A Universal Property of Axonal and Dendritic Arbors

Neuroscience: The dynamic development of dendrites

Protocadherins are cell-surface proteins that endow developing neurons with the ability to distinguish self-contacts from non-self. This recognition is critical for dendrite patterning and neuronal function. New research demonstrates the cellular basis for dendrite self-avoidance following protocadherin-mediated self-recognition.

Single-neuron analysis of axon arbors reveals distinct presynaptic organizations between feedforward and feedback projections

The morphology and spatial distribution of axon arbors and boutons are crucial for neuron presynaptic functions. However, the principles governing their whole-brain organization at the single-neuron level remain unclear. We developed a machine-learning method to separate axon arbors from passing axons in single-neuron reconstruction from fluorescence micro-optical sectioning tomography imaging data and obtained 62,374 axon arbors that displayed distinct morphology, spatial patterns, and scaling laws dependent on neuron types and targeted brain areas. Focusing on the axon arbors in the thalamus and cortex, we revealed the segregated spatial distributions and distinct morphology but shared topographic gradients between feedforward and feedback projections. Furthermore, we uncovered an association between arbor complexity and microglia density. Finally, we found that the boutons on terminal arbors show branch-specific clustering with a log-normal distribution that again differed between feedforward and feedback terminal arbors. Together, our study revealed distinct presynaptic structural organizations underlying diverse functional innervation of single projection neurons.

Topology recapitulates morphogenesis of neuronal dendrites

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.

Cell morphologies in the nervous system: Glia steal the limelight

Neurons and glia have distinct yet interactive functions but are both characterized by branching morphology. Dendritic trees have been digitally traced for over 40 years in many animal species, anatomical regions, and neuron types. Recently, long-range axons also are being reconstructed throughout the brain of many organisms from invertebrates to primates. In contrast, less attention has been paid until lately to glial morphology. Thus, although glia and neurons are similarly abundant in the nervous systems of humans and most animal models, glia have traditionally been much less represented than neurons in morphological reconstruction repositories such as NeuroMorpho.Org. This is rapidly changing with the advent of high-throughput glia tracing. NeuroMorpho.Org introduced glial cells in 2017 and today they constitute nearly a third of the database content. It took NeuroMorpho.Org 10 years to collect the first 40,000 neurons and now that amount of data can be produced in a single publication. This not only demonstrates the spectacular technological progress in data production, but also demands a corresponding advancement in informatics processing. At the same time, these publicly available data also open new opportunities for quantitative analysis and computational modeling to identify universal or cell-type-specific design principles in the cellular architecture of nervous systems. As a first application, we demonstrated that supervised machine learning of tree geometry classifies neurons and glia with practically perfect accuracy. Furthermore, we discovered a new morphometric biomarker capable of robustly separating these cell classes across multiple species, brain regions, and experimental preparations, with only sparse sampling of branch measurements.

Mapping of morpho-electric features to molecular identity of cortical inhibitory neurons

Knowledge of the cell-type-specific composition of the brain is useful in order to understand the role of each cell type as part of the network. Here, we estimated the composition of the whole cortex in terms of well characterized morphological and electrophysiological inhibitory neuron types (me-types). We derived probabilistic me-type densities from an existing atlas of molecularly defined cell-type densities in the mouse cortex. We used a well-established me-type classification from rat somatosensory cortex to populate the cortex. These me-types were well characterized morphologically and electrophysiologically but they lacked molecular marker identity labels. To extrapolate this missing information, we employed an additional dataset from the Allen Institute for Brain Science containing molecular identity as well as morphological and electrophysiological data for mouse cortical neurons. We first built a latent space based on a number of comparable morphological and electrical features common to both data sources. We then identified 19 morpho-electrical clusters that merged neurons from both datasets while being molecularly homogeneous. The resulting clusters best mirror the molecular identity classification solely using available morpho-electrical features. Finally, we stochastically assigned a molecular identity to a me-type neuron based on the latent space cluster it was assigned to. The resulting mapping was used to derive inhibitory me-types densities in the cortex.

