Self-sustained asynchronous irregular states and Up/Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons

arXiv:0809.0654v4 [q-bio.NC] 10 May 2009 Journal of Computational Neuroscience manuscript No. (will be inserted by the editor) Alain Destexhe Self-sustained asynchronous irregular states and Up–Down states in thalamic, cortical and thalamocortical networks of nonlinear integrate-and-fire neurons October 22, 2018(in press) Abstract Randomly-connected networks of integrate-and- fire (IF) neurons are known to display asynchronous ir- regular (AI) activity states, which resemble the discharge activity recorded in the cerebral cortex of awake animals. However, it is not clear whether such activity states are specific to simple IF models, or if they also exist in net- works where neurons are endowed with complex intrinsic properties similar to electrophysiological measurements. Here, we investigate the occurrence of AI states in net- works of nonlinear IF neurons, such as the adaptive expo- nential IF (Brette-Gerstner-Izhikevich) model. This model can display intrinsic properties such as low-threshold spike (LTS), regular spiking (RS) or fast-spiking (FS). We suc- cessively investigate the oscillatory and AI dynamics of thalamic, cortical and thalamocortical networks using such models. AI states can be found in each case, sometimes with surprisingly small network size of the order of a few tens of neurons. We show that the presence of LTS neurons in cortex or in thalamus, explains the robust emergence of AI states for relatively small network sizes. Finally, we investigate the role of spike-frequency adaptation (SFA). In cortical networks with strong SFA in RS cells, the AI state is transient, but when SFA is reduced, AI states can be self-sustained for long times. In thalamocortical net- works, AI states are found when the cortex is itself in an AI state, but with strong SFA, the thalamocortical network displays Up and Down state transitions, similar to intra- cellular recordings during slow-wave sleep or anesthesia. Self-sustained Up and Down states could also be gener- ated by two-layer cortical networks with LTS cells. These models suggest that intrinsic properties such as adaptation and low-threshold bursting activity are crucial for the gen- esis and control of AI states in thalamocortical networks. Keywords: Computational models; Cerebral cortex; Tha- lamus; Thalamocortical system; Intrinsic neuronal prop- erties; Network models Integrative and Computational Neuroscience Unit (UNIC), UPR2191, CNRS, Gif-sur-Yvette, France E-mail: Destexhe@unic.cnrs-gif.fr 1 Introduction In awake animals, the activity of single cortical neurons consist of seemingly noisy activity, with very irregular dis- charges at frequencies of 1-20 Hz and considerable fluctu- ations at the level of the membrane potential (Vm) (Mat- sumara et al., 1988; Steriade et al., 2001; Destexhe et al., 2003; Lee et al., 2006). Model networks of leaky integrate- and-fire (IF) neurons can display activity states similar to the irregular spike discharge seen in awake cortex. These so-called “asynchronous irregular” (AI) states contrast with the “synchronous regular” (SR) states, or with oscillatory states (Brunel, 2000). AI states have been observed more recently as a self-sustained activity in more realistic IF net- works with conductance-based synapses (Vogels and Ab- bott, 2005). Such AI states typically require large network sizes, of the order of a few thousand neurons, to display characteristics consistent with experimental data (El Bous- tani et al., 2007; Kumar et al., 2008). In reality, neurons do not behave as leaky IF models, but rather display complex intrinsic properties, such as adap- tation or bursting, and these intrinsic properties may be important for neuronal function (Llinas, 1988). However, it is not clear to what extent AI states also appear in net- works of more realistic neurons. Similarly, the genesis of AI states has never been investigated in the thalamocorti- cal system. Recent efforts have been devoted to model in- trinsic neuronal properties using variants of the IF model (Smith et al., 2000; Izhikevich, 2004; Brette and Gerstner, 2005). In the present paper, we use such models to analyze the genesis of AI states in cortical, thalamic and thalamo- cortical networks of neurons expressing complex intrinsic properties. 2 Methods We successively describe the equations used for model- ing neurons and synapses, the connectivity of the different 2 network models, as well as the methods used to quantify network activity. 2.1 Single-cell models To capture the intrinsic properties of central neurons, such as the rebound bursting capabilities of thalamic cells and the spike-frequency adaptation in cortex, we considered the adaptive exponential IF (aeIF) model. This model con- sists of the two-variable IF model proposed by Izhike- vich (2004), which was modified to include an exponential non-linearity around spike threshold, based on the expo- nential IF model of Fourcaud-Trocme et al. (2003). These two models were combined by Brette and

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