Effects of variability in anatomical reconstruction techniques on models of synaptic integration by dendrites: a comparison of three Internet archives

Compartmental distribution of GABAB receptor-mediated currents along the somatodendritic axis of hippocampal principal cells

Activity of cortical principal cells is controlled by the GABAergic system providing inhibition in a compartmentalized manner along their somatodendritic axis. While GABA_AR-mediated inhibitory synaptic transmission has been extensively characterized in hippocampal principal cells, little is known about the distribution of postsynaptic effects of GABA_BRs. In the present study, we have investigated the functional localization of GABA_BRs and their effector inwardly rectifying potassium (Kir3) channels by combining electrophysiological recordings in acute rat hippocampal slices, high-resolution immunoelectron microscopic analysis and single cell simulations. Pharmacologically isolated slow inhibitory postsynaptic currents were elicited in the three major hippocampal principal cell types by endogenous GABA released by electrical stimulation, photolysis of caged-GABA, as well as the canonical agonist baclofen, with the highest amplitudes observed in the CA3. Spatially restricted currents were assessed along the axis of principal cells by uncaging GABA in the different hippocampal layers. GABA_BR-mediated currents were present along the entire somatodendritic axis of principal cells, but non-uniformly distributed: largest currents and the highest conductance densities determined in the simulations were consistently found on the distal apical dendrites. Finally, immunocytochemical localization of GABA_BRs and Kir3 channels showed that distributions overlap but their densities diverge, particularly on the basal dendrites of pyramidal cells. GABA_BRs current amplitudes and the conductance densities correlated better with Kir3 density, suggesting a bottlenecking effect defined by the effector channel. These data demonstrate a compartmentalized distribution of the GABA_BR-Kir3 signaling cascade and suggest differential control of synaptic transmission, dendritic integration and synaptic plasticity at afferent pathways onto hippocampal principal cells.

Context-aware modeling of neuronal morphologies

Neuronal morphologies are pivotal for brain functioning: physical overlap between dendrites and axons constrain the circuit topology, and the precise shape and composition of dendrites determine the integration of inputs to produce an output signal. At the same time, morphologies are highly diverse and variant. The variance, presumably, originates from neurons developing in a densely packed brain substrate where they interact (e.g., repulsion or attraction) with other actors in this substrate. However, when studying neurons their context is never part of the analysis and they are treated as if they existed in isolation. Here we argue that to fully understand neuronal morphology and its variance it is important to consider neurons in relation to each other and to other actors in the surrounding brain substrate, i.e., their context. We propose a context-aware computational framework, NeuroMaC, in which large numbers of neurons can be grown simultaneously according to growth rules expressed in terms of interactions between the developing neuron and the surrounding brain substrate. As a proof of principle, we demonstrate that by using NeuroMaC we can generate accurate virtual morphologies of distinct classes both in isolation and as part of neuronal forests. Accuracy is validated against population statistics of experimentally reconstructed morphologies. We show that context-aware generation of neurons can explain characteristics of variation. Indeed, plausible variation is an inherent property of the morphologies generated by context-aware rules. We speculate about the applicability of this framework to investigate morphologies and circuits, to classify healthy and pathological morphologies, and to generate large quantities of morphologies for large-scale modeling.

Dendritic diameters affect the spatial variability of intracellular calcium dynamics in computer models

There is growing interest in understanding calcium dynamics in dendrites, both experimentally and computationally. Many processes influence these dynamics, but in dendrites there is a strong contribution of morphology because the peak calcium levels are strongly determined by the surface to volume ratio (SVR) of each branch, which is inversely related to branch diameter. In this study we explore the predicted variance of dendritic calcium concentrations due to local changes in dendrite diameter and how this is affected by the modeling approach used. We investigate this in a model of dendritic calcium spiking in different reconstructions of cerebellar Purkinje cells and in morphological analysis of neocortical and hippocampal pyramidal neurons. We report that many published models neglect diameter-dependent effects on calcium concentration and show how to implement this correctly in the NEURON simulator, both for phenomenological pool based models and for implementations using radial 1D diffusion. More detailed modeling requires simulation of 3D diffusion and we demonstrate that this does not dissipate the local concentration variance due to changes of dendritic diameter. In many cases 1D diffusion of models of calcium buffering give a good approximation provided an increased morphological resolution is implemented.

