skip to main content


Title: Fitting Splines to Axonal Arbors Quantifies Relationship Between Branch Order and Geometry
Neuromorphology is crucial to identifying neuronal subtypes and understanding learning. It is also implicated in neurological disease. However, standard morphological analysis focuses on macroscopic features such as branching frequency and connectivity between regions, and often neglects the internal geometry of neurons. In this work, we treat neuron trace points as a sampling of differentiable curves and fit them with a set of branching B-splines. We designed our representation with the Frenet-Serret formulas from differential geometry in mind. The Frenet-Serret formulas completely characterize smooth curves, and involve two parameters, curvature and torsion. Our representation makes it possible to compute these parameters from neuron traces in closed form. These parameters are defined continuously along the curve, in contrast to other parameters like tortuosity which depend on start and end points. We applied our method to a dataset of cortical projection neurons traced in two mouse brains, and found that the parameters are distributed differently between primary, collateral, and terminal axon branches, thus quantifying geometric differences between different components of an axonal arbor. The results agreed in both brains, further validating our representation. The code used in this work can be readily applied to neuron traces in SWC format and is available in our open-source Python package brainlit : http://brainlit.neurodata.io/ .  more » « less
Award ID(s):
2014862
NSF-PAR ID:
10331116
Author(s) / Creator(s):
; ; ; ; ;
Date Published:
Journal Name:
Frontiers in Neuroinformatics
Volume:
15
ISSN:
1662-5196
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract Recent advances in brain clearing and imaging have made it possible to image entire mammalian brains at sub-micron resolution. These images offer the potential to assemble brain-wide atlases of neuron morphology, but manual neuron reconstruction remains a bottleneck. Several automatic reconstruction algorithms exist, but most focus on single neuron images. In this paper, we present a probabilistic reconstruction method, ViterBrain, which combines a hidden Markov state process that encodes neuron geometry with a random field appearance model of neuron fluorescence. ViterBrain utilizes dynamic programming to compute the global maximizer of what we call the most probable neuron path. We applied our algorithm to imperfect image segmentations, and showed that it can follow axons in the presence of noise or nearby neurons. We also provide an interactive framework where users can trace neurons by fixing start and endpoints. ViterBrain is available in our open-source Python package . 
    more » « less
  2. 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. 
    more » « less
  3. INTRODUCTION Diverse phenotypes, including large brains relative to body size, group living, and vocal learning ability, have evolved multiple times throughout mammalian history. These shared phenotypes may have arisen repeatedly by means of common mechanisms discernible through genome comparisons. RATIONALE Protein-coding sequence differences have failed to fully explain the evolution of multiple mammalian phenotypes. This suggests that these phenotypes have evolved at least in part through changes in gene expression, meaning that their differences across species may be caused by differences in genome sequence at enhancer regions that control gene expression in specific tissues and cell types. Yet the enhancers involved in phenotype evolution are largely unknown. Sequence conservation–based approaches for identifying such enhancers are limited because enhancer activity can be conserved even when the individual nucleotides within the sequence are poorly conserved. This is due to an overwhelming number of cases where nucleotides turn over at a high rate, but a similar combination of transcription factor binding sites and other sequence features can be maintained across millions of years of evolution, allowing the function of the enhancer to be conserved in a particular cell type or tissue. Experimentally measuring the function of orthologous enhancers across dozens of species is currently infeasible, but new machine learning methods make it possible to make reliable sequence-based predictions of enhancer function across species in specific tissues and cell types. RESULTS To overcome the limits of studying individual nucleotides, we developed the Tissue-Aware Conservation Inference Toolkit (TACIT). Rather than measuring the extent to which individual nucleotides are conserved across a region, TACIT uses machine learning to test whether the function of a given part of the genome is likely to be conserved. More specifically, convolutional neural networks learn the tissue- or cell type–specific regulatory code connecting genome sequence to enhancer activity using candidate enhancers identified from only a few species. This approach allows us to accurately associate