The Self-Organization of Serotonergic Axons at the Surface of a Vertebrate Brain: A Myopic Self-Avoiding FBM Model

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Introduction Serotonergic axons (fibers) are present in virtually all brain regions of vertebrate animals (from humans to fishes). Within these regions, individual serotonergic fibers typically grow in paths that resemble random walks with memory. At the population level, they produce regionally-specific fiber meshworks that are thought to support the neuroplasticity of local, non-serotonergic neural circuits. We have recently developed a computational framework in which the trajectories of serotonergic fibers are modeled as paths of reflected fractional Brownian motion (rFBM), with simulated fiber densities approximating the biological densities in the forebrains of two phylogenetically distant species, the mouse [1] and the Pacific angelshark [2]. Methods This study focuses on the distribution of serotonergic fibers at the brain surface. Specifically, we investigate the emergence of high-density fiber bands in the dorsal pallium (including the mammalian cerebral cortex) that rFBM cannot capture accurately. We introduce a new animal model, the Pacific electric ray (Tetronarce californica), the forebrain of which has an extremely simple geometry with no ventricles or major fibers in the telencephalon. Its serotonergic fibers are visualized with immunohistochemistry, with comparisons to the mouse and angelshark brains [1,2]. We also introduce a major theoretical extension of rFBM, the reflected myopic self-avoiding FBM, based on a recently developed myopic self-avoiding FBM model [3]. Results In the electric ray telencephalon, serotonergic fibers generally accumulate at higher densities near the pial surface, consistent with findings in other vertebrate species. However, they additionally produce dense bands in the dorsal pallium (homologous to the mammalian cerebral cortex). The emergence of this biologically important feature cannot be explained by simple rFBM but is consistent with our simulations using the reflected myopic self-avoiding FBM, a stochastic process that includes a mean-density interaction between the members of the fiber ensemble. These simulations show that the interaction cuts off the divergence of the density at a reflecting boundary, producing a high-density plateau in the vicinity of the boundary. Discussion Our results suggest that FBM, with its recently developed theoretical extensions by our group [3,4], can eventually predict the key features of serotonergic fiber densities in any vertebrate brain. This approach relies on the geometry and regional viscoelasticity of the brain and is agnostic to anatomically-defined brain nuclei and their biological function. This research contributes to the understanding of the minimal set of principles that lead to the self-organization of the fundamental brain architecture. In addition, it stimulates the theoretical development of FBM-related stochastic processes, with broad applications in other fields. Acknowledgments This research was funded by an NSF-BMBF CRCNS grant (NSF #2112862 to SJ & TV). References [1] Janušonis, S., Haiman, J., Metzler, R., & Vojta, T. (2023). Predicting the distribution of serotonergic axons: a supercomputing simulation of reflected fractional Brownian motion in a 3D-mouse brain model. Frontiers in Computational Neuroscience, 17. doi: 10.3389/fncom.2023.1189853[2] Janušonis, S., Metzler, R., & Vojta, T. (2025). The organization of serotonergic fibers in the Pacific angelshark brain: neuroanatomical and supercomputing analyses. Frontiers in Neuroscience, 19. doi: 10.3389/fnins.2025.1602116[3] House, J., Bakhshizada, R., Janušonis, S., Metzler, R., & Vojta, T. (2025). Fractional Brownian motion with mean-density interaction: A myopic self-avoiding fractional stochastic process. Physical Review E, 112(3). doi: 10.1103/w5pk-bw5r[4] Wang, W., Balcerek, M., Burnecki, K., Chechkin, A., Janušonis, S., Ślęzak, J., Vojta, T., Wyłomańska, A., & Metzler, R. (2023). Memory-multi-fractional Brownian motion with continuous correlations. Physical Review Research, 5(3). doi: 10.1103/PhysRevResearch.5.L032025