Untangling dendrites with quantitative models

Key morphological features of human pyramidal neurons

The basic building block of the cerebral cortex, the pyramidal cell, has been shown to be characterized by a markedly different dendritic structure among layers, cortical areas, and species. Functionally, differences in the structure of their dendrites and axons are critical in determining how neurons integrate information. However, within the human cortex, these neurons have not been quantified in detail. In the present work, we performed intracellular injections of Lucifer Yellow and 3D reconstructed over 200 pyramidal neurons, including apical and basal dendritic and local axonal arbors and dendritic spines, from human occipital primary visual area and associative temporal cortex. We found that human pyramidal neurons from temporal cortex were larger, displayed more complex apical and basal structural organization, and had more spines compared to those in primary sensory cortex. Moreover, these human neocortical neurons displayed specific shared and distinct characteristics in comparison to previously published human hippocampal pyramidal neurons. Additionally, we identified distinct morphological features in human neurons that set them apart from mouse neurons. Lastly, we observed certain consistent organizational patterns shared across species. This study emphasizes the existing diversity within pyramidal cell structures across different cortical areas and species, suggesting substantial species-specific variations in their computational properties.

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

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

A universal workflow for creation, validation, and generalization of detailed neuronal models

Detailed single-neuron modeling is widely used to study neuronal functions. While cellular and functional diversity across the mammalian cortex is vast, most of the available computational tools focus on a limited set of specific features characteristic of a single neuron. Here, we present a generalized automated workflow for the creation of robust electrical models and illustrate its performance by building cell models for the rat somatosensory cortex. Each model is based on a 3D morphological reconstruction and a set of ionic mechanisms. We use an evolutionary algorithm to optimize neuronal parameters to match the electrophysiological features extracted from experimental data. Then we validate the optimized models against additional stimuli and assess their generalizability on a population of similar morphologies. Compared to the state-of-the-art canonical models, our models show 5-fold improved generalizability. This versatile approach can be used to build robust models of any neuronal type.

The impact of Hodgkin-Huxley models on dendritic research

For the past seven decades, the Hodgkin-Huxley (HH) formalism has been an invaluable tool in the arsenal of neuroscientists, allowing for robust and reproducible modelling of ionic conductances and the electrophysiological phenomena they underlie. Despite its apparent age, its role as a cornerstone of computational neuroscience has not waned. The discovery of dendritic regenerative events mediated by ionic and synaptic conductances has solidified the importance of HH-based models further, yielding new predictions concerning dendritic integration, synaptic plasticity and neuronal computation. These predictions are often validated through in vivo and in vitro experiments, advancing our understanding of the neuron as a biological system and emphasizing the importance of HH-based detailed computational models as an instrument of dendritic research. In this article, we discuss recent studies in which the HH formalism is used to shed new light on dendritic function and its role in neuronal phenomena.

Microgeometrical dendritic factors predict electrical decoupling between somatic and dendritic compartments in magnocellular neurosecretory neurons

It is generally assumed that dendritic release of neuropeptides from magnocellular neurosecretory neurons (MNNs), a critical process involved in homeostatic functions, is an activity-dependent process that requires backpropagating action potentials (APs). Still, growing evidence indicates that dendritic release can occur in the absence of APs, and axonal APs have been shown to fail to evoke dendritic release. These inconsistencies strongly suggest that APs in MNNs may fail to backpropagating into dendrites. Here we tested whether simple factors of electrical signal attenuation could lead to effective decoupling between cell's body and dendritic release site within typical geometrical characteristics of MNN. We developed a family of linear mathematical models of MNNs and evaluated whether the somato-dendritic transfer of electrical signals is influenced by the geometrical characteristics. We determined the prerequisites for critically strong dendritic attenuation of the somatic input which are sufficient to explain the failure of APs initiated in the soma to backpropagating into dendritic compartments. Being measured in 100 μm from soma voltage attenuations down to 0.1 and 0.01 of the input value were chosen as the markers of electrical decoupling of dendritic sites from the soma, considering 0.1 insufficient for triggering dendritic spikes and 0.01 indistinguishable from background noise. The tested micro-geometrical factors were the dendritic stem diameter, varicosities, and size of peri-dendritic space limited by glial sheath wrapping. Varicosities increased the attenuation along homogeneous proximal dendrites by providing an increased current leak at the junction with the proximal dendritic section. The glial sheath wrapping a dendrite section promoted greater attenuation by increasing longitudinal resistance of the interstitial peri-dendritic space thus playing the insulating role. These decoupling effects were strengthened in the case of the dendritic stems with thinner diameters of and/or increased conductivity of the membrane. These micro-geometrical factors are biophysically realistic and predict electrical decoupling between somatic and dendritic compartments in MNNs.

Neurons as hierarchies of quantum reference frames

Conceptual and mathematical models of neurons have lagged behind empirical understanding for decades. Here we extend previous work in modeling biological systems with fully scale-independent quantum information-theoretic tools to develop a uniform, scalable representation of synapses, dendritic and axonal processes, neurons, and local networks of neurons. In this representation, hierarchies of quantum reference frames act as hierarchical active-inference systems. The resulting model enables specific predictions of correlations between synaptic activity, dendritic remodeling, and trophic reward. We summarize how the model may be generalized to nonneural cells and tissues in developmental and regenerative contexts.

Modeling material transport regulation and traffic jam in neurons using PDE-constrained optimization

The intracellular transport process plays an important role in delivering essential materials throughout branched geometries of neurons for their survival and function. Many neurodegenerative diseases have been associated with the disruption of transport. Therefore, it is essential to study how neurons control the transport process to localize materials to necessary locations. Here, we develop a novel optimization model to simulate the traffic regulation mechanism of material transport in complex geometries of neurons. The transport is controlled to avoid traffic jam of materials by minimizing a pre-defined objective function. The optimization subjects to a set of partial differential equation (PDE) constraints that describe the material transport process based on a macroscopic molecular-motor-assisted transport model of intracellular particles. The proposed PDE-constrained optimization model is solved in complex tree structures by using isogeometric analysis (IGA). Different simulation parameters are used to introduce traffic jams and study how neurons handle the transport issue. Specifically, we successfully model and explain the traffic jam caused by reduced number of microtubules (MTs) and MT swirls. In summary, our model effectively simulates the material transport process in healthy neurons and also explains the formation of a traffic jam in abnormal neurons. Our results demonstrate that both geometry and MT structure play important roles in achieving an optimal transport process in neuron.

