Synaptic input statistics tune the variability and reproducibility of neuronal responses

Synaptic waveforms, constructed from excitatory and inhibitory presynaptic Poisson trains, are presented to living and computational neurons. We review how the average output of a neuron (e.g., the firing rate) is set by the difference between excitatory and inhibitory event rates while neuronal variability is set by their sum. We distinguish neuronal variability from reproducibility. Variability quantifies how much an output measure is expected to vary; for example, the interspike interval coefficient of variation quantifies the typical range of interspike intervals. Reproducibility quantifies the similarity of neuronal outputs in response to repeated presentations of identical stimuli. Although variability and reproducibility are conceptually distinct, we show that, for ideal current source synapses, reproducibility is defined entirely by variability. For physiologically realistic conductance-based synapses, however, reproducibility is distinct from variability and average output, set by the Poisson rate and the degree of synchrony within the synaptic waveform.