# Extending Mathematical Frameworks to Investigate Neuronal Dynamics in the Presence of Microglial Ensheathment

## TL;DR

This paper explores how microglial cells affect brain networks by wrapping around synapses, changing how neurons communicate and influencing overall brain activity.

## Contribution

The study introduces a new mathematical framework that incorporates microglial ensheathment into large-scale neuronal network models.

## Key findings

- Microglial ensheathment accelerates synaptic transmission but reduces its strength and reliability.
- A mean-field approximation accurately captures network statistics despite significant heterogeneity.
- The model reproduces experimental findings of post-anesthesia hyperactivity in mice excitatory neurons.

## Abstract

Recent experimental evidence has shown that glial cells, including microglia and astrocytes, can ensheathe specific synapses, positioning them to disrupt neurotransmitter flow between pre- and post-synaptic terminals. This study, as part of the special issue “Problems, Progress and Perspectives in Mathematical and Computational Biology,” expands micro- and network-scale theoretical frameworks to incorporate these new experimental observations that introduce substantial heterogeneities into the system. Specifically, we aim to explore how varying degrees of synaptic ensheathment affect synaptic communication and network dynamics. Consistent with previous studies, our microscale model shows that ensheathment accelerates synaptic transmission while reducing its strength and reliability, with the potential to effectively switch off synaptic connections. Building on these findings, we integrate an “effective” glial cell model into a large-scale neuronal network. Specifically, we analyze a network with highly heterogeneous synaptic strengths and time constants, where glial proximity parametrizes synaptic properties. This parametrization results in a multimodal distribution of synaptic parameters across the network, introducing significantly greater variability compared to previous modeling efforts that assumed a normal distribution. This framework is applied to large networks of exponential integrate-and-fire neurons, extending linear response theory to analyze not only firing rate distributions but also noise correlations across the network. Despite the significant heterogeneity in the system, a mean-field approximation accurately captures network statistics. We demonstrate the utility of our model by reproducing experimental findings, showing that microglial ensheathment leads to post-anesthesia hyperactivity in excitatory neurons of mice. Furthermore, we explore how glial ensheathment may be used in the visual cortex to target specific neuronal subclasses, tuning higher-order network statistics.