Untangling dendrites with quantitative models

Counting Synapses Using FIB/SEM Microscopy: A True Revolution for Ultrastructural Volume Reconstruction

The advent of transmission electron microscopy (TEM) in the 1950s represented a fundamental step in the study of neuronal circuits. The application of this technique soon led to the realization that the number of synapses changes during the course of normal life, as well as under certain pathological or experimental circumstances. Since then, one of the main goals in neurosciences has been to define simple and accurate methods to estimate the magnitude of these changes. Contrary to analysing single sections, TEM reconstructions are extremely time-consuming and difficult. Therefore, most quantitative studies use stereological methods to define the three-dimensional characteristics of synaptic junctions that are studied in two dimensions. Here, to count the exact number of synapses per unit of volume we have applied a new three-dimensional reconstruction method that involves the combination of focused ion beam milling and scanning electron microscopy (FIB/SEM). We show that the images obtained with FIB/SEM are similar to those obtained with TEM, but with the advantage that FIB/SEM permits serial reconstructions of large volumes of tissue to be generated rapidly and automatically. Furthermore, we compared the estimates of the number of synapses obtained with stereological methods with the values obtained by FIB/SEM reconstructions. We concluded that FIB/SEM not only provides the actual number of synapses per volume but it is also much easier and faster to use than other currently available TEM methods. More importantly, it also avoids most of the errors introduced by stereological methods and overcomes the difficulties associated with these techniques.

A bushy cell network in the rat ventral cochlear nucleus

Geometry of the dendritic tree and synaptic organization of afferent inputs are essential factors in determining how synaptic input is integrated by neurons. This information remains elusive for one of the first brainstem neurons involved in processing of the primary auditory signal from the ear, the bushy cells (BCs) of the ventral cochlear nucleus (VCN). Here, we labeled the BC dendritic trees with retrograde tracing techniques to analyze their geometry and synaptic organization after immunofluorescence for excitatory and inhibitory synaptic markers, electron microscopy, morphometry, double tract-tracing methods, and 3D reconstructions. Our study revealed that BC dendrites provide space for a large number of compartmentalized excitatory and inhibitory synaptic interactions. The dendritic inputs on BCs are of cochlear and noncochlear origin, and their proportion and distribution are dependent on the branching pattern and orientation of the dendritic tree in the VCN. Three-dimensional reconstructions showed that BC dendrites branch and cluster with those of other BCs in the core of the VCN. Within the cluster, incoming synaptic inputs establish divergent multiple-contact synapses (dyads and triads) between BCs. Furthermore, neuron-neuron connections including puncta adherentia, sarcoplasmic junctions, and gap junctions are common between BCs, which suggests that these neurons are electrically coupled. Overall, our study demonstrates the existence of a BC network in the rat VCN. This network may establish the neuroanatomical basis for acoustic information processing by individual BCs as well as for enhanced synchronization of the output signal of the VCN.

Generation of Spike Trains with Controlled Auto- and Cross-Correlation Functions

Emerging evidence indicates that information processing, as well as learning and memory processes, in both the network and single-neuron levels are highly dependent on the correlation structure of multiple spike trains. Contemporary experimental as well as theoretical studies that involve quasi-realistic neuronal stimulation thus require a method for controlling spike train correlations. This letter introduces a general new strategy for generating multiple spike trains with exactly controlled mean firing rates and correlation structure (defined in terms of auto- and cross-correlation functions). Our approach nonlinearly transforms random gaussian-distributed processes with a predistorted correlation structure into nonnegative rate processes, which are then used to generate doubly stochastic Poisson point processes with the required correlation structure. We show how this approach can be used to generate stationary or nonstationary spike trains from small or large groups of neurons with diverse auto- and cross-correlation structures. We analyze and derive analytical formulas for the high-order correlation structure of generated spike trains and discuss the limitations of this approach.

Subcellular topography of visually driven dendritic activity in the vertebrate visual system

Neural pathways projecting from sensory organs to higher brain centers form topographic maps in which neighbor relationships are preserved from a sending to a receiving neural population. Sensory input can generate compartmentalized electrical and biochemical activity in the dendrites of a receiving neuron. Here, we show that in the developing retinotectal projection of young Xenopus tadpoles, visually driven Ca2+ signals are topographically organized at the subcellular, dendritic scale. Functional in vivo two-photon Ca2+ imaging revealed that the sensitivity of dendritic Ca2+ signals to stimulus location in visual space is correlated with their anatomical position within the dendritic tree of individual neurons. This topographic distribution was dependent on NMDAR activation, whereas global Ca2+ signals were mediated by Ca2+ influx through dendritic, voltage-dependent Ca2+ channels. These findings suggest a framework for plasticity models that invoke local dendritic Ca2+ signaling in the elaboration of neural connectivity and dendrite-specific information storage.

ERK mediates activity dependent neuronal complexity via sustained activity and CREB-mediated signaling

A major question in the process of dendrite development and complexity is not whether neuronal activity plays a role, but how it contributes to specific components of the mature dendrite pattern. Neurons interpret activity into the influx of calcium ions leading to activation of signaling pathways. The dynamics of calcium-activated signaling pathways after neuronal activity and the contribution to formation of dendrite complexity remain unclear. Here, we show that one calcium activated signaling pathway, extracellular signal-regulated kinase (ERK), showed differential activity in cortical neurons. In response to depolarizing stimuli, ERK was active for less than an hour in most neurons, whereas in others ERK remained active for several hours. Further, neurons in which ERK activity was sustained, displayed greater dendrite complexity than neurons that did not display sustained ERK activity. Interestingly, this difference in dendrite complexity was detected in some, but not all, morphological parameters. Pharmacological inhibition of sustained ERK activity inhibited calcium-activated dendrite complexity. Increasing the duration and degree of ERK phosphorylation, and thus activity, with dominant negative MAP kinase phosphatase-1 accentuated dendrite complexity. Neurons in which ERK activity was sustained activated downstream nuclear targets including RSK, MSK, cAMP response element binding protein (CREB), CRE-mediated gene transcription, and stabilized c-Fos. Further, the increase in dendrite complexity mediated by sustained ERK activity was inhibited by expression of a dominant negative CREB. These data indicate that ERK-mediated activity induced dendrite complexity via sustained signaling and CREB-mediated signaling.