differences between species in tissue or cell type–specific enhancer activity with genome sequence differences at enhancer orthologs. We then connect these predictions of enhancer function to phenotypes across hundreds of mammals in a way that accounts for species’ phylogenetic relatedness. We applied TACIT to identify candidate enhancers from motor cortex and parvalbumin neuron open chromatin data that are associated with brain size relative to body size, solitary living, and vocal learning across 222 mammals. Our results include the identification of multiple candidate enhancers associated with brain size relative to body size, several of which are located in linear or three-dimensional proximity to genes whose protein-coding mutations have been implicated in microcephaly or macrocephaly in humans. We also identified candidate enhancers associated with the evolution of solitary living near a gene implicated in separation anxiety and other enhancers associated with the evolution of vocal learning ability. We obtained distinct results for bulk motor cortex and parvalbumin neurons, demonstrating the value in applying TACIT to both bulk tissue and specific minority cell type populations. To facilitate future analyses of our results and applications of TACIT, we released predicted enhancer activity of >400,000 candidate enhancers in each of 222 mammals and their associations with the phenotypes we investigated. CONCLUSION TACIT leverages predicted enhancer activity conservation rather than nucleotide-level conservation to connect genetic sequence differences between species to phenotypes across large numbers of mammals. TACIT can be applied to any phenotype with enhancer activity data available from at least a few species in a relevant tissue or cell type and a whole-genome alignment available across dozens of species with substantial phenotypic variation. Although we developed TACIT for transcriptional enhancers, it could also be applied to genomic regions involved in other components of gene regulation, such as promoters and splicing enhancers and silencers. As the number of sequenced genomes grows, machine learning approaches such as TACIT have the potential to help make sense of how conservation of, or changes in, subtle genome patterns can help explain phenotype evolution. Tissue-Aware Conservation Inference Toolkit (TACIT) associates genetic differences between species with phenotypes. TACIT works by generating open chromatin data from a few species in a tissue related to a phenotype, using the sequences underlying open and closed chromatin regions to train a machine learning model for predicting tissue-specific open chromatin and associating open chromatin predictions across dozens of mammals with the phenotype. [Species silhouettes are from PhyloPic] 
    more » « less
  4. Morrison, Abigail (Ed.)
    Assessing directional influences between neurons is instrumental to understand how brain circuits process information. To this end, Granger causality, a technique originally developed for time-continuous signals, has been extended to discrete spike trains. A fundamental assumption of this technique is that the temporal evolution of neuronal responses must be due only to endogenous interactions between recorded units, including self-interactions. This assumption is however rarely met in neurophysiological studies, where the response of each neuron is modulated by other exogenous causes such as, for example, other unobserved units or slow adaptation processes. Here, we propose a novel point-process Granger causality technique that is robust with respect to the two most common exogenous modulations observed in real neuronal responses: within-trial temporal variations in spiking rate and between-trial variability in their magnitudes. This novel method works by explicitly including both types of modulations into the generalized linear model of the neuronal conditional intensity function (CIF). We then assess the causal influence of neuron i onto neuron j by measuring the relative reduction of neuron j ’s point process likelihood obtained considering or removing neuron i . CIF’s hyper-parameters are set on a per-neuron basis by minimizing Akaike’s information criterion. In synthetic data sets, generated by means of random processes or networks of integrate-and-fire units, the proposed method recovered with high accuracy, sensitivity and robustness the underlying ground-truth connectivity pattern. Application of presently available point-process Granger causality techniques produced instead a significant number of false positive connections. In real spiking responses recorded from neurons in the monkey pre-motor cortex (area F5), our method revealed many causal relationships between neurons as well as the temporal structure of their interactions. Given its robustness our method can be effectively applied to real neuronal data. Furthermore, its explicit estimate of the effects of unobserved causes on the recorded neuronal firing patterns can help decomposing their temporal variations into endogenous and exogenous components. 
