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Dendritic tiling of cultured Purkinje cells. (A) Left: Purkinje cells juxtaposed to other Purkinje cells in culture avoid dendritic overlaps. Right: graphic image of dendrite arbors. (B) Dendrites of a Purkinje cell (calbindin, green) and granule cells (magenta) crossed with each other in the dissociation culture at 11 DIV. The shape of Pax6-positive granule cells (white) were visualized by transfecting TdTomato. Arrowheads point to cell bodies of the labeled granule cells. Arrows indicate dendrite crossings between the Purkinje cell and granule cells. Scale bars: 20 μm.
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Neurons develop dendritic arbors in cell type-specific patterns. Using growing Purkinje cells in culture as a model, we performed a long-term time-lapse observation of dendrite branch dynamics to understand the rules that govern the characteristic space-filling dendrites. We found that dendrite architecture was sculpted by a combination of reproduc...
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... shown to act not only between branches of the same cell but also between neighboring cells of the same type. Similarly, dendro-dendritic contacts between neighboring Purkinje cells induced retraction and stalling of branches (Fig. 4F, Fig. 5A). By contrast, dendrites of granule cells frequently overlapped with Purkinje cell dendrites in culture (Fig. 5B). In addition, contacts with the axon did not change the behavior of growing dendrites, indicating that contact-dependent repulsion is specific for homotypic dendro-dendritic interactions in Purkinje cells (Fig. ...Citations
... 36 Because the genetic networks responsible for pattern formation are frequently conserved through evolution, organisms of different size often have neuronal structures that scale geometrically. 37 Even for individual neurons, one might anticipate that repetitive application of a single set of pattern-formation rules 6,7,38 could generate arbors with similar geometric properties at different length scales, such as the fractal dimension. 39,40 Are there analogous topological properties that scale, and are these features functionally important? ...
... By contrast, Purkinje cells in culture grow predominantly by tip branching. 6 We therefore analyzed so-called QS growth processes 32 that have a balance between internal and tip branching (here we considered the one-parameter model 54 ; Figure S6). We found that internal branching, provided its frequency is less than tip branching, still gives rise to a power law, and that the perfection index decreases as the relative frequency of internal branching increases ( Figure S6B). ...
Branching allows neurons to make synaptic contacts with large numbers of other neurons, facilitating the high connectivity of nervous systems. Neuronal arbors have geometric properties such as branch lengths and diameters that are optimal in that they maximize signaling speeds while minimizing construction costs. In this work, we asked whether neuronal arbors have topological properties that may also optimize their growth or function. We discovered that for a wide range of invertebrate and vertebrate neurons the distributions of their subtree sizes follow power laws, implying that they are scale invariant. The power-law exponent distinguishes different neuronal cell types. Postsynaptic spines and branchlets perturb scale invariance. Through simulations, we show that the subtree-size distribution depends on the symmetry of the branching rules governing arbor growth and that optimal morphologies are scale invariant. Thus, the subtree-size distribution is a topological property that recapitulates the functional morphology of dendrites.
... Adult Purkinje cells have a uniquely flat dendrite, which is optimal to maximize connectivity with perpendicular parallel fibers [14][15][16][17], with usually a single root segment. But during early postnatal development, each Purkinje cell grows multiple dendritic trees (defined as the arbor connected to a dendritic root) ( Fig 1B1) and then selects a primary tree among them by retracting most of the newly grown dendrites (Fig 1 B2) [18][19][20][21][22]. This is followed by additional growth and development of a more monoplanar tree in the third postnatal week [23]. ...
... In isolated in vitro environments, Purkinje cells do not fully retract excessive dendritic trees, resulting in persistent multiple primary dendrites [21,24]. Granule cells and their parallel fibers are strong environmental factors to regulate the dendritic arborizations and retractions in terms of physical and synaptic interactions with Purkinje cells [25][26][27][28]. ...
We investigate the relationship between primary dendrite selection of Purkinje cells and migration of their presynaptic partner granule cells during early cerebellar development. During postnatal development, each Purkinje cell grows more than three dendritic trees, from which a primary tree is selected for development, whereas the others completely retract. Experimental studies suggest that this selection process is coordinated by physical and synaptic interactions with granule cells, which undergo a massive migration at the same time. However, technical limitations hinder continuous experimental observation of multiple cell populations. To explore possible mechanisms underlying this selection process, we constructed a computational model using a new computational framework, NeuroDevSim. The study presents the first computational model that simultaneously simulates Purkinje cell growth and the dynamics of granule cell migrations during the first two postnatal weeks, allowing exploration of the role of physical and synaptic interactions upon dendritic selection. The model suggests that interaction with parallel fibers is important to establish the distinct planar morphology of Purkinje cell dendrites. Specific rules to select which dendritic trees to keep or retract result in larger winner trees with more synaptic contacts than using random selection. A rule based on afferent synaptic activity was less effective than rules based on dendritic size or numbers of synapses.