A general principle of dendritic constancy: A neuron's size- and shape-invariant excitability

Reducing neuronal size results in less membrane and therefore lower input conductance. Smaller neurons are thus more excitable, as seen in their responses to somatic current injections. However, the impact of a neuron's size and shape on its voltage responses to dendritic synaptic activation is much less understood. Here we use analytical cable theory to predict voltage responses to distributed synaptic inputs in unbranched cables, showing that these are entirely independent of dendritic length. For a given synaptic density, neuronal responses depend only on the average dendritic diameter and intrinsic conductivity. This remains valid for a wide range of morphologies irrespective of their arborization complexity. Spiking models indicate that morphology-invariant numbers of spikes approximate the percentage of active synapses. In contrast to spike rate, spike times do depend on dendrite morphology. In summary, neuronal excitability in response to distributed synaptic inputs is largely unaffected by dendrite length or complexity.

Dissecting Sholl Analysis into Its Functional Components

Sholl analysis has been an important technique in dendritic anatomy for more than 60 years. The Sholl intersection profile is obtained by counting the number of dendritic branches at a given distance from the soma and is a key measure of dendritic complexity; it has applications from evaluating the changes in structure induced by pathologies to estimating the expected number of anatomical synaptic contacts. We find that the Sholl intersection profiles of most neurons can be reproduced from three basic, functional measures: the domain spanned by the dendritic arbor, the total length of the dendrite, and the angular distribution of how far dendritic segments deviate from a direct path to the soma (i.e., the root angle distribution). The first two measures are determined by axon location and hence microcircuit structure; the third arises from optimal wiring and represents a branching statistic estimating the need for conduction speed in a neuron.

Combining local and global evolutionary trajectories of brain-behaviour relationships through game theory

The study of the evolution of brain-behaviour relationships concerns understanding the causes and repercussions of cross- and within-species variability. Understanding such variability is a main objective of evolutionary and cognitive neuroscience, and it may help explaining the appearance of psychopathological phenotypes. Although brain evolution is related to the progressive action of selection and adaptation through multiple paths (e.g. mosaic vs. concerted evolution, metabolic vs. structural and functional constraints), a coherent, integrative framework is needed to combine evolutionary paths and neuroscientific evidence. Here, we review the literature on evolutionary pressures focusing on structural-functional changes and developmental constraints. Taking advantage of recent progress in neuroimaging and cognitive neuroscience, we propose a twofold hypothetical model of brain evolution. Within this model, global and local trajectories imply rearrangements of neural subunits and subsystems and of behavioural repertoires of a species, respectively. We incorporate these two processes in a game in which the global trajectory shapes the structural-functional neural substrates (i.e. players), while the local trajectory shapes the behavioural repertoires (i.e. stochastic payoffs).

A Statistical Growth Property of Plant Root Architectures

Numerous types of biological branching networks, with varying shapes and sizes, are used to acquire and distribute resources. Here, we show that plant root and shoot architectures share a fundamental design property. We studied the spatial density function of plant architectures, which specifies the probability of finding a branch at each location in the 3-dimensional volume occupied by the plant. We analyzed 1645 root architectures from four species and discovered that the spatial density functions of all architectures are population-similar. This means that despite their apparent visual diversity, all of the roots studied share the same basic shape, aside from stretching and compression along orthogonal directions. Moreover, the spatial density of all architectures can be described as variations on a single underlying function: a Gaussian density truncated at a boundary of roughly three standard deviations. Thus, the root density of any architecture requires only four parameters to specify: the total mass of the architecture and the standard deviations of the Gaussian in the three (x, y, z) growth directions. Plant shoot architectures also follow this design form, suggesting that two basic plant transport systems may use similar growth strategies.

A Topological Representation of Branching Neuronal Morphologies

Many biological systems consist of branching structures that exhibit a wide variety of shapes. Our understanding of their systematic roles is hampered from the start by the lack of a fundamental means of standardizing the description of complex branching patterns, such as those of neuronal trees. To solve this problem, we have invented the Topological Morphology Descriptor (TMD), a method for encoding the spatial structure of any tree as a "barcode", a unique topological signature. As opposed to traditional morphometrics, the TMD couples the topology of the branches with their spatial extents by tracking their topological evolution in 3-dimensional space. We prove that neuronal trees, as well as stochastically generated trees, can be accurately categorized based on their TMD profiles. The TMD retains sufficient global and local information to create an unbiased benchmark test for their categorization and is able to quantify and characterize the structural differences between distinct morphological groups. The use of this mathematically rigorous method will advance our understanding of the anatomy and diversity of branching morphologies.

