Untangling dendrites with quantitative models

Dendritic patch-clamp recordings from cerebellar granule cells demonstrate electrotonic compactness

Cerebellar granule cells (GCs), the smallest neurons in the brain, have on average four short dendrites that receive high-frequency mossy fiber inputs conveying sensory information. The short length of the dendrites suggests that GCs are electrotonically compact allowing unfiltered integration of dendritic inputs. The small average diameter of the dendrites (~0.7 µm), however, argues for dendritic filtering. Previous studies based on somatic recordings and modeling indicated that GCs are electrotonically extremely compact. Here, we performed patch-clamp recordings from GC dendrites in acute brain slices of mice to directly analyze the electrotonic properties of GCs. Strikingly, the input resistance did not differ significantly between dendrites and somata of GCs. Furthermore, spontaneous excitatory postsynaptic potentials (EPSP) were similar in amplitude at dendritic and somatic recording sites. From the dendritic and somatic input resistances we determined parameters characterizing the electrotonic compactness of GCs. These data directly demonstrate that cerebellar GCs are electrotonically compact and thus ideally suited for efficient high-frequency information transfer.

Synaptic clustering within dendrites: an emerging theory of memory formation

It is generally accepted that complex memories are stored in distributed representations throughout the brain, however the mechanisms underlying these representations are not understood. Here, we review recent findings regarding the subcellular mechanisms implicated in memory formation, which provide evidence for a dendrite-centered theory of memory. Plasticity-related phenomena which affect synaptic properties, such as synaptic tagging and capture, synaptic clustering, branch strength potentiation and spinogenesis provide the foundation for a model of memory storage that relies heavily on processes operating at the dendrite level. The emerging picture suggests that clusters of functionally related synapses may serve as key computational and memory storage units in the brain. We discuss both experimental evidence and theoretical models that support this hypothesis and explore its advantages for neuronal function.

Neural population coding: combining insights from microscopic and mass signals

Behavior relies on the distributed and coordinated activity of neural populations. Population activity can be measured using multi-neuron recordings and neuroimaging. Neural recordings reveal how the heterogeneity, sparseness, timing, and correlation of population activity shape information processing in local networks, whereas neuroimaging shows how long-range coupling and brain states impact on local activity and perception. To obtain an integrated perspective on neural information processing we need to combine knowledge from both levels of investigation. We review recent progress of how neural recordings, neuroimaging, and computational approaches begin to elucidate how interactions between local neural population activity and large-scale dynamics shape the structure and coding capacity of local information representations, make them state-dependent, and control distributed populations that collectively shape behavior.

Neurite, a finite difference large scale parallel program for the simulation of electrical signal propagation in neurites under mechanical loading

With the growing body of research on traumatic brain injury and spinal cord injury, computational neuroscience has recently focused its modeling efforts on neuronal functional deficits following mechanical loading. However, in most of these efforts, cell damage is generally only characterized by purely mechanistic criteria, functions of quantities such as stress, strain or their corresponding rates. The modeling of functional deficits in neurites as a consequence of macroscopic mechanical insults has been rarely explored. In particular, a quantitative mechanically based model of electrophysiological impairment in neuronal cells, Neurite, has only very recently been proposed. In this paper, we present the implementation details of this model: a finite difference parallel program for simulating electrical signal propagation along neurites under mechanical loading. Following the application of a macroscopic strain at a given strain rate produced by a mechanical insult, Neurite is able to simulate the resulting neuronal electrical signal propagation, and thus the corresponding functional deficits. The simulation of the coupled mechanical and electrophysiological behaviors requires computational expensive calculations that increase in complexity as the network of the simulated cells grows. The solvers implemented in Neurite--explicit and implicit--were therefore parallelized using graphics processing units in order to reduce the burden of the simulation costs of large scale scenarios. Cable Theory and Hodgkin-Huxley models were implemented to account for the electrophysiological passive and active regions of a neurite, respectively, whereas a coupled mechanical model accounting for the neurite mechanical behavior within its surrounding medium was adopted as a link between electrophysiology and mechanics. This paper provides the details of the parallel implementation of Neurite, along with three different application examples: a long myelinated axon, a segmented dendritic tree, and a damaged axon. The capabilities of the program to deal with large scale scenarios, segmented neuronal structures, and functional deficits under mechanical loading are specifically highlighted.

Bilinearity in spatiotemporal integration of synaptic inputs

Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conductance inputs, we derive a bilinear spatiotemporal dendritic integration rule. The summed somatic potential can be well approximated by the linear summation of the two postsynaptic potentials elicited separately, plus a third additional bilinear term proportional to their product with a proportionality coefficient [Formula: see text]. The rule is valid for a pair of synaptic inputs of all types, including excitation-inhibition, excitation-excitation, and inhibition-inhibition. In addition, the rule is valid during the whole dendritic integration process for a pair of synaptic inputs with arbitrary input time differences and input locations. The coefficient [Formula: see text] is demonstrated to be nearly independent of the input strengths but is dependent on input times and input locations. This rule is then verified through simulation of a realistic pyramidal neuron model and in electrophysiological experiments of rat hippocampal CA1 neurons. The rule is further generalized to describe the spatiotemporal dendritic integration of multiple excitatory and inhibitory synaptic inputs. The integration of multiple inputs can be decomposed into the sum of all possible pairwise integration, where each paired integration obeys the bilinear rule. This decomposition leads to a graph representation of dendritic integration, which can be viewed as functionally sparse.

Dendritic orientation and branching distinguish a class of multifunctional turtle spinal interneurons

Spinal interneurons can integrate diverse propriospinal and supraspinal inputs that trigger or modulate locomotion and other limb movements. These synaptic inputs can occur on distal dendrites and yet must remain effective at the soma. Active dendritic conductances may amplify distal dendritic inputs, but appear to play a minimal role during scratching, at least. Another possibility is that spinal interneurons that integrate inputs on distal dendrites have unusually simple dendritic trees that effectively funnel current to the soma. We previously described a class of spinal interneurons, called transverse interneurons (or T neurons), in adult turtles. T neurons were defined as having dendrites that extend further in the transverse plane than rostrocaudally and a soma that extends further mediolaterally than rostrocaudally. T neurons are multifunctional, as they were activated during both swimming and scratching motor patterns. T neurons had higher peak firing rates and larger membrane potential oscillations during scratching than scratch-activated interneurons with different dendritic morphologies (“non-T” neurons). These characteristics make T neurons good candidates to play an important role in integrating diverse inputs and generating or relaying rhythmic motor patterns. Here, we quantitatively investigated additional dendritic morphological characteristics of T neurons as compared to non-T neurons. We found that T neurons have less total dendritic length, a greater proportion of dendritic length in primary dendrites, and dendrites that are oriented more mediolaterally. Thus, T neuron dendritic trees extend far mediolaterally, yet are unusually simple, which may help channel synaptic current from distal dendrites in the lateral and ventral funiculi to the soma. In combination with T neuron physiological properties, these dendritic properties may help integrate supraspinal and propriospinal inputs and generate and/or modulate rhythmic limb movements.

