Impact of dendritic size and dendritic topology on burst firing in pyramidal cells

Branching morphology determines signal propagation dynamics in neurons

Computational modeling of signal propagation in neurons is critical to our understanding of basic principles underlying brain organization and activity. Exploring these models is used to address basic neuroscience questions as well as to gain insights for clinical applications. The seminal Hodgkin Huxley model is a common theoretical framework to study brain activity. It was mainly used to investigate the electrochemical and physical properties of neurons. The influence of neuronal structure on activity patterns was explored, however, the rich dynamics observed in neurons with different morphologies is not yet fully understood. Here, we study signal propagation in fundamental building blocks of neuronal branching trees, unbranched and branched axons. We show how these simple axonal elements can code information on spike trains, and how asymmetric responses can emerge in axonal branching points. This asymmetric phenomenon has been observed experimentally but until now lacked theoretical characterization. Together, our results suggest that axonal morphological parameters are instrumental in activity modulation and information coding. The insights gained from this work lay the ground for better understanding the interplay between function and form in real-world complex systems. It may also supply theoretical basis for the development of novel therapeutic approaches to damaged nervous systems.

Basal tree complexity shapes functional pathways in the prefrontal cortex

While the morphology of basal dendritic trees in cortical pyramidal neurons varies, the functional implications of this diversity are just starting to emerge. In layer 5 pyramidal neurons of the prefrontal cortex, for example, increased basal tree complexity determines the recruitment of these neurons into functional circuits. Here, we use a modeling approach to investigate whether and how the morphology of the basal tree mediates the functional output of neurons. We implemented 57 basal tree morphologies of layer 5 prefrontal pyramidal neurons of the rat and identified morphological types that were characterized by different response features, forming distinct functional types. These types were robust to a wide range of manipulations (distribution of active ionic mechanisms, NMDA conductance, somatic and apical tree morphology, or the number of activated synapses) and supported different temporal coding schemes at both the single neuron and the microcircuit level. We predict that the basal tree morphological diversity among neurons of the same class mediates their segregation into distinct functional pathways. Extension of our approach/findings to other cortical areas and/or layers or under pathological conditions may provide a generalized role of the basal trees for neuronal function.NEW & NOTEWORTHY Our results suggest that the segregation of neurons to different functional types based on their basal tree morphology is in large part independent of the distribution of active ionic mechanisms, NMDA conductance, somatic and apical tree morphology, and the number of activated synapses; different functional types support distinct temporal coding schemes. This can be exploited to create networks with diverse coding characteristics, thus contributing to the functional heterogeneity within the same layer and area.

Universal features of dendrites through centripetal branch ordering

Dendrites form predominantly binary trees that are exquisitely embedded in the networks of the brain. While neuronal computation is known to depend on the morphology of dendrites, their underlying topological blueprint remains unknown. Here, we used a centripetal branch ordering scheme originally developed to describe river networks—the Horton-Strahler order (SO)–to examine hierarchical relationships of branching statistics in reconstructed and model dendritic trees. We report on a number of universal topological relationships with SO that are true for all binary trees and distinguish those from SO-sorted metric measures that appear to be cell type-specific. The latter are therefore potential new candidates for categorising dendritic tree structures. Interestingly, we find a faithful correlation of branch diameters with centripetal branch orders, indicating a possible functional importance of SO for dendritic morphology and growth. Also, simulated local voltage responses to synaptic inputs are strongly correlated with SO. In summary, our study identifies important SO-dependent measures in dendritic morphology that are relevant for neural function while at the same time it describes other relationships that are universal for all dendrites.

Similarly to river beds, dendritic trees of nerve cells form elaborate networks that branch out to cover extensive areas. In the 1940s, ecologist Robert E. Horton developed an ordering system for branches in river networks that was refined in the 1950s by geoscientist Arthur N. Strahler, the Horton-Strahler order (SO). Branches at the tips start with order 1 and increase their order in a systematic way when encountering new branches on the way to the root. SO relationships have recently become popular for quantifying dendritic morphologies. Various branching statistics can be studied as a function of SO. Here we describe that topological measures such as the number of branches, the branch bifurcation ratio and the size of subtrees exhibit stereotypical relations with SO in dendritic trees independently of cell type, mirroring universal features of binary trees. Other functionally more relevant features such as mean branch lengths, local diameters and simulated voltage responses to synaptic inputs directly correlate with SO in a cell type-specific manner, indicating the importance of SO for understanding dendrite growth as well as neural computation.

Is realistic neuronal modeling realistic?

Scientific models are abstractions that aim to explain natural phenomena. A successful model shows how a complex phenomenon arises from relatively simple principles while preserving major physical or biological rules and predicting novel experiments. A model should not be a facsimile of reality; it is an aid for understanding it. Contrary to this basic premise, with the 21st century has come a surge in computational efforts to model biological processes in great detail. Here we discuss the oxymoronic, realistic modeling of single neurons. This rapidly advancing field is driven by the discovery that some neurons don't merely sum their inputs and fire if the sum exceeds some threshold. Thus researchers have asked what are the computational abilities of single neurons and attempted to give answers using realistic models. We briefly review the state of the art of compartmental modeling highlighting recent progress and intrinsic flaws. We then attempt to address two fundamental questions. Practically, can we realistically model single neurons? Philosophically, should we realistically model single neurons? We use layer 5 neocortical pyramidal neurons as a test case to examine these issues. We subject three publically available models of layer 5 pyramidal neurons to three simple computational challenges. Based on their performance and a partial survey of published models, we conclude that current compartmental models are ad hoc, unrealistic models functioning poorly once they are stretched beyond the specific problems for which they were designed. We then attempt to plot possible paths for generating realistic single neuron models.

Hydrocephalus compacted cortex and hippocampus and altered their output neurons in association with spatial learning and memory deficits in rats

Hydrocephalus is a common neurological disorder in children characterized by abnormal dilation of cerebral ventricles as a result of the impairment of cerebrospinal fluid flow or absorption. Clinical presentation of hydrocephalus varies with chronicity and often shows cognitive dysfunction. Here we used a kaolin-induction method in rats and studied the effects of hydrocephalus on cerebral cortex and hippocampus, the two regions highly related to cognition. Hydrocephalus impaired rats' performance in Morris water maze task. Serial three-dimensional reconstruction from sections of the whole brain freshly froze in situ with skull shows that the volumes of both structures were reduced. Morphologically, pyramidal neurons of the somatosensory cortex and hippocampus appear to be distorted. Intracellular dye injection and subsequent three-dimensional reconstruction and analyses revealed that the dendritic arbors of layer III and V cortical pyramid neurons were reduced. The total dendritic length of CA1, but not CA3, pyramidal neurons was also reduced. Dendritic spine densities on both cortical and hippocampal pyramidal neurons were decreased, consistent with our concomitant findings that the expressions of both synaptophysin and postsynaptic density protein 95 were reduced. These cortical and hippocampal changes suggest reductions of excitatory connectivity, which could underlie the learning and memory deficits in hydrocephalus.

