Predicting the distribution of serotonergic axons: a supercomputing simulation of reflected fractional Brownian motion in a 3D-mouse brain model

Abstract

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.

Qualitative Observations of Transgenically Individualized Serotonergic Fibers in the Mouse Telencephalon

“…The latter two possibilities are supported by observations that serotonergic fibers can regenerate in the adult brain 27 and that the current extension of a fiber may depend of the history of its previous extensions. 15,34 .…”

“…In particular, it is known to support transitions among global brain states such as wakefulness and sleep. 14 The regional densities of serotonergic fibers have been described in many neuroanatomical studies, 15 but their self-organization remains an unsolved problem. A number of signaling pathways appear to contribute to this process; the reported factors include Lmx1b, 16 protocadherin-αC2, [17][18][19] neurexins, 20 S100β, 21 the brain-derived neurotrophic factor (BDNF), 22 and serotonin.…”

“…23,24 Some aspects of this self-organization can be captured by models that treat the trajectories of serotonergic fibers as paths of stochastic processes. 15,25,26 Ultimately, a comprehensive mechanistic explanation should bridge the dynamics of single serotonergic fibers – as they extend, branch, and react to chemical and mechanical signals – and their resultant densities in the adult brain. These densities may represent a dynamic equilibrium rather than a static distribution: serotonergic fibers can robustly regenerate in the adult mammalian brain, with new paths, 27,28 which suggests that some individual fiber segments may continue to grow in the normal (injury-free) brain, with the accompanying degeneration of other segments.…”

Subdiffusion in an array of solid obstacles

“…Another recently emerging field of study related to the interplay of the brain's anatomic features and models of fractional random walks in a medium with obstacles, unrelated to diffusive spread, is the analogy between the shape of serotogenic axons and the random walker's trajectories. To simulate the shape and local density of axons, the authors of [25,26] modeled them by trajectories of the fractional Brownian motion (fBm) reflected by impenetrable curved boundaries and small, not very densely packed, scatterers. It should be pointed out that such a discussion poses a specific problem of adequate simulation of reflections at the boundaries [27].…”

An Experimental Platform for Stochastic Analyses of Single Serotonergic Fibers in the Mouse Brain

“…Individual trajectories may represent "sample paths" (realizations) of rigorously-definable spatial stochastic processes, which again implies computational constrains. We have demonstrated the potential of this approach in recent studies in which serotonergic axons were modeled as paths of reflected fractional Brownian motion (FBM), a stochastic continuous-time process (Janušonis et al, 2020;Janušonis et al, 2023). In these supercomputing simulations, performed in geometric shapes based on the mouse brain, the resultant fiber densities approximated the actual serotonergic fiber densities, with no other biological information.…”