Analytical Investigation of Long-time Diffusion Dynamics in a Synaptic Channel with Glial Cells

TL;DR

This paper derives and validates an analytical model for long-time diffusion dynamics in synaptic channels with glial cells, enhancing understanding of post-communication cleanup processes.

Contribution

It introduces a novel analytical approximation for the long-time decay rate of synaptic diffusion, validated against numerical solutions.

Findings

Analytical channel impulse response derived and validated.

Accurate approximation for long-time decay rate provided.

Enhanced understanding of synaptic cleanup processes.

Abstract

In this letter, we first derive the analytical channel impulse response for a cylindrical synaptic channel surrounded by glial cells and validate it with particle-based simulations. Afterwards, we provide an accurate analytical approximation for the long-time decay rate of the channel impulse response by employing Taylor expansion to the characteristic equations that determine the decay rates of the system. We validate our approximation by comparing it with the numerical decay rate obtained from the characteristic equation. Overall, we provide a fully analytical description for the long-time behavior of synaptic diffusion, e.g., the clean-up processes inside the channel after communication has long concluded.