Correlations and Synchrony in threshold neuron models

Abstract

Event Abstract Back to Event Correlations and Synchrony in threshold neuron models Tatjana Tchumatchenko1*, Aleksey Malyshe2, Theo Geisel1, Maxim Volgushev3, 4 and Fred Wolf1 1 BCCN Göttingen and Max Planck Institute for Dynamics and Self-Organization, Germany 2 Inst. of Higher Nervous Activity and Neurophysiology, RAS, Russia 3 Ruhr-University, Dep. of Neurophysiology, Germany 4 University of Connecticut, United States Experimental studies reveal significant temporal and interneuronal correlations of subthreshold Membrane Potential (MP) fluctuations of cortical neurons in vivo. How temporal input correlations are transferred to interneuronal spike correlations is largely unknown and inferring the underlying input correlations from observed spike correlations is a challenge. To understand this relation, we used a simple analytical framework for the analysis of spike correlations between neurons driven by correlated inputs [1] to examine the quantitative determinants of the synchronization strength and acuity of a pair of neurons subject to a variable percentage of common fluctuating input of different correlation times. We calculated the autoconditional firing rate of an individual neuron and analyzed its short and long time asymptotics. In the limit of small times, we find an algebraic rise out of period of intrinsic silence after each spike that reflects the temporal correlations of the inputs and is independent of refractory properties of the AP generator. For large time lags, we find a substantial influence of the second derivative of the voltage correlation function. Furthermore, we evaluated the cross conditional firing rate of a pair of neurons for low and high common input fraction and with firing rate heterogeneity. In the low correlation regime, we identified a rate dependence of the rate of synchronous firing corroborating previous observations [2]. In the high correlation regime, however, the synchronous rate ceases to depend on the stationary firing rate and voltage correlation function of individual neurons. For all strengths of correlations the model predicts the appearance of a systematic delay of firing of the lower rate neuron relative to the higher rate neuron. To test these theoretical predictions, we performed in vitro experiments in slices of rat visual cortex and injected in pyramidal neurons fluctuating currents with a varying degree of common input. Cross and autoconditional firing rates computed from these recordings, confirmed all basic theoretical predictions of our formalism.