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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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Brain serotonergic fibers suggest anomalous diffusion-based dropout in artificial neural networks
Random dropout has become a standard regularization technique in artificial neural networks (ANNs), but it is currently unknown whether an analogous mechanism exists in biological neural networks (BioNNs). If it does, its structure is likely to be optimized by hundreds of millions of years of evolution, which may suggest novel dropout strategies in large-scale ANNs. We propose that the brain serotonergic fibers (axons) meet some of the expected criteria because of their ubiquitous presence, stochastic structure, and ability to grow throughout the individual’s lifespan. Since the trajectories of serotonergic fibers can be modeled as paths of anomalous diffusion processes, in this proof-of-concept study we investigated a dropout algorithm based on the superdiffusive fractional Brownian motion (FBM). The results demonstrate that serotonergic fibers can potentially implement a dropout-like mechanism in brain tissue, supporting neuroplasticity. They also suggest that mathematical theories of the structure and dynamics of serotonergic fibers can contribute to the design of dropout algorithms in ANNs.
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- PAR ID:
- 10381575
- Date Published:
- Journal Name:
- Frontiers in Neuroscience
- Volume:
- 16
- ISSN:
- 1662-453X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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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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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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.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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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fnins.2022.949934
