Dendritic anatomy and electrotonic transfer properties of cat superior colliculus neurons

Detailed morphometrical and corresponding electrotonic characteristics on three classes of cat superior colliculus (SC) neurons have been derived. The sample of cells selected for analysis comprised ascending projection neurons (APNs), inter-layer neurons (ILNs) and tecto-reticulo-spinal neurons (TRSNs) recorded intracellularly and stained with HRP. Superficial SC neurons (APNs, ILNs) could be attached to the allo- and idiodendritic type while deep layer neurons (TRSNs) belong to the isodendritic type. For each neuron, the branching pattern, lengths and diameters of the dendritic trees were determined. These data served as input to the computer program "DENDRIT" from which electrotonic membrane and transfer properties were calculated. Both the morphometrical data and the electronic properties underline the contrasting features of superficial vs deep layer neurons in the SC. Our results support the hypothesis that on the neuron level a close relationship between dendritic pattern and neuron function might exist.     

Local Diameter Fully Constrains Dendritic Size in Basal but not Apical Trees of CA1 Pyramidal Neurons

Computational modeling of dendritic morphology is a powerful tool for quantitatively describing complex geometrical relationships, uncovering principles of dendritic development, and synthesizing virtual neurons to systematically investigate cellular biophysics and network dynamics. A feature common to many morphological models is a dependence of the branching probability on local diameter. Previous models of this type have been able to recreate a wide variety of dendritic morphologies. However, these diameter-dependent models have so far failed to properly constrain branching when applied to hippocampal CA1 pyramidal cells, leading to explosive growth. Here we present a simple modification of this basic approach, in which all parameter sampling, not just bifurcation probability, depends on branch diameter. This added constraint prevents explosive growth in both apical and basal trees of simulated CA1 neurons, yielding arborizations with average numbers and patterns of bifurcations extremely close to those observed in real cells. However, simulated apical trees are much more varied in size than the corresponding real dendrites. We show that, in this model, the excessive variability of simulated trees is a direct consequence of the natural variability of diameter changes at and between bifurcations observed in apical, but not basal, dendrites. Conversely, some aspects of branch distribution were better matched by virtual apical trees than by virtual basal trees. Dendritic morphometrics related to spatial position, such as path distance from the soma or branch order, may be necessary to fully constrain CA1 apical tree size and basal branching pattern.     

Statistical evaluation of dendritic growth models

A mathematical model (Kliemann, W. 1987.Bull. math. Biol. 49, 135–152.) that predicts the quantitative branching pattern of dendritic tree was evaluated using the apical and basal dendrites of rat hippocampal neurons. The Wald statistics for χ²-test was developed for the branching pattern of dendritic trees and for the distribution of the maximal order of the tree. Using this statistic, we obtained a reasonable, but not excellent, fit of the mathematical model for the dendritic data. The model's predictability of branching patterns was greatly enhanced by replacing one of the assumptions used for the original model “splitting of branches for all dendritic orders is stochastically independent”, with a new assumption “branches are more likely to split in areas where there is already a high density of branches”. The modified model delivered an excellent fit for basal dendrites and for the apical dendrites of hippocampal neurons from young rats (30–34 days postpartum). This indicates that for these cells the development of dendritic patterns is the result of a purely random and a systematic component, where the latter one depends on the density of dendritic branches in the brain area considered. For apical dendrites there is a trend towards decreasing pattern predictability with increasing age. This appears to reflect the late arrival of afferents and subsequent synaptogenesis proximal on the apical dendritic tree of hippocampal neurons.     

