A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions

Neural connectivity at the cellular and mesoscopic level appears very specific and is presumed to arise from highly specific developmental mechanisms. However, there are general shared features of connectivity in systems as different as the networks formed by individual neurons in Caenorhabditis elegans or in rat visual cortex and the mesoscopic circuitry of cortical areas in the mouse, macaque, and human brain. In all these systems, connection length distributions have very similar shapes, with an initial large peak and a long flat tail representing the admixture of long-distance connections to mostly short-distance connections. Furthermore, not all potentially possible synapses are formed, and only a fraction of axons (called filling fraction) establish synapses with spatially neighboring neurons. We explored what aspects of these connectivity patterns can be explained simply by random axonal outgrowth. We found that random axonal growth away from the soma can already reproduce the known distance distribution of connections. We also observed that experimentally observed filling fractions can be generated by competition for available space at the target neurons--a model markedly different from previous explanations. These findings may serve as a baseline model for the development of connectivity that can be further refined by more specific mechanisms.Comment: 31 pages (incl. supplementary information); Cerebral Cortex Advance Access published online on May 12, 200

Developmental time windows for axon growth influence neuronal network topology

Early brain connectivity development consists of multiple stages: birth of neurons, their migration and the subsequent growth of axons and dendrites. Each stage occurs within a certain period of time depending on types of neurons and cortical layers. Forming synapses between neurons either by growing axons starting at similar times for all neurons (much-overlapped time windows) or at different time points (less-overlapped) may affect the topological and spatial properties of neuronal networks. Here, we explore the extreme cases of axon formation especially concerning short-distance connectivity during early development, either starting at the same time for all neurons (parallel, i.e. maximally-overlapped time windows) or occurring for each neuron separately one neuron after another (serial, i.e. no overlaps in time windows). For both cases, the number of potential and established synapses remained comparable. Topological and spatial properties, however, differed: neurons that started axon growth early on in serial growth achieved higher out-degrees, higher local efficiency, and longer axon lengths while neurons demonstrated more homogeneous connectivity patterns for parallel growth. Second, connection probability decreased more rapidly with distance between neurons for parallel growth than for serial growth. Third, bidirectional connections were more numerous for parallel growth. Finally, we tested our predictions with C. elegans data. Together, this indicates that time windows for axon growth influence the topological and spatial properties of neuronal networks opening the possibility to a posteriori estimate developmental mechanisms based on network properties of a developed network.Comment: Biol Cybern. 2015 Jan 30. [Epub ahead of print

Modeling Brain Circuitry over a Wide Range of Scales

If we are ever to unravel the mysteries of brain function at its most fundamental level, we will need a precise understanding of how its component neurons connect to each other. Electron Microscopes (EM) can now provide the nanometer resolution that is needed to image synapses, and therefore connections, while Light Microscopes (LM) see at the micrometer resolution required to model the 3D structure of the dendritic network. Since both the topology and the connection strength are integral parts of the brain's wiring diagram, being able to combine these two modalities is critically important. In fact, these microscopes now routinely produce high-resolution imagery in such large quantities that the bottleneck becomes automated processing and interpretation, which is needed for such data to be exploited to its full potential. In this paper, we briefly review the Computer Vision techniques we have developed at EPFL to address this need. They include delineating dendritic arbors from LM imagery, segmenting organelles from EM, and combining the two into a consistent representation

Spatial embedding of neuronal trees modeled by diffusive growth

The relative importance of the intrinsic and extrinsic factors determining the variety of geometric shapes exhibited by dendritic trees remains unclear. This question was addressed by developing a model of the growth of dendritic trees based on diffusion-limited aggregation process. The model reproduces diverse neuronal shapes (i.e., granule cells, Purkinje cells, the basal and apical dendrites of pyramidal cells, and the axonal trees of interneurons) by changing only the size of the growth area, the time span of pruning, and the spatial concentration of 'neurotrophic particles'. Moreover, the presented model shows how competition between neurons can affect the shape of the dendritic trees. The model reveals that the creation of complex (but reproducible) dendrite-like trees does not require precise guidance or an intrinsic plan of the dendrite geometry. Instead, basic environmental factors and the simple rules of diffusive growth adequately account for the spatial embedding of different types of dendrites observed in the cortex. An example demonstrating the broad applicability of the algorithm to model diverse types of tree structures is also presented. Key words: Diffusion-limited aggregation; Neuronal morphology; Dendrites; Growth model; tree; dendritic geometry.Comment: 9 pages, 6 figure

