The relationship between neuronal calcium concentration and firing rate during stochastic synaptic inputs

We propose a novel, nonlinear theory about reading neuronal information using intracellular calcium concentrations, which includes the linear theory already developed in the literature as a special case. The theory is numerically confirmed using the Pinsky-Rinzel and integrate-and-fire models with constant rate Poisson inputs. Applying the theory to models with non-constant inputs, we find that there is a time lag equal to the calcium buffering time constant between the instantaneous firing rate and the firing rate estimated using calcium concentrations.