Achieving functional neuronal dendrite structure through sequential stochastic growth and retraction

Stochastic growth and selective stabilization generate stereotyped dendritic arbors

Stereotyped dendritic arbors are shaped by dynamic and stochastic growth during neuronal development. It remains unclear how guidance receptors and ligands coordinate branch dynamic growth, retraction, and stabilization to specify dendritic arbors. We previously showed that extracellular ligand SAX-7/LICAM dictates the shape of the PVD sensory neuron via binding to the dendritic guidance receptor DMA-1, a single transmembrane adhesion molecule. Here, we perform structure-function analyses of DMA-1 and unexpectedly find that robust, stochastic dendritic growth does not require ligand-binding. Instead, ligand-binding inhibits growth, prevents retraction, and specifies arbor shape. Furthermore, we demonstrate that dendritic growth requires a pool of ligand-free DMA-1, which is maintained by receptor endocytosis and reinsertion to the plasma membrane via recycling endosomes. Mutants defective of DMA-1 endocytosis show severely truncated dendritic arbors. We present a model in which ligand-free guidance receptor mediates intrinsic, stochastic dendritic growth, while extracellular ligands instruct dendrite shape by inhibiting growth.

Augmin complex activity finetunes dendrite morphology through non-centrosomal microtubule nucleation in vivo

During development, neurons achieve a stereotyped neuron type-specific morphology, which relies on dynamic support by microtubules (MTs). An important player is the augmin complex (hereafter augmin), which binds to existing MT filaments and recruits the γ-tubulin ring complex (γ-TuRC), to form branched MTs. In cultured neurons, augmin is important for neurite formation. However, little is known about the role of augmin during neurite formation in vivo. Here, we have revisited the role of mammalian augmin in culture and then turned towards the class four Drosophila dendritic arborization (c4da) neurons. We show that MT density is maintained through augmin in cooperation with the γ-TuRC in vivo. Mutant c4da neurons show a reduction of newly emerging higher-order dendritic branches and in turn also a reduced number of their characteristic space-filling higher-order branchlets. Taken together, our data reveal a cooperative function for augmin with the γ-TuRC in forming enough MTs needed for the appropriate differentiation of morphologically complex dendrites in vivo.

A biologically inspired repair mechanism for neuronal reconstructions with a focus on human dendrites

Investigating and modelling the functionality of human neurons remains challenging due to the technical limitations, resulting in scarce and incomplete 3D anatomical reconstructions. Here we used a morphological modelling approach based on optimal wiring to repair the parts of a dendritic morphology that were lost due to incomplete tissue samples. In Drosophila, where dendritic regrowth has been studied experimentally using laser ablation, we found that modelling the regrowth reproduced a bimodal distribution between regeneration of cut branches and invasion by neighbouring branches. Interestingly, our repair model followed growth rules similar to those for the generation of a new dendritic tree. To generalise the repair algorithm from Drosophila to mammalian neurons, we artificially sectioned reconstructed dendrites from mouse and human hippocampal pyramidal cell morphologies, and showed that the regrown dendrites were morphologically similar to the original ones. Furthermore, we were able to restore their electrophysiological functionality, as evidenced by the recovery of their firing behaviour. Importantly, we show that such repairs also apply to other neuron types including hippocampal granule cells and cerebellar Purkinje cells. We then extrapolated the repair to incomplete human CA1 pyramidal neurons, where the anatomical boundaries of the particular brain areas innervated by the neurons in question were known. Interestingly, the repair of incomplete human dendrites helped to simulate the recently observed increased synaptic thresholds for dendritic NMDA spikes in human versus mouse dendrites. To make the repair tool available to the neuroscience community, we have developed an intuitive and simple graphical user interface (GUI), which is available in the TREES toolbox (www.treestoolbox.org).

Sculpting the dendritic landscape: Actin, microtubules, and the art of arborization

Dendrites are intricately designed neuronal compartments that play a vital role in the gathering and processing of sensory or synaptic inputs. Their diverse and elaborate structures are distinct features of neuronal organization and function. Central to the generation of these dendritic arbors is the neuronal cytoskeleton. In this review, we delve into the current progress toward our understanding of how dendrite arbors are generated and maintained, focusing on the role of the actin and microtubule cytoskeleton.