Effects of Morphology Constraint on Electrophysiological Properties of Cortical Neurons

There is growing interest in engineering nerve cells in vitro to control architecture and connectivity of cultured neuronal networks or to build neuronal networks with predictable computational function. Pattern technologies, such as micro-contact printing, have been developed to design ordered neuronal networks. However, electrophysiological characteristics of the single patterned neuron haven't been reported. Here, micro-contact printing, using polyolefine polymer (POP) stamps with high resolution, was employed to grow cortical neurons in a designed structure. The results demonstrated that the morphology of patterned neurons was well constrained, and the number of dendrites was decreased to be about 2. Our electrophysiological results showed that alterations of dendritic morphology affected firing patterns of neurons and neural excitability. When stimulated by current, though both patterned and un-patterned neurons presented regular spiking, the dynamics and strength of the response were different. The un-patterned neurons exhibited a monotonically increasing firing frequency in response to injected current, while the patterned neurons first exhibited frequency increase and then a slow decrease. Our findings indicate that the decrease in dendritic complexity of cortical neurons will influence their electrophysiological characteristics and alter their information processing activity, which could be considered when designing neuronal circuitries.

Specific cytoarchitectureal changes in hippocampal subareas in daDREAM mice

Background

Transcriptional repressor DREAM (downstream regulatory element antagonist modulator) is a Ca²⁺-binding protein that regulates Ca²⁺ homeostasis through gene regulation and protein-protein interactions. It has been shown that a dominant active form (daDREAM) is implicated in learning-related synaptic plasticity such as LTP and LTD in the hippocampus. Neuronal spines are reported to play important roles in plasticity and memory. However, the possible role of DREAM in spine plasticity has not been reported.

Results

Here we show that potentiating DREAM activity, by overexpressing daDREAM, reduced dendritic basal arborization and spine density in CA1 pyramidal neurons and increased spine density in dendrites in dentate gyrus granule cells. These microanatomical changes are accompanied by significant modifications in the expression of specific genes encoding the cytoskeletal proteins Arc, Formin 1 and Gelsolin in daDREAM hippocampus.

Conclusions

Our results strongly suggest that DREAM plays an important role in structural plasticity in the hippocampus.

Electronic supplementary material

The online version of this article (doi:10.1186/s13041-016-0204-8) contains supplementary material, which is available to authorized users.

A general homeostatic principle following lesion induced dendritic remodeling

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.

Neuron Morphology Influences Axon Initial Segment Plasticity

In most vertebrate neurons, action potentials are initiated in the axon initial segment (AIS), a specialized region of the axon containing a high density of voltage-gated sodium and potassium channels.

In most vertebrate neurons, action potentials are initiated in the axon initial segment (AIS), a specialized region of the axon containing a high density of voltage-gated sodium and potassium channels. It has recently been proposed that neurons use plasticity of AIS length and/or location to regulate their intrinsic excitability. Here we quantify the impact of neuron morphology on AIS plasticity using computational models of simplified and realistic somatodendritic morphologies. In small neurons (e.g., dentate granule neurons), excitability was highest when the AIS was of intermediate length and located adjacent to the soma. Conversely, neurons having larger dendritic trees (e.g., pyramidal neurons) were most excitable when the AIS was longer and/or located away from the soma. For any given somatodendritic morphology, increasing dendritic membrane capacitance and/or conductance favored a longer and more distally located AIS. Overall, changes to AIS length, with corresponding changes in total sodium conductance, were far more effective in regulating neuron excitability than were changes in AIS location, while dendritic capacitance had a larger impact on AIS performance than did dendritic conductance. The somatodendritic influence on AIS performance reflects modest soma-to-AIS voltage attenuation combined with neuron size-dependent changes in AIS input resistance, effective membrane time constant, and isolation from somatodendritic capacitance. We conclude that the impact of AIS plasticity on neuron excitability will depend largely on somatodendritic morphology, and that, in some neurons, a shorter or more distally located AIS may promote, rather than limit, action potential generation.

Laminar Differences in Dendritic Structure of Pyramidal Neurons in the Juvenile Rat Somatosensory Cortex

Pyramidal cell structure varies between different cortical areas and species, indicating that the cortical circuits that these cells participate in are likely to be characterized by different functional capabilities. Structural differences between cortical layers have been traditionally reported using either the Golgi method or intracellular labeling, but the structure of pyramidal cells has not previously been systematically analyzed across all cortical layers at a particular age. In the present study, we investigated the dendritic architecture of complete basal arbors of pyramidal neurons in layers II, III, IV, Va, Vb, and VI of the hindlimb somatosensory cortical region of postnatal day 14 rats. We found that the characteristics of basal dendritic morphologies are statistically different in each cortical layer. The variations in size and branching pattern that exist between pyramidal cells of different cortical layers probably reflect the particular functional properties that are characteristic of the cortical circuit in which they participate. This new set of complete basal dendritic arbors of 3D-reconstructed pyramidal cell morphologies across each cortical layer will provide new insights into interlaminar information processing in the cerebral cortex.

Targeted pruning of a neuron's dendritic tree via femtosecond laser dendrotomy

Neurons are classified according to action potential firing in response to current injection. While such firing patterns are shaped by the composition and distribution of ion channels, modelling studies suggest that the geometry of dendritic branches also influences temporal firing patterns. Verifying this link is crucial to understanding how neurons transform their inputs to output but has so far been technically challenging. Here, we investigate branching-dependent firing by pruning the dendritic tree of pyramidal neurons. We use a focused ultrafast laser to achieve highly localized and minimally invasive cutting of dendrites, thus keeping the rest of the dendritic tree intact and the neuron functional. We verify successful dendrotomy via two-photon uncaging of neurotransmitters before and after dendrotomy at sites around the cut region and via biocytin staining. Our results show that significantly altering the dendritic arborisation, such as by severing the apical trunk, enhances excitability in layer V cortical pyramidal neurons as predicted by simulations. This method may be applied to the analysis of specific relationships between dendritic structure and neuronal function. The capacity to dynamically manipulate dendritic topology or isolate inputs from various dendritic domains can provide a fresh perspective on the roles they play in shaping neuronal output.

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.

The influence of stress and gonadal hormones on neuronal structure and function

This article is part of a Special Issue "SBN 2014". The brain is highly plastic, allowing us to adapt and respond to environmental and physiological challenges and experiences. In this review, we discuss the relationships among alterations in dendritic arborization, spine morphology, and behavior due to stress exposure, endogenous hormone fluctuation, or exogenous hormonal manipulation. Very few studies investigate structure-function associations directly in the same cohort of animals, and there are notable inconsistencies in evidence of structure-function relationships in the prefrontal cortex and hippocampus. Moreover, little work has been done to probe the causal relationship between dendritic morphology and neuronal excitability, leaving only speculation about the adaptive versus maladaptive nature of experience-dependent dendritic remodeling. We propose that future studies combine electrophysiology with a circuit-level approach to better understand how dendritic structure contributes to neuronal functional properties and behavioral outcomes.

