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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 the many available transcriptional programs. This “individuality” of serotonergic neurons necessitates the development of specialized methods for single-fiber analyses, both at the experimental and theoretical levels. We developed an integrated platform 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. 

ABSTRACT The matrix of serotonergic axons (fibers) is a constant feature of neural tissue in vertebrate brains. Its fundamental role appears to be associated with the spatiotemporal control of neuroplasticity. The densities of serotonergic fibers vary across brain regions, but their development and maintenance remain poorly understood. A specific fiber concentration is achieved as the result of the dynamics of a large number of individual fibers, each of which can make trajectory decisions independently of other fibers. Bridging these processes, operating on very different spatial scales, remains a challenge in neuroscience. The study provides the first qualitative description of individually-tagged serotonergic axons in four selected telencephalic regions (cortical and subcortical) of the mouse brain. Based on our previous implementation of the Brainbow toolbox in this system, serotonergic fibers were labeled with random intensity combinations of three fluorophores and imaged with high-resolution confocal microscopy. All examined regions contained serotonergic fibers of diverse identities and morphologies, often traveling in close proximity to one another. Some fibers transitioned among several morphologies in the same imaged volume. High fiber densities appeared to be associated with highly tortuous fiber segments produced by some individual fibers. This study supports efforts to predictively model the self-organization of the serotonergic matrix in all vertebrates, including regenerative processes in the adult human brain. 

In vertebrate brains, virtually all neural circuits operate inside a dense matrix of axons (fibers) that have a strongly stochastic character. These fibers originate in the brainstem raphe region, produce highly tortuous trajectories, and release serotonin (5-hydroxytryptamine, 5-HT), with other neurotransmitters. They can robustly regenerate in the adult mammalian brain and appear to support neuroplasticity [1], with implications for mental disorders [2] and artificial neural networks [3]. The self-organization of this “serotonergic” matrix remains poorly understood. In our previous study, we have shown that serotonergic fibers can be modeled as paths of fractional Brownian motion (FBM), a continuous-time stochastic process. FBM is parametrized by the Hurst index, which defines three distinctive regimes: subdiffusion (H < 0.5), normal diffusion (H = 0.5), and superdiffusion (H > 0.5). In two-dimensional (2D) shapes based on the adult mouse brain, simulated FBM-fibers (with H = 0.8) have produced regional distributions similar to those of the actual serotonergic fibers [4]. However, increments of superdiffusive FBM trajectories have long-range positive correlations, which implies that a fiber path in one 2D-section depends on its history in other sections. In a major extension of this study, we used a supercomputing simulation to generate 960 fibers in a complex, three-dimensional shape based on the late-embryonic mouse brain (at embryonic day 17.5). The fibers were modeled as paths of reflected FBM with H = 0.8. The reflection was caused by natural neuroanatomical borders such as the pia and ventricles. The resultant regional densities were compared to the actual fiber densities in the corresponding neuroanatomically-defined regions, based on a recently published comprehensive map [5]. The relative simulated densities showed strong similarities to the actual densities in the telencephalon, diencephalon, and mesencephalon. The current simulation does not include tissue heterogeneities, but it can be further improved with novel models of multifractional FBM, such as the one introduced by our group [6]. The study demonstrates that serotonergic fiber densities can be strongly influenced by the geometry of the brain, with implications for neurodevelopment, neuroplasticity, and brain evolution. Acknowledgements: This research was funded by an NSF-BMBF CRCNS grant (NSF #2112862 to SJ & TV; BMBF #STAXS to RM). References: 1. Lesch KP, Waider J. Serotonin in the modulation of neural plasticity and networks: implications for neurodevelopmental disorders. Neuron. 2012, 76, 175-191. 2. Daws RE, Timmermann C, Giribaldi B, et al. Increased global integration in the brain after psilocybin therapy for depression. Nat. Med. 2022, 28, 844-851. 3. Lee C, Zhang Z, Janušonis S. Brain serotonergic fibers suggest anomalous diffusion-based dropout in artificial neural networks. Front. Neurosci. 2022, 16, 949934. 4. Janušonis S, Detering N, Metzler R, Vojta T. Serotonergic axons as fractional Brownian motion paths: Insights Into the self-organization of regional densities. Front. Comput. Neurosci. 2020, 14, 56. 5. Awasthi JR, Tamada K, Overton ETN, Takumi T. Comprehensive topographical map of the serotonergic fibers in the male mouse brain. J. Comp. Neurol. 2021, 529, 1391-1429. 6. Wang W, Balcerek M, Burnecki K, et al. Memory-multi-fractional Brownian motion with continuous correlation. arXiv. 2023, 2303.01551. 