Minimizing activation of overlying axons with epiretinal stimulation: The role of fiber orientation and electrode configuration

Currently, a challenge in electrical stimulation of the retina with a visual prosthesis (bionic eye) is to excite only the cells lying directly under the electrode in the ganglion cell layer, while avoiding excitation of axon bundles that pass over the surface of the retina in the nerve fiber layer. Stimulation of overlying axons results in irregular visual percepts, limiting perceptual efficacy. This research explores how differences in fiber orientation between the nerve fiber layer and ganglion cell layer leads to differences in the electrical activation of the axon initial segment and axons of passage. Approach. Axons of passage of retinal ganglion cells in the nerve fiber layer are characterized by a narrow distribution of fiber orientations, causing highly anisotropic spread of applied current. In contrast, proximal axons in the ganglion cell layer have a wider distribution of orientations. A four-layer computational model of epiretinal extracellular stimulation that captures the effect of neurite orientation in anisotropic tissue has been developed using a volume conductor model known as the cellular composite model. Simulations are conducted to investigate the interaction of neural tissue orientation, stimulating electrode configuration, and stimulation pulse duration and amplitude. Main results. Our model shows that simultaneous stimulation with multiple electrodes aligned with the nerve fiber layer can be used to achieve selective activation of axon initial segments rather than passing fibers. This result can be achieved while reducing required stimulus charge density and with only modest increases in the spread of activation in the ganglion cell layer, and is shown to extend to the general case of arbitrary electrode array positioning and arbitrary target volume. Significance. These results elucidate a strategy for more targeted stimulation of retinal ganglion cells with experimentally-relevant multi-electrode geometries and achievable stimulation requirements.

A Statistical Description of Plant Shoot Architecture

Plant architectures can be characterized statistically by their spatial density function, which specifies the probability of finding a branch at each location in the territory occupied by a plant. Using high-precision 3D scanning, we analyzed 557 plant shoot architectures, representing three species, grown across three to five environmental conditions, and through 20-30 developmental time points. We found two elegant properties in the spatial density functions of these architectures: all functions could be nearly modified in one direction without affecting the density in orthogonal directions (called "separability"), and all functions shared the same underlying shape, aside from stretching and compression (called "self-similarity"). Surprisingly, despite their striking visual diversity, we discovered that all architectures could be described as variations on a single underlying function: a Gaussian density function truncated at roughly two SDs. We also observed systematic variation in the spatial density functions across species, growth conditions, and time, which suggests functional specialization despite following the same general design form.

Cortical Composition Hierarchy Driven by Spine Proportion Economical Maximization or Wire Volume Minimization

The structure and quantitative composition of the cerebral cortex are interrelated with its computational capacity. Empirical data analyzed here indicate a certain hierarchy in local cortical composition. Specifically, neural wire, i.e., axons and dendrites take each about 1/3 of cortical space, spines and glia/astrocytes occupy each about (1/3)², and capillaries around (1/3)⁴. Moreover, data analysis across species reveals that these fractions are roughly brain size independent, which suggests that they could be in some sense optimal and thus important for brain function. Is there any principle that sets them in this invariant way? This study first builds a model of local circuit in which neural wire, spines, astrocytes, and capillaries are mutually coupled elements and are treated within a single mathematical framework. Next, various forms of wire minimization rule (wire length, surface area, volume, or conduction delays) are analyzed, of which, only minimization of wire volume provides realistic results that are very close to the empirical cortical fractions. As an alternative, a new principle called “spine economy maximization” is proposed and investigated, which is associated with maximization of spine proportion in the cortex per spine size that yields equally good but more robust results. Additionally, a combination of wire cost and spine economy notions is considered as a meta-principle, and it is found that this proposition gives only marginally better results than either pure wire volume minimization or pure spine economy maximization, but only if spine economy component dominates. However, such a combined meta-principle yields much better results than the constraints related solely to minimization of wire length, wire surface area, and conduction delays. Interestingly, the type of spine size distribution also plays a role, and better agreement with the data is achieved for distributions with long tails. In sum, these results suggest that for the efficiency of local circuits wire volume may be more primary variable than wire length or temporal delays, and moreover, the new spine economy principle may be important for brain evolutionary design in a broader context.