Development of dendritic form and function

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

Modeling spontaneous activity across an excitable epithelium: Support for a coordination scenario of early neural evolution

Internal coordination models hold that early nervous systems evolved in the first place to coordinate internal activity at a multicellular level, most notably the use of multicellular contractility as an effector for motility. A recent example of such a model, the skin brain thesis, suggests that excitable epithelia using chemical signaling are a potential candidate as a nervous system precursor. We developed a computational model and a measure for whole body coordination to investigate the coordinative properties of such excitable epithelia. Using this measure we show that excitable epithelia can spontaneously exhibit body-scale patterns of activation. Relevant factors determining the extent of patterning are the noise level for exocytosis, relative body dimensions, and body size. In smaller bodies whole-body coordination emerges from cellular excitability and bidirectional excitatory transmission alone. Our results show that basic internal coordination as proposed by the skin brain thesis could have arisen in this potential nervous system precursor, supporting that this configuration may have played a role as a proto-neural system and requires further investigation.

A simple transfer function for nonlinear dendritic integration

Relatively recent advances in patch clamp recordings and iontophoresis have enabled unprecedented study of neuronal post-synaptic integration ("dendritic integration"). Findings support a separate layer of integration in the dendritic branches before potentials reach the cell's soma. While integration between branches obeys previous linear assumptions, proximal inputs within a branch produce threshold nonlinearity, which some authors have likened to the sigmoid function. Here we show the implausibility of a sigmoidal relation and present a more realistic transfer function in both an elegant artificial form and a biophysically derived form that further considers input locations along the dendritic arbor. As the distance between input locations determines their ability to produce nonlinear interactions, models incorporating dendritic topology are essential to understanding the computational power afforded by these early stages of integration. We use the biophysical transfer function to emulate empirical data using biophysical parameters and describe the conditions under which the artificial and biophysically derived forms are equivalent.

Dendritic and Axonal Architecture of Individual Pyramidal Neurons across Layers of Adult Human Neocortex

The size and shape of dendrites and axons are strong determinants of neuronal information processing. Our knowledge on neuronal structure and function is primarily based on brains of laboratory animals. Whether it translates to human is not known since quantitative data on "full" human neuronal morphologies are lacking. Here, we obtained human brain tissue during resection surgery and reconstructed basal and apical dendrites and axons of individual neurons across all cortical layers in temporal cortex (Brodmann area 21). Importantly, morphologies did not correlate to etiology, disease severity, or disease duration. Next, we show that human L(ayer) 2 and L3 pyramidal neurons have 3-fold larger dendritic length and increased branch complexity with longer segments compared with temporal cortex neurons from macaque and mouse. Unsupervised cluster analysis classified 88% of human L2 and L3 neurons into human-specific clusters distinct from mouse and macaque neurons. Computational modeling of passive electrical properties to assess the functional impact of large dendrites indicates stronger signal attenuation of electrical inputs compared with mouse. We thus provide a quantitative analysis of "full" human neuron morphologies and present direct evidence that human neurons are not "scaled-up" versions of rodent or macaque neurons, but have unique structural and functional properties.

Altered sensory processing and dendritic remodeling in hyperexcitable visual cortical networks

Epilepsy is characterized by impaired circuit function and a propensity for spontaneous seizures, but how plastic rearrangements within the epileptic focus trigger cortical dysfunction and hyperexcitability is only partly understood. Here we have examined alterations in sensory processing and the underlying biochemical and neuroanatomical changes in tetanus neurotoxin (TeNT)-induced focal epilepsy in mouse visual cortex. We documented persistent epileptiform electrographic discharges and upregulation of GABAergic markers at the completion of TeNT effects. We also found a significant remodeling of the dendritic arbors of pyramidal neurons, with increased dendritic length and branching, and overall reduction in spine density but significant preservation of mushroom, mature spines. Functionally, spontaneous neuronal discharge was increased, visual responses were less reliable, and electrophysiological and behavioural visual acuity was consistently impaired in TeNT-injected mice. These data demonstrate robust, long-term remodeling of both inhibitory and excitatory circuitry associated with specific disturbances of network function in neocortical epilepsy.

Analogous synaptic plasticity profiles emerge from disparate channel combinations

An open question within the Bienenstock-Cooper-Munro theory for synaptic modification concerns the specific mechanism that is responsible for regulating the sliding modification threshold (SMT). In this conductance-based modeling study on hippocampal pyramidal neurons, we quantitatively assessed the impact of seven ion channels (R- and T-type calcium, fast sodium, delayed rectifier, A-type, and small-conductance calcium-activated (SK) potassium and HCN) and two receptors (AMPAR and NMDAR) on a calcium-dependent Bienenstock-Cooper-Munro-like plasticity rule. Our analysis with R- and T-type calcium channels revealed that differences in their activation-inactivation profiles resulted in differential impacts on how they altered the SMT. Further, we found that the impact of SK channels on the SMT critically depended on the voltage dependence and kinetics of the calcium sources with which they interacted. Next, we considered interactions among all the seven channels and the two receptors through global sensitivity analysis on 11 model parameters. We constructed 20,000 models through uniform randomization of these parameters and found 360 valid models based on experimental constraints on their plasticity profiles. Analyzing these 360 models, we found that similar plasticity profiles could emerge with several nonunique parametric combinations and that parameters exhibited weak pairwise correlations. Finally, we used seven sets of virtual knock-outs on these 360 models and found that the impact of different channels on the SMT was variable and differential. These results suggest that there are several nonunique routes to regulate the SMT, and call for a systematic analysis of the variability and state dependence of the mechanisms underlying metaplasticity during behavior and pathology.

Functional consequences of age-related morphologic changes to pyramidal neurons of the rhesus monkey prefrontal cortex

Layer 3 (L3) pyramidal neurons in the lateral prefrontal cortex (LPFC) of rhesus monkeys exhibit dendritic regression, spine loss and increased action potential (AP) firing rates during normal aging. The relationship between these structural and functional alterations, if any, is unknown. To address this issue, morphological and electrophysiological properties of L3 LPFC pyramidal neurons from young and aged rhesus monkeys were characterized using in vitro whole-cell patch-clamp recordings and high-resolution digital reconstruction of neurons. Consistent with our previous studies, aged neurons exhibited significantly reduced dendritic arbor length and spine density, as well as increased input resistance and firing rates. Computational models using the digital reconstructions with Hodgkin-Huxley and AMPA channels allowed us to assess relationships between demonstrated age-related changes and to predict physiological changes that have not yet been tested empirically. For example, the models predict that in both backpropagating APs and excitatory postsynaptic currents (EPSCs), attenuation is lower in aged versus young neurons. Importantly, when identical densities of passive parameters and voltage- and calcium-gated conductances were used in young and aged model neurons, neither input resistance nor firing rates differed between the two age groups. Tuning passive parameters for each model predicted significantly higher membrane resistance (R m ) in aged versus young neurons. This R m increase alone did not account for increased firing rates in aged models, but coupling these R m values with subtle differences in morphology and membrane capacitance did. The predicted differences in passive parameters (or parameters with similar effects) are mathematically plausible, but must be tested empirically.