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.

Stochastic ion channel gating in dendritic neurons: morphology dependence and probabilistic synaptic activation of dendritic spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites.

The activity of neurons in the brain is mediated through changes in the probability of random transitions between open and closed states of ion channels. Since differences in morphology define distinct types of neuron and may underlie neurological disorders, it is important to understand how morphology influences the functional consequences of these random transitions. However, the complexities of neuronal morphology, together with the large number of ion channels expressed by a single neuron, have made this issue difficult to explore systematically. We introduce and validate new computational tools that enable efficient generation and simulation of models containing ion channels distributed across complex neuronal morphologies. Using these tools we demonstrate that the impact of random ion channel opening depends on neuronal morphology and ion channel kinetics. We show that in a realistic model of a neuron important for navigation and memory random gating of ion channels substantially modifies responses to synaptic input. Our results suggest a new and general perspective, whereby output from a neuron is a probabilistic rather than a fixed function of synaptic input to its dendrites. These results and new tools will contribute to the understanding of how intrinsic properties of neurons influence computations carried out within the brain.

Non-parametric algorithmic generation of neuronal morphologies

Generation algorithms allow for the generation of Virtual Neurons (VNs) from a small set of morphological properties. The set describes the morphological properties of real neurons in terms of statistical descriptors such as the number of branches and segment lengths (among others). The majority of reconstruction algorithms use the observed properties to estimate the parameters of a priori fixed probability distributions in order to construct statistical descriptors that fit well with the observed data. In this article, we present a non-parametric generation algorithm based on kernel density estimators (KDEs). The new algorithm is called KDE-NEURON: and has three advantages over parametric reconstruction algorithms: (1) no a priori specifications about the distributions underlying the real data, (2) peculiarities in the biological data will be reflected in the VNs, and (3) ability to reconstruct different cell types. We experimentally generated motor neurons and granule cells, and statistically validated the obtained results. Moreover, we assessed the quality of the prototype data set and observed that our generated neurons are as good as the prototype data in terms of the used statistical descriptors. The opportunities and limitations of data-driven algorithmic reconstruction of neurons are discussed.

A classification method to distinguish cell-specific responses elicited by current pulses in hippocampal CA1 pyramidal cells

The suprathreshold electrophysiological responses of pyramidal cells have been grouped into large classes such as bursting and spiking. However, it is not known whether, within a class, response variability ranges uniformly across all cells or whether each cell has a unique and consistent profile that can be differentiated. A major difficulty when comparing suprathreshold responses is that slight variations in spike timing in otherwise very similar traces render traditional metrics ineffective. To address these issues, we developed a novel distance measure based on fiducial points to quantify the similarity among traces with trains of action potentials and applied it together with classification techniques to a set of in vitro patch clamp recordings from CA1 pyramidal cells. We tested if responses to repeated current stimulation of a given cell would cluster together yet remain distinct from those of other cells. We found that depolarizing and hyperpolarizing current pulses elicited responses in each cell that clustered and were systematically distinguishable from responses in other cells. The fiducial-point distance measure was more effective than other methods based on spike times and voltage-gradient phase planes. Depolarizing traces were more reliably differentiated than hyperpolarizing traces, and combining both scores was even more effective. These results suggest that each CA1 pyramidal cell has unique properties that can be detected and quantified with methods discussed here. This uniqueness may be due to slight variations in morphology or membrane channel densities and kinetics, or to large, coordinated variations in these elements. Ascertaining the actual sources and their degree of variability is important when constructing network models of neural function to ensure that key mechanisms are robust in the face of variations within these ranges. The analytical tools presented here can assist in constructing detailed cell models to match experimental records to elucidate the sources of electrophysiological variability in neurons.