Contacts among non-sister dendritic branches at bifurcations shape neighboring dendrites and pattern their synaptic inputs

The size and shape of neuronal dendritic arbors affect the number and pattern of synaptic inputs, as well as the complexity and function of brain circuits. However, the means by which different dendritic arbors take their final shape and how these shapes are associated with distinct synaptic patterns is still largely unknown. Dendritic ramification is influenced by dendrite-dendrite interactions that stabilize specific branching directions and ensure appropriate synaptic contacts. Yet, it is not clear by which mechanism these contacts are allocated. We found that stable dendro-dendritic contacts occur preferentially between non-sister dendritic branches at sites of bifurcations, and that this process is promoted by synaptic activity. Moreover, these contacts are associated with synaptic connections of higher density, higher level of synaptophysin, NR1, GluR2 subunits of glutamate receptors and elevated secretion capability than synaptic connections found on contacts made by non-bifurcating branches or along non-contacting parts of the dendrites. Thus, in cultured neurons, stabilization of hetero-neuronal dendro-dendritic contacts at bifurcations is a new mean to pattern and associate morphogenesis and synaptic input distribution in neighboring dendritic trees.

Bifurcation analysis of solitary and synchronized pulses and formation of reentrant waves in laterally coupled excitable fibers

We study the dynamics of a reaction-diffusion system comprising two mutually coupled excitable fibers. We consider a case in which the dynamical properties of the two fibers are nonidentical due to the parameter mismatch between them. By using the spatially one-dimensional FitzHugh-Nagumo equations as a model of a single excitable fiber, synchronized pulses are found to be stable in some parameter regime. Furthermore, there exists a critical coupling strength beyond which the synchronized pulses are stable for any amount of parameter mismatch. We show the bifurcation structures of the synchronized and solitary pulses and identify a codimension-2 cusp singularity as the source of the destabilization of synchronized pulses. When stable solitary pulses in both fibers disappear via a saddle-node bifurcation on increasing the coupling strength, a reentrant wave is formed. The parameter region, where a stable reentrant wave is observed in direct numerical simulation, is consistent with that obtained by bifurcation analysis.

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane's inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite-soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.

NeuroMorpho.Org implementation of digital neuroscience: dense coverage and integration with the NIF

Neuronal morphology affects network connectivity, plasticity, and information processing. Uncovering the design principles and functional consequences of dendritic and axonal shape necessitates quantitative analysis and computational modeling of detailed experimental data. Digital reconstructions provide the required neuromorphological descriptions in a parsimonious, comprehensive, and reliable numerical format. NeuroMorpho.Org is the largest web-accessible repository service for digitally reconstructed neurons and one of the integrated resources in the Neuroscience Information Framework (NIF). Here we describe the NeuroMorpho.Org approach as an exemplary experience in designing, creating, populating, and curating a neuroscience digital resource. The simple three-tier architecture of NeuroMorpho.Org (web client, web server, and relational database) encompasses all necessary elements to support a large-scale, integrate-able repository. The data content, while heterogeneous in scientific scope and experimental origin, is unified in format and presentation by an in house standardization protocol. The server application (MRALD) is secure, customizable, and developer-friendly. Centralized processing and expert annotation yields a comprehensive set of metadata that enriches and complements the raw data. The thoroughly tested interface design allows for optimal and effective data search and retrieval. Availability of data in both original and standardized formats ensures compatibility with existing resources and fosters further tool development. Other key functions enable extensive exploration and discovery, including 3D and interactive visualization of branching, frequently measured morphometrics, and reciprocal links to the original PubMed publications. The integration of NeuroMorpho.Org with version-1 of the NIF (NIFv1) provides the opportunity to access morphological data in the context of other relevant resources and diverse subdomains of neuroscience, opening exciting new possibilities in data mining and knowledge discovery. The outcome of such coordination is the rapid and powerful advancement of neuroscience research at both the conceptual and technological level.

Regulation of information passing by synaptic transmission: a short review

The largest part of information passed among neurons in the brain occurs by the means of chemical synapses connecting the axons of presynaptic neurons to the dendritic tree of the postsynaptic ones. In the present paper, the most relevant open problems related to the mechanisms of control of the information passing among neurons by synaptic transmission will be shortly reviewed. The "cross talking" between synapses, their mutual interactions and the control of the information flow between different areas of the dendritic tree will be also considered. The threshold mechanism based on the "reversal potential" will be considered for its role in the control of information transfer among neurons and also for its contribution to the information flow among different areas of the dendritic tree and to the computational ability of the single neuron. The concept of "competition for plasticity" will be proposed as a mechanism of competition based on the synaptic activation time.

Active dendrites: colorful wings of the mysterious butterflies

Santiago Ramón y Cajal had referred to neurons as the 'mysterious butterflies of the soul.' Wings of these butterflies--their dendrites--were traditionally considered as passive integrators of synaptic information. Owing to a growing body of experimental evidence, it is now widely accepted that these wings are colorful, endowed with a plethora of active conductances, with each family of these butterflies made of distinct hues and shades. Furthermore, rapidly evolving recent literature also provides direct and indirect demonstrations for activity-dependent plasticity of these active conductances, pointing toward chameleonic adaptability in these hues. These experimental findings firmly establish the immense computational power of a single neuron, and thus constitute a turning point toward the understanding of various aspects of neuronal information processing. In this brief historical perspective, we track important milestones in the chameleonic transmogrification of these mysterious butterflies.