Scaling properties of pyramidal neurons in mice neocortex

Dendritic morphology is the structural correlate for receiving and processing inputs to a neuron. An interesting question then is what the design principles and the functional consequences of enlarged or shrinked dendritic trees might be. As yet, only a few studies have examined the effects of neuron size changes. Two theoretical scaling modes have been analyzed, conservative (isoelectrotonic) scaling (preserves the passive and active response properties) and isometric scaling (steps up low pass-filtering of inputs). It has been suggested that both scaling modes were verified in neuroanatomical studies. To overcome obvious limitations of these studies like small size of analyzed samples and restricted validity of utilized scaling measures, we considered the scaling problem of neurons on the basis of large sample data and by employing a more general method of scaling analysis. This method consists in computing the morphoelectrotonic transform (MET) of neurons. The MET maps the neuron from anatomical space into electrotonic space using the logarithm of voltage attenuation as the distance metric. The theory underlying this approach is described and then applied to two samples of morphologically reconstructed pyramidal neurons (cells from neocortex of wildtype and synRas transgenic mice) using the NEURON simulator. In a previous study, we could verify a striking increase of dendritic tree size in synRas pyramidal neurons. Surprisingly, in this study the statistical analysis of the sample MET dendrograms revealed that the electrotonic architecture of these neurons scaled roughly in a MET-conserving mode. In conclusion, our results suggest only a minor impact of the Ras protein on dendritic electroanatomy, with non-significant changes of most regions of the corresponding METs.     

Dendritic morphology is altered in hippocampal neurons following prenatal compromise

Chronic placental insufficiency (CPI), a known cause of intrauterine growth restriction, can lead to structural alterations in the developing brain that might underlie postnatal neurological deficits. We have previously demonstrated significant reductions in the volumes of hippocampal neuropil layers in fetal guinea pig brains following experimentally induced growth restriction. To determine the components of the neuropil affected in the brains of growth restricted (GR) fetuses, the dendritic morphology of CA1 pyramidal neurons and dentate granule cells was examined. CPI was induced by unilateral uterine artery ligation in pregnant guinea pigs at midgestation (term approximately 67 days). Hippocampi from control and GR fetuses were stained using the Rapid Golgi technique and the growth and branching of the dendritic arbors were quantified using the Sholl method. In addition, the density of dendritic spines was determined on the apical arbors of each population. In GR brains (n = 7) compared to controls (n = 7), there was a reduction in dendritic elongation (p < 0.005) and an alteration in the branch point distribution in CA1 basal arbors, and a reduction both in the outgrowth (p < 0.05) and branch point number (p < 0.05) of CA1 apical arbors. Dentate granule cells from GR brains also demonstrated reduced dendritic outgrowth (p < 0.05). There was an increase in dendritic spine density in both neuronal populations; this might be due either to altered synaptic pruning or as a compensatory mechanism for reduced dendritic length. These findings demonstrate that a chronic prenatal insult causes selective changes in the morphology of hippocampal cell dendrites and may lead to alterations in hippocampal function in the postnatal period.     

Synaptic integration gradients in single cortical pyramidal cell dendrites

Cortical pyramidal neurons receive thousands of synaptic inputs arriving at different dendritic locations with varying degrees of temporal synchrony. It is not known if different locations along single cortical dendrites integrate excitatory inputs in different ways. Here we have used two-photon glutamate uncaging and compartmental modeling to reveal a gradient of nonlinear synaptic integration in basal and apical oblique dendrites of cortical pyramidal neurons. Excitatory inputs to the proximal dendrite sum linearly and require precise temporal coincidence for effective summation, whereas distal inputs are amplified with high gain and integrated over broader time windows. This allows distal inputs to overcome their electrotonic disadvantage, and become surprisingly more effective than proximal inputs at influencing action potential output. Thus, single dendritic branches can already exhibit nonuniform synaptic integration, with the computational strategy shifting from temporal coding to rate coding along the dendrite.     

Cell type-specific dendritic polarity in the absence of spatially organized external cues

Pyramidal neurons of the hippocampus and cortex have polarized dendritic arbors, but little is known about the cellular mechanisms distinguishing apical and basal dendrites. We used morphometric analysis and time lapse imaging of cultured hippocampal neurons to show that glutamatergic neurons develop progressive dendritic asymmetry in the absence of polarized extrinsic cues. Thus, pyramidal neurons have a cellular program for polarized dendrite growth independent of tissue microenvironment.     