Reprogramming of HUVECs into induced pluripotent stem cells (HiPSCs), generation and characterization of HiPSC-derived neurons and astrocytes

Neurodegenerative diseases are characterized by chronic and progressive structural or functional loss of neurons. Limitations related to the animal models of these human diseases have impeded the development of effective drugs. This emphasizes the need to establish disease models using human-derived cells. The discovery of induced pluripotent stem cell (iPSC) technology has provided novel opportunities in disease modeling, drug development, screening, and the potential for “patient-matched” cellular therapies in neurodegenerative diseases. In this study, with the objective of establishing reliable tools to study neurodegenerative diseases, we reprogrammed human umbilical vein endothelial cells (HUVECs) into iPSCs (HiPSCs). Using a novel and direct approach, HiPSCs were differentiated into cells of central nervous system (CNS) lineage, including neuronal, astrocyte and glial cells, with high efficiency. HiPSCs expressed embryonic genes such as nanog, sox2 and Oct-3/4, and formed embryoid bodies that expressed markers of the 3 germ layers. Expression of endothelial-specific genes was not detected in HiPSCs at RNA or protein levels. HiPSC-derived neurons possess similar morphology but significantly longer neurites compared to primary human fetal neurons. These stem cell-derived neurons are susceptible to inflammatory cell-mediated neuronal injury. HiPSC-derived neurons express various amino acids that are important for normal function in the CNS. They have functional receptors for a variety of neurotransmitters such as glutamate and acetylcholine. HiPSC-derived astrocytes respond to ATP and acetylcholine by elevating cytosolic Ca²⁺ concentrations. In summary, this study presents a novel technique to generate differentiated and functional HiPSC-derived neurons and astrocytes. These cells are appropriate tools for studying the development of the nervous system, the pathophysiology of various neurodegenerative diseases and the development of potential drugs for their treatments.

Dendritic atrophy constricts functional maps in resonance and impedance properties of hippocampal model neurons

A gradient in the density of hyperpolarization-activated cyclic-nucleotide gated (HCN) channels is necessary for the emergence of several functional maps within hippocampal pyramidal neurons. Here, we systematically analyzed the impact of dendritic atrophy on nine such functional maps, related to input resistance and local/transfer impedance properties, using conductance-based models of hippocampal pyramidal neurons. We introduced progressive dendritic atrophy in a CA1 pyramidal neuron reconstruction through a pruning algorithm, measured all functional maps in each pruned reconstruction, and arrived at functional forms for the dependence of underlying measurements on dendritic length. We found that, across frequencies, atrophied neurons responded with higher efficiency to incoming inputs, and the transfer of signals across the dendritic tree was more effective in an atrophied reconstruction. Importantly, despite the presence of identical HCN-channel density gradients, spatial gradients in input resistance, local/transfer resonance frequencies and impedance profiles were significantly constricted in reconstructions with dendritic atrophy, where these physiological measurements across dendritic locations converged to similar values. These results revealed that, in atrophied dendritic structures, the presence of an ion channel density gradient alone was insufficient to sustain homologous functional maps along the same neuronal topograph. We assessed the biophysical basis for these conclusions and found that this atrophy-induced constriction of functional maps was mediated by an enhanced spatial spread of the influence of an HCN-channel cluster in atrophied trees. These results demonstrated that the influence fields of ion channel conductances need to be localized for channel gradients to express themselves as homologous functional maps, suggesting that ion channel gradients are necessary but not sufficient for the emergence of functional maps within single neurons.

High-conductance states and A-type K+ channels are potential regulators of the conductance-current balance triggered by HCN channels

An increase in the hyperpolarization-activated cyclic nucleotide-gated (HCN) channel conductance reduces input resistance, whereas the consequent increase in the inward h current depolarizes the membrane. This results in a delicate and unique conductance-current balance triggered by the expression of HCN channels. In this study, we employ experimentally constrained, morphologically realistic, conductance-based models of hippocampal neurons to explore certain aspects of this conductance-current balance. First, we found that the inclusion of an experimentally determined gradient in A-type K+ conductance, but not in M-type K+ conductance, tilts the HCN conductance-current balance heavily in favor of conductance, thereby exerting an overall restorative influence on neural excitability. Next, motivated by the well-established modulation of neuronal excitability by synaptically driven high-conductance states observed under in vivo conditions, we inserted thousands of excitatory and inhibitory synapses with different somatodendritic distributions. We measured the efficacy of HCN channels, independently and in conjunction with other channels, in altering resting membrane potential (RMP) and input resistance ( Rin) when the neuron received randomized or rhythmic synaptic bombardments through variable numbers of synaptic inputs. We found that the impact of HCN channels on average RMP, Rin, firing frequency, and peak-to-peak voltage response was severely weakened under high-conductance states, with the impinging synaptic drive playing a dominant role in regulating these measurements. Our results suggest that the debate on the role of HCN channels in altering excitability should encompass physiological and pathophysiological neuronal states under in vivo conditions and the spatiotemporal interactions of HCN channels with other channels.

Trigeminal intersubnuclear neurons: morphometry and input-dependent structural plasticity in adult rats

Intersubnuclear neurons in the caudal division of the spinal trigeminal nucleus that project to the principal nucleus (Pr5) play an active role in shaping the receptive fields of other neurons, at different levels in the ascending sensory system that processes information originating from the vibrissae. By using retrograde labeling and digital reconstruction, we investigated the morphometry and topology of the dendritic trees of these neurons and the changes induced by long-term experience-dependent plasticity in adult male rats. Primary afferent input was either eliminated by transection of the right infraorbital nerve (IoN), or selectively altered by repeated whisker clipping on the right side. These neurons do not display asymmetries between sides in basic metric and topologic parameters (global number of trees, nodes, spines, or dendritic ends), although neurons on the left tend to have longer terminal segments. Ipsilaterally, both deafferentation (IoN transection) and deprivation (whisker trimming) reduced the density of spines, and the former also caused a global increase in total dendritic length and a relative increase in more complex arbors. Contralaterally, deafferentation reduced more complex dendritic trees, and caused a moderate decline in dendritic length and spatial reach, and a loss of spines in number and density. Deprivation caused a similar, but more profound, effect on spines. Our findings provide original quantitative descriptions of a scarcely known cell population, and show that denervation- or deprivation-derived plasticity is expressed not only by neurons at higher levels of the sensory pathways, but also by neurons in key subcortical circuits for sensory processing.

