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. Author Summary: Neurons of sensory systems encode signals from the environment by sequences of electrical pulses — so-called spikes. This coding of information is fundamentally limited by the presence of intrinsic neural noise. One major noise source is “channel noise” that is generated by the random activity of various types of ion channels in the cell membrane. Slow adaptation currents can also be a source of channel noise. Adaptation currents profoundly shape the signal transmission properties of a neuron by emphasizing fast changes in the stimulus but adapting the spiking frequency to slow stimulus components. Here, we mathematically analyze the effects of both slow adaptation channel noise and fast channel noise on the statistics of spike times in adapting neuron models. Surprisingly, the two noise sources result in qualitatively different distributions and correlations of time intervals between spikes. Our findings add a novel aspect to the function of adaptation currents and can also be used to experimentally distinguish adaptation noise and fast channel noise on the basis of spike sequences.