Self-organized and directed branching results in optimal coverage in developing dermal lymphatic networks

Branching morphogenesis is a ubiquitous process that gives rise to high exchange surfaces in the vasculature and epithelial organs. Lymphatic capillaries form branched networks, which play a key role in the circulation of tissue fluid and immune cells. Although mouse models and correlative patient data indicate that the lymphatic capillary density directly correlates with functional output, i.e., tissue fluid drainage and trafficking efficiency of dendritic cells, the mechanisms ensuring efficient tissue coverage remain poorly understood. Here, we use the mouse ear pinna lymphatic vessel network as a model system and combine lineage-tracing, genetic perturbations, whole-organ reconstructions and theoretical modeling to show that the dermal lymphatic capillaries tile space in an optimal, space-filling manner. This coverage is achieved by two complementary mechanisms: initial tissue invasion provides a non-optimal global scaffold via self-organized branching morphogenesis, while VEGF-C dependent side-branching from existing capillaries rapidly optimizes local coverage by directionally targeting low-density regions. With these two ingredients, we show that a minimal biophysical model can reproduce quantitatively whole-network reconstructions, across development and perturbations. Our results show that lymphatic capillary networks can exploit local self-organizing mechanisms to achieve tissue-scale optimization.

Efficient simulation of neural development using shared memory parallelization

The Neural Development Simulator, NeuroDevSim, is a Python module that simulates the most important aspects of brain development: morphological growth, migration, and pruning. It uses an agent-based modeling approach inherited from the NeuroMaC software. Each cycle has agents called fronts execute model-specific code. In the case of a growing dendritic or axonal front, this will be a choice between extension, branching, or growth termination. Somatic fronts can migrate to new positions and any front can be retracted to prune parts of neurons. Collision detection prevents new or migrating fronts from overlapping with existing ones. NeuroDevSim is a multi-core program that uses an innovative shared memory approach to achieve parallel processing without messaging. We demonstrate linear strong parallel scaling up to 96 cores for large models and have run these successfully on 128 cores. Most of the shared memory parallelism is achieved without memory locking. Instead, cores have only write privileges to private sections of arrays, while being able to read the entire shared array. Memory conflicts are avoided by a coding rule that allows only active fronts to use methods that need writing access. The exception is collision detection, which is needed to avoid the growth of physically overlapping structures. For collision detection, a memory-locking mechanism was necessary to control access to grid points that register the location of nearby fronts. A custom approach using a serialized lock broker was able to manage both read and write locking. NeuroDevSim allows easy modeling of most aspects of neural development for models simulating a few complex or thousands of simple neurons or a mixture of both.

Code available at

https://github.com/CNS-OIST/NeuroDevSim.

Local Microtubule and F-Actin Distributions Fully Constrain the Spatial Geometry of Drosophila Sensory Dendritic Arbors

Dendritic morphology underlies the source and processing of neuronal signal inputs. Morphology can be broadly described by two types of geometric characteristics. The first is dendrogram topology, defined by the length and frequency of the arbor branches; the second is spatial embedding, mainly determined by branch angles and straightness. We have previously demonstrated that microtubules and actin filaments are associated with arbor elongation and branching, fully constraining dendrogram topology. Here, we relate the local distribution of these two primary cytoskeletal components with dendritic spatial embedding. We first reconstruct and analyze 167 sensory neurons from the Drosophila larva encompassing multiple cell classes and genotypes. We observe that branches with a higher microtubule concentration tend to deviate less from the direction of their parent branch across all neuron types. Higher microtubule branches are also overall straighter. F-actin displays a similar effect on angular deviation and branch straightness, but not as consistently across all neuron types as microtubule. These observations raise the question as to whether the associations between cytoskeletal distributions and arbor geometry are sufficient constraints to reproduce type-specific dendritic architecture. Therefore, we create a computational model of dendritic morphology purely constrained by the cytoskeletal composition measured from real neurons. The model quantitatively captures both spatial embedding and dendrogram topology across all tested neuron groups. These results suggest a common developmental mechanism regulating diverse morphologies, where the local cytoskeletal distribution can fully specify the overall emergent geometry of dendritic arbors.

Semi-Automated Quantitative Evaluation of Neuron Developmental Morphology In Vitro Using the Change-Point Test

Neuron morphology gives rise to distinct axons and dendrites and plays an essential role in neuronal functionality and circuit dynamics. In rat hippocampal neurons, morphological development occurs over roughly one week in vitro. This development has been qualitatively described as occurring in 5 stages. Still, there is a need to quantify cell growth to monitor cell culture health, understand cell responses to sensory cues, and compare experimental results and computational growth model predictions. To address this need, embryonic rat hippocampal neurons were observed in vitro over six days, and their processes were quantified using both standard morphometrics (degree, number of neurites, total length, and tortuosity) and new metrics (distance between change points, relative turning angle, and the number of change points) based on the Change-Point Test to track changes in path trajectories. Of the standard morphometrics, the total length of neurites per cell and the number of endpoints were significantly different between 0.5, 1.5, and 4 days in vitro, which are typically associated with Stages 2-4. Using the Change-Point Test, the number of change points and the average distance between change points per cell were also significantly different between those key time points. This work highlights key quantitative characteristics, both among common and novel morphometrics, that can describe neuron development in vitro and provides a foundation for analyzing directional changes in neurite growth for future studies.

