903-2923). This paper deals with attractor neural networks and the main result of it is the analysis of the switching between different attractors due to synaptic depression.

While we agree that the paper by Pantic et al deals with transitions between different states in networks with synaptic depression, it has some major differences with our model. Most importantly, as standard in Hopfield-like modeling, Pantic et al are interested in transitions between different attractors, i.e. different groups of neurons that compete with each other due to mutual inhibition, as a result of which the activity switches between these different groups. There is no experimental evidence that Up-Down transitions result from switching between different neuronal groups. In our model, we consider one homogeneous population that undergoes transitions between high- and low-activity states without switching to another population attractor. In addition to this major difference, the dynamical mechanism of transitions is also different between our models. In Pantic et al, transitions occur when the system acquires a stable limit cycle, thus the period of the transition is a function of the period of this limit cycle. In our model, on the other hand, we considered a bistable regime with two stable fixed points that are separated by an unstable limit cycle. The transitions between the two attractors were therefore exclusively noise-driven, and hence did not have a periodic behavior.
This is why in our model the transitions were characterized by a wide distribution of dwelling times in the Up and Down states, as indeed observed in the experiments.
Despite of these major differences, we still feel that we should have cited the work by Pantic et al in our paper, because they address related questions and apply similar mathematical analysis. We therefore apologize for having missed the opportunity to credit Pantic et al for their important contribution.

Submitted by: David Holcman