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Introduction: Neuronal death and subsequent denervation of target areas are hallmarks of many neurological disorders. Denervated neurons lose part of their dendritic tree, and are considered "atrophic", i.e. pathologically altered and damaged. The functional consequences of this phenomenon are poorly understood.
Results: Using computational modelling of 3D-reconstructed granule cells we show that denervation-induced dendritic atrophy also subserves homeostatic functions: By shortening their dendritic tree, granule cells compensate for the loss of inputs by a precise adjustment of excitability. As a consequence, surviving afferents are able to activate the cells, thereby allowing information to flow again through the denervated area. In addition, action potentials backpropagating from the soma to the synapses are enhanced specifically in reorganized portions of the dendritic arbor, resulting in their increased synaptic plasticity. These two observations generalize to any given dendritic tree undergoing structural changes.
Conclusions: Structural homeostatic plasticity, i.e. homeostatic dendritic remodeling, is operating in long-term denervated neurons to achieve functional homeostasis.
Important brain functions need to be conserved throughout organisms of extremely varying sizes. Here we study the scaling properties of an essential component of computation in the brain: the single neuron. We compare morphology and signal propagation of a uniquely identifiable interneuron, the HS cell, in the blowfly (Calliphora) with its exact counterpart in the fruit fly (Drosophila) which is about four times smaller in each dimension. Anatomical features of the HS cell scale isometrically and minimise wiring costs but, by themselves, do not scale to preserve the electrotonic behaviour. However, the membrane properties are set to conserve dendritic as well as axonal delays and attenuation as well as dendritic integration of visual information. In conclusion, the electrotonic structure of a neuron, the HS cell in this case, is surprisingly stable over a wide range of morphological scales.
Abstract: Integration of synaptic currents across an extensive dendritic tree is a prerequisite for computation in the brain. Dendritic tapering away from the soma has been suggested to both equalise contributions from synapses at different locations and maximise the current transfer to the soma. To find out how this is achieved precisely, an analytical solution for the current transfer in dendrites with arbitrary taper is required. We derive here an asymptotic approximation that accurately matches results from numerical simulations. From this we then determine the diameter profile that maximises the current transfer to the soma. We find a simple quadratic form that matches diameters obtained experimentally, indicating a fundamental architectural principle of the brain that links dendritic diameters to signal transmission.
Author Summary: Neurons take a great variety of shapes that allow them to perform their different computational roles across the brain. The most distinctive visible feature of many neurons is the extensively branched network of cable-like projections that make up their dendritic tree. A neuron receives current-inducing synaptic contacts from other cells across its dendritic tree. As in the case of botanical trees, dendritic trees are strongly tapered towards their tips. This tapering has previously been shown to offer a number of advantages over a constant width, both in terms of reduced energy requirements and the robust integration of inputs at different locations. However, in order to predict the computations that neurons perform, analytical solutions for the flow of input currents tend to assume constant dendritic diameters. Here we introduce an asymptotic approximation that accurately models the current transfer in dendritic trees with arbitrary, continuously changing, diameters. When we then determine the diameter profiles that maximise current transfer towards the cell body we find diameters similar to those observed in real neurons. We conclude that the tapering in dendritic trees to optimise signal transmission is a fundamental architectural principle of the brain.
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.
Dendritic morphology has been shown to have a dramatic impact on neuronal function. However, population features such as the inherent variability in dendritic morphology between cells belonging to the same neuronal type are often overlooked when studying computation in neural networks. While detailed models for morphology and electrophysiology exist for many types of single neurons, the role of detailed single cell morphology in the population has not been studied quantitatively or computationally. Here we use the structural context of the neural tissue in which dendritic trees exist to drive their generation in silico. We synthesize the entire population of dentate gyrus granule cells, the most numerous cell type in the hippocampus, by growing their dendritic trees within their characteristic dendritic fields bounded by the realistic structural context of (1) the granule cell layer that contains all somata and (2) the molecular layer that contains the dendritic forest. This process enables branching statistics to be linked to larger scale neuroanatomical features. We find large differences in dendritic total length and individual path length measures as a function of location in the dentate gyrus and of somatic depth in the granule cell layer. We also predict the number of unique granule cell dendrites invading a given volume in the molecular layer. This work enables the complete population-level study of morphological properties and provides a framework to develop complex and realistic neural network models.