CD44 regulates dendrite morphogenesis through Src tyrosine kinase-dependent positioning of the Golgi

The acquisition of proper dendrite morphology is a crucial aspect of neuronal development towards the formation of a functional network. The role of the extracellular matrix and its cellular receptors in this process has remained enigmatic. We report that the CD44 adhesion molecule, the main hyaluronan receptor, is localized in dendrites and plays a crucial inhibitory role in dendritic tree arborization in vitro and in vivo. This novel function is exerted by the activation of Src tyrosine kinase, leading to the alteration of Golgi morphology. The mechanism operates during normal brain development, but its inhibition might have a protective influence on dendritic trees under toxic conditions, during which the silencing of CD44 expression prevents dendritic shortening induced by glutamate exposure. Overall, our results indicate a novel role for CD44 as an essential regulator of dendritic arbor complexity in both health and disease.

LEMS: a language for expressing complex biological models in concise and hierarchical form and its use in underpinning NeuroML 2

Computational models are increasingly important for studying complex neurophysiological systems. As scientific tools, it is essential that such models can be reproduced and critically evaluated by a range of scientists. However, published models are currently implemented using a diverse set of modeling approaches, simulation tools, and computer languages making them inaccessible and difficult to reproduce. Models also typically contain concepts that are tightly linked to domain-specific simulators, or depend on knowledge that is described exclusively in text-based documentation. To address these issues we have developed a compact, hierarchical, XML-based language called LEMS (Low Entropy Model Specification), that can define the structure and dynamics of a wide range of biological models in a fully machine readable format. We describe how LEMS underpins the latest version of NeuroML and show that this framework can define models of ion channels, synapses, neurons and networks. Unit handling, often a source of error when reusing models, is built into the core of the language by specifying physical quantities in models in terms of the base dimensions. We show how LEMS, together with the open source Java and Python based libraries we have developed, facilitates the generation of scripts for multiple neuronal simulators and provides a route for simulator free code generation. We establish that LEMS can be used to define models from systems biology and map them to neuroscience-domain specific simulators, enabling models to be shared between these traditionally separate disciplines. LEMS and NeuroML 2 provide a new, comprehensive framework for defining computational models of neuronal and other biological systems in a machine readable format, making them more reproducible and increasing the transparency and accessibility of their underlying structure and properties.

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

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

An Augmented Two-Layer Model Captures Nonlinear Analog Spatial Integration Effects in Pyramidal Neuron Dendrites

In pursuit of the goal to understand and eventually reproduce the diverse functions of the brain, a key challenge lies in reverse engineering the peculiar biology-based "technology" that underlies the brain's remarkable ability to process and store information. The basic building block of the nervous system is the nerve cell, or "neuron," yet after more than 100 years of neurophysiological study and 60 years of modeling, the information processing functions of individual neurons, and the parameters that allow them to engage in so many different types of computation (sensory, motor, mnemonic, executive, etc.) remain poorly understood. In this paper, we review both historical and recent findings that have led to our current understanding of the analog spatial processing capabilities of dendrites, the major input structures of neurons, with a focus on the principal cell type of the neocortex and hippocampus, the pyramidal neuron (PN). We encapsulate our current understanding of PN dendritic integration in an abstract layered model whose spatially sensitive branch-subunits compute multidimensional sigmoidal functions. Unlike the 1-D sigmoids found in conventional neural network models, multidimensional sigmoids allow the cell to implement a rich spectrum of nonlinear modulation effects directly within their dendritic trees.

Versatile morphometric analysis and visualization of the three-dimensional structure of neurons

The computational properties of a neuron are intimately related to its morphology. However, unlike electrophysiological properties, it is not straightforward to collapse the complexity of the three-dimensional (3D) structure into a small set of measurements accurately describing the structural properties. This strong limitation leads to the fact that many studies involving morphology related questions often rely solely on empirical analysis and qualitative description. It is possible however to acquire hierarchical lists of positions and diameters of points describing the spatial structure of the neuron. While there is a number of both commercially and freely available solutions to import and analyze this data, few are extendable in the sense of providing the possibility to define novel morphometric measurements in an easy to use programming environment. Fewer are capable of performing morphometric analysis where the output is defined over the topology of the neuron, which naturally requires powerful visualization tools. The computer application presented here, Py3DN, is an open-source solution providing novel tools to analyze and visualize 3D data collected with the widely used Neurolucida (MBF) system. It allows the construction of mathematical representations of neuronal topology, detailed visualization and the possibility to define non-standard morphometric analysis on the neuronal structures. Above all, it provides a flexible and extendable environment where new types of analyses can be easily set up allowing a high degree of freedom to formulate and test new hypotheses. The application was developed in Python and uses Blender (open-source software) to produce detailed 3D data representations.

Semi-automatic quantification of neurite fasciculation in high-density neurite images by the neurite directional distribution analysis (NDDA)

BACKGROUND

Bundling of neurite extensions occur during nerve development and regeneration. Understanding the factors that drive neurite bundling is important for designing biomaterials for nerve regeneration toward the innervation target and preventing nociceptive collateral sprouting. High-density neuron cultures including dorsal root ganglia explants are employed for in vitro screening of biomaterials designed to control directional outgrowth. Although some semi-automated image processing methods exist for quantification of neurite outgrowth, methods to quantify axonal fasciculation in terms of direction of neurite outgrowth are lacking.

NEW METHOD

This work presents a semi-automated program to analyze micrographs of high-density neurites; the program aims to quantify axonal fasciculation by determining the orientational distribution function of the tangent vectors of the neurites and calculating its Fourier series coefficients ('c' values).