An autism-associated variant of Epac2 reveals a role for Ras/Epac2 signaling in controlling basal dendrite maintenance in mice

The architecture of dendritic arbors determines circuit connectivity, receptive fields, and computational properties of neurons, and dendritic structure is impaired in several psychiatric disorders. While apical and basal dendritic compartments of pyramidal neurons are functionally specialized and differentially regulated, little is known about mechanisms that selectively maintain basal dendrites. Here we identified a role for the Ras/Epac2 pathway in maintaining basal dendrite complexity of cortical neurons. Epac2 is a guanine nucleotide exchange factor (GEF) for the Ras-like small GTPase Rap, and it is highly enriched in the adult mouse brain. We found that in vivo Epac2 knockdown in layer 2/3 cortical neurons via in utero electroporation reduced basal dendritic architecture, and that Epac2 knockdown in mature cortical neurons in vitro mimicked this effect. Overexpression of an Epac2 rare coding variant, found in human subjects diagnosed with autism, also impaired basal dendritic morphology. This mutation disrupted Epac2's interaction with Ras, and inhibition of Ras selectively interfered with basal dendrite maintenance. Finally, we observed that components of the Ras/Epac2/Rap pathway exhibited differential abundance in the basal versus apical dendritic compartments. These findings define a role for Epac2 in enabling crosstalk between Ras and Rap signaling in maintaining basal dendrite complexity, and exemplify how rare coding variants, in addition to their disease relevance, can provide insight into cellular mechanisms relevant for brain connectivity.     

Computational simulation of the input-output relationship in hippocampal pyramidal cells

The precise mapping of how complex patterns of synaptic inputs are integrated into specific patterns of spiking output is an essential step in the characterization of the cellular basis of network dynamics and function. Relative to other principal neurons of the hippocampus, the electrophysiology of CA1 pyramidal cells has been extensively investigated. Yet, the precise input-output relationship is to date unknown even for this neuronal class. CA1 pyramidal neurons receive laminated excitatory inputs from three distinct pathways: recurrent CA1 collaterals on basal dendrites, CA3 Schaffer collaterals, mostly on oblique and proximal apical dendrites, and entorhinal perforant pathway on distal apical dendrites. We implemented detailed computer simulations of pyramidal cell electrophysiology based on three-dimensional anatomical reconstructions and compartmental models of available biophysical properties from the experimental literature. To investigate the effect of synaptic input on axosomatic firing, we stochastically distributed a realistic number of excitatory synapses in each of the three dendritic layers. We then recorded the spiking response to different stimulation patterns. For all dendritic layers, synchronous stimuli resulted in trains of spiking output and a linear relationship between input and output firing frequencies. In contrast, asynchronous stimuli evoked non-bursting spike patterns and the corresponding firing frequency input-output function was logarithmic. The regular/irregular nature of the input synaptic intervals was only reflected in the regularity of output inter-burst intervals in response to synchronous stimulation, and never affected firing frequency. Synaptic stimulations in the basal and proximal apical trees across individual neuronal morphologies yielded remarkably similar input-output relationships. Results were also robust with respect to the detailed distributions of dendritic and synaptic conductances within a plausible range constrained by experimental evidence. In contrast, the input-output relationship in response to distal apical stimuli showed dramatic differences from the other dendritic locations as well as among neurons, and was more sensible to the exact channel densities. Action Editor: Alain Destexhe     

An empirical assessment of tree branching networks and implications for plant allometric scaling models

Several theories predict whole‐tree function on the basis of allometric scaling relationships assumed to emerge from traits of branching networks. To test this key assumption, and more generally, to explore patterns of external architecture within and across trees, we measure branch traits (radii/lengths) and calculate scaling exponents from five functionally divergent species. Consistent with leading theories, including metabolic scaling theory, branching is area preserving and statistically self‐similar within trees. However, differences among scaling exponents calculated at node‐ and whole‐tree levels challenge the assumption of an optimised, symmetrically branching tree. Furthermore, scaling exponents estimated for branch length change across branching orders, and exponents for scaling metabolic rate with plant size (or number of terminal tips) significantly differ from theoretical predictions. These findings, along with variability in the scaling of branch radii being less than for branch lengths, suggest extending current scaling theories to include asymmetrical branching and differential selective pressures in plant architectures.     