Novel processes invaginate the pre-synaptic terminal of retinal bipolar cells

Mixed-rod cone bipolar (Mb) cells of goldfish retina have large synaptic terminals (10 microm in diameter) that make 60-90 ribbon synapses mostly onto amacrine cells and rarely onto ganglion cells and, in return, receive 300-400 synapses from gamma-aminobutyric acid (GABA)-ergic amacrine cells. Tissue viewed by electron microscopy revealed the presence of double-membrane-bound processes deep within Mb terminals. No membrane specializations were apparent on these invaginating processes, although rare vesicular fusion was observed. These invaginating dendrites were termed "InDents". Mb bipolar cells were identified by their immunoreactivity for protein kinase C. Double-label immunofluorescence with other cell-type-specific labels eliminated Müller cells, efferent fibers, other Mb bipolar cells, dopaminergic interplexiform cells, and somatostatin amacrine cells as a source of the InDents. Confocal analysis of double-labeled tissue clearly showed dendrites of GABA amacrine cells, backfilled ganglion cells, and dendrites containing PanNa immunoreactivity extending into and passing through Mb terminals. Nearly all Mb terminals showed evidence for the presence of InDents, indicating their common presence in goldfish retina. No PanNa immunoreactivity was found on GABA or ganglion cell InDents, suggesting that a subtype of glycine amacrine cell contained voltage-gated Na channels. Thus, potassium and calcium voltage-gated channels might be present on the InDents and on the Mb terminal membrane opposed to the InDents. In addition to synaptic signaling at ribbon and conventional synapses, Mb bipolar cells may exchange information with InDents by an alternative signaling mechanism.

Coincidence detection of convergent perforant path and mossy fibre inputs by CA3 interneurons

We performed whole-cell recordings from CA3 s. radiatum (R) and s. lacunosum-moleculare (L-M) interneurons in hippocampal slices to examine the temporal aspects of summation of converging perforant path (PP) and mossy fibre (MF) inputs. PP EPSPs were evoked from the s. lacunosum-moleculare in area CA1. MF EPSPs were evoked from the medial extent of the suprapyramidal blade of the dentate gyrus. Summation was strongly supralinear when examining PP EPSP with MF EPSP in a heterosynaptic pair at the 10 ms ISI, and linear to sublinear at longer ISIs. This pattern of nonlinearities suggests that R and L-M interneurons act as coincidence detectors for input from PP and MF. Summation at all ISIs was linear in voltage clamp mode demonstrating that nonlinearities were generated by postsynaptic voltage-dependent conductances. Supralinearity was not detected when the first EPSP in the pair was replaced by a simulated EPSP injected into the soma, suggesting that the conductances underlying the EPSP boosting were located in distal dendrites. Supralinearity was selectively eliminated with either Ni2+ (30 microm), mibefradil (10 microm) or nimodipine (15 microm), but was unaffected by QX-314. This pharmacological profile indicates that supralinearity is due to recruitment of dendritic T-type Ca2+channels by the first subthreshold EPSP in the pair. Results with the hyperpolarization-activated (Ih) channel blocker ZD 7288 (50 microm) revealed that Ih restricted the time course of supralinearity for coincidently summed EPSPs, and promoted linear to sublinear summation for asynchronous EPSPs. We conclude that coincidence detection results from the counterbalanced activation of T-type Ca2+ channels and inactivation of Ih.

Fractional cable models for spiny neuronal dendrites

Cable equations with fractional order temporal operators are introduced to model electrotonic properties of spiny neuronal dendrites. These equations are derived from Nernst-Planck equations with fractional order operators to model the anomalous subdiffusion that arises from trapping properties of dendritic spines. The fractional cable models predict that postsynaptic potentials propagating along dendrites with larger spine densities can arrive at the soma faster and be sustained at higher levels over longer times. Calibration and validation of the models should provide new insight into the functional implications of altered neuronal spine densities, a hallmark of normal aging and many neurodegenerative disorders.

Translating neuronal activity into dendrite elaboration: signaling to the nucleus

Growth and elaboration of neuronal processes is key to establishing neuronal connectivity critical for an optimally functioning nervous system. Neuronal activity clearly influences neuronal connectivity and does so via intracellular calcium signaling. A number of CaMKs and MAPKs convey the calcium signal initiated by neuronal activity. Several of these kinases interact with substrates in close proximity to the plasma membrane and alter dendrite structure locally via these local interactions. However, many calcium-activated kinases, such as Ras-MAPK and CaMKIV, target proteins in the nucleus, either by activating a downstream substrate that is a component of a signaling cascade or by directly acting within the nucleus. It is the activation of nuclear signaling and gene transcription that is thought to mediate global changes in dendrite complexity. The identification of calcium-sensitive transcription factors and transcriptional coactivators provides substantial evidence that gene transcription is a prevalent mechanism by which neuronal activity is translated into changes in dendrite complexity. The present review presents an overview of the role of neuronal activity in the development of neuronal dendrites, the signaling mechanisms that translate neuronal activity into gene transcription, and the transcribed effectors that regulate dendrite complexity.

A Very Simple Spiking Neuron Model That Allows for Modeling of Large, Complex Systems

This letter introduces a biologically inspired very simple spiking neuron model. The model retains only crucial aspects of biological neurons: a network of time-delayed weighted connections to other neurons, a threshold-based generation of action potentials, action potential frequency proportional to stimulus intensity, and interneuron communication that occurs with time-varying potentials that last longer than the associated action potentials. The key difference between this model and existing spiking neuron models is its great simplicity: it is basically a collection of linear and discontinuous functions with no differential equations to solve.

