Estimation of Thalamocortical and Intracortical Network Models from Joint Thalamic Single-Electrode and Cortical Laminar-Electrode Recordings in the Rat Barrel System Patrick Blomquist 1 , Anna Devor 2,3 , Ulf G. Indahl 1 , Istvan Ulbert 4,5 , Gaute T. Einevoll 1 *, Anders M. Dale 3 1 Department of Mathematical Sciences and Technology and Center for Integrative Genetics, Norwegian University of Life Sciences, A ˚ s, Norway, 2 Athinoula A. Martinos Center, Massachusetts General Hospital, Charlestown, Massachusetts, United States of America, 3 Departments of Radiology and Neurosciences, University of California San Diego, La Jolla, California, United States of America, 4 Institute for Psychology of the Hungarian Academy of Sciences, Budapest, Hungary, 5 Peter Pazmany Catholic University, Department of Information Technology, Budapest, Hungary Abstract A new method is presented for extraction of population firing-rate models for both thalamocortical and intracortical signal transfer based on stimulus-evoked data from simultaneous thalamic single-electrode and cortical recordings using linear (laminar) multielectrodes in the rat barrel system. Time-dependent population firing rates for granular (layer 4), supragranular (layer 2/3), and infragranular (layer 5) populations in a barrel column and the thalamic population in the homologous barreloid are extracted from the high-frequency portion (multi-unit activity; MUA) of the recorded extracellular signals. These extracted firing rates are in turn used to identify population firing-rate models formulated as integral equations with exponentially decaying coupling kernels, allowing for straightforward transformation to the more common firing-rate formulation in terms of differential equations. Optimal model structures and model parameters are identified by minimizing the deviation between model firing rates and the experimentally extracted population firing rates. For the thalamocortical transfer, the experimental data favor a model with fast feedforward excitation from thalamus to the layer-4 laminar population combined with a slower inhibitory process due to feedforward and/or recurrent connections and mixed linear-parabolic activation functions. The extracted firing rates of the various cortical laminar populations are found to exhibit strong temporal correlations for the present experimental paradigm, and simple feedforward population firing-rate models combined with linear or mixed linear-parabolic activation function are found to provide excellent fits to the data. The identified thalamocortical and intracortical network models are thus found to be qualitatively very different. While the thalamocortical circuit is optimally stimulated by rapid changes in the thalamic firing rate, the intracortical circuits are low- pass and respond most strongly to slowly varying inputs from the cortical layer-4 population. Citation: Blomquist P, Devor A, Indahl UG, Ulbert I, Einevoll GT, et al. (2009) Estimation of Thalamocortical and Intracortical Network Models from Joint Thalamic Single-Electrode and Cortical Laminar-Electrode Recordings in the Rat Barrel System. PLoS Comput Biol 5(3): e1000328. doi:10.1371/journal.pcbi.1000328 Editor: Karl J. Friston, University College London, United Kingdom Received October 10, 2008; Accepted February 10, 2009; Published March 27, 2009 Copyright: ß 2009 Blomquist et al. 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. Funding: Work was financially supported by the Research Council of Norway under the BeMatA and eVITA programmes, and by the National Institute of Health [R01 EB00790, NS051188]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: Gaute.Einevoll@umb.no Introduction Following pioneering work in the 1970s by, e.g., Wilson and Cowan [1] and Amari [2] a substantial effort has been put into the investigation of neural network models, particularly in the form of firing-rate or neural field models [3]. Some firing-rate network models, in particular for the early visual system ([4], Ch.2), have been developed to account for particular physiological data. However, for strongly interconnected cortical networks, few mechanistic network models directly accounting for specific neurobiological data have been identified. Instead most work has been done on generic network models and has focused on the investigation of generic features, such as the generation and stability of localized bumps, oscillatory patterns, traveling waves and pulses and other coherent structures, for reviews see Ermentrout [5] or Coombes [6]. We here (1) present a new method for identification of specific population firing-rate network models from extracellular record- ings, (2) apply the method to extract network models for thalamocortical and intracortical signal processing based on stimulus-evoked data from simultaneous single-electrode and multielectrode extracellular recordings in the rat somatosensory (barrel) system, and (3) analyze and interpret the identified firing- rate models using techniques from dynamical systems analysis. Our study reveals large differences in the transfer function between thalamus (VPM) and layer 4 of the barrel column, compared to that between cortical layers, and thus sheds direct light on how whisker stimuli is encoded in population firing- activity in the somatosensory system. The derivation of biologically realistic, cortical neural-network models has generally been hampered by the lack of relevant experimental data to constrain and test the models. Single electrodes can generally only measure the firing activity of individual neurons, not the joint activity of populations of cells typically predicted by population firing-rate models. Kyriazi and Simons [7] and Pinto et al. [8,9] thus developed models for the somatosensory thalamocortical signal transformation based on pooled data from single-unit recordings from numerous animals. PLoS Computational Biology | www.ploscompbiol.org 1 March 2009 | Volume 5 | Issue 3 | e1000328