Compartmental-reaction diffusion framework for microscale dynamics of extracellular serotonin in brain tissue

TL;DR

This paper introduces a mathematical framework to model the complex extracellular serotonin dynamics in brain tissue, capturing reaction-diffusion processes at microscale levels for better understanding of neurotransmitter signaling.

Contribution

The authors develop a novel compartmental-reaction diffusion model with efficient computational methods to analyze serotonin signaling microenvironments.

Findings

Varicosities form diffusively coupled microdomains acting as serotonin reservoirs.

The model predicts how firing frequency and uptake kinetics influence serotonin levels.

Results clarify local versus volume transmission mechanisms.

Abstract

Serotonin (5-hydroxytryptamine) is a major neurotransmitter whose release from densely distributed serotonergic varicosities shapes plasticity and network integration throughout the brain, yet its extracellular dynamics remain poorly understood due to the sub-micrometer and millisecond scales involved. We develop a mathematical framework that captures the coupled reaction-diffusion processes governing serotonin signaling in realistic tissue microenvironments. Formulating a two-dimensional compartmental-reaction diffusion system, we use strong localized perturbation theory to derive an asymptotically equivalent set of nonlinear integro-ODEs that preserve diffusive coupling while enabling efficient computation. We analyze period-averaged steady states, establish bounds using Jensen's inequality, obtain closed-form spike maxima and minima, and implement a fast marching-scheme solver based on sum-of-exponentials kernels. These mathematical results provide quantitative insight into how firing frequency, varicosity geometry, and uptake kinetics shape extracellular serotonin. The model reveals that varicosities form diffusively coupled microdomains capable of generating spatial "serotonin reservoirs," clarifies aspects of local versus volume transmission, and yields predictions relevant to interpreting high-resolution serotonin imaging and the actions of selective serotonin-reuptake inhibitors.