Poster presentation: Twenty Second Annual Computational Neuroscience Meeting: CNS*2013. Paris, France. 13-18 July 2013.
Neuronal death and subsequent denervation of target areas is a major feature of several neurological conditions such as brain trauma, ischemia or neurodegeneration. The denervation-induced axonal loss results in reorganization of the dendritic tree of denervated neurons. Dendritic reorganization of denervated neurons has been previously studied using entorhinal cortex lesion (ECL).
ECL leads to shortening and loss of dendritic segments in the denervated outer molecular layer of the dentate gyrus [1]. However, the functional importance of these long-term dendritic alterations is not yet understood and their impact on neuronal electrical properties remains unclear. Therefore, in this study we analyzed what happens to the electrotonic structure and excitability of dentate granule cells after denervation-induced alterations of their dendritic morphology, assuming all other parameters remain equal.
To perform comparative electrotonic analysis we used computer simulations in anatomically and biophysically realistic compartmental models of 3D-reconstructed healthy and denervated granule cells. Our results show that somatofugal and somatopetal voltage attenuation due to passive cable properties was strongly reduced in denervated granule cells. In line with these predictions, the attenuation of simulated backpropagating action potentials and forward propagating EPSPs was significantly reduced in dendrites of denervated neurons. In addition, simulations of somatic and dendritic frequency-current (f-I) curves revealed increased excitability in deafferentated granule cells.
Taken together, our results indicate that unless counterbalanced by a compensatory adjustment of passive and/or active membrane properties, the plastic remodeling of dendrites following lesion of entorhinal cortex inputs to granule cells will boost their electrotonic compactness and excitability.
Neurogenesis of hippocampal granule cells (GCs) persists throughout mammalian life and is important for learning and memory. How newborn GCs differentiate and mature into an existing circuit during this time period is not yet fully understood. We established a method to visualize postnatally generated GCs in organotypic entorhino-hippocampal slice cultures (OTCs) using retroviral (RV) GFP-labeling and performed time-lapse imaging to study their morphological development in vitro. Using anterograde tracing we could, furthermore, demonstrate that the postnatally generated GCs in OTCs, similar to adult born GCs, grow into an existing entorhino-dentate circuitry. RV-labeled GCs were identified and individual cells were followed for up to four weeks post injection. Postnatally born GCs exhibited highly dynamic structural changes, including dendritic growth spurts but also retraction of dendrites and phases of dendritic stabilization. In contrast, older, presumably prenatally born GCs labeled with an adeno-associated virus (AAV), were far less dynamic. We propose that the high degree of structural flexibility seen in our preparations is necessary for the integration of newborn granule cells into an already existing neuronal circuit of the dentate gyrus in which they have to compete for entorhinal input with cells generated and integrated earlier.
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.
Artificial neural networks, taking inspiration from biological neurons, have become an invaluable tool for machine learning applications. Recent studies have developed techniques to effectively tune the connectivity of sparsely-connected artificial neural networks, which have the potential to be more computationally efficient than their fully-connected counterparts and more closely resemble the architectures of biological systems. We here present a normalisation, based on the biophysical behaviour of neuronal dendrites receiving distributed synaptic inputs, that divides the weight of an artificial neuron’s afferent contacts by their number. We apply this dendritic normalisation to various sparsely-connected feedforward network architectures, as well as simple recurrent and self-organised networks with spatially extended units. The learning performance is significantly increased, providing an improvement over other widely-used normalisations in sparse networks. The results are two-fold, being both a practical advance in machine learning and an insight into how the structure of neuronal dendritic arbours may contribute to computation.
Achieving functional neuronal dendrite structure through sequential stochastic growth and retraction
(2020)
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.