Successes and rewards in sharing digital reconstructions of neuronal morphology

The computer-assisted three-dimensional reconstruction of neuronal morphology is becoming an increasingly popular technique to quantify the arborization patterns of dendrites and axons. The resulting digital files are suitable for comprehensive morphometric analyses as well as for building anatomically realistic compartmental models of membrane biophysics and neuronal electrophysiology. The digital tracings acquired in a lab for a specific purpose can be often re-used by a different research group to address a completely unrelated scientific question, if the original investigators are willing to share the data. Since reconstructing neuronal morphology is a labor-intensive process, data sharing and re-analysis is particularly advantageous for the neuroscience and biomedical communities. Here we present numerous cases of "success stories" in which digital reconstructions of neuronal morphology were shared and re-used, leading to additional, independent discoveries and publications, and thus amplifying the impact of the "source" study for which the data set was first collected. In particular, we overview four main applications of this kind of data: comparative morphometric analyses, statistical estimation of potential synaptic connectivity, morphologically accurate electrophysiological simulations, and computational models of neuronal shape and development.

MorphML: level 1 of the NeuroML standards for neuronal morphology data and model specification

Quantitative neuroanatomical data are important for the study of many areas of neuroscience, and the complexity of problems associated with neuronal structure requires that research from multiple groups across many disciplines be combined. However, existing neuron-tracing systems, simulation environments, and tools for the visualization and analysis of neuronal morphology data use a variety of data formats, making it difficult to exchange data in a readily usable way. The NeuroML project was initiated to address these issues, and here we describe an extensible markup language standard, MorphML, which defines a common data format for neuronal morphology data and associated metadata to facilitate data and model exchange, database creation, model publication, and data archiving. We describe the elements of the standard in detail and outline the mappings between this format and those used by a number of popular applications for reconstruction, simulation, and visualization of neuronal morphology.

Dendritic amplification of inhibitory postsynaptic potentials in a model Purkinje cell

In neurons with large dendritic arbors, the postsynaptic potentials interact in a complex manner with active and passive membrane properties, causing not easily predictable transformations during the propagation from synapse to soma. Previous theoretical and experimental studies in both cerebellar Purkinje cells and neocortical pyramidal neurons have shown that voltage-dependent ion channels change the amplitude and time-course of postsynaptic potentials. We investigated the mechanisms involved in the propagation of inhibitory postsynaptic potentials (IPSPs) along active dendrites in a model of the Purkinje cell. The amplitude and time-course of IPSPs recorded at the soma were dependent on the synaptic distance from the soma, as predicted by passive cable theory. We show that the effect of distance on the amplitude and width of the IPSP was significantly reduced by the dendritic ion channels, whereas the rise time was not affected. Somatic IPSPs evoked by the activation of the most distal synapses were up to six times amplified owing to the presence of voltage-gated channels and the IPSP width became independent of the covered distance. A transient deactivation of the Ca(2+) channels and the Ca(2+)-dependent K(+) channels, triggered by the hyperpolarization following activation of the inhibitory synapse, was found to be responsible for these dynamics. Nevertheless, the position of activated synapses had a marked effect on the Purkinje cell firing pattern, making stellate cells and basket cells most suitable for controlling the firing rate and spike timing, respectively, of their target Purkinje cells.

Complex parameter landscape for a complex neuron model

The electrical activity of a neuron is strongly dependent on the ionic channels present in its membrane. Modifying the maximal conductances from these channels can have a dramatic impact on neuron behavior. But the effect of such modifications can also be cancelled out by compensatory mechanisms among different channels. We used an evolution strategy with a fitness function based on phase-plane analysis to obtain 20 very different computational models of the cerebellar Purkinje cell. All these models produced very similar outputs to current injections, including tiny details of the complex firing pattern. These models were not completely isolated in the parameter space, but neither did they belong to a large continuum of good models that would exist if weak compensations between channels were sufficient. The parameter landscape of good models can best be described as a set of loosely connected hyperplanes. Our method is efficient in finding good models in this complex landscape. Unraveling the landscape is an important step towards the understanding of functional homeostasis of neurons.