Cerebral cortex is an outer layer of the brain in mammals, and it plays a critical part in various cognitive processes such as learning, memory, attention, language, and consciousness. The cerebral cortex contains a number of neuroanatomical parameters whose values are essentially conserved across species and brain sizes, which suggests that these particular parameters are somehow important for brain efficient functioning. This study shows that the fractional volumes of five major cortical components both neuronal and non-neuronal (axons, dendrites, spines, glia/astrocytes, capillaries) are also approximately conserved across mammals, and neural wire (axons and dendrites) occupies the most of cortical space. Moreover, the fractional volumes form a special hierarchy of dependencies, being approximately equal to integer powers of 1/3. Is there any evolutionary principle of cortical organization that would explain these properties? This study finds that there are two different theoretical principles that can provide answers: one standard related to minimization of neural wire fractional volume, and a new proposition associated with economical maximization of spine content. However, the latter principle produces more robust results, which suggests that spine economical maximization is potentially an alternative to the more common “wire minimization” in explaining the cortical layout. Therefore, the current study can become an important contribution to our understanding (or debating) of the main factors influencing the evolution of local cortical circuits in the brain.

Development of dendritic form and function

The nervous system is populated by numerous types of neurons, each bearing a dendritic arbor with a characteristic morphology. These type-specific features influence many aspects of a neuron's function, including the number and identity of presynaptic inputs and how inputs are integrated to determine firing properties. Here, we review the mechanisms that regulate the construction of cell type-specific dendrite patterns during development. We focus on four aspects of dendrite patterning that are particularly important in determining the function of the mature neuron: (a) dendrite shape, including branching pattern and geometry of the arbor; (b) dendritic arbor size;

The effects of neuron morphology on graph theoretic measures of network connectivity: the analysis of a two-level statistical model

We developed a two-level statistical model that addresses the question of how properties of neurite morphology shape the large-scale network connectivity. We adopted a low-dimensional statistical description of neurites. From the neurite model description we derived the expected number of synapses, node degree, and the effective radius, the maximal distance between two neurons expected to form at least one synapse. We related these quantities to the network connectivity described using standard measures from graph theory, such as motif counts, clustering coefficient, minimal path length, and small-world coefficient. These measures are used in a neuroscience context to study phenomena from synaptic connectivity in the small neuronal networks to large scale functional connectivity in the cortex. For these measures we provide analytical solutions that clearly relate different model properties. Neurites that sparsely cover space lead to a small effective radius. If the effective radius is small compared to the overall neuron size the obtained networks share similarities with the uniform random networks as each neuron connects to a small number of distant neurons. Large neurites with densely packed branches lead to a large effective radius. If this effective radius is large compared to the neuron size, the obtained networks have many local connections. In between these extremes, the networks maximize the variability of connection repertoires. The presented approach connects the properties of neuron morphology with large scale network properties without requiring heavy simulations with many model parameters. The two-steps procedure provides an easier interpretation of the role of each modeled parameter. The model is flexible and each of its components can be further expanded. We identified a range of model parameters that maximizes variability in network connectivity, the property that might affect network capacity to exhibit different dynamical regimes.

Statistical analysis and data mining of digital reconstructions of dendritic morphologies

Neuronal morphology is diverse among animal species, developmental stages, brain regions, and cell types. The geometry of individual neurons also varies substantially even within the same cell class. Moreover, specific histological, imaging, and reconstruction methodologies can differentially affect morphometric measures. The quantitative characterization of neuronal arbors is necessary for in-depth understanding of the structure-function relationship in nervous systems. The large collection of community-contributed digitally reconstructed neurons available at NeuroMorpho.Org constitutes a “big data” research opportunity for neuroscience discovery beyond the approaches typically pursued in single laboratories. To illustrate these potential and related challenges, we present a database-wide statistical analysis of dendritic arbors enabling the quantification of major morphological similarities and differences across broadly adopted metadata categories. Furthermore, we adopt a complementary unsupervised approach based on clustering and dimensionality reduction to identify the main morphological parameters leading to the most statistically informative structural classification. We find that specific combinations of measures related to branching density, overall size, tortuosity, bifurcation angles, arbor flatness, and topological asymmetry can capture anatomically and functionally relevant features of dendritic trees. The reported results only represent a small fraction of the relationships available for data exploration and hypothesis testing enabled by sharing of digital morphological reconstructions.

