Impact of Adaptation Currents on Synchronization of Coupled Exponential Integrate-and-Fire Neurons Josef Ladenbauer 1,2 *, Moritz Augustin 1 , LieJune Shiau 3 , Klaus Obermayer 1,2 1 Department of Software Engineering and Theoretical Computer Science, Technische Universita ¨t Berlin, Berlin, Germany, 2 Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany, 3 Department of Mathematics, University of Houston, Houston, Texas, United States of America Abstract The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential integrate-and-fire (aEIF) neuron model to determine how subthreshold and spike-triggered slow adaptation currents shape the PRC. Based on that, we predict how synchrony and phase locked states of coupled neurons change in presence of synaptic delays and unequal coupling strengths. We find that increased subthreshold adaptation currents cause a transition of the PRC from only phase advances to phase advances and delays in response to excitatory perturbations. Increased spike-triggered adaptation currents on the other hand predominantly skew the PRC to the right. Both adaptation induced changes of the PRC are modulated by spike frequency, being more prominent at lower frequencies. Applying phase reduction theory, we show that subthreshold adaptation stabilizes synchrony for pairs of coupled excitatory neurons, while spike-triggered adaptation causes locking with a small phase difference, as long as synaptic heterogeneities are negligible. For inhibitory pairs synchrony is stable and robust against conduction delays, and adaptation can mediate bistability of in-phase and anti-phase locking. We further demonstrate that stable synchrony and bistable in/anti-phase locking of pairs carry over to synchronization and clustering of larger networks. The effects of adaptation in aEIF neurons on PRCs and network dynamics qualitatively reflect those of biophysical adaptation currents in detailed Hodgkin-Huxley-based neurons, which underscores the utility of the aEIF model for investigating the dynamical behavior of networks. Our results suggest neuronal spike frequency adaptation as a mechanism synchronizing low frequency oscillations in local excitatory networks, but indicate that inhibition rather than excitation generates coherent rhythms at higher frequencies. Citation: Ladenbauer J, Augustin M, Shiau L, Obermayer K (2012) Impact of Adaptation Currents on Synchronization of Coupled Exponential Integrate-and-Fire Neurons. PLoS Comput Biol 8(4): e1002478. doi:10.1371/journal.pcbi.1002478 Editor: Olaf Sporns, Indiana University, United States of America Received October 26, 2011; Accepted February 27, 2012; Published April 12, 2012 Copyright: ß 2012 Ladenbauer 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: This work was supported by the DFG Collaborative Research Center SFB910 (JL,MA,KO) and the NSF grant DMS-0908528 (LS). 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: jl@ni.tu-berlin.de Introduction Synchronized oscillating neural activity has been shown to be involved in a variety of cognitive functions [1,2] such as multisensory integration [3,4], conscious perception [5,6], selective attention [7,8] and memory [9,10], as well as in pathological states including Parkinson’s disease [11], schizophrenia [12], and epilepsy [13]. These observations have led to a great interest in understanding the mechanisms of neuronal synchronization, how synchronous oscillations are initiated, maintained, and destabi- lized. The phase response curve (PRC) provides a powerful tool to study neuronal synchronization [14]. The PRC is an experimen- tally obtainable measure that characterizes the effects of transient inputs to a periodically spiking neuron on the timing of its subsequent spike. PRC based techniques have been applied widely to analyze rhythms of neuronal populations and have yielded valuable insights into, for example, motor pattern generation [15], the hippocampal theta rhythm [16], and memory retrieval [10]. The shape of the PRC is strongly affected by ionic currents that mediate spike frequency adaptation (SFA) [17,18], a prominent feature of neuronal dynamics shown by a decrease in instanta- neous spike rate during a sustained current injection [19–21]. These adaptation currents modify the PRC in distinct ways, depending on whether they operate near rest or during the spike [18]. Using biophysical neuron models, it has been shown that a low threshold outward current, such as the muscarinic voltage- dependent K z -current (I m ), can produce a type II PRC, characterized by phase advances and delays in response to excitatory stimuli, in contrast to only phase advances, defining a type I PRC. A high threshold outward current on the other hand, such as the Ca 2z -dependent afterhyperpolarization K z -current (I ahp ), flattens the PRC at early phases and skews its peak towards the end of the period [18,22,23]. Both changes of the PRC indicate an increased propensity for synchronization of coupled excitatory cells [22], and can be controlled selectively through cholinergic neuromodulation. In particular, I m and I ahp are reduced by acetylcholine with different sensitivities, which modifies the PRC shape [23–25]. In recent years substantial efforts have been exerted to develop single neuron models of reduced complexity that can reproduce a large repertoire of observed neuronal behavior, while being computationally less demanding and, more importantly, easier to understand and analyze than detailed biophysical models. Two- PLoS Computational Biology | www.ploscompbiol.org 1 April 2012 | Volume 8 | Issue 4 | e1002478