IRS1 expression in hippocampus is age-dependent and is required for mature spine maintenance and neuritogenesis

Insulin and insulin-like growth factor type I (IGF-1) play prominent roles in brain activity throughout the lifespan. Insulin/IGF1 signaling starts with the activation of the intracellular insulin receptor substrates (IRS). In this work, we performed a comparative study of IRS1 and IRS2, together with the IGF1 (IGF1R) and insulin (IR) receptor expression in the hippocampus and prefrontal cortex during development. We found that IRS1 and IRS2 expression is prominent during development and declines in the aged hippocampus, contrary to IR, which increases in adulthood and aging. In contrast, IGF1R expression is unaffected by age. Expression patterns are similar in the prefrontal cortex. Neurite development occurs postnatally in the rodent hippocampus and cortex, and it declines in the mature and aged brain and is influenced by trophic factors. In our previous work, we demonstrated that knockdown of IRS1 by shRNA impairs learning and reduces synaptic plasticity in a rat model, as measured by synaptophysin puncta in axons. In this study, we report that shIRS1 alters spine maturation in adult hilar hippocampal neurons. Lastly, to understand the role of IRS1 in neuronal neurite tree, we transfect shIRS1 into primary neuronal cultures and observed that shIRS1 reduced neurite branching and neurite length. Our results demonstrate that IRS1/2 and insulin/IGF1 receptors display different age-dependent expression profiles and that IRS1 is required for spine maturation, demonstrating a novel role for IRS1 in synaptic plasticity.

Local dendritic balance enables learning of efficient representations in networks of spiking neurons

How can neural networks learn to efficiently represent complex and high-dimensional inputs via local plasticity mechanisms? Classical models of representation learning assume that feedforward weights are learned via pairwise Hebbian-like plasticity. Here, we show that pairwise Hebbian-like plasticity works only under unrealistic requirements on neural dynamics and input statistics. To overcome these limitations, we derive from first principles a learning scheme based on voltage-dependent synaptic plasticity rules. Here, recurrent connections learn to locally balance feedforward input in individual dendritic compartments and thereby can modulate synaptic plasticity to learn efficient representations. We demonstrate in simulations that this learning scheme works robustly even for complex high-dimensional inputs and with inhibitory transmission delays, where Hebbian-like plasticity fails. Our results draw a direct connection between dendritic excitatory-inhibitory balance and voltage-dependent synaptic plasticity as observed in vivo and suggest that both are crucial for representation learning.

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.

Active Dendrites and Local Field Potentials: Biophysical Mechanisms and Computational Explorations

Neurons and glial cells are endowed with membranes that express a rich repertoire of ion channels, transporters, and receptors. The constant flux of ions across the neuronal and glial membranes results in voltage fluctuations that can be recorded from the extracellular matrix. The high frequency components of this voltage signal contain information about the spiking activity, reflecting the output from the neurons surrounding the recording location. The low frequency components of the signal, referred to as the local field potential (LFP), have been traditionally thought to provide information about the synaptic inputs that impinge on the large dendritic trees of various neurons. In this review, we discuss recent computational and experimental studies pointing to a critical role of several active dendritic mechanisms that can influence the genesis and the location-dependent spectro-temporal dynamics of LFPs, spanning different brain regions. We strongly emphasize the need to account for the several fast and slow dendritic events and associated active mechanisms - including gradients in their expression profiles, inter- and intra-cellular spatio-temporal interactions spanning neurons and glia, heterogeneities and degeneracy across scales, neuromodulatory influences, and activitydependent plasticity - towards gaining important insights about the origins of LFP under different behavioral states in health and disease. We provide simple but essential guidelines on how to model LFPs taking into account these dendritic mechanisms, with detailed methodology on how to account for various heterogeneities and electrophysiological properties of neurons and synapses while studying LFPs.

The Role of Hippo Signaling Pathway in the Development of the Nervous System

Hippo signaling pathway is a highly conserved and crucial signaling pathway that controls the size of tissues and organs by regulating the proliferation, differentiation, and apoptosis of cells. The nervous system is a complicated system that participates in information collection, integration, and procession. The balance of various aspects of the nervous system is vital for the normal regulation of physiological conditions of the body, like the population and distribution of nerve cells, nerve connections, and so on. Defects in these aspects may lead to cognitive, behavioral, and neurological dysfunction, resulting in various nervous system diseases. Recently, accumulating evidence proposes that Hippo pathway maintains numerous biological functions in the nervous system development, including modulating the proliferation and differentiation of nerve cells and promoting the development of synapse, corpus callosum, and cortex. In this review, we will summarize recent findings of Hippo pathway in the nervous system to improve our understanding on its function and to provide potential therapeutic strategies of nervous system diseases in the future.

Differential Structure of Hippocampal CA1 Pyramidal Neurons in the Human and Mouse

Pyramidal neurons are the most common cell type and are considered the main output neuron in most mammalian forebrain structures. In terms of function, differences in the structure of the dendrites of these neurons appear to be crucial in determining how neurons integrate information. To further shed light on the structure of the human pyramidal neurons we investigated the geometry of pyramidal cells in the human and mouse CA1 region-one of the most evolutionary conserved archicortical regions, which is critically involved in the formation, consolidation, and retrieval of memory. We aimed to assess to what extent neurons corresponding to a homologous region in different species have parallel morphologies. Over 100 intracellularly injected and 3D-reconstructed cells across both species revealed that dendritic and axonal morphologies of human cells are not only larger but also have structural differences, when compared to mouse. The results show that human CA1 pyramidal cells are not a stretched version of mouse CA1 cells. These results indicate that there are some morphological parameters of the pyramidal cells that are conserved, whereas others are species-specific.