Contribution of morphology and membrane resistance to integration of fast synaptic signals in two thalamic cell types

Thalamocortical cells (TCs) and interneurons (INs) in the lateral geniculate nucleus process visual information from the retina. The TCs have many short dendrites, whereas the INs have fewer and longer dendrites. Because of these morphological differences, it has been suggested that transmission of synaptic signals from dendritic synapses to soma is more efficient in TCs than in INs. However, a higher membrane resistance (R(m)) for the INs could, in theory, compensate for the attenuating effect of their long dendrites and allow distal synaptic inputs to significantly depolarize the soma. Compartmental models were made from biocytin filled TCs (n = 15) and INs (n = 3) and adjusted to fit the current- and voltage-clamp recordings from the individual cells. The confidence limits for the passive electrical parameters were explored by simulating the influence of noise, morphometric errors and non-uniform and active conductances. One of the useful findings was that R(m) was accurately estimated despite realistic levels of active conductance. Simulations to explore the somatic influence of dendritic synapses showed that a small (0.5 nS) excitatory synapse placed at different dendritic positions gave similar somatic potentials in the individual TCs, within the TC population and also between TCs and INs. A linear increase in the conductance of the synapse gave increases in somatic potentials that were more sublinear in INs than TCs. However, when the total synaptic conductance was increased by simultaneously activating many small, spatially distributed synapses, the INs converted the synaptic signals to soma potentials almost as efficiently as the TCs. Thus, INs can transfer fast synaptic signals to soma as efficiently as TCs except when the focal conductance is large.

Fitting experimental data to models that use morphological data from public databases

Ideally detailed neuron models should make use of morphological and electrophysiological data from the same cell. However, this rarely happens. Typically a modeler will choose a cell morphology from a public database, assign standard values for Ra, Cm, and other parameters and then do the modeling study. The assumption is that the model will produce results representative of what might be obtained experimentally. To test this assumption we developed models of CA1 hippocampal pyramidal neurons using 4 different morphologies obtained from 3 public databases. The multiple run fitter in NEURON was used to fit parameter values in each of the 4 morphological models to match experimental data recorded from 19 CA1 pyramidal cells. Fits with fixed standard parameter values produced results that were generally not representative of our experimental data. However, when parameter values were allowed to vary, excellent fits were obtained in almost all cases, but the fitted parameter values were very different among the 4 reconstructions and did not match standard values. The differences in fitted values can be explained by very different diameters, total lengths, membrane areas and volumes among the reconstructed cells, reflecting either cell heterogeneity or issues with the reconstruction data. The fitted values compensated for these differences to make the database cells and experimental cells more similar electrotonically. We conclude that models using fully reconstructed morphologies need to be calibrated with experimental data (even when morphological and electrophysiological data come from the same cell), model results should be generated with multiple reconstructions, morphological and experimental cells should come from the same strain of animal at the same age, and blind use of standard parameter values in models that use reconstruction data may not produce representative experimental results.

Relation of apical dendritic spikes to output decision in CA1 pyramidal cells during synchronous activation: a computational study

Recent studies on the initiation and propagation of dendritic spikes have modified the classical view of postsynaptic integration. Earlier we reported that subthreshold currents and spikes recruited by synaptic currents play a critical role in defining outputs following synchronous activation. Experimental factors strongly condition these currents due to their nonlinear behaviour. Hence, we have performed a detailed parametric study in a CA1 pyramidal cell model to explore how different variables interact and initiate dendritic spiking, and how they influence cell output. The input pattern, the relative excitability of axon and dendrites, the presence/modulation of voltage-dependent channels, and inhibition were cross analysed. Subthreshold currents and spikes on synaptically excited branches fired spikes in other branches to jointly produce different modalities of apical shaft spiking with a variable impact on cell output. Synchronous activation initiated a varying number and temporal scatter of firing branches that produced in the apical shaft-soma axis nonpropagating spikes, pseudosaltatory or continuous forward conduction, or backpropagation. As few as 6-10 local spikes within a time window of 2 ms ensure cell output. However, the activation mode varied extremely when two or more variables were cross-analysed, becoming rather unpredictable when all the variables were considered. Spatially clustered inputs and upper modulation of dendritic Na(+) or Ca(2+) electrogenesis favour apical decision. In contrast, inhibition biased the output decision toward the axon and switched between dendritic firing modes. We propose that dendrites can discriminate input patterns and decide immediate cell output depending on the particular state of a variety of endogenous parameters.