RESULTS

We found that neurite directional distribution analysis (NDDA) of fasciculated neurites yielded 'c' values of ≥∼0.25 whereas branched outgrowth led to statistically significant lesser values of <∼0.2. The 'c' values correlated directly to the width of neurite bundles and indirectly to the number of branching points.

COMPARISON WITH EXISTING METHODS

Information about the directional distribution of outgrowth is lost in simple counting methods or achieved laboriously through manual analysis. The NDDA supplements previous quantitative analyses of axonal bundling using a vector-based approach that captures new information about the directionality of outgrowth.

CONCLUSION

The NDDA is a valuable addition to open source image processing tools available to biomedical researchers offering a robust, precise approach to quantification of imaged features important in tissue development, disease, and repair.

Neural codes formed by small and temporally precise populations in auditory cortex

The encoding of sensory information by populations of cortical neurons forms the basis for perception but remains poorly understood. To understand the constraints of cortical population coding we analyzed neural responses to natural sounds recorded in auditory cortex of primates (Macaca mulatta). We estimated stimulus information while varying the composition and size of the considered population. Consistent with previous reports we found that when choosing subpopulations randomly from the recorded ensemble, the average population information increases steadily with population size. This scaling was explained by a model assuming that each neuron carried equal amounts of information, and that any overlap between the information carried by each neuron arises purely from random sampling within the stimulus space. However, when studying subpopulations selected to optimize information for each given population size, the scaling of information was strikingly different: a small fraction of temporally precise cells carried the vast majority of information. This scaling could be explained by an extended model, assuming that the amount of information carried by individual neurons was highly nonuniform, with few neurons carrying large amounts of information. Importantly, these optimal populations can be determined by a single biophysical marker-the neuron's encoding time scale-allowing their detection and readout within biologically realistic circuits. These results show that extrapolations of population information based on random ensembles may overestimate the population size required for stimulus encoding, and that sensory cortical circuits may process information using small but highly informative ensembles.

Dendritic signal transmission induced by intracellular charge inhomogeneities

Signal propagation in neuronal dendrites represents the basis for interneuron communication and information processing in the brain. Here we take into account charge inhomogeneities arising in the vicinity of ion channels in cytoplasm and obtain a modified cable equation. We show that charge inhomogeneities acting on a millisecond time scale can lead to the appearance of propagating waves with wavelengths of hundreds of micrometers. They correspond to a certain frequency band predicting the appearance of resonant properties in brain neuron signaling. We also show that membrane potential in spiny dendrites obeys the modified cable equation suggesting a crucial role of the spines in dendritic subthreshold resonance.

Induction and modulation of persistent activity in a layer V PFC microcircuit model

Working memory refers to the temporary storage of information and is strongly associated with the prefrontal cortex (PFC). Persistent activity of cortical neurons, namely the activity that persists beyond the stimulus presentation, is considered the cellular correlate of working memory. Although past studies suggested that this type of activity is characteristic of large scale networks, recent experimental evidence imply that small, tightly interconnected clusters of neurons in the cortex may support similar functionalities. However, very little is known about the biophysical mechanisms giving rise to persistent activity in small-sized microcircuits in the PFC. Here, we present a detailed biophysically—yet morphologically simplified—microcircuit model of layer V PFC neurons that incorporates connectivity constraints and is validated against a multitude of experimental data. We show that (a) a small-sized network can exhibit persistent activity under realistic stimulus conditions. (b) Its emergence depends strongly on the interplay of dADP, NMDA, and GABA_B currents. (c) Although increases in stimulus duration increase the probability of persistent activity induction, variability in the stimulus firing frequency does not consistently influence it. (d) Modulation of ionic conductances (I_h, I_D, I_sAHP, I_caL, I_caN, I_caR) differentially controls persistent activity properties in a location dependent manner. These findings suggest that modulation of the microcircuit's firing characteristics is achieved primarily through changes in its intrinsic mechanism makeup, supporting the hypothesis of multiple bi-stable units in the PFC. Overall, the model generates a number of experimentally testable predictions that may lead to a better understanding of the biophysical mechanisms of persistent activity induction and modulation in the PFC.

Matched pre- and post-synaptic changes underlie synaptic plasticity over long time scales

Modifications of synaptic efficacies are considered essential for learning and memory. However, it is not known how the underlying functional components of synaptic transmission change over long time scales. To address this question, we studied cortical synapses from young Wistar rats before and after 12 h intervals of spontaneous or glutamate-induced spiking activity. We found that, under these conditions, synaptic efficacies can increase or decrease by up to 10-fold. Statistical analyses reveal that these changes reflect modifications in the number of presynaptic release sites, together with postsynaptic changes that maintain the quantal size per release site. The quantitative relation between the presynaptic and postsynaptic transmission components was not affected when synaptic plasticity was enhanced or reduced using a broad range of pharmacological agents. These findings suggest that ongoing synaptic plasticity results in matched presynaptic and postsynaptic modifications, in which elementary modules that span the synaptic cleft are added or removed as a function of experience.

Active processing of spatio-temporal input patterns in silicon dendrites

Capturing the functionality of active dendritic processing into abstract mathematical models will help us to understand the role of complex biophysical neurons in neuronal computation and to build future useful neuromorphic analog Very Large Scale Integrated (aVLSI) neuronal devices. Previous work based on an aVLSI multi-compartmental neuron model demonstrates that the compartmental response in the presence of either of two widely studied classes of active mechanisms, is a nonlinear sigmoidal function of the degree of either input temporal synchrony OR input clustering level. Using the same silicon model, this work expounds the interaction between both active mechanisms in a compartment receiving input patterns of varying temporal AND spatial clustering structure and demonstrates that this compartmental response can be captured by a combined sigmoid and radial-basis function over both input dimensions. This paper further shows that the response to input spatio-temporal patterns in a one-dimensional multi-compartmental dendrite, can be described by a radial-basis like function of the degree of temporal synchrony between the inter-compartmental inputs.