Myosin Va but Not nNOSα is Significantly Reduced in Jejunal Musculomotor Nerve Terminals in Diabetes Mellitus

Nitric oxide (NO) mediated slow inhibitory junction potential and mechanical relaxation after electrical field stimulation (EFS) is impaired in diabetes mellitus. Externally added NO donor restore nitrergic function, indicating that this reduction result from diminution of NO synthesis within the pre-junctional nerve terminals. The present study aimed to investigate two specific aims that may potentially provide pathophysiological insights into diabetic nitrergic neuropathy. Specifically, alteration in nNOSα contents within jejunal nerve terminals and a local subcortical transporter myosin Va was tested 16 weeks after induction of diabetes by low dose streptozotocin (STZ) in male Wistar rats. The results show that diabetic rats, in contrast to vehicle treated animals, have: (a) nearly absent myosin Va expression in nerve terminals of axons innervating smooth muscles and (b) significant decrease of myosin Va in neuronal soma of myenteric plexus. In contrast, nNOSα staining in diabetic jejunum neuromuscular strips showed near intact expression in neuronal cell bodies. The space occupancy of nitrergic nerve fibers was comparable between groups. Normal concentration of nNOSα was visualized within a majority of nitrergic terminals in diabetes, suggesting intact axonal transport of nNOSα to distant nerve terminals. These results reveal the dissociation between presences of nNOSα in the nerve terminals but deficiency of its transporter myosin Va in the jejunum of diabetic rats. This significant observation of reduced motor protein myosin Va within jejunal nerve terminals may potentially explain impairment of pre-junctional NO synthesis during EFS of diabetic gut neuromuscular strips despite presence of the nitrergic synthetic enzyme nNOSα.

A general principle governs vision-dependent dendritic patterning of retinal ganglion cells

Dendritic arbors of retinal ganglion cells (RGCs) collect information over a certain area of the visual scene. The coverage territory and the arbor density of dendrites determine what fraction of the visual field is sampled by a single cell and at what resolution. However, it is not clear whether visual stimulation is required for the establishment of branching patterns of RGCs, and whether a general principle directs the dendritic patterning of diverse RGCs. By analyzing the geometric structures of RGC dendrites, we found that dendritic arbors of RGCs underwent a substantial spatial rearrangement after eye-opening. Light deprivation blocked both the dendritic growth and the branch patterning, suggesting that visual stimulation is required for the acquisition of specific branching patterns of RGCs. We further showed that vision-dependent dendritic growth and arbor refinement occurred mainly in the middle portion of the dendritic tree. This nonproportional growth and selective refinement suggest that the late-stage dendritic development of RGCs is not a passive stretching with the growth of eyes, but rather an active process of selective growth/elimination of dendritic arbors of RGCs driven by visual activity. Finally, our data showed that there was a power law relationship between the coverage territory and dendritic arbor density of RGCs on a cell-by-cell basis. RGCs were systematically less dense when they cover larger territories regardless of their cell type, retinal location, or developmental stage. These results suggest that a general structural design principle directs the vision-dependent patterning of RGC dendrites.

Scaling and coordination deficits during dynamic object manipulation in Parkinson's disease

The ability to reach for and dynamically manipulate objects in a dexterous fashion requires scaling and coordination of arm, hand, and fingertip forces during reach and grasp components of this behavior. The neural substrates underlying dynamic object manipulation are not well understood. Insight into the role of basal ganglia-thalamocortical circuits in object manipulation can come from the study of patients with Parkinson's disease (PD). We hypothesized that scaling and coordination aspects of motor control are differentially affected by this disorder. We asked 20 PD patients and 23 age-matched control subjects to reach for, grasp, and lift virtual objects along prescribed paths. The movements were subdivided into two types, intensive (scaling) and coordinative, by detecting their underlying self-similarity. PD patients off medication were significantly impaired relative to control subjects for both aspects of movement. Intensive deficits, reduced peak speed and aperture, were seen during the reach. Coordinative deficits were observed during the reach, namely, the relative position along the trajectory at which peak speed and aperture were achieved, and during the lift, when objects tilted with respect to the gravitational axis. These results suggest that basal ganglia-thalamocortical circuits may play an important role in fine motor coordination. Dopaminergic therapy significantly improved intensive but not coordinative aspects of movements. These findings are consistent with a framework in which tonic levels of dopamine in the dorsal striatum encode the energetic cost of a movement, thereby improving intensive or scaling aspects of movement. However, repletion of brain dopamine levels does not restore finely coordinated movement.