Signal propagation in oblique dendrites of CA1 pyramidal cells

The electrophysiological properties of the oblique branches of CA1 pyramidal neurons are largely unknown and very difficult to investigate experimentally. These relatively thin dendrites make up the majority of the apical tree surface area and constitute the main target of Schaffer collateral axons from CA3. Their electrogenic properties might have an important role in defining the computational functions of CA1 neurons. It is thus important to determine if and to what extent the back- and forward propagation of action potentials (AP) in these dendrites could be modulated by local properties such as morphology or active conductances. In the first detailed study of signal propagation in the full extent of CA1 oblique dendrites, we used 27 reconstructed three-dimensional morphologies and different distributions of the A-type K(+) conductance (K(A)), to investigate their electrophysiological properties by computational modeling. We found that the local K(A) distribution had a major role in modulating action potential back propagation, whereas the forward propagation of dendritic spikes originating in the obliques was mainly affected by local morphological properties. In both cases, signal processing in any given oblique was effectively independent of the rest of the neuron and, by and large, of the distance from the soma. Moreover, the density of K(A) in oblique dendrites affected spike conduction in the main shaft. Thus the anatomical variability of CA1 pyramidal cells and their local distribution of voltage-gated channels may suit a powerful functional compartmentalization of the apical tree.

Distinct properties of two major excitatory inputs to hippocampal pyramidal cells: a computational study

The two main sources of excitatory input to CA1 pyramidal cells, the Schaffer collaterals (SC) and the perforant path (PP), target different regions of the dendritic tree. This spatial segregation may have important consequences for the way in which different inputs affect the activity of principal neurons. We constructed detailed biophysical models of CA1 pyramidal cells, incorporating a variety of active conductances, and investigated the ability of synapses located in different dendritic segments to elicit a somatic voltage response. Synaptic efficacy as seen by the soma was strongly dependent on the site of the synapse, with PP inputs being more severely attenuated than SC inputs. Variability within SC inputs, but not between SC inputs and PP inputs, could be eliminated by appropriate scaling of synaptic efficacy. The spatial and temporal summation of multiple synaptic inputs was also investigated. While summation of SC inputs was linear up to the somatic spike threshold, PP inputs summed in a strongly sublinear fashion, with the somatic response remaining subthreshold even following the simultaneous activation of a large number of synapses and during stimulation with high-frequency trains. Finally, the relative impact of different pathways on somatic activity could be effectively altered by modulating the kinetic properties of dendritic transient K+ channels, corresponding to the activation of ascending modulatory neurotransmitter systems. In this case, the efficacy of the PP was enhanced by the dendritic generation and limited spread of action potentials. Strong PP activation could also evoke dendritic Ca++ spikes, which often triggered a somatic burst.

Biophysically detailed modelling of microcircuits and beyond

Realistic bottom-up modelling has been seminal to understanding which properties of microcircuits control their dynamic behaviour, such as the locomotor rhythms generated by central pattern generators. In this article of the TINS Microcircuits Special Feature, we review recent modelling work on the leech-heartbeat and lamprey-swimming pattern generators as examples. Top-down mathematical modelling also has an important role in analyzing microcircuit properties but it has not always been easy to reconcile results from the two modelling approaches. Most realistic microcircuit models are relatively simple and need to be made more detailed to represent complex processes more accurately. We review methods to add neuromechanical feedback, biochemical pathways or full dendritic morphologies to microcircuit models. Finally, we consider the advantages and challenges of full-scale simulation of networks of microcircuits.

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.