Influence of asymmetric attenuation of single and paired dendritic inputs on summation of synaptic potentials and initiation of action potentials

Previous studies revealed mechanisms of dendritic inputs leading to action potential initiation at the axon initial segment and backpropagation into the dendritic tree. This interest has recently expanded toward the communication between different parts of the dendritic tree which could preprocess information before reaching the soma. This study tested for effects of asymmetric voltage attenuation between different sites in the dendritic tree on summation of synaptic inputs and action potential initiation using the NEURON simulation environment. Passive responses due to the electrical equivalent circuit of the three-dimensional neuron architecture with leak channels were examined first, followed by the responses after adding voltage-gated channels and finally synaptic noise. Asymmetric attenuation of voltage, which is a function of asymmetric input resistance, was seen between all pairs of dendritic sites but the transfer voltages (voltage recorded at the opposite site from stimulation among a pair of dendritic sites) were equal and also summed linearly with local voltage responses during simultaneous stimulation of both sites. In neurons with voltage-gated channels, we reproduced the observations where a brief stimulus to the proximal ascending dendritic branch of a pyramidal cell triggers a local action potential but a long stimulus triggers a somal action potential. Combined stimulation of a pair of sites in this proximal dendrite did not alter this pattern. The attraction of the action potential onset toward the soma with a long stimulus in the absence of noise was due to the higher density of voltage-gated sodium channels at the axon initial segment. This attraction was, however, negligible at the most remote distal dendritic sites and was replaced by an effect due to high input resistance. Action potential onset occurred at the dendritic site of higher input resistance among a pair of remote dendritic sites, irrespective of which of these two sites received the synaptic input. Exploration of the parameter space showed how the gradient of voltage-gated channel densities and input resistances along a dendrite could draw the action potential onset away from the stimulation site. The attraction of action potential onset toward the higher density of voltage-gated channels in the soma during stimulation of the proximal dendrite was, however, reduced after the addition of synaptic noise.

Stereological and ultrastructural quantification of the afferent synaptome of individual neurons

Determining the number and placement of synaptic inputs along the distinct plasma membrane domains of neurons is essential for explaining the basis of neuronal activity and function. We detail a strategy that combines juxtacellular labeling, neuronal reconstructions and stereological sampling of inputs at the ultrastructural level to define key elements of the afferent ‘synaptome’ of a given neuron. This approach provides unbiased estimates of the total number and somato-dendritic distribution of synapses made with individual neurons. These organizational properties can be related to the activity of the same neurons previously recorded in vivo, for direct structure–function correlations at the single-cell level. The approach also provides the quantitative data required to develop biologically realistic models that simulate and predict neuronal activity and function.

Cyr61, a matricellular protein, is needed for dendritic arborization of hippocampal neurons

The shape of the dendritic arbor is one of the criteria of neuron classification and reflects functional specialization of particular classes of neurons. The development of a proper dendritic branching pattern strongly relies on interactions between the extracellular environment and intracellular processes responsible for dendrite growth and stability. We previously showed that mammalian target of rapamycin (mTOR) kinase is crucial for this process. In this work, we performed a screen for modifiers of dendritic growth in hippocampal neurons, the expression of which is potentially regulated by mTOR. As a result, we identified Cyr61, an angiogenic factor with unknown neuronal function, as a novel regulator of dendritic growth, which controls dendritic growth in a β1-integrin-dependent manner.

Responses of retinal ganglion cells to extracellular electrical stimulation, from single cell to population: model-based analysis

Retinal ganglion cells (RGCs), which survive in large numbers following neurodegenerative diseases, could be stimulated with extracellular electric pulses to elicit artificial percepts. How do the RGCs respond to electrical stimulation at the sub-cellular level under different stimulus configurations, and how does this influence the whole-cell response? At the population level, why have experiments yielded conflicting evidence regarding the extent of passing axon activation? We addressed these questions through simulations of morphologically and biophysically detailed computational RGC models on high performance computing clusters. We conducted the analyses on both large-field RGCs and small-field midget RGCs. The latter neurons are unique to primates. We found that at the single cell level the electric potential gradient in conjunction with neuronal element excitability, rather than the electrode center location per se, determined the response threshold and latency. In addition, stimulus positioning strongly influenced the location of RGC response initiation and subsequent activity propagation through the cellular structure. These findings were robust with respect to inhomogeneous tissue resistivity perpendicular to the electrode plane. At the population level, RGC cellular structures gave rise to low threshold hotspots, which limited axonal and multi-cell activation with threshold stimuli. Finally, due to variations in neuronal element excitability over space, following supra-threshold stimulation some locations favored localized activation of multiple cells, while others favored axonal activation of cells over extended space.

Wide propagation of graded signals in nonspiking neurons

Signal processing in neuritic trees is ruled by the concerted action of passive and active membrane properties that, together, determine the degree of electrical compartmentalization of these trees. We analyzed how active properties modulate spatial propagation of graded signals in a pair of nonspiking (NS) neurons of the leech. NS neurons present a very extensive neuritic tree that mediates the interaction with all the excitatory motoneurons in leech ganglia. NS cells express voltage-activated Ca(2+) conductances (VACCs) that, under certain experimental conditions, evoke low-threshold spikes. We studied the distribution of calcium transients in NS neurons loaded with fluorescent calcium probes in response to low-threshold spikes, electrical depolarizing pulses, and synaptic inputs. The three types of stimuli evoked calcium transients of similar characteristics in the four main branches of the neuron. The magnitude of the calcium transients evoked by electrical pulses was a graded function of the change in NS membrane potential and depended on the baseline potential level. The underlying VACCs were partially inactivated at rest and strongly inactivated at -20 mV. Stimulation of mechanosensory pressure cells evoked calcium transients in NS neurons whose amplitude was a linear function of the amplitude of the postsynaptic response. The results evidenced that VACCs aid an efficient propagation of graded signals, turning the vast neuritic tree of NS cells into an electrically compact structure.

