Effects of Spike-Driven Feedback on Neural Gain and Pairwise Correlation

Both single neuron and neural population spiking statistics, such as firing rate or temporal patterning, are critical aspects of manyneural codes. Tremendous experimental and theoretical effort has been devoted to understanding how nonlinear membrane dynamics and ambient synaptic activity determine the gain of single neuron firing rate responses. Furthermore, there is increasing experimental evidence that the same manipulationsthat affect firing rate gain also modulate the pairwise correlationbetween neurons. However, there is little understanding of the mechanistic links between rate and correlation modulation. In this thesis, we explore how spike-driven intrinsicfeedback co-modulates firing rate gain and spike traincorrelation. Throughout our study, we focus on excitable LIF neurons subject to Gaussian white noise fluctuations. We first review prior work which develops linear response theory for studying spectral properties of LIF neurons. This theory is used to capture the influence of weak spike driven feedback in single neuron responses. We introduce a concept of "dynamic spike count gain" and study how this property is affected by intrinsic feedback, comparing theoretical results to simulations of stochastic ODE models. We then expand our scope to a pair of such neurons receiving weakly correlated noisy inputs. Extending previous work, we study the correlation between the spike trains of these neurons, comparing theoretical and simulation results. We observe that firing rate gain modulation from feedback is largely time-scale invariant, while correlation modulation exhibits marked temporal dependence. To discern whether these effects can be solely attributed to firing rate changes, we perform a perturbative analysis to derive conditions for correlation modulation over small time scales beyond that expected from rate modulation. We find that correlation is not purely a function of firing rate change; rather it is also influenced by sufficiently fast feedback inputs. These results offer a glimpse into the connections between gain and correlation, indicating that attempts to manipulate either property via firing rates will affect both, and that achievability of modulation targets is constrained by the time scale of spike feedback