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.

The creation of protein from DNA is a dynamic process consisting of numerous reactions, such as transcription, translation and protein folding. Each of these reactions is further comprised of hundreds or thousands of sub-steps that must be completed before a protein is fully mature. Consequently, the time it takes to create a single protein depends on the number of steps in the reaction chain and the nature of each step. One way to account for these reactions in models of gene regulatory networks is to incorporate dynamical delay. However, the stochastic nature of the reactions necessary to produce protein leads to a waiting time that is randomly distributed. Here, we use queueing theory to examine the effects of such distributed delay on the propagation of information through transcriptionally regulated genetic networks. In an analytically tractable model we find that increasing the randomness in protein production delay can increase signaling speed in transcriptional networks. The effect is confirmed in stochastic simulations, and we demonstrate its impact in several common transcriptional motifs. In particular, we show that in feedforward loops signaling time and magnitude are significantly affected by distributed delay. In addition, delay has previously been shown to cause stable oscillations in circuits with negative feedback. We show that the period and the amplitude of the oscillations monotonically decrease as the variability of the delay time increases.

No abstract

We study the spike statistics of an adaptive exponential integrate-and-fire neuron stimulated by white Gaussian current noise. We derive analytical approximations for the coefficient of variation and the serial correlation coefficient of the interspike interval assuming that the neuron operates in the mean-driven tonic firing regime and that the stochastic input is weak. Our result for the serial correlation coefficient has the form of a geometric sequence and is confirmed by the comparison to numerical simulations. The theory predicts various patterns of interval correlations (positive or negative at lag one, monotonically decreasing or oscillating) depending on the strength of the spike-triggered and subthreshold components of the adaptation current. In particular, for pure subthreshold adaptation we find strong positive ISI correlations that are usually ascribed to positive correlations in the input current. Our results i) provide an alternative explanation for interspike-interval correlations observed in vivo, ii) may be useful in fitting point neuron models to experimental data, and iii) may be instrumental in exploring the role of adaptation currents for signal detection and signal transmission in single neurons.

Table of contentsA1 Functional advantages of cell-type heterogeneity in neural circuitsTatyana O. SharpeeA2 Mesoscopic modeling of propagating waves in visual cortexAlain DestexheA3 Dynamics and biomarkers of mental disordersMitsuo KawatoF1 Precise recruitment of spiking output at theta frequencies requires dendritic h-channels in multi-compartment models of oriens-lacunosum/moleculare hippocampal interneuronsVladislav Sekulić, Frances K. SkinnerF2 Kernel methods in reconstruction of current sources from extracellular potentials for single cells and the whole brainsDaniel K. Wójcik, Chaitanya Chintaluri, Dorottya Cserpán, Zoltán SomogyváriF3 The synchronized periods depend on intracellular transcriptional repression mechanisms in circadian clocks.Jae Kyoung Kim, Zachary P. Kilpatrick, Matthew R. Bennett, Kresimir JosićO1 Assessing irregularity and coordination of spiking-bursting rhythms in central pattern generatorsIrene Elices, David Arroyo, Rafael Levi, Francisco B. Rodriguez, Pablo VaronaO2 Regulation of top-down processing by cortically-projecting parvalbumin positive neurons in basal forebrainEunjin Hwang, Bowon Kim, Hio-Been Han, Tae Kim, James T. McKenna, Ritchie E. Brown, Robert W. McCarley, Jee Hyun ChoiO3 Modeling auditory stream segregation, build-up and bistabilityJames Rankin, Pamela Osborn Popp, John RinzelO4 Strong competition between tonotopic neural ensembles explains pitch-related dynamics of auditory cortex evoked fieldsAlejandro Tabas, André Rupp, Emili Balaguer-BallesterO5 A simple model of retinal response to multi-electrode stimulationMatias I. Maturana, David B. Grayden, Shaun L. Cloherty, Tatiana Kameneva, Michael R. Ibbotson, Hamish MeffinO6 Noise correlations in V4 area correlate with behavioral performance in visual discrimination taskVeronika Koren, Timm Lochmann, Valentin Dragoi, Klaus ObermayerO7 Input-location dependent gain modulation in cerebellar nucleus neuronsMaria Psarrou, Maria Schilstra, Neil Davey, Benjamin Torben-Nielsen, Volker SteuberO8 Analytic solution of cable energy function for cortical axons and dendritesHuiwen Ju, Jiao Yu, Michael L. Hines, Liang Chen, Yuguo YuO9 C. elegans interactome: interactive visualization of Caenorhabditis elegans worm neuronal networkJimin Kim, Will Leahy, Eli ShlizermanO10 Is the model any good? Objective criteria for computational neuroscience model selectionJustas Birgiolas, Richard C. Gerkin, Sharon M. CrookO11 Cooperation and competition of gamma oscillation mechanismsAtthaphon Viriyopase, Raoul-Martin Memmesheimer, Stan GielenO12 A discrete structure of the brain wavesYuri Dabaghian, Justin DeVito, Luca PerottiO13 Direction-specific silencing of the Drosophila gaze stabilization systemAnmo J. Kim, Lisa M. Fenk, Cheng Lyu, Gaby MaimonO14 What does the fruit fly think about values? A model of olfactory associative learningChang Zhao, Yves Widmer, Simon Sprecher,Walter SennO15 Effects of ionic diffusion on power spectra of local field potentials (LFP)Geir Halnes, Tuomo Mäki-Marttunen, Daniel Keller, Klas H. Pettersen,Ole A. Andreassen...