MAPping out distribution routes for kinesin couriers

In the crowded environment of eukaryotic cells, diffusion is an inefficient distribution mechanism for cellular components. Long-distance active transport is required and is performed by molecular motors including kinesins. Furthermore, in highly polarized, compartmentalized and plastic cells such as neurons, regulatory mechanisms are required to ensure appropriate spatio-temporal delivery of neuronal components. The kinesin machinery has diversified into a large number of kinesin motor proteins as well as adaptor proteins that are associated with subsets of cargo. However, many mechanisms contribute to the correct delivery of these cargos to their target domains. One mechanism is through motor recognition of subdomain-specific microtubule (MT) tracks, sign-posted by different tubulin isoforms, tubulin post-translational modifications (PTMs), tubulin GTPase activity and MT associated proteins (MAPs). With neurons as a model system, a critical review of these regulatory mechanisms is presented here, with particular focus on the emerging contribution of compartmentalised MAPs. Overall, we conclude that – especially for axonal cargo – alterations to the MT track can influence transport, although in vivo, it is likely that multiple track-based effects act synergistically to ensure accurate cargo distribution

Variation in early life maternal care predicts later long range frontal cortex synapse development in mice.

Empirical and theoretical work suggests that early postnatal experience may inform later developing synaptic connectivity to adapt the brain to its environment. We hypothesized that early maternal experience may program the development of synaptic density on long range frontal cortex projections. To test this idea, we used maternal separation (MS) to generate environmental variability and examined how MS affected 1) maternal care and 2) synapse density on virally-labeled long range axons of offspring reared in MS or control conditions. We found that MS and variation in maternal care predicted bouton density on dorsal frontal cortex axons that terminated in the basolateral amygdala (BLA) and dorsomedial striatum (DMS) with more, fragmented care associated with higher density. The effects of maternal care on these distinct axonal projections of the frontal cortex were manifest at different ages. Maternal care measures were correlated with frontal cortex → BLA bouton density at mid-adolescence postnatal (P) day 35 and frontal cortex → DMS bouton density in adulthood (P85). Meanwhile, we found no evidence that MS or maternal care affected bouton density on ascending orbitofrontal cortex (OFC) or BLA axons that terminated in the dorsal frontal cortices. Our data show that variation in early experience can alter development in a circuit-specific and age-dependent manner that may be relevant to understanding the effects of early life adversity

Neocortical Axon Arbors Trade-off Material and Conduction Delay Conservation

The brain contains a complex network of axons rapidly communicating information between billions of synaptically connected neurons. The morphology of individual axons, therefore, defines the course of information flow within the brain. More than a century ago, Ramón y Cajal proposed that conservation laws to save material (wire) length and limit conduction delay regulate the design of individual axon arbors in cerebral cortex. Yet the spatial and temporal communication costs of single neocortical axons remain undefined. Here, using reconstructions of in vivo labelled excitatory spiny cell and inhibitory basket cell intracortical axons combined with a variety of graph optimization algorithms, we empirically investigated Cajal's conservation laws in cerebral cortex for whole three-dimensional (3D) axon arbors, to our knowledge the first study of its kind. We found intracortical axons were significantly longer than optimal. The temporal cost of cortical axons was also suboptimal though far superior to wire-minimized arbors. We discovered that cortical axon branching appears to promote a low temporal dispersion of axonal latencies and a tight relationship between cortical distance and axonal latency. In addition, inhibitory basket cell axonal latencies may occur within a much narrower temporal window than excitatory spiny cell axons, which may help boost signal detection. Thus, to optimize neuronal network communication we find that a modest excess of axonal wire is traded-off to enhance arbor temporal economy and precision. Our results offer insight into the principles of brain organization and communication in and development of grey matter, where temporal precision is a crucial prerequisite for coincidence detection, synchronization and rapid network oscillations

