The conundrum of ISI variability was raised by Softky and Koch: cortical neuronal firing resembles a Poisson process, yet large numbers of inputs are being integrated. Softky and Koch suggested that neurons must function as coincidence detectors to account for this variability. Shadlen and Newsome countered that a tight balance of excitation and inhibition could produce observed variability, arguing for a noisy rate code.
The correct solution to the ISI variability conundrum in simple neuronal models, we suggest, is accurate modeling of neuronal gain. The variability in output spiking, roughly, is the variability in somatic input current, times the neuronal gain: the change in spike rate with a change in somatic input current (the slope of the f-I curve). Previous simple models used neuronal gains of about 40 Hz/nA; real cortical excitatory cells have gains around 240 +/- 120 Hz/nA.
To reproduce in vitro f-I plots, a simple conductance-based integrate-and-fire model was modified as follows: voltage after spikes was reset to 5 mV below threshold; and simple spike rate adaptation was added (as is observed in all cortical excitatory cells when firing in single-spike mode). Small reset results in input sensitivity (high gain) on short time scales; adaptation leads to wide dynamic range over longer time scales. The model displays physiological ISI variability using either delta function or temporally realistic synaptic conductances. These cells support integration and thus rate coding, but they also can be responsive to coincidence; thus, ISI variability does not by itself provide a good constraint on neural coding.
Such simple integrate-and-fire neurons that accurately reproduce in vitro data from cortical regular spiking cells can display surprisingly sophisticated behavior. Matching fast and slow time scales of neuronal gain and of synaptic conductances may allow neuronal processing on multiple time scales; we are actively investigating these possibilities.