Biol Cybern (2009) 101:325–338 DOI 10.1007/s00422-009-0339-0 ORIGINAL PAPER Inhibitory network of spiking neurons may express a sharp peak of synchrony at low frequency band Pierre Meyrand · Daniel Cattaert · Hubert Ostaszewski · Tiaza Bem Received: 10 July 2009 / Accepted: 14 September 2009 / Published online: 28 October 2009 © Springer-Verlag 2009 Abstract Spike synchronization remains an important issue in neuroscience, and inhibitory networks are the best candidates to provide such synchrony. Increasing evidence indicates that in many brain area inhibitory interneurons of similar properties make reciprocal connections. We found that a hybrid, as well as model network, consisting of two reciprocally inhibitory spiking neurons may express a peak of synchronization in a narrow range of low spiking frequen- cies in addition to classically described plateau of synchrony at a wide range of high frequencies. Occurrence of the low frequency peak of synchrony requires a moderate-to-strong inhibitory coupling and relatively fast synapses. This novel possibility of synchronization in a narrow range of network parameters may have an important implication in discrimi- nation and encoding of signals of precise intensity, as well as in altering network ability to process information. Introduction A lot of studies on the brain function have shown that syn- chronization of spikes of individual neurons or synchroniza- tion of average population activities may play an important role in the operation of sensory, cognitive, or behavioral task (Baker et al. 2003; Friedrich 2006; Friedrich et al. 2004; Gray 1994; Riehle et al. 1997; Roy et al. 2007; Singer 1999). P. Meyrand (B ) · D. Cattaert Centre de Neurosciences Intégratives et Computationnelles, Université Bordeaux 1 et Centre National de la Recherche Scientifique Unité Mixte de Recherche 5228, Avenue des Facultés, 33405 Talence cedex, France e-mail: p.meyrand@cnic.u-bordeaux1.fr H. Ostaszewski · T. Bem Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, 4 Trojdena, 02-109 Warsaw, Poland As indicated by many experimental and theoretical studies, inhibitory interneuron networks seem to play an important role in global oscillations found in such structure like hip- pocampus, thalamus, or cortex (Galarreta and Hestrin 2002; Hestrin and Galarreta 2005; Markram et al. 2004; Merriam et al. 2005; Tamas et al. 1998). The mechanism providing synchronization through inhi- bition has been understood using reduced models consist- ing of two reciprocally inhibitory cells in a weak (Lewis and Rinzel 2003; Van Vreeswijk et al. 1994) as well as strong coupling regime (Chow 1998). For example, it has been found that synchronization depends on cells’ firing frequency as well as synapse kinetics (Chow et al. 1998; Lewis and Rinzel 2003; White et al. 1998). Insights from such simplified models have been thereafter extended into understanding of more complex behavior of large scale net- works (Traub et al. 1997; Whittington et al. 1995). Weak coupling requires that to synchronize network activity, the kinetics of synapses must be slow. However, such synchrony can be very fragile to heterogeneity of neurons’ membrane and/or synaptic properties (Chow et al. 1998; Skinner et al. 2005; White et al. 1998). In contrast, with stronger coupling, synchronization can be reached even in a fairly heteroge- neous network by using fast synapses with a delay (Bartos et al. 2007) whereas slow synaptic kinetics results in de-syn- chronization of network activity. Indeed, in heterogeneous networks some neurons, of higher intrinsic frequency, sup- press the activity of the others (Chow 1998; Chow et al. 1998; Skinner et al. 2005; White et al. 1998). Moreover, even in homogenous networks with sufficiently strong and slow inhibitory synapses, the stability of both the synchronous and anti-synchronous states is broken leading to the sup- pression state (Bressloff and Coombes 2000; Chow 1998). Because anti-synchronous activity dominates in a regime of weak coupling and low-to-moderate firing frequencies 123