Deep learning of material transport in complex neurite networks

Neurons exhibit complex geometry in their branched networks of neurites which is essential to the function of individual neuron but also brings challenges to transport a wide variety of essential materials throughout their neurite networks for their survival and function. While numerical methods like isogeometric analysis (IGA) have been used for modeling the material transport process via solving partial differential equations (PDEs), they require long computation time and huge computation resources to ensure accurate geometry representation and solution, thus limit their biomedical application. Here we present a graph neural network (GNN)-based deep learning model to learn the IGA-based material transport simulation and provide fast material concentration prediction within neurite networks of any topology. Given input boundary conditions and geometry configurations, the well-trained model can predict the dynamical concentration change during the transport process with an average error less than 10% and [Formula: see text] times faster compared to IGA simulations. The effectiveness of the proposed model is demonstrated within several complex neurite networks.

Modeling Neurotransmission: Computational Tools to Investigate Neurological Disorders

The investigation of synaptic functions remains one of the most fascinating challenges in the field of neuroscience and a large number of experimental methods have been tuned to dissect the mechanisms taking part in the neurotransmission process. Furthermore, the understanding of the insights of neurological disorders originating from alterations in neurotransmission often requires the development of (i) animal models of pathologies, (ii) invasive tools and (iii) targeted pharmacological approaches. In the last decades, additional tools to explore neurological diseases have been provided to the scientific community. A wide range of computational models in fact have been developed to explore the alterations of the mechanisms involved in neurotransmission following the emergence of neurological pathologies. Here, we review some of the advancements in the development of computational methods employed to investigate neuronal circuits with a particular focus on the application to the most diffuse neurological disorders.

Small universal spiking neural P systems with dendritic/axonal delays and dendritic trunk/feedback

In spiking neural P (SN P) systems, neurons are interconnected by means of synapses, and they use spikes to communicate with each other. However, in biology, the complex structure of dendritic tree is also an important part in the communication scheme between neurons since these structures are linked to advanced neural process such as learning and memory formation. In this work, we present a new variant of the SN P systems inspired by diverse dendrite and axon phenomena such as dendritic feedback, dendritic trunk, dendritic delays and axonal delays, respectively. This new variant is referred to as a spiking neural P system with dendritic and axonal computation (DACSN P system). Specifically, we include experimentally proven biological features in the current SN P systems to reduce the computational complexity of the soma by providing it with stable firing patterns through dendritic delays, dendritic feedback and axonal delays. As a consequence, the proposed DACSN P systems use the minimum number of synapses and neurons with simple and homogeneous standard spiking rules. Here, we study the computational capabilities of a DACSN P system. In particular, we prove that DACSN P systems with dendritic and axonal behavior are universal as both number-accepting/generating devices. In addition, we constructed a small universal SN P system using 39 neurons with standard spiking rules to compute any Turing computable function.

Comparing the Electrophysiology and Morphology of Human and Mouse Layer 2/3 Pyramidal Neurons With Bayesian Networks

Pyramidal neurons are the most common neurons in the cerebral cortex. Understanding how they differ between species is a key challenge in neuroscience. We compared human temporal cortex and mouse visual cortex pyramidal neurons from the Allen Cell Types Database in terms of their electrophysiology and dendritic morphology. We found that, among other differences, human pyramidal neurons had a higher action potential threshold voltage, a lower input resistance, and larger dendritic arbors. We learned Gaussian Bayesian networks from the data in order to identify correlations and conditional independencies between the variables and compare them between the species. We found strong correlations between electrophysiological and morphological variables in both species. In human cells, electrophysiological variables were correlated even with morphological variables that are not directly related to dendritic arbor size or diameter, such as mean bifurcation angle and mean branch tortuosity. Cortical depth was correlated with both electrophysiological and morphological variables in both species, and its effect on electrophysiology could not be explained in terms of the morphological variables. For some variables, the effect of cortical depth was opposite in the two species. Overall, the correlations among the variables differed strikingly between human and mouse neurons. Besides identifying correlations and conditional independencies, the learned Bayesian networks might be useful for probabilistic reasoning regarding the morphology and electrophysiology of pyramidal neurons.

Data-driven reduction of dendritic morphologies with preserved dendro-somatic responses

Dendrites shape information flow in neurons. Yet, there is little consensus on the level of spatial complexity at which they operate. Through carefully chosen parameter fits, solvable in the least-squares sense, we obtain accurate reduced compartmental models at any level of complexity. We show that (back-propagating) action potentials, Ca²⁺ spikes, and N-methyl-D-aspartate spikes can all be reproduced with few compartments. We also investigate whether afferent spatial connectivity motifs admit simplification by ablating targeted branches and grouping affected synapses onto the next proximal dendrite. We find that voltage in the remaining branches is reproduced if temporal conductance fluctuations stay below a limit that depends on the average difference in input resistance between the ablated branches and the next proximal dendrite. Furthermore, our methodology fits reduced models directly from experimental data, without requiring morphological reconstructions. We provide software that automatizes the simplification, eliminating a common hurdle toward including dendritic computations in network models.

Spatially resolved dendritic integration: towards a functional classification of neurons

The vast tree-like dendritic structure of neurons allows them to receive and integrate input from many neurons. A wide variety of neuronal morphologies exist, however, their role in dendritic integration, and how it shapes the response of the neuron, is not yet fully understood. Here, we study the evolution and interactions of dendritic spikes in excitable neurons with complex real branch structures. We focus on dozens of digitally reconstructed illustrative neurons from the online repository NeuroMorpho.org, which contains over 130,000 neurons. Yet, our methods can be promptly extended to any other neuron. This approach allows us to estimate and map specific and heterogeneous patterns of activity observed across extensive dendritic trees with thousands of compartments. We propose a classification of neurons based on the location of the soma (centrality) and the number of branches connected to the soma. These are key topological factors in determining the neuron's energy consumption, firing rate, and the dynamic range, which quantifies the range in synaptic input rate that can be reliably encoded by the neuron's firing rate. Moreover, we find that bifurcations, the structural building blocks of complex dendrites, play a major role in increasing the dynamic range of neurons. Our results provide a better understanding of the effects of neuronal morphology in the diversity of neuronal dynamics and function.