Dynamic instability of dendrite tips generates the highly branched morphologies of sensory neurons

The highly ramified arbors of neuronal dendrites provide the substrate for the high connectivity and computational power of the brain. Altered dendritic morphology is associated with neuronal diseases. Many molecules have been shown to play crucial roles in shaping and maintaining dendrite morphology. However, the underlying principles by which molecular interactions generate branched morphologies are not understood. To elucidate these principles, we visualized the growth of dendrites throughout larval development of Drosophila sensory neurons and found that the tips of dendrites undergo dynamic instability, transitioning rapidly and stochastically between growing, shrinking, and paused states. By incorporating these measured dynamics into an agent-based computational model, we showed that the complex and highly variable dendritic morphologies of these cells are a consequence of the stochastic dynamics of their dendrite tips. These principles may generalize to branching of other neuronal cell types, as well as to branching at the subcellular and tissue levels.

The branching code: A model of actin-driven dendrite arborization

The cytoskeleton is crucial for defining neuronal-type-specific dendrite morphologies. To explore how the complex interplay of actin-modulatory proteins (AMPs) can define neuronal types in vivo, we focused on the class III dendritic arborization (c3da) neuron of Drosophila larvae. Using computational modeling, we reveal that the main branches (MBs) of c3da neurons follow general models based on optimal wiring principles, while the actin-enriched short terminal branches (STBs) require an additional growth program. To clarify the cellular mechanisms that define this second step, we thus concentrated on STBs for an in-depth quantitative description of dendrite morphology and dynamics. Applying these methods systematically to mutants of six known and novel AMPs, we revealed the complementary roles of these individual AMPs in defining STB properties. Our data suggest that diverse dendrite arbors result from a combination of optimal-wiring-related growth and individualized growth programs that are neuron-type specific.

Theory of branching morphogenesis by local interactions and global guidance

Branching morphogenesis governs the formation of many organs such as lung, kidney, and the neurovascular system. Many studies have explored system-specific molecular and cellular regulatory mechanisms, as well as self-organizing rules underlying branching morphogenesis. However, in addition to local cues, branched tissue growth can also be influenced by global guidance. Here, we develop a theoretical framework for a stochastic self-organized branching process in the presence of external cues. Combining analytical theory with numerical simulations, we predict differential signatures of global vs. local regulatory mechanisms on the branching pattern, such as angle distributions, domain size, and space-filling efficiency. We find that branch alignment follows a generic scaling law determined by the strength of global guidance, while local interactions influence the tissue density but not its overall territory. Finally, using zebrafish innervation as a model system, we test these key features of the model experimentally. Our work thus provides quantitative predictions to disentangle the role of different types of cues in shaping branched structures across scales.

Quantifying neuronal structural changes over time using dynamic morphometrics

Brain circuit development involves tremendous structural formation and rearrangement of dendrites, axons, and the synaptic connections between them. Direct studies of neuronal morphogenesis are now possible through recent developments in multiple technologies, including single-neuron labeling, time-lapse imaging in intact tissues, and 4D rendering software capable of tracking neural growth over periods spanning minutes to days. These methods allow detailed quantification of structural changes of neurons over time, called dynamic morphometrics, providing new insights into fundamental growth patterns, underlying molecular mechanisms, and the intertwined influences of external factors, including neural activity, and intrinsic genetic programs. Here, we review the methods of dynamic morphometrics sampling and analyses, focusing on their applications to studies of activity-driven dendritogenesis in vertebrate systems.

Drosophila Dendritic Arborisation Neurons: Fantastic Actin Dynamics and Where to Find Them

Neuronal dendrites receive, integrate, and process numerous inputs and therefore serve as the neuron's "antennae". Dendrites display extreme morphological diversity across different neuronal classes to match the neuron's specific functional requirements. Understanding how this structural diversity is specified is therefore important for shedding light on information processing in the healthy and diseased nervous system. Popular models for in vivo studies of dendrite differentiation are the four classes of dendritic arborization (c1da-c4da) neurons of Drosophila larvae with their class-specific dendritic morphologies. Using da neurons, a combination of live-cell imaging and computational approaches have delivered information on the distinct phases and the time course of dendrite development from embryonic stages to the fully developed dendritic tree. With these data, we can start approaching the basic logic behind differential dendrite development. A major role in the definition of neuron-type specific morphologies is played by dynamic actin-rich processes and the regulation of their properties. This review presents the differences in the growth programs leading to morphologically different dendritic trees, with a focus on the key role of actin modulatory proteins. In addition, we summarize requirements and technological progress towards the visualization and manipulation of such actin regulators in vivo.

