Irregularity in neocortical spike trains: Influence of measurement factors and another method of estimation

Variability of visual responses of superior colliculus neurons depends on stimulus velocity

Visually responding neurons in the superficial, retinorecipient layers of the cat superior colliculus receive input from two primarily parallel information processing channels, Y and W, which is reflected in their velocity response profiles. We quantified the time-dependent variability of responses of these neurons to stimuli moving with different velocities by Fano factor (FF) calculated in discrete time windows. The FF for cells responding to low-velocity stimuli, thus receiving W inputs, increased with the increase in the firing rate. In contrast, the dynamics of activity of the cells responding to fast moving stimuli, processed by Y pathway, correlated negatively with FF whether the response was excitatory or suppressive. These observations were tested against several types of surrogate data. Whereas Poisson description failed to reproduce the variability of all collicular responses, the inclusion of secondary structure to the generating point process recovered most of the observed features of responses to fast moving stimuli. Neither model could reproduce the variability of low-velocity responses, which suggests that, in this case, more complex time dependencies need to be taken into account. Our results indicate that Y and W channels may differ in reliability of responses to visual stimulation. Apart from previously reported morphological and physiological differences of the cells belonging to Y and W channels, this is a new feature distinguishing these two pathways.

Comparison of local measures of spike time irregularity and relating variability to firing rate in motor cortical neurons

Spike time irregularity can be measured by the coefficient of variation. However, it overestimates the irregularity in the case of pronounced firing rate changes. Several alternative measures that are local in time and therefore relatively rate-independent were proposed. Here we compared four such measures: CV(2), LV, IR and SI. First, we asked which measure is the most efficient for time-resolved analyses of experimental data. Analytical results show that CV(2) has the less variable estimates. Second, we derived useful properties of CV(2) for gamma processes. Third, we applied CV(2) on recordings from the motor cortex of a monkey performing a delayed motor task to characterize the irregularity, that can be modulated or not, and decoupled or not from firing rate. Neurons with a CV(2)-rate decoupling have a rather constant CV(2) and discharge mainly irregularly. Neurons with a CV(2)-rate coupling can modulate their CV(2) and explore a larger range of CV(2) values.

Measurement of variability dynamics in cortical spike trains

We propose a method for the time-resolved joint analysis of two related aspects of single neuron variability, the spiking irregularity measured by the squared coefficient of variation (CV(2)) of the ISIs and the trial-by-trial variability of the spike count measured by the Fano factor (FF). We provide a calibration of both estimators using the theory of renewal processes, and verify it for spike trains recorded in vitro. Both estimators exhibit a considerable bias for short observations that count less than about 5-10 spikes on average. The practical difficulty of measuring the CV(2) in rate modulated data can be overcome by a simple procedure of spike train demodulation which was tested in numerical simulations and in real spike trains. We propose to test neuronal spike trains for deviations from the null-hypothesis FF=CV(2). We show that cortical pyramidal neurons, recorded under controlled stationary input conditions in vitro, comply with this assumption. Performing a time-resolved joint analysis of CV(2) and FF of a single unit recording from the motor cortex of a behaving monkey we demonstrate how the dynamic change of their quantitative relation can be interpreted with respect to neuron intrinsic and extrinsic factors that influence cortical variability in vivo. Finally, we discuss the effect of several additional factors such as serial interval correlation and refractory period on the empiric relation of FF and CV(2).