Comparing basal dendrite branches in human and mouse hippocampal CA1 pyramidal neurons with Bayesian networks

Pyramidal neurons are the most common cell type in the cerebral cortex. Understanding how they differ between species is a key challenge in neuroscience. A recent study provided a unique set of human and mouse pyramidal neurons of the CA1 region of the hippocampus, and used it to compare the morphology of apical and basal dendritic branches of the two species. The study found inter-species differences in the magnitude of the morphometrics and similarities regarding their variation with respect to morphological determinants such as branch type and branch order. We use the same data set to perform additional comparisons of basal dendrites. In order to isolate the heterogeneity due to intrinsic differences between species from the heterogeneity due to differences in morphological determinants, we fit multivariate models over the morphometrics and the determinants. In particular, we use conditional linear Gaussian Bayesian networks, which provide a concise graphical representation of the independencies and correlations among the variables. We also extend the previous study by considering additional morphometrics and by formally testing whether a morphometric increases or decreases with the distance from the soma. This study introduces a multivariate methodology for inter-species comparison of morphology.

Illuminating dendritic function with computational models

Dendrites have always fascinated researchers: from the artistic drawings by Ramon y Cajal to the beautiful recordings of today, neuroscientists have been striving to unravel the mysteries of these structures. Theoretical work in the 1960s predicted important dendritic effects on neuronal processing, establishing computational modelling as a powerful technique for their investigation. Since then, modelling of dendrites has been instrumental in driving neuroscience research in a targeted manner, providing experimentally testable predictions that range from the subcellular level to the systems level, and their relevance extends to fields beyond neuroscience, such as machine learning and artificial intelligence. Validation of modelling predictions often requires - and drives - new technological advances, thus closing the loop with theory-driven experimentation that moves the field forward. This Review features the most important, to our understanding, contributions of modelling of dendritic computations, including those pending experimental verification, and highlights studies of successful interactions between the modelling and experimental neuroscience communities.

Generation of Granule Cell Dendritic Morphologies by Estimating the Spatial Heterogeneity of Dendritic Branching

Biological realism of dendritic morphologies is important for simulating electrical stimulation of brain tissue. By adding point process modeling and conditional sampling to existing generation strategies, we provide a novel means of reproducing the nuanced branching behavior that occurs in different layers of granule cell dendritic morphologies. In this study, a heterogeneous Poisson point process was used to simulate branching events. Conditional distributions were then used to select branch angles depending on the orthogonal distance to the somatic plane. The proposed method was compared to an existing generation tool and a control version of the proposed method that used a homogeneous Poisson point process. Morphologies were generated with each method and then compared to a set of digitally reconstructed neurons. The introduction of a conditionally dependent branching rate resulted in the generation of morphologies that more accurately reproduced the emergent properties of dendritic material per layer, Sholl intersections, and proximal passive current flow. Conditional dependence was critically important for the generation of realistic granule cell dendritic morphologies.

Electrical Compartmentalization in Neurons

The dendritic tree of neurons plays an important role in information processing in the brain. While it is thought that dendrites require independent subunits to perform most of their computations, it is still not understood how they compartmentalize into functional subunits. Here, we show how these subunits can be deduced from the properties of dendrites. We devised a formalism that links the dendritic arborization to an impedance-based tree graph and show how the topology of this graph reveals independent subunits. This analysis reveals that cooperativity between synapses decreases slowly with increasing electrical separation and thus that few independent subunits coexist. We nevertheless find that balanced inputs or shunting inhibition can modify this topology and increase the number and size of the subunits in a context-dependent manner. We also find that this dynamic recompartmentalization can enable branch-specific learning of stimulus features. Analysis of dendritic patch-clamp recording experiments confirmed our theoretical predictions.

A Brief History of Simulation Neuroscience

Our knowledge of the brain has evolved over millennia in philosophical, experimental and theoretical phases. We suggest that the next phase is simulation neuroscience. The main drivers of simulation neuroscience are big data generated at multiple levels of brain organization and the need to integrate these data to trace the causal chain of interactions within and across all these levels. Simulation neuroscience is currently the only methodology for systematically approaching the multiscale brain. In this review, we attempt to reconstruct the deep historical paths leading to simulation neuroscience, from the first observations of the nerve cell to modern efforts to digitally reconstruct and simulate the brain. Neuroscience began with the identification of the neuron as the fundamental unit of brain structure and function and has evolved towards understanding the role of each cell type in the brain, how brain cells are connected to each other, and how the seemingly infinite networks they form give rise to the vast diversity of brain functions. Neuronal mapping is evolving from subjective descriptions of cell types towards objective classes, subclasses and types. Connectivity mapping is evolving from loose topographic maps between brain regions towards dense anatomical and physiological maps of connections between individual genetically distinct neurons. Functional mapping is evolving from psychological and behavioral stereotypes towards a map of behaviors emerging from structural and functional connectomes. We show how industrialization of neuroscience and the resulting large disconnected datasets are generating demand for integrative neuroscience, how the scale of neuronal and connectivity maps is driving digital atlasing and digital reconstruction to piece together the multiple levels of brain organization, and how the complexity of the interactions between molecules, neurons, microcircuits and brain regions is driving brain simulation to understand the interactions in the multiscale brain.