... One can thus divide structural plasticity of dendrites into two temporal phases: plasticity during development and plasticity after reaching a steady mature shape. During development, dendrites undergo frequent, dynamic changes including elongation, branching of terminals, and retraction caused by contact with another growing dendrite (Fujishima et al. 2012). The self-organizing dynamics of the developing arbors are regulated by both local and global cues (Uçar et al. 2021). ...
Mature dendritic arbors emerge out of complex growth mechanisms involving intracellular, extracellular, and activity-dependent factors. These interactions converge on cytoskeletal effectors, mainly microtubules and actin filaments, which mediate the structural changes and stabilize the mature structure. The quantitative characterization of developmental dynamics remains challenging because current morphological descriptors are static and without explicit representation of subcellular composition. Large datasets of new time-varying reconstructions with co-registered internal cytoskeletal information are required to build statistically reliable models of dendritic growth and plasticity. In this chapter, we review the history and current state of experimental and theoretical approaches and illustrate the progress of an innovative closed-loop research design using the Drosophila larva system. Time-lapse confocal images of the fluorescently labeled cytoskeletal components are digitally reconstructed into a novel file structure, enabling comprehensive statistical analysis and data-driven computational simulations of dendritic growth. These data in turn guide the most informative genetic manipulations for testing specific hypotheses.KeywordsNeuronal reconstructionsStochastic models of dendritic growthDrosophila neurogeneticsDendrite developmentMultispectral fluorescent confocal imagingDentritic arborization of sensory neuronsCytoskeletal regulationMultichannel reconstructionTime-lapse reconstruction
... This semi-automated process ensures that the right paths are chosen and traced. Each dendritic tree was evaluated with branching grades (orders) according to the Fujishima protocol [20]. The branch orders for each analyzed Purkinje neuron were determined as follows: Microscope Leica files (.lif) were converted to TIFF files and opened with the Fiji SNT plugin. ...
Elucidation of the mechanisms involved in neurodegenerative diseases of the cerebellum has been hampered by the lack of robust single cell models to study Purkinje neurons and replicate at the same time in vivo features. Cerebellar Purkinje neurons are difficult to grow in dispersed cell culture, and only limited work has been done using rat cells. We developed a refined protocol for growing rat Purkinje neurons from embryonic and postnatal tissue ex vivo that results in well-developed, mature, functional, and synaptically active neurons. The rat Purkinje neurons generated are responsive to paracrine factors and genetic manipulation, allowing great experimental flexibility at the single-cell level. This ex vivo model can be used to investigate disease mechanisms that disturb Purkinje neuron morphology, function, and communication in high- and low-throughput screening formats.
... This fact suggests that the mechanism of PC dendrite maturation through N-WASP-Arp2/3 signaling absolutely requires Cdc42 as an upstream regulator, and may therefore be mediated to some extent by an extracellular signal(s). In support of this idea, the process of PC dendrite development in the dissociated culture and cerebellar slice culture, where extracellular signals in the cerebellum would have been disturbed, only partially recapitulates the in vivo situation; for example, many cells fail to completely reorganize their dendrites, thereby retaining multiple dendrites that are smaller than PCs in vivo even after long cultivation (Fig. 2D) (Fujishima et al., 2012). Thus, the extrinsic signals that are strictly regulated in time, space and quantity in the cerebellum, could potentially instruct the formation of a single stem dendrite via Cdc42-N-WASP-Arp2/3 signaling in PCs between P4 and P10. ...
During neural development, the actin filament network must be precisely regulated to form elaborate neurite structures. N-WASP tightly controls actin polymerization dynamics by activating an actin nucleator Arp2/3. However, the importance of N-WASP-Arp2/3 signaling in the assembly of neurite architecture in vivo has not been clarified. Here, we demonstrate that N-WASP-Arp2/3 signaling plays a crucial role in the maturation of cerebellar Purkinje cell (PC) dendrites in vivo in mice. N-WASP was expressed and activated in developing PCs. Inhibition of Arp2/3 and N-WASP from the beginning of dendrite formation severely disrupted the establishment of a single stem dendrite, which is a characteristic basic structure of PC dendrites. Inhibition of Arp2/3 after stem dendrite formation resulted in hypoplasia of the PC dendritic tree. Cdc42, an upstream activator of N-WASP, is required for N-WASP-Arp2/3 signaling-mediated PC dendrite maturation. In addition, overactivation of N-WASP is also detrimental to dendrite formation in PCs. These findings reveal that proper activation of N-WASP-Arp2/3 signaling is crucial for multiple steps of PC dendrite maturation in vivo.