    more » « less
  5. INTRODUCTION Neurons are by far the most diverse of all cell types in animals, to the extent that “cell types” in mammalian brains are still mostly heterogeneous groups, and there is no consensus definition of the term. The Drosophila optic lobes, with approximately 200 well-defined cell types, provides a tractable system with which to address the genetic basis of neuronal type diversity. We previously characterized the distinct developmental gene expression program of each of these types using single-cell RNA sequencing (scRNA-seq), with one-to-one correspondence to the known morphological types. RATIONALE The identity of fly neurons is determined by temporal and spatial patterning mechanisms in stem cell progenitors, but it remained unclear how these cell fate decisions are implemented and maintained in postmitotic neurons. It was proposed in Caenorhabditis elegans that unique combinations of terminal selector transcription factors (TFs) that are continuously expressed in each neuron control nearly all of its type-specific gene expression. This model implies that it should be possible to engineer predictable and complete switches of identity between different neurons just by modifying these sustained TFs. We aimed to test this prediction in the Drosophila visual system. RESULTS Here, we used our developmental scRNA-seq atlases to identify the potential terminal selector genes in all optic lobe neurons. We found unique combinations of, on average, 10 differentially expressed and stably maintained (across all stages of development) TFs in each neuron. Through genetic gain- and loss-of-function experiments in postmitotic neurons, we showed that modifications of these selector codes are sufficient to induce predictable switches of identity between various cell types. Combinations of terminal selectors jointly control both developmental (e.g., morphology) and functional (e.g., neurotransmitters and their receptors) features of neurons. The closely related Transmedullary 1 (Tm1), Tm2, Tm4, and Tm6 neurons (see the figure) share a similar code of terminal selectors, but can be distinguished from each other by three TFs that are continuously and specifically expressed in one of these cell types: Drgx in Tm1, Pdm3 in Tm2, and SoxN in Tm6. We showed that the removal of each of these selectors in these cell types reprograms them to the default Tm4 fate. We validated these conversions using both morphological features and molecular markers. In addition, we performed scRNA-seq to show that ectopic expression of pdm3 in Tm4 and Tm6 neurons converts them to neurons with transcriptomes that are nearly indistinguishable from that of wild-type Tm2 neurons. We also show that Drgx expression in Tm1 neurons is regulated by Klumpfuss, a TF expressed in stem cells that instructs this fate in progenitors, establishing a link between the regulatory programs that specify neuronal fates and those that implement them. We identified an intronic enhancer in the Drgx locus whose chromatin is specifically accessible in Tm1 neurons and in which Klu motifs are enriched. Genomic deletion of this region knocked down Drgx expression specifically in Tm1 neurons, leaving it intact in the other cell types that normally express it. We further validated this concept by demonstrating that ectopic expression of Vsx (visual system homeobox) genes in Mi15 neurons not only converts them morphologically to Dm2 neurons, but also leads to the loss of their aminergic identity. Our results suggest that selector combinations can be further sculpted by receptor tyrosine kinase signaling after neurogenesis, providing a potential mechanism for postmitotic plasticity of neuronal fates. Finally, we combined our transcriptomic datasets with previously generated chromatin accessibility datasets to understand the mechanisms that control brain wiring downstream of terminal selectors. We built predictive computational models of gene regulatory networks using the Inferelator framework. Experimental validations of these networks revealed how selectors interact with ecdysone-responsive TFs to activate a large and specific repertoire of cell surface proteins and other effectors in each neuron at the onset of synapse formation. We showed that these network models can be used to identify downstream effectors that mediate specific cellular decisions during circuit formation. For instance, reduced levels of cut expression in Tm2 neurons, because of its negative regulation by pdm3 , controls the synaptic layer targeting of their axons. Knockdown of cut in Tm1 neurons is sufficient to redirect their axons to the Tm2 layer in the lobula neuropil without affecting other morphological features. CONCLUSION Our results support a model in which neuronal type identity is primarily determined by a relatively simple code of continuously expressed terminal selector TFs in each cell type throughout development. Our results provide a unified framework of how specific fates are initiated and maintained in postmitotic neurons and open new avenues to understanding synaptic specificity through gene regulatory networks. The conservation of this regulatory logic in both C. elegans and Drosophila makes it likely that the terminal selector concept will also be useful in understanding and manipulating the neuronal diversity of mammalian brains. Terminal selectors enable predictive cell fate reprogramming. Tm1, Tm2, Tm4, and Tm6 neurons of the Drosophila visual system share a core set of TFs continuously expressed by each cell type (simplified). The default Tm4 fate is overridden by the expression of a single additional terminal selector to generate Tm1 ( Drgx ), Tm2 ( pdm3 ), or Tm6 ( SoxN ) fates. 
    more » « less