The model's ability to operate in a complex network was tested by using it as a basis of a network implementing a hypothetical echolocation system. The system consists of an emitter and two receivers. The outputs of the receivers are connected to a network of spiking neurons (using the proposed model) to form a detection grid that acts as a map of object locations in space. The network uses differences in the arrival times of the signals to determine the azimuthal angle of the source and time of flight to calculate the distance. The activation patterns observed indicate that for a network of spiking neurons, which uses only time delays to determine source locations, the spatial discrimination varies with the number and relative spacing of objects. These results are similar to those observed in animals that use echolocation.

Role of mTOR in physiology and pathology of the nervous system

Mammalian target of rapamycin (mTOR) is a serine-threonine protein kinase that regulates several intracellular processes in response to extracellular signals, nutrient availability, energy status of the cell and stress. mTOR regulates survival, differentiation and development of neurons. Axon growth and navigation, dendritic arborization, as well as synaptogenesis, depend on proper mTOR activity. In adult brain mTOR is crucial for synaptic plasticity, learning and memory formation, and brain control of food uptake. Recent studies reveal that mTOR activity is modified in various pathologic states of the nervous system, including brain tumors, tuberous sclerosis, cortical displasia and neurodegenerative disorders such as Alzheimer's, Parkinson's and Huntington's diseases. This review presents current knowledge about the role of mTOR in the physiology and pathology of the nervous system, with special focus on molecular targets acting downstream of mTOR that potentially contribute to neuronal development, plasticity and neuropathology.

Dendrite-to-Soma Input/Output Function of Continuous Time-Varying Signals in Hippocampal CA1 Pyramidal Neurons

We examined how hippocamal CA1 neurons process complex time-varying inputs that dendrites are likely to receive in vivo. We propose a functional model of the dendrite-to-soma input/output relationship that combines temporal integration and static-gain control mechanisms. Using simultaneous dual whole cell recordings, we injected 50 s of subthreshold and suprathreshold zero-mean white-noise current into the primary dendritic trunk along the proximal 2/3 of stratum radiatum and measured the membrane potential at the soma. Applying a nonlinear system-identification analysis, we found that a cascade of a linear filter followed by an adapting static-gain term fully accounted for the nonspiking input/output relationship between the dendrite and soma. The estimated filters contained a prominent band-pass region in the 1- to 10-Hz frequency range that remained constant as a function of stimulus variance. The gain of the dendrite-to-soma input/output relationship, in contrast, varied as a function of stimulus variance. When the contribution of the voltage-dependent current Ih was eliminated, the estimated filters lost their band-pass properties and the gain regulation was substantially altered. Our findings suggest that the dendrite-to-soma input/output relationship for proximal apical inputs to CA1 pyramidal neurons is well described as a band-pass filter in the theta frequency range followed by a gain-control nonlinearity that dynamically adapts to the statistics of the input signal.

Input-output relation of FitzHugh-Nagumo elements arranged in a trifurcated structure

In this study, the propagation of an action potential in a network of excitable elements is studied numerically. The network we consider consists of excitable elements arranged in the shape of a trifurcated structure having three cables. The system has a branch point, a Y junction, at which the three cables are joined. Two types of external stimulations are considered: a single impulsive stimulation at one of the cable terminals, and a pair of stimuli applied to two different terminals. We have found three basic phases depending on the excitability of the elements for a single external stimulus as follows: (1) signal distributor--as the excitability gets higher, the pulse generated by a stimulus splits into two at the branch point, and two pulses are transmitted to the opposite terminals, (2) propagation block--the pulse in the lower excitable chain is blocked at the branch point, and (3) transient propagation--as the excitability is decreased further, we see that the pulse vanishes before reaching the branch point. By the interaction between the pulses that originate from different sources, signal transmission is recovered if the pulses arrive at the branch point nearly synchronously or after a specific delay time. The effects of the repetition of these two types of stimulation are also investigated. Complex spatiotemporal patterns occur due to pulse-pulse interaction and collisions at the branch point. The input-output relationship, which depends crucially on the repetition period and the time lag between the pair of stimuli, is characterized by the stimulus-response ratio and the interspike interval. We also show the effects of noise on the distribution of the interspike interval.

Branching dendrites with resonant membrane: a "sum-over-trips" approach

Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. It is well known that dendritic morphology plays an important role in the function of dendrites. Another important contribution to the response characteristics of a single neuron comes from the intrinsic resonant properties of dendritic membrane. In this paper we combine the effects of dendritic branching and resonant membrane dynamics by generalising the "sum-over-trips" approach (Abbott et al. in Biol Cybernetics 66, 49-60 1991). To illustrate how this formalism can shed light on the role of architecture and resonances in determining neuronal output we consider dual recording and reconstruction data from a rat CA1 hippocampal pyramidal cell. Specifically we explore the way in which an Ih current contributes to a voltage overshoot at the soma.

Optimization principles of dendritic structure

Background

Dendrites are the most conspicuous feature of neurons. However, the principles determining their structure are poorly understood. By employing cable theory and, for the first time, graph theory, we describe dendritic anatomy solely on the basis of optimizing synaptic efficacy with minimal resources.