Neuron tracing and quantitative analyses of dendritic architecture reveal symmetrical three-way-junctions and phenotypes of git-1 in C. elegans

Complex dendritic trees are a distinctive feature of neurons. Alterations to dendritic morphology are associated with developmental, behavioral and neurodegenerative changes. The highly-arborized PVD neuron of C. elegans serves as a model to study dendritic patterning; however, quantitative, objective and automated analyses of PVD morphology are missing. Here, we present a method for neuronal feature extraction, based on deep-learning and fitting algorithms. The extracted neuronal architecture is represented by a database of structural elements for abstracted analysis. We obtain excellent automatic tracing of PVD trees and uncover that dendritic junctions are unevenly distributed. Surprisingly, these junctions are three-way-symmetrical on average, while dendritic processes are arranged orthogonally. We quantify the effect of mutation in git-1, a regulator of dendritic spine formation, on PVD morphology and discover a localized reduction in junctions. Our findings shed new light on PVD architecture, demonstrating the effectiveness of our objective analyses of dendritic morphology and suggest molecular control mechanisms.

Nerve cells (neurons) collect input signals via branched cellular projections called dendrites. A major aspect of the study of neurons, dating back over a century, involves the characterization of neuronal shapes and of their dendritic processes.

Here, we present an algorithmic approach for detection and classification of the tree-like dendrites of the PVD neuron in C. elegans worms. A key feature of our approach is to represent dendritic trees by a set of fundamental shapes, such as junctions and linear elements. By analyzing this dataset, we discovered several novel structural features. We have found that the junctions connecting branched dendrites have a three-way-symmetry, although the dendrites are arranged in a crosshatch pattern, and that the distribution of junctions varies across distinct sub-classes of the PVD’s dendritic tree. We further quantified subtle morphological effects due to mutation in the git-1 gene, a known regulator of dendritic spines. Our findings suggest molecular mechanisms for dendritic shape regulation and may help direct new avenues of research.

An imaging analysis protocol to trace, quantify, and model multi-signal neuron morphology

We describe how to reconstruct and quantify multi-signal neuronal morphology, using the dendritic distributions of microtubules and F-actin in sensory neurons from fly larvae as examples. We then provide a detailed procedure to analyze channel-specific morphometrics from these enhanced reconstructions. To illustrate applications, we demonstrate how to run a cytoskeleton-constrained simulation of dendritic tree generation and explain its validation against experimental data. This protocol is applicable to any species, developmental stage, brain region, cell class, branching process, and signal type. For complete details on the use and execution of this protocol, please refer to Nanda et al. (2020).

Dendrite enlightenment

Neuronal dendrites acquire complex morphologies during development. These are not just the product of cell-intrinsic developmental programs; rather they are defined in close interaction with the cellular environment. Thus, to understand the molecular cascades that yield appropriate morphologies, it is essential to investigate them in vivo, in the actual complex tissue environment encountered by the differentiating neuron in the developing animal. Particularly, genetic approaches have pointed to factors controlling dendrite differentiation in vivo. These suggest that localized and transient molecular cascades might underlie the formation and stabilization of dendrite branches with neuron type-specific characteristics. Here, I highlight the need for studies of neuronal dendrite differentiation in the animal, the challenges provided by such an approach, and the promising pathways that have recently opened.

Transcription factor encoding of neuron subtype: Strategies that specify arbor pattern

Dendrite and axon arbors form scaffolds that connect a neuron to its partners; they are patterned to support the specific connectivity and computational requirements of each neuron subtype. Transcription factor networks control the specification of neuron subtypes, and the consequent diversification of their stereotyped arbor patterns during differentiation. We outline how the differentiation trajectories of stereotyped arbors are shaped by hierarchical deployment of precursor cell and postmitotic transcription factors. These transcription factors exert modular control over the dendrite and axon features of a single neuron, create spatial and functional compartmentalization of an arbor, instruct implementation of developmental patterning rules, and exert operational control over the cell biological processes that construct an arbor.

Achieving functional neuronal dendrite structure through sequential stochastic growth and retraction

Class I ventral posterior dendritic arborisation (c1vpda) proprioceptive sensory neurons respond to contractions in the Drosophila larval body wall during crawling. Their dendritic branches run along the direction of contraction, possibly a functional requirement to maximise membrane curvature during crawling contractions. Although the molecular machinery of dendritic patterning in c1vpda has been extensively studied, the process leading to the precise elaboration of their comb-like shapes remains elusive. Here, to link dendrite shape with its proprioceptive role, we performed long-term, non-invasive, in vivo time-lapse imaging of c1vpda embryonic and larval morphogenesis to reveal a sequence of differentiation stages. We combined computer models and dendritic branch dynamics tracking to propose that distinct sequential phases of stochastic growth and retraction achieve efficient dendritic trees both in terms of wire and function. Our study shows how dendrite growth balances structure-function requirements, shedding new light on general principles of self-organisation in functionally specialised dendrites.