Universität zu Köln

Schwalger, Tilo ORCID: 0000-0002-5422-3723, Deger, Moritz ORCID: 0000-0002-2775-2611 and Gerstner, Wulfram (2017). Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size. PLoS Comput. Biol., 13 (4). SAN FRANCISCO: PUBLIC LIBRARY SCIENCE. ISSN 1553-7358

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Abstract

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50-2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finitesize- induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Schwalger, Tilo UNSPECIFIED orcid.org/0000-0002-5422-3723 UNSPECIFIED Deger, Moritz UNSPECIFIED orcid.org/0000-0002-2775-2611 UNSPECIFIED Gerstner, Wulfram UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-236091
DOI:	10.1371/journal.pcbi.1005507
Journal or Publication Title:	PLoS Comput. Biol.
Volume:	13
Number:	4
Date:	2017
Publisher:	PUBLIC LIBRARY SCIENCE
Place of Publication:	SAN FRANCISCO
ISSN:	1553-7358
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language RESPONSE VARIABILITY; NETWORK MODEL; FIELD-THEORY; LAYER 2/3; DYNAMICS; ADAPTATION; NOISE; STATISTICS; MEMORY; TRAINS Multiple languages Biochemical Research Methods; Mathematical & Computational Biology Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/23609