How Noisy Adaptation of Neurons Shapes Interspike Interval Histograms and Correlations

Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics

Sparse Gamma Rhythms Arising through Clustering in Adapting Neuronal Networks

Gamma rhythms (30–100 Hz) are an extensively studied synchronous brain state responsible for a number of sensory, memory, and motor processes. Experimental evidence suggests that fast-spiking interneurons are responsible for carrying the high frequency components of the rhythm, while regular-spiking pyramidal neurons fire sparsely. We propose that a combination of spike frequency adaptation and global inhibition may be responsible for this behavior. Excitatory neurons form several clusters that fire every few cycles of the fast oscillation. This is first shown in a detailed biophysical network model and then analyzed thoroughly in an idealized model. We exploit the fact that the timescale of adaptation is much slower than that of the other variables. Singular perturbation theory is used to derive an approximate periodic solution for a single spiking unit. This is then used to predict the relationship between the number of clusters arising spontaneously in the network as it relates to the adaptation time constant. We compare this to a complementary analysis that employs a weak coupling assumption to predict the first Fourier mode to destabilize from the incoherent state of an associated phase model as the external noise is reduced. Both approaches predict the same scaling of cluster number with respect to the adaptation time constant, which is corroborated in numerical simulations of the full system. Thus, we develop several testable predictions regarding the formation and characteristics of gamma rhythms with sparsely firing excitatory neurons