The self-organization of the brain matrix of serotonergic axons (fibers) remains an unsolved problem in neuroscience. The regional densities of this matrix have major implications for neuroplasticity, tissue regeneration, and the understanding of mental disorders, but the trajectories of its fibers are strongly stochastic and require novel conceptual and analytical approaches. In a major extension to our previous studies, we used a supercomputing simulation to model around one thousand serotonergic fibers as paths of superdiffusive fractional Brownian motion (FBM), a continuous-time stochastic process. The fibers produced long walks in a complex, three-dimensional shape based on the mouse brain and reflected at the outer (pial) and inner (ventricular) boundaries. The resultant regional densities were compared to the actual fiber densities in the corresponding neuroanatomically-defined regions. The relative densities showed strong qualitative similarities in the forebrain and midbrain, demonstrating the predictive potential of stochastic modeling in this system. The current simulation does not respect tissue heterogeneities but can be further improved with novel models of multifractional FBM. The study demonstrates that serotonergic fiber densities can be strongly influenced by the geometry of the brain, with implications for brain development, plasticity, and evolution.

The self-organization of the brain matrix of serotonergic axons (fibers) remains an unsolved problem in neuroscience. The regional densities of this matrix have major implications for neuroplasticity, tissue regeneration, and the understanding of mental disorders, but the trajectories of single fibers are strongly stochastic and require novel conceptual and analytical approaches. In a major extension to our previous studies, we used a supercomputing simulation to model 1000 serotonergic fibers as paths of superdiffusive fractional Brownian motion (FBM), a continuous-time stochastic process. The fibers produced long walks in a complex, three-dimensional shape based on the mouse brain and reflected at the outer (pial) and inner (ventricular) boundaries. The resultant regional densities were compared to the actual fiber densities in the corresponding neuroanatomically-defined regions. The relative densities showed strong qualitative similarities in the forebrain and midbrain, demonstrating the predictive potential of stochastic modeling in this system. The current simulation does not respect tissue heterogeneities, but can be further improved with novel models of multifractional FBM. The study demonstrates that serotonergic fiber densities can be strongly influenced by the geometry of the brain, with implications for brain development, plasticity, and evolution.

The self-organization of the serotonergic matrix, a massive axon meshwork in all vertebrate brains, is driven by the structural and dynamical properties of its constitutive elements. Each of these elements, a single serotonergic axon (fiber), has a unique trajectory and can be supported by a soma that executes one of many available transcriptional programs. It necessitates the development of specialized methods for single-fiber analyses, both at the experimental and theoretical levels. We developed an integrated system that facilitates experimental isolation of single serotonergic fibers in brain tissue, including regions with high fiber densities, and demonstrated the potential of their quantitative analyses based on stochastic modeling. Single fibers were visualized using two transgenic mouse models, one of which is the first implementation of the Brainbow toolbox in this system. The trajectories of serotonergic fibers were automatically traced in the three spatial dimensions with a novel algorithm, and their properties were captured with a single parameter associated with the directional von Mises-Fisher probability distribution. The system represents an end-to-end workflow that can be imported into various studies, including those investigating serotonergic dysfunction in brain disorders. It also supports new research directions inspired by single-fiber analyses in the serotonergic matrix, including supercomputing simulations and modeling in physics.