Dampening of hyperexcitability in CA1 pyramidal neurons by polyunsaturated fatty acids acting on voltage-gated ion channels

A ketogenic diet is an alternative treatment of epilepsy in infants. The diet, rich in fat and low in carbohydrates, elevates the level of polyunsaturated fatty acids (PUFAs) in plasma. These substances have therefore been suggested to contribute to the anticonvulsive effect of the diet. PUFAs modulate the properties of a range of ion channels, including K and Na channels, and it has been hypothesized that these changes may be part of a mechanistic explanation of the ketogenic diet. Using computational modelling, we here study how experimentally observed PUFA-induced changes of ion channel activity affect neuronal excitability in CA1, in particular responses to synaptic input of high synchronicity. The PUFA effects were studied in two pathological models of cellular hyperexcitability associated with epileptogenesis. We found that experimentally derived PUFA modulation of the A-type K (K_A) channel, but not the delayed-rectifier K channel, restored healthy excitability by selectively reducing the response to inputs of high synchronicity. We also found that PUFA modulation of the transient Na channel was effective in this respect if the channel's steady-state inactivation was selectively affected. Furthermore, PUFA-induced hyperpolarization of the resting membrane potential was an effective approach to prevent hyperexcitability. When the combined effect of PUFA on the K_A channel, the Na channel, and the resting membrane potential, was simulated, a lower concentration of PUFA was needed to restore healthy excitability. We therefore propose that one explanation of the beneficial effect of PUFAs lies in its simultaneous action on a range of ion-channel targets. Furthermore, this work suggests that a pharmacological cocktail acting on the voltage dependence of the Na-channel inactivation, the voltage dependences of K_A channels, and the resting potential can be an effective treatment of epilepsy.

SpineLab: tool for three-dimensional reconstruction of neuronal cell morphology

SpineLab is a software tool developed for reconstructing neuronal feature skeletons from three-dimensional single- or multi-photon image stacks. These images often suffer from limited resolution and a low signal-to-noise ratio, making the extraction of morphometric information difficult. To overcome this limitation, we have developed a software tool that offers the possibility to create feature skeletons in various modes-automatically as well as with manual interaction. We have named this novel tool SpineLab. In a first step, an investigator adjusts a set of parameters for automatic analysis in an interactive manner, i.e., with online visual feedback, followed by a second step, in which the neuronal feature skeleton can be modified by hand. We validate the ability of SpineLab to reconstruct the entire dendritic tree of identified GFP-expressing neurons and evaluate the accuracy of dendritic spine detection. We report that SpineLab is capable of significantly facilitating the reconstruction of dendrites and spines. Moreover, the automatic approach appears sufficient to detect spine density changes in time-lapse imaging experiments. Taken together, we conclude that SpineLab is an ideal software tool for partially automatic reconstruction of neural cell morphology.

Somato-dendritic morphology and dendritic signal transfer properties differentiate between fore- and hindlimb innervating motoneurons in the frog Rana esculenta

Background

The location specific motor pattern generation properties of the spinal cord along its rostro-caudal axis have been demonstrated. However, it is still unclear that these differences are due to the different spinal interneuronal networks underlying locomotions or there are also segmental differences in motoneurons innervating different limbs. Frogs use their fore- and hindlimbs differently during jumping and swimming. Therefore we hypothesized that limb innervating motoneurons, located in the cervical and lumbar spinal cord, are different in their morphology and dendritic signal transfer properties. The test of this hypothesis what we report here.

Results

Discriminant analysis classified segmental origin of the intracellularly labeled and three-dimensionally reconstructed motoneurons 100% correctly based on twelve morphological variables. Somata of lumbar motoneurons were rounder; the dendrites had bigger total length, more branches with higher branching orders and different spatial distributions of branch points. The ventro-medial extent of cervical dendrites was bigger than in lumbar motoneurons. Computational models of the motoneurons showed that dendritic signal transfer properties were also different in the two groups of motoneurons. Whether log attenuations were higher or lower in cervical than in lumbar motoneurons depended on the proximity of dendritic input to the soma. To investigate dendritic voltage and current transfer properties imposed by dendritic architecture rather than by neuronal size we used standardized distributions of transfer variables. We introduced a novel combination of cluster analysis and homogeneity indexes to quantify segmental segregation tendencies of motoneurons based on their dendritic transfer properties. A segregation tendency of cervical and lumbar motoneurons was detected by the rates of steady-state and transient voltage-amplitude transfers from dendrites to soma at all levels of synaptic background activities, modeled by varying the specific dendritic membrane resistance. On the other hand no segregation was observed by the steady-state current transfer except under high background activity.

Conclusions

We found size-dependent and size-independent differences in morphology and electrical structure of the limb moving motoneurons based on their spinal segmental location in frogs. Location specificity of locomotor networks is therefore partly due to segmental differences in motoneurons driving fore-, and hindlimbs.

Electrical advantages of dendritic spines

Many neurons receive excitatory glutamatergic input almost exclusively onto dendritic spines. In the absence of spines, the amplitudes and kinetics of excitatory postsynaptic potentials (EPSPs) at the site of synaptic input are highly variable and depend on dendritic location. We hypothesized that dendritic spines standardize the local geometry at the site of synaptic input, thereby reducing location-dependent variability of local EPSP properties. We tested this hypothesis using computational models of simplified and morphologically realistic spiny neurons that allow direct comparison of EPSPs generated on spine heads with EPSPs generated on dendritic shafts at the same dendritic locations. In all morphologies tested, spines greatly reduced location-dependent variability of local EPSP amplitude and kinetics, while having minimal impact on EPSPs measured at the soma. Spine-dependent standardization of local EPSP properties persisted across a range of physiologically relevant spine neck resistances, and in models with variable neck resistances. By reducing the variability of local EPSPs, spines standardized synaptic activation of NMDA receptors and voltage-gated calcium channels. Furthermore, spines enhanced activation of NMDA receptors and facilitated the generation of NMDA spikes and axonal action potentials in response to synaptic input. Finally, we show that dynamic regulation of spine neck geometry can preserve local EPSP properties following plasticity-driven changes in synaptic strength, but is inefficient in modifying the amplitude of EPSPs in other cellular compartments. These observations suggest that one function of dendritic spines is to standardize local EPSP properties throughout the dendritic tree, thereby allowing neurons to use similar voltage-sensitive postsynaptic mechanisms at all dendritic locations.

