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      The Emergence of Up and Down States in Cortical Networks

      research-article
      1 , * , 2 , 3
      PLoS Computational Biology
      Public Library of Science

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          Abstract

          The cerebral cortex is continuously active in the absence of external stimuli. An example of this spontaneous activity is the voltage transition between an Up and a Down state, observed simultaneously at individual neurons. Since this phenomenon could be of critical importance for working memory and attention, its explanation could reveal some fundamental properties of cortical organization. To identify a possible scenario for the dynamics of Up–Down states, we analyze a reduced stochastic dynamical system that models an interconnected network of excitatory neurons with activity-dependent synaptic depression. The model reveals that when the total synaptic connection strength exceeds a certain threshold, the phase space of the dynamical system contains two attractors, interpreted as Up and Down states. In that case, synaptic noise causes transitions between the states. Moreover, an external stimulation producing a depolarization increases the time spent in the Up state, as observed experimentally. We therefore propose that the existence of Up–Down states is a fundamental and inherent property of a noisy neural ensemble with sufficiently strong synaptic connections.

          Synopsis

          The cerebral cortex is continuously active in the absence of sensory stimuli. An example of this spontaneous activity is the phenomenon of voltage transitions between two distinct levels, called Up and Down states, observed simultaneously when recoding from many neurons. This phenomenon could be of a critical importance for working memory and attention. Thus, uncovering its biological mechanism could reveal fundamental properties of the cortical organization. In this theoretical contribution, Holcman and Tsodyks propose a mathematical model of cortical dynamics that exhibits spontaneous transitions between Up and Down states. The model describes an activity of a network of interconnected neurons. A crucial component of the model is synaptic depression of interneuronal connections, which is a well-known effect that characterizes many types of synaptic connections in the cortex. Despite its simplicity, the model reproduces many properties of Up–Down transitions that were experimentally observed, and makes several intriguing predictions for future experiments. In particular, the model predicts that the time that a network spends in the Up state is highly variable, changing from a fraction of a second to more than ten seconds, which could have some interesting implications for the temporal characteristics of working memory.

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          Most cited references30

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          Neural networks with dynamic synapses.

          Transmission across neocortical synapses depends on the frequency of presynaptic activity (Thomson & Deuchars, 1994). Interpyramidal synapses in layer V exhibit fast depression of synaptic transmission, while other types of synapses exhibit facilitation of transmission. To study the role of dynamic synapses in network computation, we propose a unified phenomenological model that allows computation of the postsynaptic current generated by both types of synapses when driven by an arbitrary pattern of action potential (AP) activity in a presynaptic population. Using this formalism, we analyze different regimes of synaptic transmission and demonstrate that dynamic synapses transmit different aspects of the presynaptic activity depending on the average presynaptic frequency. The model also allows for derivation of mean-field equations, which govern the activity of large, interconnected networks. We show that the dynamics of synaptic transmission results in complex sets of regular and irregular regimes of network activity.
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            Turning on and off recurrent balanced cortical activity.

            The vast majority of synaptic connections onto neurons in the cerebral cortex arise from other cortical neurons, both excitatory and inhibitory, forming local and distant 'recurrent' networks. Although this is a basic theme of cortical organization, its study has been limited largely to theoretical investigations, which predict that local recurrent networks show a proportionality or balance between recurrent excitation and inhibition, allowing the generation of stable periods of activity. This recurrent activity might underlie such diverse operations as short-term memory, the modulation of neuronal excitability with attention, and the generation of spontaneous activity during sleep. Here we show that local cortical circuits do indeed operate through a proportional balance of excitation and inhibition generated through local recurrent connections, and that the operation of such circuits can generate self-sustaining activity that can be turned on and off by synaptic inputs. These results confirm the long-hypothesized role of recurrent activity as a basic operation of the cerebral cortex.
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              Interaction of sensory responses with spontaneous depolarization in layer 2/3 barrel cortex.

              The rodent primary somatosensory cortex is spontaneously active in the form of locally synchronous membrane depolarizations (UP states) separated by quiescent hyperpolarized periods (DOWN states) both under anesthesia and during quiet wakefulness. In vivo whole-cell recordings and tetrode unit recordings were combined with voltage-sensitive dye imaging to analyze the relationship of the activity of individual pyramidal neurons in layer 2/3 to the ensemble spatiotemporal dynamics of the spontaneous depolarizations. These were either brief and localized to an area of a barrel column or occurred as propagating waves dependent on local glutamatergic synaptic transmission in layer 2/3. Spontaneous activity inhibited the sensory responses evoked by whisker deflection, accounting almost entirely for the large trial-to-trial variability of sensory-evoked postsynaptic potentials and action potentials. Subthreshold sensory synaptic responses evoked while a cortical area was spontaneously depolarized were smaller, briefer and spatially more confined. Surprisingly, whisker deflections evoked fewer action potentials during the spontaneous depolarizations despite neurons being closer to threshold. The ongoing spontaneous activity thus regulates the amplitude and the time-dependent spread of the sensory response in layer 2/3 barrel cortex.
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                Author and article information

                Contributors
                Role: Editor
                Journal
                PLoS Comput Biol
                pcbi
                PLoS Computational Biology
                Public Library of Science (San Francisco, USA )
                1553-734X
                1553-7358
                March 2006
                24 March 2006
                10 February 2006
                : 2
                : 3
                : e23
                Affiliations
                [1 ] Department of Mathematics, Weizmann Institute of Science, Rehovot, Israel
                [2 ] Department of Neurobiology, Weizmann Institute of Science, Rehovot, Israel
                [3 ] Departement d'etudes cognitives, Ecole Normale Superieure, Paris, France
                University College London, United Kingdom
                Author notes
                * To whom correspondence should be addressed. E-mail: david.holcman@ 123456weizmann.ac.il

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

                Article
                05-PLCB-RA-0211R3 plcb-02-03-07
                10.1371/journal.pcbi.0020023
                1409813
                16557293
                95bc5a4b-33da-4227-90fb-229fd1f1914f
                Copyright: © 2006 Holcman and Tsodyks. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
                History
                : 24 August 2005
                : 10 February 2006
                Page count
                Pages: 8
                Categories
                Research Article
                Bioinformatics - Computational Biology
                Neuroscience
                Systems Biology
                None
                Custom metadata
                Holcman D, Tsodyks M (2006) The emergence of Up and Down states in cortical networks. PLoS Comput Biol 2(3): e23.

                Quantitative & Systems biology
                Quantitative & Systems biology

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