Results

We show that dendritic branching topology can be well described by minimizing the path length from the neuron's dendritic root to each of its synaptic inputs while constraining the total length of wiring. Tapering of diameter toward the dendrite tip – a feature of many neurons – optimizes charge transfer from all dendritic synapses to the dendritic root while housekeeping the amount of dendrite volume. As an example, we show how dendrites of fly neurons can be closely reconstructed based on these two principles alone.

neuroConstruct: a tool for modeling networks of neurons in 3D space

Conductance-based neuronal network models can help us understand how synaptic and cellular mechanisms underlie brain function. However, these complex models are difficult to develop and are inaccessible to most neuroscientists. Moreover, even the most biologically realistic network models disregard many 3D anatomical features of the brain. Here, we describe a new software application, neuroConstruct, that facilitates the creation, visualization, and analysis of networks of multicompartmental neurons in 3D space. A graphical user interface allows model generation and modification without programming. Models within neuroConstruct are based on new simulator-independent NeuroML standards, allowing automatic generation of code for NEURON or GENESIS simulators. neuroConstruct was tested by reproducing published models and its simulator independence verified by comparing the same model on two simulators. We show how more anatomically realistic network models can be created and their properties compared with experimental measurements by extending a published 1D cerebellar granule cell layer model to 3D.

A new stochastic tridimensional model of neonatal rat spinal motoneuron for investigating compartmentalization of neuronal conductances and their influence on firing

During postnatal development spinal motoneurons play a major role in expressing basic behaviours like reflex reactions and in allowing the onset of the locomotor programme. For this purpose it is useful to clarify how various inputs are integrated at the level of the motoneuron soma to generate phasic or rhythmic firing. Although existing models of motoneurons have indicated the distributed role of certain conductances in regulating firing, it is unclear how the spatial distribution of certain currents is ultimately shaping motoneuron output. Thus, it would be helpful to build a bridge between histological and electrophysiological data. The present report is based on the construction of a 3D motoneuron model based on available parameters applicable to the neonatal spinal cord. The presented algorithm allows building up a complex, variable dendrogram which, together with the somatic and axonic compartments, enables strategic location of certain voltage or ligand gated conductances and simulation of resulting electrical behaviour. One application of the present model has been exploring the functional location of the recently reported cystic fibrosis transmembrane conductance regulator (CFTR) which controls Cl(-) homeostasis of postnatal motoneurons. The 3D model is made available for free, user friendly use via the dedicated web site http://www.mn-morphology.org.

Reversed somatodendritic I(h) gradient in a class of rat hippocampal neurons with pyramidal morphology

In CA1 and neocortical pyramidal neurons, I(h) is present primarily in the dendrites. We asked if all neurons of a pyramidal morphology have a similar density of I(h). We characterized a novel class of hippocampal neurons with pyramidal morphology found in the stratum radiatum, which we termed the 'pyramidal-like principal' (PLP) neuron. Morphological similarities to pyramidal neurons were verified by filling the neurons with biocytin. PLPs did not stain for markers associated with interneurons, and projected to both the septum and olfactory bulb. By using cell-attached patch-clamp recordings, we found that these neurons expressed a high density of I(h) in the soma that declined to a lower density in the dendrites, a pattern that is reversed compared to pyramidal neurons. The voltage-dependent activation and activation time constants of I(h) in the PLPs were similar to pyramidal neurons. Whole-cell patch-clamp recordings from the soma and dendrites of PLP neurons showed no significant differences in input resistance and local temporal summation between the two locations. Blockade of I(h) by ZD7288 increased the input resistance and temporal summation of simulated EPSPs, as in pyramidal neurons. When NMDA receptors were blocked, temporal summation at the soma of distal synaptic potentials was similar to that seen with current injections at the soma, suggesting a 'normalization' of temporal summation similar to that observed in pyramidal neurons. Thus, we have characterized a principal neuronal subtype in the hippocampus with a similar morphology but reversed I(h) somatodendritic gradient to that previously observed in CA1 hippocampal and neocortical pyramidal neurons.

Three dimensional transport lattice model for describing action potentials in axons stimulated by external electrodes

Conditions that stimulate action potentials in one or more nerves is of widespread interest. Axon and nerve models are usually based on two dimensional pre-specified lumped equivalents that assume where currents will flow. In contrast, here we illustrate creation of three dimensional (3D) system models with a transport lattice of interconnected local models for external and internal electrolyte and axon membrane. The transport lattice solves Laplace's equation in the extracellular medium and is coupled to the Hodgkin-Huxley model at local membrane sites. These space-filling models incorporate the geometric scale, which allows explicit representation of confined axons and external electrodes. The present results demonstrate feasibility of the basic approach. These models are spatially coarse and approximate, but can be straightforwardly improved. The transport lattice system models are modular and multiscale (spatial scales ranging from the membrane thickness of 5 nm to the axon segment length of 2 cm).

Functional significance of passive and active dendritic properties in the synaptic integration by an identified nonspiking interneuron of crayfish

Nonspiking interneurons control their synaptic output directly by membrane potential changes caused by synaptic activities. Although these interneurons do not generate spikes, their dendritic membrane is endowed with a variety of voltage-dependent conductances whose functional significance in synaptic integration remains unknown. We quantitatively investigated how the passive and active dendritic properties affect the synaptic integration in an identified nonspiking interneuron of crayfish by computer simulation using its multicompartment model based on electrophysiological measurements and three-dimensional morphometry. At the resting potential level, the attenuation factor (V(s)/V(t)) of a unitary synaptic potential in the course of its spread from a dendritic terminal (V(s)) to other terminals (V(t)) ranged from 4.42 to 6.30 with no substantial difference between hyperpolarizing and depolarizing potentials. The compound synaptic responses to strong mechanosensory stimulation could be reproduced in calculation only as the result of spatial summation of attenuated potentials, not as any single large potential. The characteristic response could be reproduced by assuming that the active conductances were distributed only in the dendritic region where the synaptic summation was carried out. The active conductances in other parts of the cell affected neither the shape of the compound synaptic response nor the dendritic spread of synaptic potentials. These findings suggest that the active membrane conductances do not affect the spatial distribution of synaptic potentials over dendrites but function in sculpting the summed synaptic potential to enhance temporal resolution in the synaptic output of the nonspiking interneuron.