How Dendrites Affect Online Recognition Memory

In order to record the stream of autobiographical information that defines our unique personal history, our brains must form durable memories from single brief exposures to the patterned stimuli that impinge on them continuously throughout life. However, little is known about the computational strategies or neural mechanisms that underlie the brain's ability to perform this type of "online" learning. Based on increasing evidence that dendrites act as both signaling and learning units in the brain, we developed an analytical model that relates online recognition memory capacity to roughly a dozen dendritic, network, pattern, and task-related parameters. We used the model to determine what dendrite size maximizes storage capacity under varying assumptions about pattern density and noise level. We show that over a several-fold range of both of these parameters, and over multiple orders-of-magnitude of memory size, capacity is maximized when dendrites contain a few hundred synapses-roughly the natural number found in memory-related areas of the brain. Thus, in comparison to entire neurons, dendrites increase storage capacity by providing a larger number of better-sized learning units. Our model provides the first normative theory that explains how dendrites increase the brain's capacity for online learning; predicts which combinations of parameter settings we should expect to find in the brain under normal operating conditions; leads to novel interpretations of an array of existing experimental results; and provides a tool for understanding which changes associated with neurological disorders, aging, or stress are most likely to produce memory deficits-knowledge that could eventually help in the design of improved clinical treatments for memory loss.

Amot and Yap1 regulate neuronal dendritic tree complexity and locomotor coordination in mice

The angiomotin (Amot)-Yes-associated protein 1 (Yap1) complex plays a major role in regulating the inhibition of cell contact, cellular polarity, and cell growth in many cell types. However, the function of Amot and the Hippo pathway transcription coactivator Yap1 in the central nervous system remains unclear. We found that Amot is a critical mediator of dendritic morphogenesis in cultured hippocampal cells and Purkinje cells in the brain. Amot function in developing neurons depends on interactions with Yap1, which is also indispensable for dendrite growth and arborization in vitro. The conditional deletion of Amot and Yap1 in neurons led to a decrease in the complexity of Purkinje cell dendritic trees, abnormal cerebellar morphology, and impairments in motor coordination. Our results indicate that the function of Amot and Yap1 in dendrite growth does not rely on interactions with TEA domain (TEAD) transcription factors or the expression of Hippo pathway-dependent genes. Instead, Amot and Yap1 regulate dendrite development by affecting the phosphorylation of S6 kinase and its target S6 ribosomal protein.

Differences in glutamate uptake between cortical regions impact neuronal NMDA receptor activation

Removal of synaptically-released glutamate by astrocytes is necessary to spatially and temporally limit neuronal activation. Recent evidence suggests that astrocytes may have specialized functions in specific circuits, but the extent and significance of such specialization are unclear. By performing direct patch-clamp recordings and two-photon glutamate imaging, we report that in the somatosensory cortex, glutamate uptake by astrocytes is slower during sustained synaptic stimulation when compared to lower stimulation frequencies. Conversely, glutamate uptake capacity is increased in the frontal cortex during higher frequency synaptic stimulation, thereby limiting extracellular buildup of glutamate and NMDA receptor activation in layer 5 pyramidal neurons. This efficient glutamate clearance relies on Na+/K+-ATPase function and both GLT-1 and non-GLT-1 transporters. Thus, by enhancing their glutamate uptake capacity, astrocytes in the frontal cortex may prevent excessive neuronal excitation during intense synaptic activity. These results may explain why diseases associated with network hyperexcitability differentially affect individual brain areas.

Detection of Multiway Gamma Coordination Reveals How Frequency Mixing Shapes Neural Dynamics

A principle of communication technology, frequency mixing, describes how novel oscillations are generated when rhythmic inputs converge on a nonlinearly activating target. As expected given that neurons are nonlinear integrators, it was demonstrated that neuronal networks exhibit mixing in response to imposed oscillations of known frequencies. However, determining when mixing occurs in spontaneous conditions, where weaker or more variable rhythms prevail, has remained impractical. Here, we show that, by exploiting the predicted phase (rather than frequency) relationships between oscillations, the contributions of mixing can be readily identified, even in small samples of noisy data. Assessment of extracellular data using this approach revealed that frequency mixing is widely expressed in a state- and region-dependent manner and that oscillations emerging from mixing entrain unit activity. Frequency mixing is thus intrinsic to the structure of neural activity and contributes importantly to neural dynamics.

Point Process Filtering Estimates of Branching Rate for Neural Dendritic Morphology Generation

Current parametric approaches to dendritic morphology generation are limited in their ability to replicate realistic branching. A non-parametric approach applying a point process filter and the expectation-maximization algorithm offers a data-based solution that estimates the dendritic branching rate based on observations of bifurcation events in real neurons. Point processes can then be simulated using this branching rate estimate to indicate when a generated morphology should branch. Morphologies generated using this technique match both basic and emergent property distributions of the real neurons used as input into the algorithm. Further refinement of branching angles will allow for a flexible tool to generate realistic morphologies of a variety of neuronal stereotypes.

Simultaneous dendritic voltage and calcium imaging and somatic recording from Purkinje neurons in awake mice

Spatiotemporal maps of dendritic signalling and their relationship with somatic output is fundamental to neuronal information processing, yet remain unexplored in awake animals. Here, we combine simultaneous sub-millisecond voltage and calcium two-photon imaging from distal spiny dendrites, with somatic electrical recording from spontaneously active cerebellar Purkinje neurons (PN) in awake mice. We detect discrete 1−2 ms suprathreshold voltage spikelets in the distal spiny dendrites during dendritic complex spikes. Spikelets and their calcium correlates are highly heterogeneous in number, timing and spatial distribution within and between complex spikes. Back-propagating simple spikes are highly attenuated. Highly variable 5–10 ms voltage hotspots are localized to fine dendritic processes and are reduced in size and frequency by lidocaine and CNQX. Hotspots correlated with somatic output but also, at high frequency, trigger purely dendritic calcium spikes. Summarizing, spatiotemporal signalling in PNs is far more complex, dynamic, and fine scaled than anticipated, even in resting animals.

