Adaptation with correlated noise predicts negative interval correlations in neuronal spike trains
Negative correlations in the sequential evolution of interspike intervals (ISIs) are a signature of memory in neuronal spike-trains. They provide coding benefits including firing-rate stabilization, improved detectability of weak sensory signals, and enhanced transmission of information by improving signal-to-noise ratio. Primary electrosensory afferent spike-trains in weakly electric fish fall into two categories based on the pattern of SCCs: non-bursting units have negative SCCs which remain negative but decay to zero with increasing lags (Type I SCCs), and bursting units have oscillatory (alternating sign) SCCs which damp to zero with increasing lags (Type II SCCs). Here, we predict and match observed ISI serial correlations in these afferents using a stochastic dynamic threshold model. We determine SCCs as a function of an arbitrary discrete noise correlation function Rk, where k is a multiple of the mean ISI. The function permits forward and inverse calculations of SCCs. Both types of SCCs can be generated by adding colored noise to the spike threshold with Type I SCCs generated with slow noise and Type II SCCs generated with fast noise. We show that a first-order autoregressive (AR) process with a single parameter is sufficient to predict and accurately match both types of afferent SCCs, the type being determined by the sign of the AR parameter. The predicted and experimentally observed SCCs are in geometric progression. The theory predicts that the limiting sum of SCCs is -0.5 yielding a perfect DC-block in the power spectrum of the spike train. Observed SCCs from afferents have a limiting sum that is slightly larger at -0.475 {+/-} 0.04 (mean {+/-} s.d.). We conclude that the underlying process for generating ISIs may be a simple combination of low-order autoregressive (AR) processes, and discuss the results from the perspective of optimal coding.