MeCP2 mutation results in compartment-specific reductions in dendritic branching and spine density in layer 5 motor cortical neurons of YFP-H mice

Rett Syndrome (RTT) is a neurodevelopmental disorder predominantly caused by mutations in the X-linked gene MECP2. A primary feature of the syndrome is the impaired maturation and maintenance of excitatory synapses in the central nervous system (CNS). Different RTT mouse models have shown that particular Mecp2 mutations have highly variable effects on neuronal architecture. Distinguishing MeCP2 mutant cellular phenotypes therefore demands analysis of specific mutations in well-defined neuronal subpopulations. We examined a transgenically labeled subset of cortical neurons in YFP-H mice crossed with the Mecp2(tm1.1Jae) mutant line. YFP(+) Layer 5 pyramidal neurons in the motor cortex of wildtype and hemizygous mutant male mice were examined for differences in dendrite morphology and spine density. Total basal dendritic length was decreased by 18.6% due to both shorter dendrites and reduced branching proximal to the soma. Tangential dendrite lengths in the apical tuft were reduced by up to 26.6%. Spine density was reduced by 47.4% in the apical tuft and 54.5% in secondary apical dendrites, but remained unaffected in primary apical and proximal basal dendrites. We also found that MeCP2 mutation reduced the number of YFP(+) cells in YFP-H mice by up to 72% in various cortical regions without affecting the intensity of YFP expression in individual cells. Our results support the view that the effects of MeCP2 mutation are highly context-dependent and cannot be generalized across mutation types and cell populations.     

Pyramidal neurons: dendritic structure and synaptic integration

Pyramidal neurons are characterized by their distinct apical and basal dendritic trees and the pyramidal shape of their soma. They are found in several regions of the CNS and, although the reasons for their abundance remain unclear, functional studies--especially of CA1 hippocampal and layer V neocortical pyramidal neurons--have offered insights into the functions of their unique cellular architecture. Pyramidal neurons are not all identical, but some shared functional principles can be identified. In particular, the existence of dendritic domains with distinct synaptic inputs, excitability, modulation and plasticity appears to be a common feature that allows synapses throughout the dendritic tree to contribute to action-potential generation. These properties support a variety of coincidence-detection mechanisms, which are likely to be crucial for synaptic integration and plasticity.     

HGF regulates the development of cortical pyramidal dendrites

Although hepatocyte growth factor (HGF) and its receptor tyrosine kinase MET are widely expressed in the developing and mature central nervous system, little is known about the role of MET signaling in the brain. We have used particle-mediated gene transfer in cortical organotypic slice cultures established from early postnatal mice to study the effects of HGF on the development of dendritic arbors of pyramidal neurons. Compared with untreated control cultures, exogenous HGF promoted a highly significant increase in dendritic growth and branching of layer 2 pyramidal neurons, whereas inactivation of endogenous HGF with function-blocking, anti-HGF antibody caused a marked reduction in size and complexity of the dendritic arbors of these neurons. Furthermore, pyramidal neurons transfected with an MET dominant-negative mutant receptor likewise had much smaller and less complex dendritic arbors than did control transfected neurons. Our results indicate that HGF plays a role in regulating dendritic morphology in the developing cerebral cortex.     

Phosphorylation of CRMP2 is involved in proper bifurcation of the apical dendrite of hippocampal CA1 pyramidal neurons