Extensive use of RNA-binding proteins in Drosophila sensory neuron dendrite morphogenesis

The large number of RNA-binding proteins and translation factors encoded in the Drosophila and other metazoan genomes predicts widespread use of post-transcriptional regulation in cellular and developmental processes. Previous studies identified roles for several RNA-binding proteins in dendrite branching morphogenesis of Drosophila larval sensory neurons. To determine the larger contribution of post-transcriptional gene regulation to neuronal morphogenesis, we conducted an RNA interference screen to identify additional Drosophila proteins annotated as either RNA-binding proteins or translation factors that function in producing the complex dendritic trees of larval class IV dendritic arborization neurons. We identified 88 genes encoding such proteins whose knockdown resulted in aberrant dendritic morphology, including alterations in dendritic branch number, branch length, field size, and patterning of the dendritic tree. In particular, splicing and translation initiation factors were associated with distinct and characteristic phenotypes, suggesting that different morphogenetic events are best controlled at specific steps in post-transcriptional messenger RNA metabolism. Many of the factors identified in the screen have been implicated in controlling the subcellular distributions and translation of maternal messenger RNAs; thus, common post-transcriptional regulatory strategies may be used in neurogenesis and in the generation of asymmetry in the female germline and embryo.

The molecular basis for the development of neural maps

Neural development leads to the establishment of precise connectivity in the nervous system. By contrasting the information capacities of cortical connectivity and the genome, we suggest that simplifying rules are necessary in order to create cortical connections from the limited set of instructions contained in the genome. One of these rules may be employed by the visual system, where connections are formed on the basis of the interplay of molecular gradients and activity-dependent synaptic plasticity. We show how a simple model that accounts for such interplay can create both neural topographic maps and more complex patterns of ocular dominance, that is, the segregated binary mixture of projections from two eyes converging in the same visual area. With regard to the ocular dominance patterns, we show that pattern orientation may be instructed by the direction of the gradients of molecular labels. We also show that the periodicity of ocular dominance patterns may result from the interplay of the effects of molecular gradients and correlated neural activity. Overall, we propose that simple mechanisms can account for the formation of apparently complex features of neuronal connections.

Constancy and trade-offs in the neuroanatomical and metabolic design of the cerebral cortex

Mammalian brains span about four orders of magnitude in cortical volume and have to operate in different environments that require diverse behavioral skills. Despite these geometric and behavioral diversities, the examination of cerebral cortex across species reveals that it contains a substantial number of conserved characteristics that are associated with neuroanatomy and metabolism, i.e., with neuronal connectivity and function. Some of these cortical constants or invariants have been known for a long time but not sufficiently appreciated, and others were only recently discovered. The focus of this review is to present the cortical invariants and discuss their role in the efficient information processing. Global conservation in neuroanatomy and metabolism, as well as their correlated regional and developmental variability suggest that these two parallel systems are mutually coupled. It is argued that energetic constraint on cortical organization can be strong if cerebral blood supplied is either below or above a certain level, and it is rather soft otherwise. Moreover, because maximization or minimization of parameters associated with cortical connectivity, function and cost often leads to conflicts in design, it is argued that the architecture of the cerebral cortex is a result of structural and functional compromises.

Single-neuron criticality optimizes analog dendritic computation

Active dendritic branchlets enable the propagation of dendritic spikes, whose computational functions remain an open question. Here we propose a concrete function to the active channels in large dendritic trees. Modelling the input-output response of large active dendritic arbors subjected to complex spatio-temporal inputs and exhibiting non-stereotyped dendritic spikes, we find that the dendritic arbor can undergo a continuous phase transition from a quiescent to an active state, thereby exhibiting spontaneous and self-sustained localized activity as suggested by experiments. Analogously to the critical brain hypothesis, which states that neuronal networks self-organize near criticality to take advantage of its specific properties, here we propose that neurons with large dendritic arbors optimize their capacity to distinguish incoming stimuli at the critical state. We suggest that "computation at the edge of a phase transition" is more compatible with the view that dendritic arbors perform an analog rather than a digital dendritic computation.

