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.