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 serotonergic matrix in the brain is a key unsolved problem in neuroscience. This matrix is composed of extremely long axons (fibers) that originate in the brainstem, invade nearly all brain regions, and accumulate in remarkably high densities in many of them. Serotonergic fibers possess a number of intriguing properties, including the ability to robustly regenerate in the adult brain, the strongly stochastic trajectories, and the poorly understood but consistent association with neural plasticity. We developed several experimental methods that can be used to capture the individual trajectories of serotonergic fibers in the mouse brain, including regions with high fiber densities. These data are essential for stochastic modeling efforts that currently utilize two different frameworks (a step-wise random walk based on the von Mises-Fisher directional distribution and the superdiffusive fractional Brownian motion). In one approach, we show that serotonergic fibers can be experimentally isolated by using transgenic mice with the inducible Cre (under the Tph2-promoter), crossed with a Cre reporter line. While the overall labeling intensity falls below that of the best constitutive model in the field (Migliarini et al., 2013), the inducible Cre allows for control over how many fibers are labeled in high-density regions, thus facilitating their semi-automated tracing. A particularly powerful approach is based on the Brainbow toolbox (Cai et al., 2013) which can be used to randomly “color-code” individual axons. We have developed the first implementation of Brainbow-tagging in the serotonergic system (based on intracranial AAV-injections) and demonstrate its potential in downstream stochastic analyses. In particular, we show that some apparent branching points are different fibers crossing at distances below the limit of optical resolution (even in high-power confocal imaging). Finally, we demonstrate the feasibility of imaging single serotonergic fibers with CUBIC-based tissue clearing and high-resolution light-sheet microscopy (with a 20X objective). This experimental toolbox, integrated with stochastic modeling, can advance the current understanding of the dynamics, robustness, and plasticity of the brain serotonergic system. This research was funded by NSF CRCNS (#1822517 and #2112862), NIMH (#MH117488), and the California NanoSystems Institute. 

Serotonergic axons (fibers) have a ubiquitous distribution in vertebrate brains, where they form meshworks with well-defined, regionally-specific densities. In humans, perturbations of these densities have been associated with abnormal neural processes, including neuropsychiatric conditions. The self-organization of serotonergic meshworks depends on the cumulative behavior of many serotonergic axons, each one of which has a virtually unpredictable trajectory. In order to bridge the high stochasticity at the microscopic level and the regional stability at the mesoscopic level, we are developing tunable hydrogel systems that can support causal modeling of these processes. These same systems can support future restorative efforts in neural tissue because serotonergic axons are nearly unique in their ability to robustly regenerate in the adult brain. In the study, we extended our research in 2D-primary brainstem cultures (Hingorani et al., 2022) to 3D-hydrogels. Tunable hydrogel scaffolds can closely mimic the mechanical and biochemical properties of actual neural tissue in all three dimensions and are therefore qualitatively different from 2D-environments. However, the integration of these scaffolds with highly sensitive neurons poses unique challenges. As the first step in building a hydrogel-based platform for the bioengineering of serotonergic axons, we studied primary brainstem neurons in several commercially available hydrogel platforms. The viability and dynamics of serotonergic somata and neurites were analyzed at different days in vitro with immunocytochemistry and high-resolution confocal microscopy. In addition, live imaging of neuron growth cones was performed, and the observed dynamics was compared to our extensive database of holotomographic (refractive index-based) recordings in 2D-cultures. The progress and key problems will be discussed. This research was funded by NSF CRCNS (#1822517 and #2112862), NIMH (#MH117488), and the California NanoSystems Institute. 

The neighborhood of virtually every brain neuron contains thin, meandering axons that release serotonin (5-HT). These axons, also referred to as serotonergic fibers, are present in all vertebrate species (from fish to mammals) and are an essential component of biological neural networks. In the mammalian brain, they create dense meshworks that are macroscopically described by densities. It is not known how these densities arise from the trajectories of individual fibers, each of which resembles a unique random-walk path. Solving this problem will advance our understanding of the fundamental structure of neural tissue, including its plasticity and regeneration. Our interdisciplinary program investigates the stochastic structure of serotonergic fibers, by employing a range of experimental, computational, and theoretical methods. Transgenic mouse models (e.g., Brainbow) and brainstem cell cultures are used with advanced microscopy (3D-confocal imaging, STED super-resolution microscopy, holotomography) to visualize individual serotonergic fibers and their trajectories. Serotonergic fibers are modeled as paths of a superdiffusive stochastic process, with a focus on fractional Brownian motion (FBM). The formation of regional fiber densities is tested with supercomputer modeling in neuroanatomically accurate 2D- and 3D-brain-like shapes. Within the same framework, we are developing the mathematical theory of the reflected, branching, and spatially heterogenous FBM.