Effect of burst spikes on linear and nonlinear signal transmission in spiking neurons

We study the impact of bursts on spike statistics and neural signal transmission. We propose a stochastic burst algorithm that is applied to a burst-free spike train and adds a random number of temporally-jittered burst spikes to each spike. This simple algorithm ignores any possible stimulus-dependence of bursting but allows to relate spectra and signal-transmission characteristics of burst-free and burst-endowed spike trains. By averaging over the various statistical ensembles, we find a frequency-dependent factor connecting the linear and also the second-order susceptibility of the spike trains with and without bursts. The relation between spectra is more complicated: besides a frequency-dependent multiplicative factor it also involves an additional frequency-dependent offset. We confirm these relations for the (burst-free) spike trains of a stochastic integrate-and-fire neuron and identify frequency ranges in which the transmission is boosted or diminished by bursting. We then consider bursty spike trains of electroreceptor afferents of weakly electric fish and approach the role of burst spikes as follows. We compare the spectral statistics of the bursty spike train to (i) that of a spike train with burst spikes removed and to (ii) that of the spike train in (i) endowed by bursts according to our algorithm. Significant spectral features are explained by our signal-independent burst algorithm, e.g. the burst-induced boosting of the nonlinear response. A difference is seen in the information transfer for the original bursty spike train and our burst-endowed spike train. Our algorithm is thus helpful to identify different effects of bursting.