Mathematical modelling and numerical simulation of the morphological development of neurons

BACKGROUND: The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other. METHODS: A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described. RESULTS: Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development. CONCLUSION: A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity

Synaptic activity and the formation and maintenance of neuronal circuits

One of the most fundamental features of neurons is their polarized organization with two types of neurites extending from the cell body, axons and dendrites that are both functionally and morphologically distinct. During development, both axons and dendrites possess highly dynamic and actin-rich growth cones and filopodia extending from their shafts, which are subsequently replace by fundamentally stable axonal varicosities and dendritic spines. Together they form the basic elements of mature synapses. To mimic in vivo neuronal development, I have used organotypic cultures of brain tissue from transgenic mice expressing either green fluorescent protein (GFP) bearing a surface membrane localization signal or actin-GFP in combination with live cell imaging system. This approach provided me with high-resolution images of developing neurons’ fine structure in organized tissue. Co-cultures of fluorescent and non-fluorescent hippocampal slices enabled me then to examine simultaneously dendrite differentiation in the fluorescent slice and to track the fate of fluorescent axons growing into the non-fluorescent slice. Together this granted me a powerful tool to study neuronal network formation and developmental maturation of axons and dendrites. Co-cultures of embryonic tissue showed a sustained cross-innervation of axonal projections. Over time neurons in these co-cultures formed a dense axonal network with numerous axonal varicosities along their shaft. This axonal plexus remained present beyond 2 months in vitro. Dendrites in these embryonic co-cultures subsequently switched from producing labile filopodia to fundamentally stable dendritic spines. These mature dendritic spines had morphologies similar to those reported from studies of adult brain. Both axons and dendrites exhibited a successive focalisation of actin-based dynamics to the site of the synaptic junction. The observed changes in shape of mature axonal varicosities and dendritic spines together with the rapidly extension and retraction of actin-rich protrusions from the top of varicosities and spine heads suggest a retained capacity for experience-dependent fine-tuning e.g. during either periods of learning and memory or during brain damage resulting in an altered connectivity for both pre- and postsynaptic compartments in the mature mammalian central nervous system. The observed morphological dynamics suggest a high degree of preservation of morphological plasticity at the synapse in mature neuronal networks. Co-cultures of postnatal brain slices showed intensive invasion of axonal projections during the first two weeks in culture, followed by dramatic axonal regression and resulting in a near complete absence of cross-innervating axons after 1 month in vitro. In contrast, dendrite development in each of these postnatal cultures was fundamentally normal and occurred similar to that observed in embryonic co-cultures. I then co-cultured embryonic and postnatal slices to investigate whether the difference in capacity to cross-innervate between postnatal co-cultures and embryonic co-cultures were the result of tissue maturation. We found that the postnatal slice degenerated so that after 1 month in culture it had almost disappeared whereas the neighbouring embryonic slice had matured without noticeable problems. Staining these co-cultures of embryonic and postnatal slices showed a massive invasion of microglial cells into the dying postnatal slice. The difference between embryonic and postnatal neurons in their capacity to maintain cross-innervating synaptic connection suggests the existence of a developmental switch resulting in the inability of sustained afferent cross-innervation between postnatal brain slices. At the same time, in heterochronic co-cultures it causes miscommunication between postnatal and embryonic cells leading to profound degeneration of postnatal tissue. The thick layer of microglia surrounding postnatal tissue suggests their involvement in neuronal degeneration similar to that observed in axotomy-induced neuronal death and various neurodegenerative conditions such as Alzheimer’s disease. The earlier suggested preservation of morphological plasticity at the synapse in mature neuronal networks was illustrated by cooling mature hippocampal slices, either acutely cut brain slices or organotypic cultures, to room temperature. Dendritic spines are highly sensitive to reduced temperature with rapid loss of actin-based motility followed by disappearance of the entire spine structure within 12 hours. However, rewarming these cooled slices to 37˚C resulted in the rapid extension of filopodia from the surface of dendrites and re-establishment of dendritic spines within several of hours. These data underline the high degree of plasticity retained by neuronal connections in the mature CNS and suggest a link between dendritic spine structure and global brain function