Dendritic integration is important for information processing in the brain. Here, in awake mice, authors combine simultaneous dendritic recording of voltage and calcium signals, with somatic recording from Purkinje neurons, enabling characterization of dendritic spiking, action potential backpropagation, and ‘hotspots’ in spiny dendrites.

Parameter Optimization Using Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES), an Approach to Investigate Differences in Channel Properties Between Neuron Subtypes

Computational models in neuroscience can be used to predict causal relationships between biological mechanisms in neurons and networks, such as the effect of blocking an ion channel or synaptic connection on neuron activity. Since developing a biophysically realistic, single neuron model is exceedingly difficult, software has been developed for automatically adjusting parameters of computational neuronal models. The ideal optimization software should work with commonly used neural simulation software; thus, we present software which works with models specified in declarative format for the MOOSE simulator. Experimental data can be specified using one of two different file formats. The fitness function is customizable as a weighted combination of feature differences. The optimization itself uses the covariance matrix adaptation-evolutionary strategy, because it is robust in the face of local fluctuations of the fitness function, and deals well with a high-dimensional and discontinuous fitness landscape. We demonstrate the versatility of the software by creating several model examples of each of four types of neurons (two subtypes of spiny projection neurons and two subtypes of globus pallidus neurons) by tuning to current clamp data. Optimizations reached convergence within 1,600-4,000 model evaluations (200-500 generations × population size of 8). Analysis of the parameters of the best fitting models revealed differences between neuron subtypes, which are consistent with prior experimental results. Overall our results suggest that this easy-to-use, automatic approach for finding neuron channel parameters may be applied to current clamp recordings from neurons exhibiting different biochemical markers to help characterize ionic differences between other neuron subtypes.

Redundancy in synaptic connections enables neurons to learn optimally

Recent experimental studies suggest that, in cortical microcircuits of the mammalian brain, the majority of neuron-to-neuron connections are realized by multiple synapses. However, it is not known whether such redundant synaptic connections provide any functional benefit. Here, we show that redundant synaptic connections enable near-optimal learning in cooperation with synaptic rewiring. By constructing a simple dendritic neuron model, we demonstrate that with multisynaptic connections synaptic plasticity approximates a sample-based Bayesian filtering algorithm known as particle filtering, and wiring plasticity implements its resampling process. Extending the proposed framework to a detailed single-neuron model of perceptual learning in the primary visual cortex, we show that the model accounts for many experimental observations. In particular, the proposed model reproduces the dendritic position dependence of spike-timing-dependent plasticity and the functional synaptic organization on the dendritic tree based on the stimulus selectivity of presynaptic neurons. Our study provides a conceptual framework for synaptic plasticity and rewiring.

Voltage-dependent K+ channels improve the energy efficiency of signalling in blowfly photoreceptors

Voltage-dependent conductances in many spiking neurons are tuned to reduce action potential energy consumption, so improving the energy efficiency of spike coding. However, the contribution of voltage-dependent conductances to the energy efficiency of analogue coding, by graded potentials in dendrites and non-spiking neurons, remains unclear. We investigate the contribution of voltage-dependent conductances to the energy efficiency of analogue coding by modelling blowfly R1-6 photoreceptor membrane. Two voltage-dependent delayed rectifier K⁺ conductances (DRs) shape the membrane's voltage response and contribute to light adaptation. They make two types of energy saving. By reducing membrane resistance upon depolarization they convert the cheap, low bandwidth membrane needed in dim light to the expensive high bandwidth membrane needed in bright light. This investment of energy in bandwidth according to functional requirements can halve daily energy consumption. Second, DRs produce negative feedback that reduces membrane impedance and increases bandwidth. This negative feedback allows an active membrane with DRs to consume at least 30% less energy than a passive membrane with the same capacitance and bandwidth. Voltage-dependent conductances in other non-spiking neurons, and in dendrites, might be organized to make similar savings.

Maternal autoimmune antibodies alter the dendritic arbor and spine numbers in the infragranular layers of the cortex

An association between maternal IgG antibodies reactive against proteins in fetal brain and an outcome of autism in the child has been identified. Using a mouse model of prenatal intraventricular administration of autism-specific maternal IgG, we demonstrated that these antibodies produce behavioral alterations similar to those in children with ASD. We previously demonstrated that these antibodies bind to radial glial stem cells (RG) and observed an increase in the number of divisions of translocating RG in the developing cortex. We also showed an alteration in brain size and as well as a generalized increased of neuronal volume in adult mice. Here, we used our intraventricular mouse model of antibody administration, followed by Golgi and Neurolucida analysis to demonstrate that during midstages of neurogenesis these maternal autism-specific antibodies produced a consistent decrease in the number of spines in the infragranular layers in the adult cortical areas analyzed. Specifically, in the frontal cortex basal dendrites of layer V neurons were decreased in length and volume, and both the total number of spines-mature and immature-and the spine density were lower than in the control neurons from the same region. Further, in the occipital cortex layer VI neurons presented with a decrease in the total number of spines and in the spine density in the apical dendrite, as well as decrease in the number of mature spines in the apical and basal dendrites. Interestingly, the time of exposure to these antibodies (E14.5) coincides with the generation of pyramidal neurons in layer V in the frontal cortex and in layer VI in the occipital cortex, following the normal rostro-caudal pattern of cortical cell generation. We recently demonstrated that one of the primary antigens recognized by these antibodies corresponds to stress-induced phosphoprotein 1 (STIP1). Here we hypothesize that the reduction in the access of newborn cells to STIP1 in the developing cortex may be responsible for the reduced dendritic arborization and number of spines we noted in the adult cortex.