Dendritic morphology predicts pattern recognition performance in multi-compartmental model neurons with and without active conductances

In this paper we examine how a neuron’s dendritic morphology can affect its pattern recognition performance. We use two different algorithms to systematically explore the space of dendritic morphologies: an algorithm that generates all possible dendritic trees with 22 terminal points, and one that creates representative samples of trees with 128 terminal points. Based on these trees, we construct multi-compartmental models. To assess the performance of the resulting neuronal models, we quantify their ability to discriminate learnt and novel input patterns. We find that the dendritic morphology does have a considerable effect on pattern recognition performance and that the neuronal performance is inversely correlated with the mean depth of the dendritic tree. The results also reveal that the asymmetry index of the dendritic tree does not correlate with the performance for the full range of tree morphologies. The performance of neurons with dendritic tapering is best predicted by the mean and variance of the electrotonic distance of their synapses to the soma. All relationships found for passive neuron models also hold, even in more accentuated form, for neurons with active membranes.

Linking macroscopic with microscopic neuroanatomy using synthetic neuronal populations

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.

Computational models of neurons and neural networks provide a valuable avenue to test our understanding of brain regions and to make predictions to guide future experimentation. Each neuron has a unique dendritic tree, features of which can vary depending on the location of the neuron within the particular brain region. In this study, we generated a complete population of dendritic trees for the most numerous type of neuron in the hippocampus, the dentate gyrus granule cell, using a realistic three-dimensional structural context to drive the generation process. Morphological properties can now be studied at the level of complete neuronal populations, and this work provides a foundation to build upon in the construction of large-scale, data-driven neuroanatomical and network models.

A simulation study on the effects of dendritic morphology on layer V prefrontal pyramidal cell firing behavior

Pyramidal cells, the most abundant neurons in neocortex, exhibit significant structural variability across different brain areas and layers in different species. Moreover, in response to a somatic step current, these cells display a range of firing behaviors, the most common being (1) repetitive action potentials (Regular Spiking-RS), and (2) an initial cluster of 2-5 action potentials with short interspike interval (ISIs) followed by single spikes (Intrinsic Bursting-IB). A correlation between firing behavior and dendritic morphology has recently been reported. In this work we use computational modeling to investigate quantitatively the effects of the basal dendritic tree morphology on the firing behavior of 112 three-dimensional reconstructions of layer V PFC rat pyramidal cells. Particularly, we focus on how different morphological (diameter, total length, volume, and branch number) and passive [Mean Electrotonic Path length (MEP)] features of basal dendritic trees shape somatic firing when the spatial distribution of ionic mechanisms in the basal dendritic trees is uniform or non-uniform. Our results suggest that total length, volume and branch number are the best morphological parameters to discriminate the cells as RS or IB, regardless of the distribution of ionic mechanisms in basal trees. The discriminatory power of total length, volume, and branch number remains high in the presence of different apical dendrites. These results suggest that morphological variations in the basal dendritic trees of layer V pyramidal neurons in the PFC influence their firing patterns in a predictive manner and may in turn influence the information processing capabilities of these neurons.

Asymmetry in signal propagation between the soma and dendrites plays a key role in determining dendritic excitability in motoneurons

It is widely recognized that propagation of electrophysiological signals between the soma and dendrites of neurons differs depending on direction, i.e. it is asymmetric. How this asymmetry influences the activation of voltage-gated dendritic channels, and consequent neuronal behavior, remains unclear. Based on the analysis of asymmetry in several types of motoneurons, we extended our previous methodology for reducing a fully reconstructed motoneuron model to a two-compartment representation that preserved asymmetric signal propagation. The reduced models accurately replicated the dendritic excitability and the dynamics of the anatomical model involving a persistent inward current (PIC) dispersed over the dendrites. The relationship between asymmetric signal propagation and dendritic excitability was investigated using the reduced models while varying the asymmetry in signal propagation between the soma and the dendrite with PIC density constant. We found that increases in signal attenuation from soma to dendrites increased the activation threshold of a PIC (hypo-excitability), whereas increases in signal attenuation from dendrites to soma decreased the activation threshold of a PIC (hyper-excitability). These effects were so strong that reversing the asymmetry in the soma-to-dendrite vs. dendrite-to-soma attenuation, reversed the correlation between PIC threshold and distance of this current source from the soma. We propose the tight relation of the asymmetric signal propagation to the input resistance in the dendrites as a mechanism underlying the influence of the asymmetric signal propagation on the dendritic excitability. All these results emphasize the importance of maintaining the physiological asymmetry in dendritic signaling not only for normal function of the cells but also for biophysically realistic simulations of dendritic excitability.

Antidepressant-like effects of cortical deep brain stimulation coincide with pro-neuroplastic adaptations of serotonin systems

BACKGROUND

Cortical deep brain stimulation (DBS) is a promising therapeutic option for treatment-refractory depression, but its mode of action remains enigmatic. Serotonin (5-HT) systems are engaged indirectly by ventromedial prefrontal cortex (vmPFC) DBS. Resulting neuroplastic changes in 5-HT systems could thus coincide with the long-term therapeutic activity of vmPFC DBS.

METHODS

We tested this hypothesis by evaluating the antidepressant-like activity of vmPFC DBS in the chronic social defeat stress (CSDS) model of depression (n = 8-13 mice/group). Circuit-wide activation induced by vmPFC DBS was mapped with c-Fos immunolabeling. The effects of chronic vmPFC DBS on the physiology and morphology of genetically identified 5-HT cells from the dorsal raphe nucleus (DRN) were examined with whole-cell recording, somatodendritic three-dimensional reconstructions and morphometric analyses of presynaptic boutons along 5-HT axons.

RESULTS

Acute DBS drove c-Fos expression locally in the vmPFC and in several distal monosynaptically connected regions, including the DRN. Chronic DBS reversed CSDS-induced social avoidance, restored the disrupted balance of excitatory/inhibitory inputs onto 5-HT neurons, and reversed 5-HT hypoexcitability observed after CSDS. Furthermore, vmPFC DBS reversed CSDS-induced arborization of 5-HT dendrites in the DRN and increased the size and density of 5-HT presynaptic terminals in the dentate gyrus and vmPFC.

CONCLUSIONS

We validate a new preclinical paradigm to examine cellular mechanisms underlying the antidepressant-like activity of vmPFC DBS and identify dramatic circuit-mediated cellular adaptations that coincide with this treatment. These neuroplastic changes of 5-HT neurons might contribute to the progressive mood improvements reported in patients treated with chronic courses of cortical DBS.

