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1. Single serotonergic axons: From a convolutional neural network for trajectory analysis to a neuroscience-inspired dropout in machine learning

   Madinei, P.; Mays, Kasie C.; Janusonis, Skirmantas (November 2022, Abstracts Society for Neuroscience)

   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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2. An experimental toolbox for the analysis of single serotonergic axons in the mouse brain

   Mays, Kasie C.; Haiman, Justin H.; Janusonis, Skirmantas. (November 2022, Abstracts Society for Neuroscience)

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

   https://doi.org/10.3389/fncom.2023.1189853  

   Janušonis, Skirmantas; Haiman, Justin H.; Metzler, Ralf; Vojta, Thomas (May 2023, Frontiers in Computational Neuroscience)

   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. 

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4. The Self-Organization of the Brain Serotonergic Matrix: From Stochastic Axon Paths to Regional Densities

   Janusonis, Skirmantas; Vojta, Thomas; Metzler, Ralf; Haiman, Justin H.; Wang, Wei (January 2022, NSF CRCNS PI Meeting)

   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. 

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5. Reflected Fractional Brownian Motion in 3D-Brain Shapes: Insights into the Distribution of Serotonergic Axons

   Janusonis, Skirmantas; Metzler, Ralf; Vojta, Thomas (January 2022, Organization for Computational Neurosciences (OCNS))

   The immediate 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 nearly all studied nervous systems (both vertebrate and invertebrate) and appear to be a key 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. This poses interesting theoretical questions, solving which will advance our understanding of brain plasticity and regeneration. For example, serotonin-associated psychedelics have recently been shown to promote global brain integration in depression [1], and serotonergic fibers are nearly unique in their ability to robustly regenerate in the adult mammalian brain [2]. We have recently introduced a conceptual framework that treats the serotonergic axons as “stochastic axons.” Stochastic axons are different from axons that support point-to-point connectivity (often studied with graph-theoretical methods) and require novel theoretical approaches. We have shown that serotonergic axons can be potentially modeled as paths of fractional Brownian motion (FBM) in the superdiffusive regime (with the Hurst exponent H > 0.5). Our supercomputing simulations demonstrate that particles driven by reflected FBM (rFBM) accumulate at the border enclosing the shape [3]. Likewise, serotonergic fibers tend to accumulate at the border of neural tissue, in addition to their general similarity to simulated FBM paths [4]. This work expands our previous simulations in 2D-brain-like shapes by considering the full 3D-geometry of the brain. This transition is not trivial and cannot be reduced to independent 2D-sections because increments of FBM trajectories exhibit long-range correlation. Supercomputing simulations of rFMB (H > 0.5) were performed in the reconstructed 3D-geometry of a mouse brain at embryonic day 17 (serotonergic fibers are already well developed at this age and begin to invade the cortical plate). The obtained results were compared to the actual distribution of fibers in the mouse brain. In addition, we obtained preliminary results by simulating rFBM with a region-dependent H. This next step in complexity presents challenges (e.g., it can be highly sensitive to mathematical specifications), but it is necessary for the predictive modeling of interior fiber densities in heterogenous brain tissue. 

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