Impact of the localization of dendritic calcium persistent inward current on the input-output properties of spinal motoneuron pool: a computational study

The goal of this study is to investigate how the dendritic Ca-PIC location influences nonlinear input-output properties and depends on the type of motoneurons across the motoneuron pool. A model motoneuron pool consisting of 10 motoneurons was constructed using a recently developed two-compartment modeling approach that reflected key cell type-associated properties experimentally identified. The dendritic excitability and firing output depended systematically on both the PIC location and the motoneuron type. The PIC onset and offset in the current-voltage (I-V) relationship tended to occur at more hyperpolarized voltages as the path length to the PIC channels from the soma increased and as the cell type shifted from high- to low-threshold motoneurons. At the same time, the firing acceleration and frequency hysteresis in the frequency-current (F-I) relationship became faster and larger, respectively. However, the PIC onset-offset hysteresis increased as the path length and the recruitment threshold increased. Furthermore, the gain of frequency-current function before full PIC activation was larger for PIC channels located over distal dendritic regions in low- compared with high-threshold motoneurons. When compared with previously published experimental observations, the modeling concurred when Ca-PIC channels were placed closer to the soma in high- than low-threshold motoneurons in the model motoneuron pool. All of these results suggest that the negative relationship of Ca-PIC location and cell recruitment threshold may underlie the systematic variation in I-V and F-I transformation across the motoneuron pool.NEW & NOTEWORTHY How does the dendritic location of calcium persistent inward current (Ca-PIC) influence dendritic excitability and firing behavior across the spinal motoneuron pool? This issue was investigated developing a model motoneuron pool that reflected key motoneuron type-specific properties experimentally identified. The simulation results point out the negative relationship between the distance of Ca-PIC source from the soma and cell recruitment threshold as a basis underlying the systematic variation in input-output properties of motoneurons over the motoneuron pool.

Dendrite and spine modifications in autism and related neurodevelopmental disorders in patients and animal models

Dendrites and spines are the main neuronal structures receiving input from other neurons and glial cells. Dendritic and spine number, size, and morphology are some of the crucial factors determining how signals coming from individual synapses are integrated. Much remains to be understood about the characteristics of neuronal dendrites and dendritic spines in autism and related disorders. Although there have been many studies conducted using autism mouse models, few have been carried out using postmortem human tissue from patients. Available animal models of autism include those generated through genetic modifications and those non-genetic models of the disease. Here, we review how dendrite and spine morphology and number is affected in autism and related neurodevelopmental diseases, both in human, and genetic and non-genetic animal models of autism. Overall, data obtained from human and animal models point to a generalized reduction in the size and number, as well as an alteration of the morphology of dendrites; and an increase in spine densities with immature morphology, indicating a general spine immaturity state in autism. Additional human studies on dendrite and spine number and morphology in postmortem tissue are needed to understand the properties of these structures in the cerebral cortex of patients with autism. © 2016 Wiley Periodicals, Inc. Develop Neurobiol 77: 419-437, 2017.

Pyramidal Neurons Are Not Generalizable Building Blocks of Cortical Networks

A key challenge in cortical neuroscience is to gain a comprehensive understanding of how pyramidal neuron heterogeneity across different areas and species underlies the functional specialization of individual neurons, networks, and areas. Comparative studies have been important in this endeavor, providing data relevant to the question of which of the many inherent properties of individual pyramidal neurons are necessary and sufficient for species-specific network and areal function. In this mini review, the importance of pyramidal neuron structural properties for signaling are outlined, followed by a summary of our recent work comparing the structural features of mouse (C57/BL6 strain) and rhesus monkey layer 3 (L3) pyramidal neurons in primary visual and frontal association cortices and their implications for neuronal and areal function. Based on these and other published data, L3 pyramidal neurons plausibly might be considered broadly “generalizable” from one area to another in the mouse neocortex due to their many similarities, but major differences in the properties of these neurons in diverse areas in the rhesus monkey neocortex rules this out in the primate. Further, fundamental differences in the dendritic topology of mouse and rhesus monkey pyramidal neurons highlight the implausibility of straightforward scaling and/or extrapolation from mouse to primate neurons and cortical networks.

Unique membrane properties and enhanced signal processing in human neocortical neurons

The advanced cognitive capabilities of the human brain are often attributed to our recently evolved neocortex. However, it is not known whether the basic building blocks of the human neocortex, the pyramidal neurons, possess unique biophysical properties that might impact on cortical computations. Here we show that layer 2/3 pyramidal neurons from human temporal cortex (HL2/3 PCs) have a specific membrane capacitance (C_m) of ~0.5 µF/cm², half of the commonly accepted 'universal' value (~1 µF/cm²) for biological membranes. This finding was predicted by fitting in vitro voltage transients to theoretical transients then validated by direct measurement of C_m in nucleated patch experiments. Models of 3D reconstructed HL2/3 PCs demonstrated that such low C_m value significantly enhances both synaptic charge-transfer from dendrites to soma and spike propagation along the axon. This is the first demonstration that human cortical neurons have distinctive membrane properties, suggesting important implications for signal processing in human neocortex.

DOI:http://dx.doi.org/10.7554/eLife.16553.001

The influence of postsynaptic structure on missing quanta at the Drosophila neuromuscular junction

Background

Synaptic transmission requires both pre- and post-synaptic elements for neural communication. The postsynaptic structure contributes to the ability of synaptic currents to induce voltage changes in postsynaptic cells. At the Drosophila neuromuscular junction (NMJ), the postsynaptic structure, known as the subsynaptic reticulum (SSR), consists of elaborate membrane folds that link the synaptic contacts to the muscle, but its role in synaptic physiology is poorly understood.

Results

In this study, we investigate the role of the SSR with simultaneous intra- and extra-cellular recordings that allow us to identify the origin of spontaneously occurring synaptic events. We compare data from Type 1b and 1s synaptic boutons, which have naturally occurring variations of the SSR, as well as from genetic mutants that up or down-regulate SSR complexity. We observed that some synaptic currents do not result in postsynaptic voltage changes, events we called ‘missing quanta’. The frequency of missing quanta is positively correlated with SSR complexity in both natural and genetically-induced variants. Rise-time and amplitude data suggest that passive membrane properties contribute to the observed differences in synaptic effectiveness.

