Serotonergic Axons as Fractional Brownian Motion Paths: Insights Into the Self-Organization of Regional Densities.

All vertebrate brains contain a dense matrix of thin fibers that release serotonin (5-hydroxytryptamine), a neurotransmitter that modulates a wide range of neural, glial, and vascular processes. Perturbations in the density of this matrix have been associated with a number of mental disorders, including autism and depression, but its self-organization and plasticity remain poorly understood. We introduce a model based on reflected Fractional Brownian Motion (FBM), a rigorously defined stochastic process, and show that it recapitulates some key features of regional serotonergic fiber densities. Specifically, we use supercomputing simulations to model fibers as FBM-paths in two-dimensional brain-like domains and demonstrate that the resultant steady state distributions approximate the fiber distributions in physical brain sections immunostained for the serotonin transporter (a marker for serotonergic axons in the adult brain). We suggest that this framework can support predictive descriptions and manipulations of the serotonergic matrix and that it can be further extended to incorporate the detailed physical properties of the fibers and their environment.

A stochastic approach to serotonergic fibers in mental disorders.

Virtually all brain circuits are physically embedded in a three-dimensional matrix of fibers that release 5-hydroxytryptamine (5-HT, serotonin). The density of this matrix varies across brain regions and cortical laminae, and it is altered in some mental disorders, including Major Depressive Disorder and Autism Spectrum Disorder. We investigate how the regional structure of the serotonergic matrix depends on the stochastic behavior of individual serotonergic fibers and introduce a new framework for the quantitative analysis of this behavior. In particular, we show that a step-wise random walk, based on the von Mises-Fisher probability distribution, can provide a realistic and mathematically concise description of these fibers. We also consider other stochastic models, including the fractional Brownian motion. The proposed approach seeks to advance the current understanding of the ascending reticular activating system (ARAS) and may also support future theory-guided therapeutic approaches.