Effects of Neural Heterogeneity on the Low-Dimensional Dynamics of Spiking Neural Networks

The physiological properties of neurons influence their population dynamics to shape neural computation and behavior.
These physiological properties are diverse: the brain is composed of many genetically distinct neuronal cell types with pronounced physiological and functional differences.
But neurons of the same cell type are also not identical, and exhibit heterogeneity in their physiological properties.
We call this "within-type" heterogeneity, in contrast to the former, "between-type" heterogeneity.
Whereas the contributions of distinct neuron types to neural network dynamics has been studied intensely, within-type heterogeneity has received less attention.
Recent results suggest, however, that the loss of within-type heterogeneity might underlie pathological brain dynamics seen in epilepsy \cite{rich_loss_2022}. We provide insight into the computational consequences of within-type heterogeneity by studying the effect of distributed physiological properties of neurons on emergent dynamics in networks of one or more cell type.
Specifically, we derive a novel mean-field model that incorporates heterogeneity in the spiking thresholds of neurons, a measurable property that has been associated with the sigmoidal input-output relationship that many neural populations exhibit \cite{robinson_propagation_1997}.
Our model allows us to determine a direct relationship between the variance of the spike thresholds across neurons and the resulting low-dimensional mean-field network dynamics. Building on this model, we use bifurcation analysis to show that the heterogeneity of inhibitory interneurons plays a crucial role in shaping the dynamic regimes of neural circuits: heterogeneous inhibitory interneuron populations promote asynchronous, multistable regimes, whereas homogeneous interneurons facilitate synchronized dynamics.
We also show that spike threshold heterogeneity interacts with synaptic input heterogeneity in sparse networks to alter the community structure of the network and the effective dimensionality of the network dynamics.
We thus show that continuously distributed, within-type heterogeneity can dramatically impact neural population dynamics, and introduce a new mean-field model for future studies of heterogeneous neural networks.