Motoneuron model of self-sustained firing after spinal cord injury

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

An Ultrascalable Solution to Large-scale Neural Tissue Simulation

Neural tissue simulation extends requirements and constraints of previous neuronal and neural circuit simulation methods, creating a tissue coordinate system. We have developed a novel tissue volume decomposition, and a hybrid branched cable equation solver. The decomposition divides the simulation into regular tissue blocks and distributes them on a parallel multithreaded machine. The solver computes neurons that have been divided arbitrarily across blocks. We demonstrate thread, strong, and weak scaling of our approach on a machine with more than 4000 nodes and up to four threads per node. Scaling synapses to physiological numbers had little effect on performance, since our decomposition approach generates synapses that are almost always computed locally. The largest simulation included in our scaling results comprised 1 million neurons, 1 billion compartments, and 10 billion conductance-based synapses and gap junctions. We discuss the implications of our ultrascalable Neural Tissue Simulator, and with our results estimate requirements for a simulation at the scale of a human brain.

Multiple clusters of release sites formed by individual thalamic afferents onto cortical interneurons ensure reliable transmission

Thalamic afferents supply the cortex with sensory information by contacting both excitatory neurons and inhibitory interneurons. Interestingly, thalamic contacts with interneurons constitute such a powerful synapse that even one afferent can fire interneurons, thereby driving feedforward inhibition. However, the spatial representation of this potent synapse on interneuron dendrites is poorly understood. Using Ca imaging and electron microscopy we show that an individual thalamic afferent forms multiple contacts with the interneuronal proximal dendritic arbor, preferentially near branch points. More contacts are correlated with larger amplitude synaptic responses. Each contact, consisting of a single bouton, can release up to seven vesicles simultaneously, resulting in graded and reliable Ca transients. Computational modeling indicates that the release of multiple vesicles at each contact minimally reduces the efficiency of the thalamic afferent in exciting the interneuron. This strategy preserves the spatial representation of thalamocortical inputs across the dendritic arbor over a wide range of release conditions.

Effective stimuli for constructing reliable neuron models

The rich dynamical nature of neurons poses major conceptual and technical challenges for unraveling their nonlinear membrane properties. Traditionally, various current waveforms have been injected at the soma to probe neuron dynamics, but the rationale for selecting specific stimuli has never been rigorously justified. The present experimental and theoretical study proposes a novel framework, inspired by learning theory, for objectively selecting the stimuli that best unravel the neuron's dynamics. The efficacy of stimuli is assessed in terms of their ability to constrain the parameter space of biophysically detailed conductance-based models that faithfully replicate the neuron's dynamics as attested by their ability to generalize well to the neuron's response to novel experimental stimuli. We used this framework to evaluate a variety of stimuli in different types of cortical neurons, ages and animals. Despite their simplicity, a set of stimuli consisting of step and ramp current pulses outperforms synaptic-like noisy stimuli in revealing the dynamics of these neurons. The general framework that we propose paves a new way for defining, evaluating and standardizing effective electrical probing of neurons and will thus lay the foundation for a much deeper understanding of the electrical nature of these highly sophisticated and non-linear devices and of the neuronal networks that they compose.

Turtle functions downstream of Cut in differentially regulating class specific dendrite morphogenesis in Drosophila

Background

Dendritic morphology largely determines patterns of synaptic connectivity and electrochemical properties of a neuron. Neurons display a myriad diversity of dendritic geometries which serve as a basis for functional classification. Several types of molecules have recently been identified which regulate dendrite morphology by acting at the levels of transcriptional regulation, direct interactions with the cytoskeleton and organelles, and cell surface interactions. Although there has been substantial progress in understanding the molecular mechanisms of dendrite morphogenesis, the specification of class-specific dendritic arbors remains largely unexplained. Furthermore, the presence of numerous regulators suggests that they must work in concert. However, presently, few genetic pathways regulating dendrite development have been defined.

Methodology/Principal Findings

The Drosophila gene turtle belongs to an evolutionarily conserved class of immunoglobulin superfamily members found in the nervous systems of diverse organisms. We demonstrate that Turtle is differentially expressed in Drosophila da neurons. Moreover, MARCM analyses reveal Turtle acts cell autonomously to exert class specific effects on dendritic growth and/or branching in da neuron subclasses. Using transgenic overexpression of different Turtle isoforms, we find context-dependent, isoform-specific effects on mediating dendritic branching in class II, III and IV da neurons. Finally, we demonstrate via chromatin immunoprecipitation, qPCR, and immunohistochemistry analyses that Turtle expression is positively regulated by the Cut homeodomain transcription factor and via genetic interaction studies that Turtle is downstream effector of Cut-mediated regulation of da neuron dendrite morphology.

Conclusions/Significance

Our findings reveal that Turtle proteins differentially regulate the acquisition of class-specific dendrite morphologies. In addition, we have established a transcriptional regulatory interaction between Cut and Turtle, representing a novel pathway for mediating class specific dendrite development.

Zipcode binding protein 1 regulates the development of dendritic arbors in hippocampal neurons

The pattern of dendritic branching, together with the density of synapses and receptor composition, defines the electrical properties of a neuron. The development of the dendritic arbor and its additional stabilization are highly orchestrated at the molecular level and are guided by intrinsic mechanisms and extracellular information. Although protein translation is known to contribute to these processes, the role of its local component has not been fully explored. For local translation, mRNAs are transported to dendrites in their dormant form as ribonucleoparticles (RNPs). We hypothesized that disturbing spatial mRNA distribution via RNP targeting may result in severe underdevelopment of the dendritic arbor. Zipcode binding protein 1 (ZBP1) controls β-actin mRNA transport and translation in dendrites. We showed that proper cellular levels of ZBP1, its ability to engage in mRNA binding, and Src-dependent release of mRNA cargo from ZBP1 are vital for dendritic arbor development in cultured rat hippocampal neurons. Moreover, β-actin overexpression significantly alleviated the effects of ZBP1 knockdown. These results suggest that ZBP1-dependent dendritic mRNA transport contributes to proper dendritic branching.

Critical issues in state-of-the-art brain-computer interface signal processing

This paper reviews several critical issues facing signal processing for brain-computer interfaces (BCIs) and suggests several recent approaches that should be further examined. The topics were selected based on discussions held during the 4th International BCI Meeting at a workshop organized to review and evaluate the current state of, and issues relevant to, feature extraction and translation of field potentials for BCIs. The topics presented in this paper include the relationship between electroencephalography and electrocorticography, novel features for performance prediction, time-embedded signal representations, phase information, signal non-stationarity, and unsupervised adaptation.