Conclusion

We conclude that electrotonic decay within the postsynaptic structure contributes to the phenomenon of missing quanta. Further studies directed at understanding the role of the SSR in synaptic transmission and the potential for regulating ‘missing quanta’ will yield important information about synaptic transmission at the Drosophila NMJ.

Physical connections between different SSVEP neural networks

This work investigates the mechanism of the Steady-State Visual Evoked Potential (SSVEP). One theory suggests that different SSVEP neural networks exist whose strongest response are located in different frequency bands. This theory is based on the fact that there are similar SSVEP frequency-amplitude response curves in these bands. Previous studies that employed simultaneous stimuli of different frequencies illustrated that the distribution of these networks were similar, but did not discuss the physical connection between them. By comparing the SSVEP power and distribution under a single-eye stimulus and a simultaneous, dual-eye stimulus, this work demonstrates that the distributions of different SSVEP neural networks are similar to each other and that there should be physical overlapping between them. According to the band-pass filter theory in a signal transferring channel, which we propose in this work for the first time, there are different amounts of neurons that are involved under repetitive stimuli of different frequencies and that the response intensity of each neuron is similar to each other so that the total response (i.e., the SSVEP) that is observed from the scalp is different.

Foundational dendritic processing that is independent of the cell type-specific structure in model primary neurons

It has long been known that primary neurons in the brain and spinal cord exhibit very distinctive dendritic structures. However, it remains unclear whether dendritic processing for signal propagation and channel activation over dendrites is a function of the cell type-specific dendritic structure. By applying an extended analysis of signal attenuation for the physiological distributions of synaptic inputs and active channels on dendritic branches, we first demonstrate that regardless of their specific structure, all anatomically reconstructed models of primary neurons display a similar pattern of directional signal attenuation and locational channel activation over their dendrites. Then, using a novel modeling approach that allows direct comparison of the anatomically reconstructed primary neurons with their reduced models that exclusively retain anatomical dendritic signaling without being associated with structural specificity, we show that the reduced model can accurately predict dendritic excitability of the anatomical model in both passive and active mode. These results indicate that the directional signaling, locational excitability and their relationship are foundational features of dendritic processing that are independent of the cell type-specific structure across primary neurons.

A Sparse Reformulation of the Green's Function Formalism Allows Efficient Simulations of Morphological Neuron Models

We prove that when a class of partial differential equations, generalized from the cable equation, is defined on tree graphs and the inputs are restricted to a spatially discrete, well chosen set of points, the Green's function (GF) formalism can be rewritten to scale as O(n) with the number n of inputs locations, contrary to the previously reported O(n(2)) scaling. We show that the linear scaling can be combined with an expansion of the remaining kernels as sums of exponentials to allow efficient simulations of equations from the aforementioned class. We furthermore validate this simulation paradigm on models of nerve cells and explore its relation with more traditional finite difference approaches. Situations in which a gain in computational performance is expected are discussed.

Modeling the effect of dendritic input location on MEG and EEG source dipoles

The cerebral sources of magneto- and electroencephalography (MEG, EEG) signals can be represented by current dipoles. We used computational modeling of realistically shaped passive-membrane dendritic trees of pyramidal cells from the human cerebral cortex to examine how the spatial distribution of the synaptic inputs affects the current dipole. The magnitude of the total dipole moment vector was found to be proportional to the vertical location of the synaptic input. The dipole moment had opposite directions for inputs above and below a reversal point located near the soma. Inclusion of shunting-type inhibition either suppressed or enhanced the current dipole, depending on whether the excitatory and inhibitory synapses were on the same or opposite side of the reversal point. Relating the properties of the macroscopic current dipoles to dendritic current distributions can help to provide means for interpreting MEG and EEG data in terms of synaptic connection patterns within cortical areas.

Anatomy and physiology of the thick-tufted layer 5 pyramidal neuron

The thick-tufted layer 5 (TTL5) pyramidal neuron is one of the most extensively studied neuron types in the mammalian neocortex and has become a benchmark for understanding information processing in excitatory neurons. By virtue of having the widest local axonal and dendritic arborization, the TTL5 neuron encompasses various local neocortical neurons and thereby defines the dimensions of neocortical microcircuitry. The TTL5 neuron integrates input across all neocortical layers and is the principal output pathway funneling information flow to subcortical structures. Several studies over the past decades have investigated the anatomy, physiology, synaptology, and pathophysiology of the TTL5 neuron. This review summarizes key discoveries and identifies potential avenues of research to facilitate an integrated and unifying understanding on the role of a central neuron in the neocortex.

Neural precursor lineages specify distinct neocortical pyramidal neuron types

Several neural precursor populations contemporaneously generate neurons in the developing neocortex. Specifically, radial glial stem cells of the dorsal telencephalon divide asymmetrically to produce excitatory neurons, but also indirectly to produce neurons via three types of intermediate progenitor cells. Why so many precursor types are needed to produce neurons has not been established; whether different intermediate progenitor cells merely expand the output of radial glia or instead generate distinct types of neurons is unknown. Here we use a novel genetic fate mapping technique to simultaneously track multiple precursor streams in the developing mouse brain and show that layer 2 and 3 pyramidal neurons exhibit distinctive electrophysiological and structural properties depending upon their precursor cell type of origin. These data indicate that individual precursor subclasses synchronously produce functionally different neurons, even within the same lamina, and identify a primary mechanism leading to cortical neuronal diversity.

What is the most realistic single-compartment model of spike initiation?

A large variety of neuron models are used in theoretical and computational neuroscience, and among these, single-compartment models are a popular kind. These models do not explicitly include the dendrites or the axon, and range from the Hodgkin-Huxley (HH) model to various flavors of integrate-and-fire (IF) models. The main classes of models differ in the way spikes are initiated. Which one is the most realistic? Starting with some general epistemological considerations, I show that the notion of realism comes in two dimensions: empirical content (the sort of predictions that a model can produce) and empirical accuracy (whether these predictions are correct). I then examine the realism of the main classes of single-compartment models along these two dimensions, in light of recent experimental evidence.