Conductance Based Integrate and Fire Model with Correlated Inputs Captures Neural Variability

The spiking activity of neurons is highly variable and is often described as a Poisson
process. This variability comes from random fluctuations within the membrane potential (V) that leads
to random spike times. Prior analysis has shown that the variability of V, in response to stimuli, became
quenched, where the variance (σ2) decreased as the mean (μ) increased. However, recent in-vivo
primate data has shown that σ2 also can increase with μ. Here we propose a new analytical and
computational framework to show that conductance-based integrate-and-fire (C-IF) neurons can
accurately capture μ and σ2 as well as the skewness (γ) of V. Specifically, we show that when subjected
to uncorrelated Poissonian inputs, μ and σ2 simultaneously increase whereas γ decreases in response
to stimulus drive. However, for biophysical parameters, we find that σ2 and γ are an order-of-magnitude
smaller than in-vivo estimates. We then show that accounting for realistic values of σ2 and γ requires
the inclusion of weak but nonzero spiking input correlations. To do so, we model the impact of spiking
input correlations via Levy-process-based synaptic drives, leveraging the theory of statistical
exchangeability. We then perform an exact moment analysis of the stationary neural response using
techniques from queueing theory. Practically, our approach produces closed-form expressions for μ, σ2
and γ, which can be used to estimate network-level features such as input synaptic numbers and
spiking correlations. Theoretically, our approach suggests that mean-field description of neural activity
shall be revised to include nonzero spiking correlation.