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The brain serotonergic axons (fibers) are quintessential “stochastic” axons in the sense that their individual trajectories are best described as sample paths of a spatial stochastic process. These fibers are present in high densities in virtually all regions of vertebrate brains; more generally, they appear to be an obligatory component of all nervous systems on this planet (from the dominating arthropods to such small phyla as the kinorhynchs). In mammals, serotonergic fibers are nearly unique in their ability to robustly regenerate in the adult brain, and they have been strongly associated with neural plasticity. We have recently developed several experimental approaches to trace individual serotonergic fibers in the mouse brain (Mays et al., 2022). To further advance the theoretical analyses of their stochastic properties (e.g., the increment covariance structure), we developed a convolutional neural network (CNN) that performs high-throughput analysis of experimental data collected with sub-micrometer resolution. In contrast to a recently developed mesoscale platform that can separate large-caliber fiber segments from the background on the whole-brain scale (Friedmann et al., 2020), our microscale model prioritizes the accuracy and continuity of individual fiber trajectories, an essential element in downstream stochastic analyses. In particular, it seamlessly integrates information about the physical properties of serotonergic fibers and high-resolution experimental data to achieve reliable, fully-automated tracing of trajectories in brain regions with different fiber densities. This 3D-spatial information supports our current theoretical frameworks based on step-wise random walks (Janusonis & Detering, 2019) and continuous-time processes (Janusonis et al., 2020). In a complementary approach, we also investigated whether the structure of the serotonergic fibers may provide useful information for machine learning architectures. Specifically, we studied whether dropout, a standard regularization technique in artificial neural networks, can be matched or improved by virtual serotonergic fibers moving through CNN layers (endowed with the Euclidean metric) and triggering spatially correlated dropout events. This research was funded by NSF CRCNS (#1822517 and #2112862), NIMH (#MH117488), and the California NanoSystems Institute.
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An experimental toolbox for the analysis of single serotonergic axons in the mouse brain
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.
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- PAR ID:
- 10381577
- Date Published:
- Journal Name:
- Abstracts Society for Neuroscience
- ISSN:
- 0190-5295
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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.more » « less
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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.more » « less
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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.more » « less
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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.more » « less
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