Characterization of the NT2-derived neuronal and astrocytic cell lines as alternative in vitro models for primary human neurons and astrocytes

Primary human fetal neurons and astrocytes (HFNs and HFAs, respectively) provide relevant cell types with which to study in vitro the mechanisms involved in various human neurological diseases, such as multiple sclerosis, Parkinson's disease, and Alzheimer's disease. However, the limited availability of human fetal cells poses a significant problem for the study of these diseases when a human cell model system is required. Thus, generating a readily available alternative cell source with the essential features of human neurons and astrocytes is necessary. The human teratoma-derived NTera2/D1 (NT2) cell line is a promising tool from which both neuronal and glial cells can be generated. Nevertheless, a direct comparison of NT2 neurons and primary HFNs in terms of their morphology physiological and chemical properties is still missing. This study directly compares NT2-derived neurons and primary HFNs using immunocytochemistry, confocal calcium imaging, high-performance liquid chromatography, and high-content analysis techniques. We investigated the morphological similarities and differences, levels of relevant amino acids, and internal calcium fluctuations in response to certain neurotransmitters/stimuli. We also compared NT2-derived astrocytes and HFAs. In most of the parameters tested, both neuronal and astrocytic cell types exhibited similarities to primary human fetal neurons and astrocytes. NT2-derived neurons and astrocytes are reliable in vitro tools and a renewable cell source that can serve as a valid alternative to HFNs/HFAs for mechanistic studies of neurological diseases.

Development of dendritic tonic GABAergic inhibition regulates excitability and plasticity in CA1 pyramidal neurons

Synaptic plasticity rules change during development: while hippocampal synapses can be potentiated by a single action potential pairing protocol in young neurons, mature neurons require burst firing to induce synaptic potentiation. An essential component for spike timing-dependent plasticity is the backpropagating action potential (BAP). BAP along the dendrites can be modulated by morphology and ion channel composition, both of which change during late postnatal development. However, it is unclear whether these dendritic changes can explain the developmental changes in synaptic plasticity induction rules. Here, we show that tonic GABAergic inhibition regulates dendritic action potential backpropagation in adolescent, but not preadolescent, CA1 pyramidal neurons. These developmental changes in tonic inhibition also altered the induction threshold for spike timing-dependent plasticity in adolescent neurons. This GABAergic regulatory effect on backpropagation is restricted to distal regions of apical dendrites (>200 μm) and mediated by α5-containing GABA(A) receptors. Direct dendritic recordings demonstrate α5-mediated tonic GABA(A) currents in adolescent neurons which can modulate BAPs. These developmental modulations in dendritic excitability could not be explained by concurrent changes in dendritic morphology. To explain our data, model simulations propose a distally increasing or localized distal expression of dendritic α5 tonic inhibition in mature neurons. Overall, our results demonstrate that dendritic integration and plasticity in more mature dendrites are significantly altered by tonic α5 inhibition in a dendritic region-specific and developmentally regulated manner.

Coding and decoding with dendrites

Since the discovery of complex, voltage dependent mechanisms in the dendrites of multiple neuron types, great effort has been devoted in search of a direct link between dendritic properties and specific neuronal functions. Over the last few years, new experimental techniques have allowed the visualization and probing of dendritic anatomy, plasticity and integrative schemes with unprecedented detail. This vast amount of information has caused a paradigm shift in the study of memory, one of the most important pursuits in Neuroscience, and calls for the development of novel theories and models that will unify the available data according to some basic principles. Traditional models of memory considered neural cells as the fundamental processing units in the brain. Recent studies however are proposing new theories in which memory is not only formed by modifying the synaptic connections between neurons, but also by modifications of intrinsic and anatomical dendritic properties as well as fine tuning of the wiring diagram. In this review paper we present previous studies along with recent findings from our group that support a key role of dendrites in information processing, including the encoding and decoding of new memories, both at the single cell and the network level.

Continuation-Based Numerical Detection of After-Depolarization and Spike-Adding Thresholds

The changes in neuronal firing pattern are signatures of brain function, and it is of interest to understand how such changes evolve as a function of neuronal biophysical properties. We address this important problem by the analysis and numerical investigation of a class of mechanistic mathematical models. We focus on a hippocampal pyramidal neuron model and study the occurrence of bursting related to the after-depolarization (ADP) that follows a brief current injection. This type of burst is a transient phenomenon that is not amenable to the classical bifurcation analysis done, for example, for periodic bursting oscillators. In this letter, we show how to formulate such transient behavior as a two-point boundary value problem (2PBVP), which can be solved using well-known continuation methods. The 2PBVP is formulated such that the transient response is represented by a finite orbit segment for which onsets of ADP and additional spikes in a burst can be detected as bifurcations during a one-parameter continuation. This in turn provides us with a direct method to approximate the boundaries of regions in a two-parameter plane where certain model behavior of interest occurs. More precisely, we use two-parameter continuation of the detected onset points to identify the boundaries between regions with and without ADP and bursts with different numbers of spikes. Our 2PBVP formulation is a novel approach to parameter sensitivity analysis that can be applied to a wide range of problems.

Preserving axosomatic spiking features despite diverse dendritic morphology

Throughout the nervous system, cells belonging to a certain electrical class (e-class)-sharing high similarity in firing response properties-may nevertheless have widely variable dendritic morphologies. To quantify the effect of this morphological variability on the firing of layer 5 thick-tufted pyramidal cells (TTCs), a detailed conductance-based model was constructed for a three-dimensional reconstructed exemplar TTC. The model exhibited spike initiation in the axon and reproduced the characteristic features of individual spikes, as well as of the firing properties at the soma, as recorded in a population of TTCs in young Wistar rats. When using these model parameters over the population of 28 three-dimensional reconstructed TTCs, both axonal and somatic ion channel densities had to be scaled linearly with the conductance load imposed on each of these compartments. Otherwise, the firing of model cells deviated, sometimes very significantly, from the experimental variability of the TTC e-class. The study provides experimentally testable predictions regarding the coregulation of axosomatic membrane ion channels density for cells with different dendritic conductance load, together with a simple and systematic method for generating reliable conductance-based models for the whole population of modeled neurons belonging to a particular e-class, with variable morphology as found experimentally.

Influence of highly distinctive structural properties on the excitability of pyramidal neurons in monkey visual and prefrontal cortices

Whole-cell patch-clamp recordings and high-resolution 3D morphometric analyses of layer 3 pyramidal neurons in in vitro slices of monkey primary visual cortex (V1) and dorsolateral granular prefrontal cortex (dlPFC) revealed that neurons in these two brain areas possess highly distinctive structural and functional properties. Area V1 pyramidal neurons are much smaller than dlPFC neurons, with significantly less extensive dendritic arbors and far fewer dendritic spines. Relative to dlPFC neurons, V1 neurons have a significantly higher input resistance, depolarized resting membrane potential, and higher action potential (AP) firing rates. Most V1 neurons exhibit both phasic and regular-spiking tonic AP firing patterns, while dlPFC neurons exhibit only tonic firing. Spontaneous postsynaptic currents are lower in amplitude and have faster kinetics in V1 than in dlPFC neurons, but are no different in frequency. Three-dimensional reconstructions of V1 and dlPFC neurons were incorporated into computational models containing Hodgkin-Huxley and AMPA receptor and GABA(A) receptor gated channels. Morphology alone largely accounted for observed passive physiological properties, but led to AP firing rates that differed more than observed empirically, and to synaptic responses that opposed empirical results. Accordingly, modeling predicts that active channel conductances differ between V1 and dlPFC neurons. The unique features of V1 and dlPFC neurons are likely fundamental determinants of area-specific network behavior. The compact electrotonic arbor and increased excitability of V1 neurons support the rapid signal integration required for early processing of visual information. The greater connectivity and dendritic complexity of dlPFC neurons likely support higher level cognitive functions including working memory and planning.

