  Heterogeneity of firing rate statistics is known to have severe consequences
on neural coding. Recent experimental recordings in weakly electric fish
indicate that the distribution-width of superficial pyramidal cell firing rates
(trial- and time-averaged) in the electrosensory lateral line lobe (ELL)
depends on the stimulus, and also that network inputs can mediate changes in
the firing rate distribution across the population. We previously developed
theoretical methods to understand how two attributes (synaptic and intrinsic
heterogeneity) interact and alter the firing rate distribution in a population
of integrate-and-fire neurons with random recurrent coupling. Inspired by our
experimental data, we extend these theoretical results to a delayed feedforward
spiking network that qualitatively capture the changes of firing rate
heterogeneity observed in in-vivo recordings. We demonstrate how heterogeneous
neural attributes alter firing rate heterogeneity, accounting for the effect
with various sensory stimuli. The model predicts how the strength of the
effective network connectivity is related to intrinsic heterogeneity in such
delayed feedforward networks: the strength of the feedforward input is
positively correlated with excitability (threshold value for spiking) with low
firing rate heterogeneity and is negatively correlated with excitability with
high firing rate heterogeneity. We also show how our theory can be use to
predict effective neural architecture. We demonstrate that neural attributes do
not interact in a simple manner but rather in a complex stimulus-dependent
fashion to control neural heterogeneity and discuss how it can ultimately shape
population codes.