... Throughout multiple lobules of the cerebellum, it was possible to observe the somata of Purkinje cells located in a thin layer (Purkinje cell layer). One or two primary dendrites extending from each soma, arborizing into a distinctive highly branched, planar, fan-shaped structure, were also visualized, as described in the literature [46][47][48][49]. Additionally, for multiple Purkinje cells, a single long axon was visualized by EGFP fluorescence leaving the respective cell body towards the granule cell layer (Fig. 5D and Supplementary Movie 4), a feature that could not be observed by standard IHC. ...
... Following an intravenous administration of rAAV9 in neonatal mice, in this study we observed an extensive EGFP expression within cerebellar Purkinje cells, which is in agreement with previous reports [11,62]. This observation suggests that these vectors could be valuable tools not only for the elucidation of Purkinje cell development in vitro and in vivo [47,48,63], but also for research and preclinical studies of several diseases, including multiple forms of ataxia, Huntington's disease, schizophrenia and autism spectrum disorders, where Purkinje cells are profoundly affected [64,65]. Moreover, the clearing methodology could help to further characterize and monitor disease progression by circumventing standard IHC limitations. ...
Recombinant adeno-associated virus (rAAV) has become one of the most promising gene delivery systems for both in vitro and in vivo applications. However, a key challenge is the lack of suitable imaging technologies to evaluate delivery, biodistribution and tropism of rAAVs and efficiently monitor disease amelioration promoted by AAV-based therapies at a whole-organ level with single-cell resolution. Therefore, we aimed to establish a new pipeline for the biodistribution analysis of natural and new variants of AAVs at a whole-brain level by tissue clearing and light-sheet fluorescence microscopy (LSFM). To test this platform, neonatal C57BL/6 mice were intravenously injected with rAAV9 encoding EGFP and, after sacrifice, brains were processed by standard immunohistochemistry and a recently released aqueous-based clearing procedure. This clearing technique required no dedicated equipment and rendered highly cleared brains, while simultaneously preserving endogenous fluorescence. Moreover, three-dimensional imaging by LSFM allowed the quantitative analysis of EGFP at a whole-brain level, as well as the reconstruction of Purkinje cells for the retrieval of valuable morphological information inaccessible by standard immunohistochemistry. In conclusion, the pipeline herein described takes the AAVs to a new level when coupled to LSFM, proving its worth as a bioimaging tool in tropism and gene therapy studies.
... The growth environment plays a central role in the determination of neuronal dendritic morphology. Previous studies have shown that when neurons are isolated from the in vivo environment and induced to regenerate in culture dishes, certain specific dendritic morphology of neurons can be preserved, such as Purkinje cells from the cerebellum [40]. But this only happens in neurons with extremely specialized dendritic morphology. ...
The back-propagating action potential (bpAP) is crucial for neuronal signal integration and synaptic plasticity in dendritic trees. Its properties (velocity and amplitude) can be affected by dendritic morphology. Due to limited spatial resolution, it has been difficult to explore the specific propagation process of bpAPs along dendrites and examine the influence of dendritic morphology, such as the dendrite diameter and branching pattern, using patch-clamp recording. By taking advantage of Optopatch, an all-optical electrophysiological method, we made detailed recordings of the real-time propagation of bpAPs in dendritic trees. We found that the velocity of bpAPs was not uniform in a single dendrite, and the bpAP velocity differed among distinct dendrites of the same neuron. The velocity of a bpAP was positively correlated with the diameter of the dendrite on which it propagated. In addition, when bpAPs passed through a dendritic branch point, their velocity decreased significantly. Similar to velocity, the amplitude of bpAPs was also positively correlated with dendritic diameter, and the attenuation patterns of bpAPs differed among different dendrites. Simulation results from neuron models with different dendritic morphology corresponded well with the experimental results. These findings indicate that the dendritic diameter and branching pattern significantly influence the properties of bpAPs. The diversity among the bpAPs recorded in different neurons was mainly due to differences in dendritic morphology. These results may inspire the construction of neuronal models to predict the propagation of bpAPs in dendrites with enormous variation in morphology, to further illuminate the role of bpAPs in neuronal communication.