Spike timing-dependent plasticity: from synapse to perception

Information in the nervous system may be carried by both the rate and timing of neuronal spikes. Recent findings of spike timing-dependent plasticity (STDP) have fueled the interest in the potential roles of spike timing in processing and storage of information in neural circuits. Induction of long-term potentiation (LTP) and long-term depression (LTD) in a variety of in vitro and in vivo systems has been shown to depend on the temporal order of pre- and postsynaptic spiking. Spike timing-dependent modification of neuronal excitability and dendritic integration was also observed. Such STDP at the synaptic and cellular level is likely to play important roles in activity-induced functional changes in neuronal receptive fields and human perception.

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.

Branch-specific Ca2+ influx from Na+-dependent dendritic spikes in olfactory granule cells

Two-photon laser scanning microscopy was used to correlate electrical events detected with whole-cell somatic recordings to Ca2+ transients in dendrites of olfactory bulb granule cells. A subset of spontaneous subthreshold depolarizing events recorded at the soma were shown to correspond to suprathreshold dendritic, Na-dependent action potentials [APs; dendritic spikes (D-spikes)]. These potentials were blocked by intracellular QX-314 (lidocaine N-ethyl bromide), hyperpolarizing current injection at the soma, and by partial inhibition of AMPA/kainate receptors with 0.75 microM DNQX. They were affected only slightly by 100 microM NiCl2. The majority of D-spikes recorded at the soma had a time to peak of <4 ms, comparable with somatic APs, a nonexponential decay, and amplitudes between 3 and 21 mV. Somatically recorded APs produced Ca2+ transients that were observed in spines and dendrites in all parts of the cell. Ca2+ transients from D-spikes were restricted to subsets of distal dendrites and their associated spines but were absent from the soma and dendrite within approximately 50-80 microm of the soma. Ca2+ transients in different branches could be correlated with different-sized D-spikes. D-spike and backpropagating AP-induced Ca2+ transients summed in dendrites, provided the interval between them was >5-6 ms. Generation of a D-spike in a particular dendrite <5-6 ms before a somatic AP blocked backpropagation of the somatic AP into that dendrite. The temporally specific interplay between D-spikes and backpropagating APs may play a role in regulating feedback and feedforward inhibition of groups of mitral cells synapsing on different granule cell dendrites.

A biopolymer transistor: electrical amplification by microtubules

Microtubules (MTs) are important cytoskeletal structures engaged in a number of specific cellular activities, including vesicular traffic, cell cyto-architecture and motility, cell division, and information processing within neuronal processes. MTs have also been implicated in higher neuronal functions, including memory and the emergence of "consciousness". How MTs handle and process electrical information, however, is heretofore unknown. Here we show new electrodynamic properties of MTs. Isolated, taxol-stabilized MTs behave as biomolecular transistors capable of amplifying electrical information. Electrical amplification by MTs can lead to the enhancement of dynamic information, and processivity in neurons can be conceptualized as an "ionic-based" transistor, which may affect, among other known functions, neuronal computational capabilities.

Coincidence detection of synaptic inputs is facilitated at the distal dendrites after long-term potentiation induction

Two major aspects of dendritic integration, coincidence detection and temporal integration, depend critically on the spatial and temporal properties of the dendritic summation of synaptic inputs. Neuronal activity capable of inducing synaptic long-term potentiation (LTP) leads to increased linearity of the spatial summation of synchronous EPSPs. Whether such activity can also modulate the temporal summation of EPSPs is unknown. In the present study, we examined the linearity of the summation of EPSPs spaced by different time intervals in hippocampal CA1 pyramidal neurons, before and after LTP induction. We found that LTP induction resulted in an increased linearity of summation of the potentiated input with another synchronous or asynchronous input, with a striking dendritic location-specific selectivity for the timing of the summed inputs. At distal dendrites, LTP induction led to an increased linearity of summation only for EPSPs arriving within 5 ms, thus favoring the summation of coincident inputs. In contrast, LTP induction at proximal dendrites increased the linearity of summation for EPSPs arriving within a time window of >20 ms. Furthermore, for synaptic inputs at the distal dendrite, enhanced spiking output after LTP induction was observed only for coincidently summed EPSPs, suggesting facilitated coincidence detection. In contrast, for proximal inputs, enhanced spiking output after LTP induction occurred for EPSPs arriving within a broader time window of approximately 20 ms, favoring temporal integration. Such dendritic location-dependent differential modulation of coincidence detection and temporal integration by neuronal activity represents a form of activity-dependent and domain-specific plasticity in the function of dendritic information processing.

Cellular signalling properties in microcircuits

Molecules and cells are the signalling elements in microcircuits. Recent studies have uncovered bewildering diversity in postsynaptic signalling properties in all areas of the vertebrate nervous system. Major effort is now being invested in establishing the specialized signalling properties at the cellular and molecular levels in microcircuits in specific brain regions. This review is part of the TINS Microcircuits Special Feature.

Cylindrical cell membranes in uniform applied electric fields: validation of a transport lattice method

The frequency and time domain transmembrane voltage responses of a cylindrical cell in an external electric field are calculated using a transport lattice, which allows solution of a variety of biologically relevant transport problems with complex cell geometry and field interactions. Here we demonstrate the method for a cylindrical membrane geometry and compare results with known analytical solutions. Results of transport lattice simulations on a Cartesian lattice are found to have discrepancies with the analytical solutions due to the limited volume of the system model and approximations for the local membrane model on the Cartesian lattice. Better agreement is attained when using a triangular mesh to represent the geometry rather than a Cartesian lattice. The transport lattice method can be readily extended to more sophisticated cell, organelle, and tissue configurations. Local membrane models within a system lattice can also include nonlinear responses such as electroporation and ion-channel gating.