Semiautomated analysis of dendrite morphology in cell culture

Quantifying dendrite morphology is a method for determining the effect of biochemical pathways and extracellular agents on neuronal development and differentiation. Quantification can be performed using Sholl analysis, dendrite counting, and length quantification. These procedures can be performed on dendrite-forming cell lines or primary neurons grown in culture. In this protocol, we describe the use of a set of computer programs to assist in quantifying many aspects of dendrite morphology, including changes in total and localized arbor complexity.

Morphological alterations in newly born dentate gyrus granule cells that emerge after status epilepticus contribute to make them less excitable

Computer simulations of external current stimulations of dentate gyrus granule cells of rats with Status Epilepticus induced by pilocarpine and control rats were used to evaluate whether morphological differences alone between these cells have an impact on their electrophysiological behavior. The cell models were constructed using morphological information from tridimensional reconstructions with Neurolucida software. To evaluate the effect of morphology differences alone, ion channel conductances, densities and distributions over the dendritic trees of dentate gyrus granule cells were the same for all models. External simulated currents were injected in randomly chosen dendrites belonging to one of three different areas of dentate gyrus granule cell molecular layer: inner molecular layer, medial molecular layer and outer molecular layer. Somatic membrane potentials were recorded to determine firing frequencies and inter-spike intervals. The results show that morphologically altered granule cells from pilocarpine-induced epileptic rats are less excitable than control cells, especially when they are stimulated in the inner molecular layer, which is the target area for mossy fibers that sprout after pilocarpine-induced cell degeneration. This suggests that morphological alterations may act as a protective mechanism to allow dentate gyrus granule cells to cope with the increase of stimulation caused by mossy fiber sprouting.

Altered dendritic complexity affects firing properties of cortical layer 2/3 pyramidal neurons in mice lacking the 5-HT3A receptor

We have previously shown that the serotonergic input on Cajal-Retzius cells, mediated by 5-HT(3) receptors, plays an important role in the early postnatal maturation of the apical dendritic trees of layer 2/3 pyramidal neurons. We reported that knockout mice lacking the 5-HT(3A) receptor showed exuberant apical dendrites of these cortical pyramidal neurons. Because model studies have shown the role of dendritic morphology on neuronal firing pattern, we used the 5-HT(3A) knockout mouse to explore the impact of dendritic hypercomplexity on the electrophysiological properties of this specific class of neurons. Our experimental results show that hypercomplexity of the apical dendritic tuft of layer 2/3 pyramidal neurons affects neuronal excitability by reducing the amount of spike frequency adaptation. This difference in firing pattern, related to a higher dendritic complexity, was accompanied by an altered development of the afterhyperpolarization slope with successive action potentials. Our abstract and realistic neuronal models, which allowed manipulation of the dendritic complexity, showed similar effects on neuronal excitability and confirmed the impact of apical dendritic complexity. Alterations of dendritic complexity, as observed in several pathological conditions such as neurodegenerative diseases or neurodevelopmental disorders, may thus not only affect the input to layer 2/3 pyramidal neurons but also shape their firing pattern and consequently alter the information processing in the cortex.

Dynamical systems analysis of spike-adding mechanisms in transient bursts

Transient bursting behaviour of excitable cells, such as neurons, is a common feature observed experimentally, but theoretically, it is not well understood. We analyse a five-dimensional simplified model of after-depolarisation that exhibits transient bursting behaviour when perturbed with a short current injection. Using one-parameter continuation of the perturbed orbit segment formulated as a well-posed boundary value problem, we show that the spike-adding mechanism is a canard-like transition that has a different character from known mechanisms for periodic burst solutions. The biophysical basis of the model gives a natural time-scale separation, which allows us to explain the spike-adding mechanism using geometric singular perturbation theory, but it does not involve actual bifurcations as for periodic bursts. We show that unstable sheets of the critical manifold, formed by saddle equilibria of the system that only exist in a singular limit, are responsible for the spike-adding transition; the transition is organised by the slow flow on the critical manifold near folds of this manifold. Our analysis shows that the orbit segment during the spike-adding transition includes a fast transition between two unstable sheets of the slow manifold that are of saddle type. We also discuss a different parameter regime where the presence of additional saddle equilibria of the full system alters the spike-adding mechanism.

Neuromantic - from semi-manual to semi-automatic reconstruction of neuron morphology

The ability to create accurate geometric models of neuronal morphology is important for understanding the role of shape in information processing. Despite a significant amount of research on automating neuron reconstructions from image stacks obtained via microscopy, in practice most data are still collected manually. This paper describes Neuromantic, an open source system for three dimensional digital tracing of neurites. Neuromantic reconstructions are comparable in quality to those of existing commercial and freeware systems while balancing speed and accuracy of manual reconstruction. The combination of semi-automatic tracing, intuitive editing, and ability of visualizing large image stacks on standard computing platforms provides a versatile tool that can help address the reconstructions availability bottleneck. Practical considerations for reducing the computational time and space requirements of the extended algorithm are also discussed.

Oxytocin and dendrite remodeling in the hypothalamus

For most people, their quality of life depends on their successful interdependence with others, which requires sophisticated social cognition, communication, and emotional bonds. Across the lifespan, new bonds must be forged and maintained, and conspecific menaces must be managed. The dynamic nature of the human social landscape suggests ongoing specific alterations in neural circuitry across several brain systems to subserve social behavior. To discover the biological mechanisms that contribute to normal social activities, animal models of social behavior have been developed. One valuable model system has been female rat sexual behavior, which is governed by cyclic variation of ovarian hormones. This behavior is modulated by the neuropeptide oxytocin (OT) through its actions in the hypothalamic ventromedial nucleus (VMH). The fluctuation of this behavior is associated with dendrite remodeling, like several other examples of behavioral plasticity. This review compares hormone-induced plasticity in the VMH with other examples of dendrite plasticity across the mammalian nervous system, namely the neurobehavioral paradigms of environmental enrichment, chronic stress, and incentive sensitization, which affect the neocortex, hippocampal formation, and ventral striatum, respectively. This comparison suggests that the effects of ovarian hormones on VMH neurons in rats, given the simple dendritic arbor and short time course for dendrite remodeling, provide a dual opportunity for mechanistic and functional studies that will shed light on i) the neural actions of OT that regulate social behavior and, ii) behaviorally relevant dendrite regulation in a variety of brain structures. This article is part of a Special Issue entitled Oxytocin, Vasopressin, and Social Behavior.