Neuronal morphology goes digital: a research hub for cellular and system neuroscience

The importance of neuronal morphology in brain function has been recognized for over a century. The broad applicability of "digital reconstructions" of neuron morphology across neuroscience subdisciplines has stimulated the rapid development of numerous synergistic tools for data acquisition, anatomical analysis, three-dimensional rendering, electrophysiological simulation, growth models, and data sharing. Here we discuss the processes of histological labeling, microscopic imaging, and semiautomated tracing. Moreover, we provide an annotated compilation of currently available resources in this rich research "ecosystem" as a central reference for experimental and computational neuroscience.

Communication and wiring in the cortical connectome

In cerebral cortex, the huge mass of axonal wiring that carries information between near and distant neurons is thought to provide the neural substrate for cognitive and perceptual function. The goal of mapping the connectivity of cortical axons at different spatial scales, the cortical connectome, is to trace the paths of information flow in cerebral cortex. To appreciate the relationship between the connectome and cortical function, we need to discover the nature and purpose of the wiring principles underlying cortical connectivity. A popular explanation has been that axonal length is strictly minimized both within and between cortical regions. In contrast, we have hypothesized the existence of a multi-scale principle of cortical wiring where to optimize communication there is a trade-off between spatial (construction) and temporal (routing) costs. Here, using recent evidence concerning cortical spatial networks we critically evaluate this hypothesis at neuron, local circuit, and pathway scales. We report three main conclusions. First, the axonal and dendritic arbor morphology of single neocortical neurons may be governed by a similar wiring principle, one that balances the conservation of cellular material and conduction delay. Second, the same principle may be observed for fiber tracts connecting cortical regions. Third, the absence of sufficient local circuit data currently prohibits any meaningful assessment of the hypothesis at this scale of cortical organization. To avoid neglecting neuron and microcircuit levels of cortical organization, the connectome framework should incorporate more morphological description. In addition, structural analyses of temporal cost for cortical circuits should take account of both axonal conduction and neuronal integration delays, which appear mostly of the same order of magnitude. We conclude the hypothesized trade-off between spatial and temporal costs may potentially offer a powerful explanation for cortical wiring patterns.

Orientation specificity of contrast adaptation in mouse primary visual cortex

Contrast adaptation is a commonly studied phenomenon in vision, where prolonged exposure to spatial contrast alters perceived stimulus contrast and produces characteristic shifts in the contrast response functions of primary visual cortex neurons in cats and primates. In this study we investigated contrast adaptation in mouse primary visual cortex with two goals in mind. First, we sought to establish a quantitative description of contrast adaptation in an animal model, where genetic tools are more readily applicable to this phenomenon. Second, the orientation specificity of contrast adaptation was studied to comparatively assess the possible role of local cortical networks in contrast adaptation. In cats and primates, predictable differences in visual processing across the cortical surface are thought to be caused by inhomogeneous local network membership that arises from the pinwheel organization of orientation columns. Because mice lack this pinwheel organization, we predicted that local cortical networks would have access to a broad spectrum of orientation signals, and contrast adaptation in mice would not be specific to the recorded cell's preferred orientation. We found that most mouse V1 neurons showed contrast adaptation that was robust regardless of whether the adapting stimulus matched the cell's preferred orientation or was orthogonal to it.

The dendritic density field of a cortical pyramidal cell

Much is known about the computation in individual neurons in the cortical column. Also, the selective connectivity between many cortical neuron types has been studied in great detail. However, due to the complexity of this microcircuitry its functional role within the cortical column remains a mystery. Some of the wiring behavior between neurons can be interpreted directly from their particular dendritic and axonal shapes. Here, I describe the dendritic density field (DDF) as one key element that remains to be better understood. I sketch an approach to relate DDFs in general to their underlying potential connectivity schemes. As an example, I show how the characteristic shape of a cortical pyramidal cell appears as a direct consequence of connecting inputs arranged in two separate parallel layers.

