  The spiking activity of neocortical neurons exhibits a striking level of
variability, even when these networks are driven by identical stimuli. The
approximately Poisson firing of neurons has led to the hypothesis that these
neural networks operate in the asynchronous state. In the asynchronous state
neurons fire independently from one another, so that the probability that a
neuron experience synchronous synaptic inputs is exceedingly low. While the
models of asynchronous neurons lead to observed spiking variability, it is not
clear whether the asynchronous state can also account for the level of
subthreshold membrane potential variability. We propose a new analytical
framework to rigorously quantify the subthreshold variability of a single
conductance-based neuron in response to synaptic inputs with prescribed degrees
of synchrony. Technically we leverage the theory of exchangeability to model
input synchrony via jump-process-based synaptic drives; we then perform a
moment analysis of the stationary response of a neuronal model with all-or-none
conductances that neglects post-spiking reset. As a result, we produce exact,
interpretable closed forms for the first two stationary moments of the membrane
voltage, with explicit dependence on the input synaptic numbers, strengths, and
synchrony. For biophysically relevant parameters, we find that the asynchronous
regime only yields realistic subthreshold variability (voltage variance $\simeq
4-9\mathrm{mV^2}$) when driven by a restricted number of large synapses,
compatible with strong thalamic drive. By contrast, we find that achieving
realistic subthreshold variability with dense cortico-cortical inputs requires
including weak but nonzero input synchrony, consistent with measured pairwise
spiking correlations.