The neural circuit in the hippocampus is important for higher brain functions. Dendrites of CA1 pyramidal neurons mainly receive input from the axons of CA3 pyramidal neurons in this neural circuit. A CA1 pyramidal neuron has a single apical dendrite and multiple basal dendrites. In wild‐type mice, most of CA1 pyramidal neurons extend a single trunk, or alternatively, the apical dendrite bifurcates into two daughter trunks at the stratum radiatum layer. We previously reported the proximal bifurcation phenotype in Sema3A?/?, p35?/?, and CRMP4?/? mice. Cdk5/p35 phosphorylates CRMP2 at Ser522, and inhibition of this phosphorylation suppressed Sema3A‐induced growth cone collapse. In this study, we analyzed the bifurcation points of the apical dendrites of hippocampal CA1 pyramidal neurons in CRMP2KI/KI mice in which the Cdk5/p35‐phosphorylation site Ser522 was mutated into an Ala residue. The proximal bifurcation phenotype was not observed in CRMP2KI/KI mice; however, severe proximal bifurcation of apical dendrites was found in CRMP2KI/KI;CRMP4?/? mice. Cultured hippocampal neurons from CRMP2KI/KI and CRMP2KI/KI;CRMP4?/? embryos showed an increased number of dendritic branching points compared to those from wild‐type embryos. Sema3A increased the number of branching points and the total length of dendrites in wild‐type hippocampal neurons, but these effects of Sema3A for dendrites were notobserved in CRMP2KI/KI and CRMP2KI/KI;CRMP4?/?hippocampal neurons. Binding of CRMP2 to tubulin increased in both CRMP2KI/KI and CRMP2KI/KI:CRMP4?/? brain lysates. These results suggest that CRMP2 and CRMP4 synergistically regulate dendritic development, and CRMP2 phosphorylation is critical for proper bifurcation of apical dendrite of CA1 pyramidal neurons. © 2012 Wiley Periodicals, Inc. Develop Neurobiol, 2013     

A new approach to reconstruction models of dendritic branching patterns

Quantitative models for characterising the detailed branching patterns of dendritic trees aim to explain these patterns either in terms of growth models based on principles of dendritic development or reconstruction models that describe an existing structure by means of a canonical set of elementary properties of dendritic morphology, which when incorporated into an algorithmic procedure will generate samples of dendrites that are statistically indistinguishable in both canonical and emergent features from those of the original sample of real neurons. This article introduces a conceptually new approach to reconstruction modelling based on the single assumption that dendritic segments are built from sequences of units of constant diameter, and that the distribution of the lengths of units of similar diameter is independent of location within a dendritic tree. This assumption in combination with non-parametric methods for estimating univariate and multivariate probability densities leads to an algorithm that significantly reduces the number of basic parameters required to simulate dendritic morphology. It is not necessary to distinguish between stem and terminal segments or to specify daughter branch ratios or dendritic taper. The procedure of sampling probability densities conditioned on local morphological features eliminates the need, for example, to specify daughter branch ratios and dendritic taper since these emerge naturally as a consequence of the conditioning process. Thus several basic parameters of previous reconstruction algorithms become emergent parameters of the new reconstruction process. The new procedure was applied successfully to a sample of 51 interneurons from lamina II/III of the spinal dorsal horn.     

Characteristics of electrotonic spread along the dendritic tree of retinal ganglion cells

Morphometric investigations of four types of dendritic trees of frog retinal ganglion cells show that these trees cannot be satisfactorily represented by an equivalent cable cylinder. In calculations of the electrotonic characteristics the geometric properties of the dendritic trees were accordingly considered. The following electrotonic characteristics were calculated for steady-state excitation: input resistances, coefficients of electrotonic transmission, and electrotonic efficiency of the bifurcations and the middle and end of the dendritic segments, as well as the electrotonic length of the dendritic tree and input resistances of the cell body. Model investigations showed that the electrotonic characteristics are determined mainly by extensiveness. The calculated values of electrotonic efficiency point to the physiological importance of the electrotonic spread of excitation in the dendrites of the retinal ganglion cells.Kaunas Medical Institute. Translated from Neirofiziologiya, Vol. 6, No. 3, pp. 304–311, May–June, 1974.     

Dendritic analysis of lobster stretch receptor neurons: Electrotonic properties with single and distributed inputs

Using steady-state cable analysis as derived by Rall, electrotonic properties of the dendritic trees of the tonic stretch receptor neuron of the spiny lobster, Panulirus interruptus,have been examined. By directly measuring the somatic input resistance and by visualizing the dendritic trees of this neuron by backfilling the axon with cobalt, the electrotonic properties of the dendritic trees have been derived. The calculated membrane resistivity is 800-3600 -cm ². Voltage and current transfer functions were calculated for (a) single dendritic tips the size observed in the cobalt preparations and (b) for processes 2 µm or smaller, as observed in electron microscopy. Current transfer to the soma was high in both cases (greater than 80%). Voltage transfer was 22% for large and 4% for small dendrites. When a more natural simultaneous conductance change at the tips of all major dendrites was modeled, voltage transfer was 84% and current transfer 56%. But the dynamic range of the cell (rheobase to saturation) is well-predicted by varying the simultaneous inputs, not by scaling up a single input, thus illustrating that convenient indices of electrotonic properties may not prove useful in appreciating the integrative properties of a neuron.     