Encoding of spatio-temporal input characteristics by a CA1 pyramidal neuron model

The in vivo activity of CA1 pyramidal neurons alternates between regular spiking and bursting, but how these changes affect information processing remains unclear. Using a detailed CA1 pyramidal neuron model, we investigate how timing and spatial arrangement variations in synaptic inputs to the distal and proximal dendritic layers influence the information content of model responses. We find that the temporal delay between activation of the two layers acts as a switch between excitability modes: short delays induce bursting while long delays decrease firing. For long delays, the average firing frequency of the model response discriminates spatially clustered from diffused inputs to the distal dendritic tree. For short delays, the onset latency and inter-spike-interval succession of model responses can accurately classify input signals as temporally close or distant and spatially clustered or diffused across different stimulation protocols. These findings suggest that a CA1 pyramidal neuron may be capable of encoding and transmitting presynaptic spatiotemporal information about the activity of the entorhinal cortex-hippocampal network to higher brain regions via the selective use of either a temporal or a rate code.

Pyramidal neurons in the hippocampus are crucially involved in learning and memory functions, but the ways in which they contribute to the processing of sensory inputs and their internal representation remain mostly unclear. The principal neurons of the CA1 region of the hippocampus are surrounded by at least 21 different types of interneurons. This feature, together with the fact that CA1 pyramidal dendrites associate two major glutamatergic inputs arriving from the entorhinal cortex, makes it laborious to track the ‘how’ and ‘what’ of synaptic integration. The present study tries to shed light on the ‘what’, that is, the information content of the CA1 discharge pattern. Using a detailed biophysical CA1 neuron model, we show that the output of the model neuron contains spatial and temporal features of the incoming synaptic input. This information lies in the temporal pattern of the inter-spike intervals produced during the bursting activity which is induced by the temporal coincidence of the two activated synaptic streams. Our findings suggest that CA1 pyramidal neurons may be capable of capturing features of the ongoing network activity via the use of a temporal code for information transfer.

Multilayer processing of spatiotemporal spike patterns in a neuron with active dendrites

With the advent of new experimental evidence showing that dendrites play an active role in processing a neuron's inputs, we revisit the question of a suitable abstraction for the computing function of a neuron in processing spatiotemporal input patterns. Although the integrative role of a neuron in relation to the spatial clustering of synaptic inputs can be described by a two-layer neural network, no corresponding abstraction has yet been described for how a neuron processes temporal input patterns on the dendrites. We address this void using a real-time aVLSI (analog very-large-scale-integrated) dendritic compartmental model, which incorporates two widely studied classes of regenerative event mechanisms: one is mediated by voltage-gated ion channels and the other by transmitter-gated NMDA channels. From this model, we find that the response of a dendritic compartment can be described as a nonlinear sigmoidal function of both the degree of input temporal synchrony and the synaptic input spatial clustering. We propose that a neuron with active dendrites can be modeled as a multilayer network that selectively amplifies responses to relevant spatiotemporal input spike patterns.

An inverse approach for elucidating dendritic function

We outline an inverse approach for investigating dendritic function-structure relationships by optimizing dendritic trees for a priori chosen computational functions. The inverse approach can be applied in two different ways. First, we can use it as a "hypothesis generator" in which we optimize dendrites for a function of general interest. The optimization yields an artificial dendrite that is subsequently compared to real neurons. This comparison potentially allows us to propose hypotheses about the function of real neurons. In this way, we investigated dendrites that optimally perform input-order detection. Second, we can use it as a "function confirmation" by optimizing dendrites for functions hypothesized to be performed by classes of neurons. If the optimized, artificial, dendrites resemble the dendrites of real neurons the artificial dendrites corroborate the hypothesized function of the real neuron. Moreover, properties of the artificial dendrites can lead to predictions about yet unmeasured properties. In this way, we investigated wide-field motion integration performed by the VS cells of the fly visual system. In outlining the inverse approach and two applications, we also elaborate on the nature of dendritic function. We furthermore discuss the role of optimality in assigning functions to dendrites and point out interesting future directions.

A mechanism for ultra-slow oscillations in the cortical default network

When the brain is in its noncognitive "idling" state, functional MRI measurements reveal the activation of default cortical networks whose activity is suppressed during cognitive processing. This default or background mode is characterized by ultra-slow BOLD oscillations (∼0.05 Hz), signaling extremely slow cycling in cortical metabolic demand across distinct cortical regions. Here we describe a model of the cortex which predicts that slow cycling of cortical activity can arise naturally as a result of nonlinear interactions between temporal (Hopf) and spatial (Turing) instabilities. The Hopf instability is triggered by delays in the inhibitory postsynaptic response, while the Turing instability is precipitated by increases in the strength of the gap-junction coupling between interneurons. We comment on possible implications for slow dendritic computation and information processing.

One rule to grow them all: a general theory of neuronal branching and its practical application

Understanding the principles governing axonal and dendritic branching is essential for unravelling the functionality of single neurons and the way in which they connect. Nevertheless, no formalism has yet been described which can capture the general features of neuronal branching. Here we propose such a formalism, which is derived from the expression of dendritic arborizations as locally optimized graphs. Inspired by Ramón y Cajal's laws of conservation of cytoplasm and conduction time in neural circuitry, we show that this graphical representation can be used to optimize these variables. This approach allows us to generate synthetic branching geometries which replicate morphological features of any tested neuron. The essential structure of a neuronal tree is thereby captured by the density profile of its spanning field and by a single parameter, a balancing factor weighing the costs for material and conduction time. This balancing factor determines a neuron's electrotonic compartmentalization. Additions to this rule, when required in the construction process, can be directly attributed to developmental processes or a neuron's computational role within its neural circuit. The simulations presented here are implemented in an open-source software package, the “TREES toolbox,” which provides a general set of tools for analyzing, manipulating, and generating dendritic structure, including a tool to create synthetic members of any particular cell group and an approach for a model-based supervised automatic morphological reconstruction from fluorescent image stacks. These approaches provide new insights into the constraints governing dendritic architectures. They also provide a novel framework for modelling and analyzing neuronal branching structures and for constructing realistic synthetic neural networks.