... The presence of ATOH1-, TBR1-, Calbindin-, and PCP4-positive cell populations in the established brain organoids with 40-50 days was evaluated through immunohistochemistry. Data indicated that ATOH1, TBR1, PCP4, and Calbindin are present both in CNT and MJD organoids, indicating the presence of cells positive for cerebellar neuronal progenitors (Fig. 3e-j), deep cerebellar neurons (Fig. 3k-p), and Purkinje cells (Fig. 3q-v) markers; even though the latter, mainly calbindinpositive cells, are less abundant. Purkinje cells are the largest neurons in the human cerebellum and exhibit a characteristic morphology, namely, Purkinje cells extend one primary dendrite from the soma, which arborizes into a highly branched structure 39 . To evaluate the presence of Purkinje cell dendritic arbors, organoids with 120 days were evaluated for Calbindin- (Fig. 3w-z) and PCP4-positive dendritic arborization (Fig. 3aa-ad). ...
The establishment of robust human brain organoids to model cerebellar diseases is essential to study new therapeutic strategies for cerebellum-associated disorders. Machado-Joseph disease (MJD) is a cerebellar hereditary neurodegenerative disease, without therapeutic options able to prevent the disease progression. In the present work, control and MJD induced-pluripotent stem cells were used to establish human brain organoids. These organoids were characterized regarding brain development, cell type composition, and MJD-associated neuropathology markers, to evaluate their value for cerebellar diseases modeling. Our data indicate that the organoids recapitulated, to some extent, aspects of brain development, such as astroglia emerging after neurons and the presence of ventricular-like zones surrounded by glia and neurons that are found only in primate brains. Moreover, the brain organoids presented markers of neural progenitors proliferation, neuronal differentiation, inhibitory and excitatory synapses, and firing neurons. The established brain organoids also exhibited markers of cerebellar neurons progenitors and mature cerebellar neurons. Finally, MJD brain organoids showed higher ventricular-like zone numbers, an indication of lower maturation, and an increased number of ataxin-3-positive aggregates, compared with control organoids. Altogether, our data indicate that the established organoids recapitulate important characteristics of human brain development and exhibit cerebellar features, constituting a resourceful tool for testing therapeutic approaches for cerebellar diseases.
... In particular, the failure of these processes has been associated with developmental abnormalities and cognitive impairment as observed, for example, in Down syndrome (Haydar and Reeves 2012;Mrak and Griffin 2004). Many generative models have been proposed to characterize and mimic the morphological diversity of neuritic trees (Ascoli 2002), using formalism such as Lindenmeyer grammars (Hamilton 1993;Ascoli 2002;Donohue et al. 2002) and other stochastic branching systems (Torben-Nielsen and De Schutter 2014;Carriquiry et al. 1991;Nowakowski et al. 1992;Uemura et al. 1995;Dityatev et al. 1995;Van Pelt et al. 1997;Van Pelt and Uylings 2005;Villacorta et al. 2007;Fujishima et al. 2012); or cellular automata (Luczak 2006;Albinet and Pelce 1996). A parsimonious example is the BESTL model which describes branching probability as a function of node depth (its centrifugal order) and the current number of terminal nodes in the tree (Van Pelt and Uylings 2005;Van Ooyen 2003). ...
The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites—axons and dendrites—to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.
... To analyze the influence of both the local self-organizing (intrinsic) cues and the global (extrinsic) guidance on the formation of branched structures, we first turned to a modelling approach inspired by the physics of branching random walks, which represents tips as particles undergoing both stochastic and deterministic elongation movements (which generates branches at a constant speed), as well as stochastic branching events into two tips with probability p b . This type of model 20,22,[33][34][35] has the advantage of coarsening many microscopic features of branching regulation (for instance that have been addressed via reaction-diffusion models 36,37 ) into simple sets of rules. In this work, we include both the possibility for global guidance via gradients quantified by a guidance strength f c (which acts as an external force on tip motion) as well as local self-avoidance of neighboring branch segments. ...
... A strength of our "mesoscopic" approach is that it extracts a small number of such coarse-grained parameters, to identify which ones are key at the scale of the overall branching pattern, and thus guiding subsequent, more detailed modelling. Our proposed framework builds upon previous simulations of stochastic branching morphogenesis, which had considered local cues such as branching and repulsion 20,22,33,35 . We find that adding global extrinsic guidance-a key element in different contexts to break the isotropy in tissue growth-in the model gives rise to significantly different dynamics, enriching the phase diagram of possible branching patterns. ...
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.
