Definition of fluctuation– and mean–driven spiking

Neuronal spiking has traditionally been considered to occur when the mean inward current of the cellular membrane is large enough to cross the rheobase such that the mean membrane potential (V_m) is above threshold (V_thres). In practice, the mean V_m will not exceed V_thres by very much due to the active spiking and after–hyperpolarization, but if this mechanism was turned off the mean membrane current (I_m) would drive V_m across threshold, formally written as I_m > V_thres/R_m where R_m is the membrane resistance. Spikes elicited in this manner are in the mean–driven regime (Gerstner et al., 2014; Renart et al., 2007). They have shorter inter–spike intervals (ISIs) because of the large I_m and regular spiking due to the after–hyperpolarization. In contrast, when the mean V_m is below threshold, i.e. I_m  <  V_thres/R_m, spikes are elicited by temporary fluctuations in V_m due to synaptic bombardment. Such spiking is in the fluctuation–driven regime (Kuhn et al., 2004; Tiesinga et al., 2000; Gerstner et al., 2014; Roxin et al., 2011). The random synaptic fluctuations cause the spiking to be more irregular, which results in a higher coefficient of variation (CV, defined as the standard deviation (σ) divided by the mean of ISIs), than for the mean–driven regime (cf. Figure 1D–E). Therefore irregularity is an indicator of the spiking regime. Another indicator of the fluctuation–driven regime is positive skewness of the firing rate distribution (Figure 1A–B). These indicators are used to quantify the fraction of the population that is in one versus the other regime.