Dendritic computation

One of the central questions in neuroscience is how particular tasks, or computations, are implemented by neural networks to generate behavior. The prevailing view has been that information processing in neural networks results primarily from the properties of synapses and the connectivity of neurons within the network, with the intrinsic excitability of single neurons playing a lesser role. As a consequence, the contribution of single neurons to computation in the brain has long been underestimated. Here we review recent work showing that neuronal dendrites exhibit a range of linear and nonlinear mechanisms that allow them to implement elementary computations. We discuss why these dendritic properties may be essential for the computations performed by the neuron and the network and provide theoretical and experimental examples to support this view.

Synaptic integration in dendritic trees

Most neurons have elaborate dendritic trees that receive tens of thousands of synaptic inputs. Because postsynaptic responses to individual synaptic events are usually small and transient, the integration of many synaptic responses is needed to depolarize most neurons to action potential threshold. Over the past decade, advances in electrical and optical recording techniques have led to new insights into how synaptic responses propagate and interact within dendritic trees. In addition to their passive electrical and morphological properties, dendrites express active conductances that shape individual synaptic responses and influence synaptic integration locally within dendrites. Dendritic voltage-gated Na(+) and Ca(2+) channels support action potential backpropagation into the dendritic tree and local initiation of dendritic spikes, whereas K(+) conductances act to dampen dendritic excitability. While all dendrites investigated to date express active conductances, different neuronal types show specific patterns of dendritic channel expression leading to cell-specific differences in the way synaptic responses are integrated within dendritic trees. This review explores the way active and passive dendritic properties shape synaptic responses in the dendrites of central neurons, and emphasizes their role in synaptic integration.

Functionally relevant measures of spatial complexity in neuronal dendritic arbors

We introduce a set of scaling exponents for characterizing global 3D morphologic properties of mass distribution, branching and taper in neuronal dendritic arbors, capable of distinguishing functionally relevant changes in dendritic complexity that standard Sholl analysis and fractal analysis cannot. We demonstrate that the scaling exponent for mass distribution, d(M), comprises a sum of independent scaling exponents for branching, d(N), and taper, d(T). The accuracy of experimental measurements of the scaling exponents was verified using computer generated self-similar binary trees of known fractal dimension, and with prescribed amounts of branching and taper. The theory was applied to measuring 3D spatial complexity in the apical and basal dendritic trees of two functionally distinct types of macaque monkey neocortical pyramidal neurons: long corticocortical projection neurons from superior temporal cortex to area 46 of the prefrontal cortex (PFC), and local projection neurons within area 46 of the PFC. Two distinct scaling subregions (proximal and medial) were identified in both apical and basal trees of the two neuron types, and scaling exponents were fitted. A small but significant difference in mass scaling in the proximal region distinguished long from local projection neurons. Interestingly, both classes of neuron exhibited a homeostatic pattern of mass distribution across the two regions: despite large differences between proximal and medial regions in branching and tapering exponents, these effects were compensatory, resulting in a uniform, slow reduction of mass with distance from the soma, over both scaling regions of the apical and basal trees. Given a uniformly excitable membrane, the electrotonic properties of dendritic arbors depend entirely upon mass distribution, and its relative contributions from dendritic branching and taper. By capturing each of these complex morphologic properties in a single, globally descriptive parameter, the new 3D scaling exponents introduced in this study permit efficient morphometric characterization of complex dendritic arbors in the fewest possible parameters, that can be directly related to their electrotonic properties, and hence to neuronal function.

Single-neuron theory of consciousness

By most accounts, the mind arises from the integrated activity of large populations of neurons distributed across multiple brain regions. A contrasting model is presented in the present paper that places the mind/brain interface not at the whole brain level but at the level of single neurons. Specifically, it is proposed that each neuron in the nervous system is independently conscious, with conscious content corresponding to the spatial pattern of a portion of that neuron's dendritic electrical activity. For most neurons, such as those in the hypothalamus or posterior sensory cortices, the conscious activity would be assumed to be simple and unable to directly affect the organism's macroscopic conscious behavior. For a subpopulation of layer 5 pyramidal neurons in the lateral prefrontal cortices, however, an arrangement is proposed to be present such that, at any given moment: (i) the spatial pattern of electrical activity in a portion of the dendritic tree of each neuron in the subpopulation individually manifests a complexity and diversity sufficient to account for the complexity and diversity of conscious experience; (ii) the dendritic trees of the neurons in the subpopulation all contain similar spatial electrical patterns; (iii) the spatial electrical pattern in the dendritic tree of each neuron interacts non-linearly with the remaining ambient dendritic electrical activity to determine the neuron's overall axonal response; (iv) the dendritic spatial pattern is reexpressed at the population level by the spatial pattern exhibited by a synchronously firing subgroup of the conscious neurons, thereby providing a mechanism by which conscious activity at the neuronal level can influence overall behavior. The resulting scheme is one in which conscious behavior appears to be the product of a single macroscopic mind, but is actually the integrated output of a chorus of minds, each associated with a different neuron.

Dynamic spatiotemporal synaptic integration in cortical neurons: neuronal gain, revisited

Gain modulation is a ubiquitous phenomenon in cortical neurons, providing flexibility to operate under changing conditions. The prevailing view is that this modulation reflects a change in the relationship between mean input and output firing rate brought about by variation in neuronal membrane characteristics. An alternative mechanism is proposed for neuronal gain modulation that takes into account the capability of cortical neurons to process spatiotemporal synaptic correlations. Through the use of numerical simulations, it is shown that voltage-gated and leak conductances, membrane potential, noise, and input firing rate modify the sensitivity of cortical neurons to the degree of temporal correlation between their synaptic inputs. These changes are expressed in a change of the temporal window for synaptic integration and the range of input correlation over which response probability is graded. The study also demonstrates that temporal integration depends on the distance between the inputs and that this interplay of space and time is modulated by voltage-gated and leak conductances. Thus, gain modulation may reflect a change in the relationship between spatiotemporal synaptic correlations and output firing probability. It is further proposed that by acting synergistically with the network, dynamic spatiotemporal synaptic integration in cortical neurons may serve a functional role in the formation of dynamic cell assemblies.