Bergmann glia and the recognition molecule CHL1 organize GABAergic axons and direct innervation of Purkinje cell dendrites

The geometric and subcellular organization of axon arbors distributes and regulates electrical signaling in neurons and networks, but the underlying mechanisms have remained elusive. In rodent cerebellar cortex, stellate interneurons elaborate characteristic axon arbors that selectively innervate Purkinje cell dendrites and likely regulate dendritic integration. We used GFP BAC transgenic reporter mice to examine the cellular processes and molecular mechanisms underlying the development of stellate cell axons and their innervation pattern. We show that stellate axons are organized and guided towards Purkinje cell dendrites by an intermediate scaffold of Bergmann glial (BG) fibers. The L1 family immunoglobulin protein Close Homologue of L1 (CHL1) is localized to apical BG fibers and stellate cells during the development of stellate axon arbors. In the absence of CHL1, stellate axons deviate from BG fibers and show aberrant branching and orientation. Furthermore, synapse formation between aberrant stellate axons and Purkinje dendrites is reduced and cannot be maintained, leading to progressive atrophy of axon terminals. These results establish BG fibers as a guiding scaffold and CHL1 a molecular signal in the organization of stellate axon arbors and in directing their dendritic innervation.     

A comparative computer simulation of dendritic morphology

Computational modeling of neuronal morphology is a powerful tool for understanding developmental processes and structure-function relationships. We present a multifaceted approach based on stochastic sampling of morphological measures from digital reconstructions of real cells. We examined how dendritic elongation, branching, and taper are controlled by three morphometric determinants: Branch Order, Radius, and Path Distance from the soma. Virtual dendrites were simulated starting from 3,715 neuronal trees reconstructed in 16 different laboratories, including morphological classes as diverse as spinal motoneurons and dentate granule cells. Several emergent morphometrics were used to compare real and virtual trees. Relating model parameters to Branch Order best constrained the number of terminations for most morphological classes, except pyramidal cell apical trees, which were better described by a dependence on Path Distance. In contrast, bifurcation asymmetry was best constrained by Radius for apical, but Path Distance for basal trees. All determinants showed similar performance in capturing total surface area, while surface area asymmetry was best determined by Path Distance. Grouping by other characteristics, such as size, asymmetry, arborizations, or animal species, showed smaller differences than observed between apical and basal, pointing to the biological importance of this separation. Hybrid models using combinations of the determinants confirmed these trends and allowed a detailed characterization of morphological relations. The differential findings between morphological groups suggest different underlying developmental mechanisms. By comparing the effects of several morphometric determinants on the simulation of different neuronal classes, this approach sheds light on possible growth mechanism variations responsible for the observed neuronal diversity.     

Sez-6 proteins affect dendritic arborization patterns and excitability of cortical pyramidal neurons

Development of appropriate dendritic arbors is crucial for neuronal information transfer. We show, using seizure-related gene 6 (sez-6) null mutant mice, that Sez-6 is required for normal dendritic arborization of cortical neurons. Deep-layer pyramidal neurons in the somatosensory cortex of sez-6 null mice exhibit an excess of short dendrites, and cultured cortical neurons lacking Sez-6 display excessive neurite branching. Overexpression of individual Sez-6 isoforms in knockout neurons reveals opposing actions of membrane-bound and secreted Sez-6 proteins, with membrane-bound Sez-6 exerting an antibranching effect under both basal and depolarizing conditions. Layer V pyramidal neurons in knockout brain slices show reduced excitatory postsynaptic responses and a reduced dendritic spine density, reflected by diminished punctate staining for postsynaptic density 95 (PSD-95). In behavioral tests, the sez-6 null mice display specific exploratory, motor, and cognitive deficits. In conclusion, cell-surface protein complexes involving Sez-6 help to sculpt the dendritic arbor, in turn enhancing synaptic connectivity.