Motoneuron model of self-sustained firing after spinal cord injury

Under many conditions spinal motoneurons produce plateau potentials, resulting in self-sustained firing and providing a mechanism for translating short-lasting synaptic inputs into long-lasting motor output. During the acute-stage of spinal cord injury (SCI), the endogenous ability to generate plateaus is lost; however, during the chronic-stage of SCI, plateau potentials reappear with prolonged self-sustained firing that has been implicated in the development of spasticity. In this work, we extend previous modeling studies to systematically investigate the mechanisms underlying the generation of plateau potentials in motoneurons, including the influences of specific ionic currents, the morphological characteristics of the soma and dendrite, and the interactions between persistent inward currents and synaptic input. In particular, the goal of these computational studies is to explore the possible interactions between morphological and electrophysiological changes that occur after incomplete SCI. Model results predict that some of the morphological changes generally associated with the chronic-stage for some types of spinal cord injuries can cause a decrease in self-sustained firing. This and other computational results presented here suggest that the observed increases in self-sustained firing following some types of SCI may occur mainly due to changes in membrane conductances and changes in synaptic activity, particularly changes in the strength and timing of inhibition.

Burst firing transitions in two-compartment pyramidal neuron induced by the perturbation of membrane capacitance

Neuronal membrane capacitance C (m) is one of the prominent factors in action potential initiation and propagation and then influences the firing patterns of neurons. Exploring the roles that C (m) plays in different firing patterns can facilitate the understanding of how different factors might influence neuronal firing behaviors. However, the impacts of variations in C (m) on neuronal firing patterns have been only partly explored until now. In this study, the influence of C (m) on burst firing behaviors of a two-compartment pyramidal neuron (including somatic compartment and dendritic compartment) was investigated by means of computer simulation, the value of C (m) in each compartment was denoted as C (m,s) and C (m,d), respectively. Two cases were considered, in the first case, we let C (m,s) =C (m,d), and then changed them simultaneously. While in the second case, we assumed C (m,s) ≠C (m,d), and then changed them, respectively. From the simulation results obtained from these two cases, it was found that the variation of C (m) in the somatic compartment and the dendritic compartment show much difference, simulated results obtained from the variation of C (m,d) have much more similarities than that of C (m,s) when comparing with the results obtained in the first case under which C (m,s) =C (m,d). These different effects of C (m,s) and C (m,d) on neuronal firing behaviors may result from the different topology and functional roles of soma and dendrites. Numerical results demonstrated in this paper may give us some inspiration in understanding the possible roles of C (m) in burst firing patterns, especially their transitions in compartmental neurons.

Conserved properties of dendritic trees in four cortical interneuron subtypes

Dendritic trees influence synaptic integration and neuronal excitability, yet appear to develop in rather arbitrary patterns. Using electron microscopy and serial reconstructions, we analyzed the dendritic trees of four morphologically distinct neocortical interneuron subtypes to reveal two underlying organizational principles common to all. First, cross-sectional areas at any given point within a dendrite were proportional to the summed length of all dendritic segments distal to that point. Consistent with this observation, total cross-sectional area was almost perfectly conserved at bifurcation points. Second, dendritic cross-sections became progressively more elliptical at more proximal, larger diameter, dendritic locations. Finally, computer simulations revealed that these conserved morphological features limit distance dependent filtering of somatic EPSPs and facilitate distribution of somatic depolarization into all dendritic compartments. Because these features were shared by all interneurons studied, they may represent common organizational principles underlying the otherwise diverse morphology of dendritic trees.

Theory of electric resonance in the neocortical apical dendrite

Pyramidal neurons of the neocortex display a wide range of synchronous EEG rhythms, which arise from electric activity along the apical dendrites of neocortical pyramidal neurons. Here we present a theoretical description of oscillation frequency profiles along apical dendrites which exhibit resonance frequencies in the range of 10 to 100 Hz. The apical dendrite is modeled as a leaky coaxial cable coated with a dielectric, in which a series of compartments act as coupled electric circuits that gradually narrow the resonance profile. The tuning of the peak frequency is assumed to be controlled by the average amplitude of voltage-gated outward currents, which in turn are regulated by the subthreshold noise in the thousands of synaptic spines that are continuously bombarded by local circuits. The results of simulations confirmed the ability of the model both to tune the peak frequency in the 10–100 Hz range and to gradually narrow the resonance profile. Considerable additional narrowing of the resonance profile is provided by repeated looping through the apical dendrite via the corticothalamocortical circuit, which reduced the width of each resonance curve (at half-maximum) to approximately 1 Hz. Synaptic noise in the neural circuit is discussed in relation to the ways it can influence the narrowing process.

Stochastic continuous time neurite branching models with tree and segment dependent rates

In this paper we introduce a continuous time stochastic neurite branching model closely related to the discrete time stochastic BES-model. The discrete time BES-model is underlying current attempts to simulate cortical development, but is difficult to analyze. The new continuous time formulation facilitates analytical treatment thus allowing us to examine the structure of the model more closely. We derive explicit expressions for the time dependent probabilities p(γ,t) for finding a tree γ at time t, valid for arbitrary continuous time branching models with tree and segment dependent branching rates. We show, for the specific case of the continuous time BES-model, that as expected from our model formulation, the sums needed to evaluate expectation values of functions of the terminal segment number μ(f(n),t) do not depend on the distribution of the total branching probability over the terminal segments. In addition, we derive a system of differential equations for the probabilities p(n,t) of finding n terminal segments at time t. For the continuous BES-model, this system of differential equations gives direct numerical access to functions only depending on the number of terminal segments, and we use this to evaluate the development of the mean and standard deviation of the number of terminal segments at a time t. For comparison we discuss two cases where mean and variance of the number of terminal segments are exactly solvable. Then we discuss the numerical evaluation of the S-dependence of the solutions for the continuous time BES-model. The numerical results show clearly that higher S values, i.e. values such that more proximal terminal segments have higher branching rates than more distal terminal segments, lead to more symmetrical trees as measured by three tree symmetry indicators.

Humanized Foxp2 specifically affects cortico-basal ganglia circuits

It has been proposed that two amino acid substitutions in the transcription factor FOXP2 have been positively selected during human evolution and influence aspects of speech and language. Recently it was shown that when these substitutions are introduced into the endogenous Foxp2 gene of mice, they increase dendrite length and long-term depression (LTD) in medium spiny neurons of the striatum. Here we investigated if these effects are found in other brain regions. We found that neurons in the cerebral cortex, the thalamus and the striatum have increased dendrite lengths in the humanized mice whereas neurons in the amygdala and the cerebellum do not. In agreement with previous work we found increased LTD in medium spiny neurons, but did not detect alterations of synaptic plasticity in Purkinje cells. We conclude that although Foxp2 is expressed in many brain regions and has multiple roles during mammalian development, the evolutionary changes that occurred in the protein in human ancestors specifically affect brain regions that are connected via cortico-basal ganglia circuits.