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The spiking activity of neocortical neurons exhibits a striking level ofvariability, even when these networks are driven by identical stimuli. Theapproximately Poisson firing of neurons has led to the hypothesis that theseneural networks operate in the asynchronous state. In the asynchronous stateneurons fire independently from one another, so that the probability that aneuron experience synchronous synaptic inputs is exceedingly low. While themodels of asynchronous neurons lead to observed spiking variability, it is notclear whether the asynchronous state can also account for the level ofsubthreshold membrane potential variability. We propose a new analyticalframework to rigorously quantify the subthreshold variability of a singleconductance-based neuron in response to synaptic inputs with prescribed degreesof synchrony. Technically we leverage the theory of exchangeability to modelinput synchrony via jump-process-based synaptic drives; we then perform amoment analysis of the stationary response of a neuronal model with all-or-noneconductances that neglects post-spiking reset. As a result, we produce exact,interpretable closed forms for the first two stationary moments of the membranevoltage, with explicit dependence on the input synaptic numbers, strengths, andsynchrony. For biophysically relevant parameters, we find that the asynchronousregime only yields realistic subthreshold variability (voltage variance $\simeq4-9\mathrm{mV^2}$) when driven by a restricted number of large synapses,compatible with strong thalamic drive. By contrast, we find that achievingrealistic subthreshold variability with dense cortico-cortical inputs requiresincluding weak but nonzero input synchrony, consistent with measured pairwisespiking correlations.

Exact analysis of the subthreshold variability for conductance-based neuronal models with synchronous synaptic inputs