Dynamical mean-field theory for a highly heterogeneous neural population with graded persistent activity of the entorhinal cortex

The entorhinal cortex serves as a major gateway connecting the hippocampus and neocortex, playing a pivotal role in episodic memory formation. Neurons in the entorhinal cortex exhibit two notable features associated with temporal information processing: a population-level ability to encode long temporal signals and a single-cell characteristic known as graded-persistent activity, where some neurons maintain activity for extended periods even without external inputs. However, the relationship between these single-cell characteristics and population dynamics has remained unclear, largely due to the absence of a framework to describe the dynamics of neural populations with highly heterogeneous time scales. To address this gap, we extend the dynamical mean field theory, a powerful framework for analyzing large-scale population dynamics, to study the dynamics of heterogeneous neural populations. By proposing an analytically tractable model of graded-persistent activity, we demonstrate that the introduction of graded-persistent neurons shifts the chaos-order phase transition point and expands the network’s dynamical region, a preferable region for temporal information computation. Furthermore, we validate our framework by applying it to a system with heterogeneous adaptation, demonstrating that such heterogeneity can reduce the dynamical regime, contrary to previous simplified approximations. These findings establish a theoretical foundation for understanding the functional advantages of diversity in biological systems and offer insights applicable to a wide range of heterogeneous networks beyond neural populations.Author summary: Neurons in the brain exhibit a high degree of diversity in their intrinsic properties, including their characteristic time scales. However, little is known about how this diversity influences population dynamics. This study explores how a specific type of neuron in the entorhinal cortex, which can maintain firing activity for several minutes, even without external input, affects population dynamics. We develop a theory to describe large-scale recurrent networks of heterogeneous neurons and reveal that the introduction of these neurons shifts the network toward a more dynamic regime, which is preferable for temporal information processing. Our theory was also applied to other heterogeneous populations, offering new perspectives on the significance of diversity in neural population dynamics.