A probabilistic framework for region-specific remodeling of dendrites in three-dimensional neuronal reconstructions

Dendritic arborization is an important determinant of single-neuron function as well as the circuitry among neurons. Dendritic trees undergo remodeling during development, aging, and many pathological conditions, with many of the morphological changes being confined to certain regions of the dendritic tree. In order to analyze the functional consequences of such region-specific dendritic remodeling, it is essential to develop techniques that can systematically manipulate three-dimensional reconstructions of neurons. Hence, in this study, we develop an algorithm that uses statistics from precise morphometric analyses to systematically remodel neuronal reconstructions. We use the distribution function of the ratio of two normal distributed random variables to specify the probabilities of remodeling along various regions of the dendritic arborization. We then use these probabilities to drive an iterative algorithm for manipulating the dendritic tree in a region-specific manner. As a test, we apply this framework to a well-characterized example of dendritic remodeling: stress-induced dendritic atrophy in hippocampal CA3 pyramidal cells. We show that our pruning algorithm is capable of eliciting atrophy that matches biological data from rodent models of chronic stress.

Computational models of epileptiform activity in single neurons

A series of original computational models written in NEURON of increasing physiological and morphological complexity were developed to determine the dominant causes of epileptiform behavior. Current injections to a model hippocampal pyramidal neuron consisting of three compartments produced the sustained depolarizations (SD) and simple paroxysmal depolarizing shifts (PDS) characteristic of ictal and interictal behavior in a cell, respectively. Our results indicate that SDs are the result of the semi-saturation of Na+, Ca2+ and K+ active channels, particularly the CaN, with regular Na+/K+ spikes riding atop a saturated depolarization; PDS rides on a similar semi-saturated depolarization whose shape depends more heavily on interactions between low-threshold voltage-gated Ca2+ channels (CaT) and Ca(2+)-dependent K+ channels. Our results reflect and predict recent physiological data, and we report here a cellular basis of epilepsy whose mechanisms reside mainly in the membrane channels, and not in specific morphology or network interactions, advancing a possible resolution to the cellular/network debate over the etiology of epileptiform activity.

Progress in Functional Neuroanatomy: Precise Automatic Geometric Reconstruction of Neuronal Morphology From Confocal Image Stacks

Dendritic architecture provides the structural substrate for myriads of input and output synapses in the brain and for the integration of presynaptic inputs. Understanding mechanisms of evolution and development of neuronal shape and its respective function is thus a formidable problem in neuroscience. A fundamental prerequisite for finding answers is a precise quantitative analysis of neuronal structure in situ and in vivo. Therefore we have developed a tool set for automatic geometric reconstruction of neuronal architecture from stacks of confocal images. It provides exact midlines, diameters, surfaces, volumes, and branch point locations and allows analysis of labeled molecule distribution along neuronal surfaces as well as direct export into modeling software. We show the high accuracy of geometric reconstruction and the analysis of putative input synapse distribution throughout entire dendritic trees from in situ light microscopy preparations as a possible application. The binary version of the reconstruction module is downloadable at no cost.

Reconstruct: a free editor for serial section microscopy

Many microscopy studies require reconstruction from serial sections, a method of analysis that is sometimes difficult and time-consuming. When each section is cut, mounted and imaged separately, section images must be montaged and realigned to accurately analyse and visualize the three-dimensional (3D) structure. Reconstruct is a free editor designed to facilitate montaging, alignment, analysis and visualization of serial sections. The methods used by Reconstruct for organizing, transforming and displaying data enable the analysis of series with large numbers of sections and images over a large range of magnifications by making efficient use of computer memory. Alignments can correct for some types of non-linear deformations, including cracks and folds, as often encountered in serial electron microscopy. A large number of different structures can be easily traced and placed together in a single 3D scene that can be animated or saved. As a flexible editor, Reconstruct can reduce the time and resources expended for serial section studies and allows a larger tissue volume to be analysed more quickly.

Spike-timing-dependent synaptic plasticity depends on dendritic location

In the neocortex, each neuron receives thousands of synaptic inputs distributed across an extensive dendritic tree. Although postsynaptic processing of each input is known to depend on its dendritic location, it is unclear whether activity-dependent synaptic modification is also location-dependent. Here we report that both the magnitude and the temporal specificity of spike-timing-dependent synaptic modification vary along the apical dendrite of rat cortical layer 2/3 pyramidal neurons. At the distal dendrite, the magnitude of long-term potentiation is smaller, and the window of pre-/postsynaptic spike interval for long-term depression (LTD) is broader. The spike-timing window for LTD correlates with the window of action potential-induced suppression of NMDA (N-methyl-D-aspartate) receptors; this correlation applies to both their dendritic location-dependence and pharmacological properties. Presynaptic stimulation with partial blockade of NMDA receptors induced LTD and occluded further induction of spike-timing-dependent LTD, suggesting that NMDA receptor suppression underlies LTD induction. Computer simulation studies showed that the dendritic inhomogeneity of spike-timing-dependent synaptic modification leads to differential input selection at distal and proximal dendrites according to the temporal characteristics of presynaptic spike trains. Such location-dependent tuning of inputs, together with the dendritic heterogeneity of postsynaptic processing, could enhance the computational capacity of cortical pyramidal neurons.