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1. High-resolution spatiotemporal dynamics of serotonergic axons in primary brainstem cultures

   Hingorani, M.; Janusonis, S. (November 2022, Abstracts Society for Neuroscience)

   Recent experimental and theoretical work by our group has shown that the self-organization of the brain serotonergic matrix is strongly driven by the spatiotemporal dynamics of single serotonergic axons (fibers). The trajectories of these axons are often stochastic in character and can be described by step-wise random walks or time-continuous processes (e.g., fractional Brownian motion). The success of these modeling efforts depends on experimental data that can validate the proposed mathematical frameworks and constrain their parameters. In particular, further progress requires reliable experimental tracking of individual serotonergic axons in time and space. Visualizing this dynamic behavior in vivo is currently extremely difficult because of the high axon densities and other resolution limitations. In this study, we used in vitro systems of mouse primary brainstem neurons to examine serotonergic axons with unprecedented spatiotemporal precision. The high-resolution methods included confocal microscopy, STED super-resolution microscopy, and live imaging with holotomography. We demonstrate that the extension of developing serotonergic axons strongly relies on discrete attachments points on other, non-serotonergic neurons. These membrane anchors are remarkably stable but can be stretched into nano-scale tethers that accommodate the axon’s transitions from neuron to neuron, as it advances through neural tissue. We also show that serotonergic axons can be flat (ribbon-like) and produce screw-like rotations along their trajectory, perhaps to accommodate mechanical constraints. We conclude that the stochastic dynamics of serotonergic axons may be conditioned by the stochastic geometry of neural tissue and, consequently, may reflect it. Our current research includes hydrogels to better understand these processes in controlled artificial environments. Since serotonergic axons are nearly unique in their ability to regenerate in the adult mammalian brain and they support neural plasticity, this research not only advances fundamental neuroscience but can also inform efforts to restore injured neural tissue. This research was funded by NSF CRCNS (#1822517 and #2112862), NIMH (#MH117488), and the California NanoSystems Institute. 

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2. 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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3. 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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4. High-resolution spatiotemporal analysis of single serotonergic axons in an in vitro system

   https://doi.org/10.3389/fnins.2022.994735  

   Hingorani, Melissa; Viviani, Adele M.; Sanfilippo, Jenna E.; Janušonis, Skirmantas (October 2022, Frontiers in Neuroscience)

   Vertebrate brains have a dual structure, composed of ( i ) axons that can be well-captured with graph-theoretical methods and ( ii ) axons that form a dense matrix in which neurons with precise connections operate. A core part of this matrix is formed by axons (fibers) that store and release 5-hydroxytryptamine (5-HT, serotonin), an ancient neurotransmitter that supports neuroplasticity and has profound implications for mental health. The self-organization of the serotonergic matrix is not well understood, despite recent advances in experimental and theoretical approaches. In particular, individual serotonergic axons produce highly stochastic trajectories, fundamental to the construction of regional fiber densities, but further advances in predictive computer simulations require more accurate experimental information. This study examined single serotonergic axons in culture systems (co-cultures and monolayers), by using a set of complementary high-resolution methods: confocal microscopy, holotomography (refractive index-based live imaging), and super-resolution (STED) microscopy. It shows that serotonergic axon walks in neural tissue may strongly reflect the stochastic geometry of this tissue and it also provides new insights into the morphology and branching properties of serotonergic axons. The proposed experimental platform can support next-generation analyses of the serotonergic matrix, including seamless integration with supercomputing approaches. 

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5. The stochastic self-organization of serotonergic densities

   Janusonis, Skirmantas; Metzler, Ralf; Vojta, Thomas (July 2023, NSF CRCNS PI Meeting)

   Neural networks in adult vertebrate brains are physically embedded in meshworks of thin, functionally active axons (fibers) that originate in the brainstem. As these fibers weave through neural tissue, releasing serotonin (5-HT) with glutamate and other neurotransmitters, they produce a dense matrix macroscopically described by regional fiber densities. This matrix is fundamentally associated with neuroplasticity, with implications for mental disorders and artificial neural networks. We have recently shown that its self-organization strongly depends on the stochastic properties of single fibers and their interaction with the three-dimensional (3D) geometry of the brain. Specifically, the trajectories of individual fibers can be described as paths of reflected fractional Brownian motion (FBM) [1, 2]. We are currently using transgenic, in vitro [3], and other experimental approaches to guide further modeling efforts and to motivate the development of the FBM theory itself [4]. In a major extension of our previous studies, we used supercomputing to simulate 960 fibers in a complex, 3D-dimensional shape constructed from serial sections of the late-embryonic mouse brain (at E17.5) [5]. The fibers were modeled as paths of reflected FBM (H = 0.8) which interacted with pial and ventricular borders. The simulated densities were compared to the actual regional fiber densities in a recently published comprehensive map. Strong similarities were found in the forebrain and midbrain. This study demonstrates that regional “serotonergic” fiber densities can achieve a substantial degree of self-organization with no biological guiding signals, with implications for neurodevelopment, neuroplasticity, and brain evolution. Support: NSF-BMBF CRCNS (NSF #2112862 to SJ & TV; BMBF #STAXS to RM). References: [1] Janušonis et al. (2020) Front. Comput. Neurosci. 14: 56; [2] Vojta et al. (2020) Phys. Rev. E 102: 032108; [3] Hingorani et al. (2022) Front. Neurosci. 16: 994735; [4] Wang et al. (2023) arXiv 2303.01551; [5] Janušonis et al. (2023) bioRxiv 10.1101/2023.03.19.533385. 

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