Wnt/PCP proteins regulate stereotyped axon branch extension in Drosophila

Branching morphology is a hallmark feature of axons and dendrites and is essential for neuronal connectivity. To understand how this develops, I analyzed the stereotyped pattern of Drosophila mushroom body (MB) neurons, which have single axons branches that extend dorsally and medially. I found that components of the Wnt/Planar Cell Polarity (PCP) pathway control MB axon branching. frizzled mutant animals showed a predominant loss of dorsal branch extension, whereas strabismus (also known as Van Gogh) mutants preferentially lost medial branches. Further results suggest that Frizzled and Strabismus act independently. Nonetheless, branching fates are determined by complex Wnt/PCP interactions, including interactions with Dishevelled and Prickle that function in a context-dependent manner. Branching decisions are MB-autonomous but non-cell-autonomous as mutant and non-mutant neurons regulate these decisions collectively. I found that Wnt/PCP components do not need to be asymmetrically localized to distinct branches to execute branching functions. However, Prickle axonal localization depends on Frizzled and Strabismus.

The cytoskeletal and signaling mechanisms of axon collateral branching

During development, axons are guided to their appropriate targets by a variety of guidance factors. On arriving at their synaptic targets, or while en route, axons form branches. Branches generated de novo from the main axon are termed collateral branches. The generation of axon collateral branches allows individual neurons to make contacts with multiple neurons within a target and with multiple targets. In the adult nervous system, the formation of axon collateral branches is associated with injury and disease states and may contribute to normally occurring plasticity. Collateral branches are initiated by actin filament– based axonal protrusions that subsequently become invaded by microtubules, thereby allowing the branch to mature and continue extending. This article reviews the current knowledge of the cellular mechanisms of the formation of axon collateral branches. The major conclusions of this review are (1) the mechanisms of axon extension and branching are not identical; (2) active suppression of protrusive activity along the axon negatively regulates branching; (3) the earliest steps in the formation of axon branches involve focal activation of signaling pathways within axons, which in turn drive the formation of actin-based protrusions; and (4) regulation of the microtubule array by microtubule-associated and severing proteins underlies the development of branches. Linking the activation of signaling pathways to specific proteins that directly regulate the axonal cytoskeleton underlying the formation of collateral branches remains a frontier in the field.

A general principle of neural arbor branch density

The tree-like structures of a neuron that are responsible for distributing (axons) or collecting (dendrites) information over a region of the brain are called arbors. The size of the territory occupied by an arbor and the density of the arbor branches within that territory are important for computation because these factors determine what fraction of a neural map is sampled by a single cell and at what resolution [1]. Arbor territory size and branch density can vary by many orders of magnitude; however, we have identified a universal relationship between these two physical properties revealing a general neural architectural design principle. All of the arbors (axons and dendrites) we have studied (including fish retinal ganglion cells, rodent Purkinje cells, and the cortical arbors of various neural classes from rat, cat, monkey, and human) are found to be systematically less dense when they cover larger territories. This relationship can be described as a power law. Of several simple biological explanations explored, we find that this relationship is most consistent with a design principle that conserves the average number of connections between pairs of arbors of different sizes.

The DIADEM data sets: representative light microscopy images of neuronal morphology to advance automation of digital reconstructions

The comprehensive characterization of neuronal morphology requires tracing extensive axonal and dendritic arbors imaged with light microscopy into digital reconstructions. Considerable effort is ongoing to automate this greatly labor-intensive and currently rate-determining process. Experimental data in the form of manually traced digital reconstructions and corresponding image stacks play a vital role in developing increasingly more powerful reconstruction algorithms. The DIADEM challenge (short for DIgital reconstruction of Axonal and DEndritic Morphology) successfully stimulated progress in this area by utilizing six data set collections from different animal species, brain regions, neuron types, and visualization methods. The original research projects that provided these data are representative of the diverse scientific questions addressed in this field. At the same time, these data provide a benchmark for the types of demands automated software must meet to achieve the quality of manual reconstructions while minimizing human involvement. The DIADEM data underwent extensive curation, including quality control, metadata annotation, and format standardization, to focus the challenge on the most substantial technical obstacles. This data set package is now freely released ( http://diademchallenge.org ) to train, test, and aid development of automated reconstruction algorithms.

Is universal coverage good for neurons?

In this issue of Neuron, Snider et al., analyze dendritic and axonal arbors of several cell types in several species. They show that general features of arbor structure are shared by the diverse cell populations, suggesting that the growth of these arbors is guided by universal principles.