A network model with pyramidal cells and GABAergic non-FS cells in the cerebral cortex
Introduction
There are a wide variety of GABAergic interneurons in the cerebral cortex. Recent experiments using intracellular dual recordings revealed that these GABAergic neurons are divided into mainly two classes, fast spiking (FS) cells and non-FS cells including low threshold spiking (LTS) cells, according to their electrophysiological features. Additionally, this physiological grouping largely accords with the anatomical grouping based on the difference in the locations where they make the synapses on the target pyramidal cells; while FS cells tend to make their synapses at the somata or proximal regions of the dendrites, non-FS cells are apt to target the distal sites of the dendrites [2], [3], [4], [21]. Therefore, as for non-FS cells, localized interaction between the excitatory synaptic inputs and inhibitory ones on each dendritic branch could occur, raising the possibility of the local computation, proposed by Koch et al. as “dendritic gate” [10], such that inhibitory inputs on a certain dendritic branch effectively shunt excitatory inputs on the same branch but do not have effects on other branches. Increasing evidences indicate that the non-FS GABAergic system is functionally different in many situations from the FS system [2], [3], [26], and so it seems to be important to analyze the interaction between pyramidal cells and non-FS cells not only in the single cell level but also in the network level. In this paper, we propose a firing rate-based neural network model of cortical local circuits consisting of pyramidal cells and non-FS GABAergic cells, in which we include location-restricted effects of dendritic inhibitions mediated by non-FS cells. We examine the dynamical properties of the model, showing that this nonlinearity of single neurons changes the network behavior from those of conventional lateral inhibition networks.
Section snippets
The model
We propose a neural network model that corresponds to relatively small regions of the cerebral cortex, possibly cortical columns [22], [23], including excitatory pyramidal cells and inhibitory GABAergic interneurons of such types as LTS or other non-FS cells that make synapses on to the distal dendrites of the target pyramidal cells (Fig. 1). We consider four types of connections: (1) excitatory feedforward connections from input sources such as thalamus, other subcortical regions, or other
Simulation results
In both the conventional model (Eq. (2)) and our new model (Eq. (1)), there are two regimes about the strength of the self-excitation (). If , whenever the input is absent, all the neurons are quiet because the decay term (−x) exceeds the self-excitation term (). If , on the other hand, the self-excitation term exceeds the decay term so that activities of some neurons persist even after the input is turned off. In this paper, we concentrate on the latter case, namely , in which the
Discussion
We discuss here the possibility that our simplified network model is related to the real neocortical neuronal networks. At first, consider the problem that though our model includes only non-FS type of GABAergic cells, actually there coexist both types, non-FS and FS, of GABAergic cells in the cerebral cortex. In general, it goes without saying that models including both types of GABAergic cells should be constructed. Nevertheless, the network model with only the non-FS cells, as those proposed
Acknowledgements
This study is partially supported by a Grant-in-Aid No. 15016023 on priority areas (C) Advanced Brain Science Project from the Ministry of Education, Sports, Science, and Technology, the Japanese Government. K.M. is supported by JSPS Research Fellowships for Young Scientists (10834).
References (26)
- et al.
Competition and cooperation in neural nets
On the piecewise analysis of networks of linear threshold neurons
Neural Networks
(1998)- et al.
Differences between somatic and dendritic inhibition in the hippocampus
Neuron
(1996) - et al.
Pyramidal neuron as two-layer neural network
Neuron
(2003) - et al.
Coincident pre- and postsynaptic activity modifies GABAergic synapses by postsynaptic changes in Cl-transporter activity
Neuron
(2003) - et al.
Major differences in inhibitory synaptic transmission onto two neocortical interneuron subclasses
J. Neurosci.
(2003) - et al.
Two dynamically distinct inhibitory networks in layer 4 of the neocortex
J. Neurophysiol.
(2003) - et al.
number and location of synapses made by single pyramidal cells onto aspiny interneurones of cat visual cortex
J. Phys.
(1997) - et al.
Qualitative behaviour of some simple networks
J. Phys. A
(1996) - et al.
Dopamine modulation of perisomatic and peridendritic inhibition in prefrontal cortex
J. Neurosci.
(2003)
Two networks of electrically coupled inhibitory neurons in neocortex
Nature
Principles of Neural Science
Nonlinear interactions in a dendritic treelocalization, timing, and role in information processing
Proc. Nat. Acad. Sci. U.S.A.
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