More than a century has passed since Ramón y Cajal presented a set of fundamental biological laws of neuronal branching. He described how the shape of the core elements of the neural circuitry – axons and dendrites – are constrained by physical parameters such as space, cytoplasmic volume, and conduction time. The existence of these laws enabled him to organize his histological observations, to formulate the neuron doctrine, and to infer directionality in signal flow in the nervous system. We show that Cajal's principles can be used computationally to generate synthetic neural circuits. These principles rigorously constrain the shape of real neuronal structures, providing direct validation of his theories. At the same time, this strategy provides us with a powerful set of tools for generating synthetic neurons, as well as a model-based approach for automated reconstructions of neuronal trees from confocal image stacks.

Dendritic synapse location and neocortical spike-timing-dependent plasticity

While it has been appreciated for decades that synapse location in the dendritic tree has a powerful influence on signal processing in neurons, the role of dendritic synapse location on the induction of long-term synaptic plasticity has only recently been explored. Here, we review recent work revealing how learning rules for spike-timing-dependent plasticity (STDP) in cortical neurons vary with the spatial location of synaptic input. A common principle appears to be that proximal synapses show conventional STDP, whereas distal inputs undergo plasticity according to novel learning rules. One crucial factor determining location-dependent STDP is the backpropagating action potential, which tends to decrease in amplitude and increase in width as it propagates into the dendritic tree of cortical neurons. We discuss additional location-dependent mechanisms as well as the functional implications of heterogeneous learning rules at different dendritic locations for the organization of synaptic inputs.

Control of submillisecond synaptic timing in binaural coincidence detectors by K(v)1 channels

Neurons in the medial superior olive process sound-localization cues via binaural coincidence detection, in which excitatory synaptic inputs from each ear are segregated onto different branches of a bipolar dendritic structure and summed at the soma and axon with submillisecond time resolution. Although synaptic timing and dynamics critically shape this computation, synaptic interactions with intrinsic ion channels have received less attention. Using paired somatic and dendritic patch-clamp recordings in gerbil brainstem slices together with compartmental modeling, we found that activation of K(v)1 channels by dendritic excitatory postsynaptic potentials (EPSPs) accelerated membrane repolarization in a voltage-dependent manner and actively improved the time resolution of synaptic integration. We found that a somatically biased gradient of K(v)1 channels underlies the degree of compensation for passive cable filtering during propagation of EPSPs in dendrites. Thus, both the spatial distribution and properties of K(v)1 channels are important for preserving binaural synaptic timing.

Dendritic excitability modulates dendritic information processing in a purkinje cell model

Using an electrophysiological compartmental model of a Purkinje cell we quantified the contribution of individual active dendritic currents to processing of synaptic activity from granule cells. We used mutual information as a measure to quantify the information from the total excitatory input current (I_Glu) encoded in each dendritic current. In this context, each active current was considered an information channel. Our analyses showed that most of the information was encoded by the calcium (I_CaP) and calcium activated potassium (I_Kc) currents. Mutual information between I_Glu and I_CaP and I_Kc was sensitive to different levels of excitatory and inhibitory synaptic activity that, at the same time, resulted in the same firing rate at the soma. Since dendritic excitability could be a mechanism to regulate information processing in neurons we quantified the changes in mutual information between I_Glu and all Purkinje cell currents as a function of the density of dendritic Ca (g_CaP) and Kca (g_Kc) conductances. We extended our analysis to determine the window of temporal integration of I_Glu by I_CaP and I_Kc as a function of channel density and synaptic activity. The window of information integration has a stronger dependence on increasing values of g_Kc than on g_CaP, but at high levels of synaptic stimulation information integration is reduced to a few milliseconds. Overall, our results show that different dendritic conductances differentially encode synaptic activity and that dendritic excitability and the level of synaptic activity regulate the flow of information in dendrites.

Dendritic vulnerability in neurodegenerative disease: insights from analyses of cortical pyramidal neurons in transgenic mouse models

In neurodegenerative disorders, such as Alzheimer's disease, neuronal dendrites and dendritic spines undergo significant pathological changes. Because of the determinant role of these highly dynamic structures in signaling by individual neurons and ultimately in the functionality of neuronal networks that mediate cognitive functions, a detailed understanding of these changes is of paramount importance. Mutant murine models, such as the Tg2576 APP mutant mouse and the rTg4510 tau mutant mouse have been developed to provide insight into pathogenesis involving the abnormal production and aggregation of amyloid and tau proteins, because of the key role that these proteins play in neurodegenerative disease. This review showcases the multidimensional approach taken by our collaborative group to increase understanding of pathological mechanisms in neurodegenerative disease using these mouse models. This approach includes analyses of empirical 3D morphological and electrophysiological data acquired from frontal cortical pyramidal neurons using confocal laser scanning microscopy and whole-cell patch-clamp recording techniques, combined with computational modeling methodologies. These collaborative studies are designed to shed insight on the repercussions of dystrophic changes in neocortical neurons, define the cellular phenotype of differential neuronal vulnerability in relevant models of neurodegenerative disease, and provide a basis upon which to develop meaningful therapeutic strategies aimed at preventing, reversing, or compensating for neurodegenerative changes in dementia.

The passive cable properties of hair cell stereocilia and their contribution to somatic capacitance measurements

Somatic measurements of whole-cell capacitance are routinely used to understand physiologic events occurring in remote portions of cells. These studies often assume the intracellular space is voltage-clamped. We questioned this assumption in auditory and vestibular hair cells with respect to their stereocilia based on earlier studies showing that neurons, with radial dimensions similar to stereocilia, are not always isopotential under voltage-clamp. To explore this, we modeled the stereocilia as passive cables with transduction channels located at their tips. We found that the input capacitance measured at the soma changes when the transduction channels at the tips of the stereocilia are open compared to when the channels are closed. The maximum capacitance is felt with the transducer closed but will decrease as the transducer opens due to a length-dependent voltage drop along the stereocilium length. This potential drop is proportional to the intracellular resistance and stereocilium tip conductance and can produce a maximum capacitance error on the order of fF for single stereocilia and pF for the bundle.

An arithmetic rule for spatial summation of excitatory and inhibitory inputs in pyramidal neurons

Dendritic integration of excitatory and inhibitory inputs is critical for neuronal computation, but the underlying rules remain to be elucidated. Based on realistic modeling and experiments in rat hippocampal slices, we derived a simple arithmetic rule for spatial summation of concurrent excitatory glutamatergic inputs (E) and inhibitory GABAergic inputs (I). The somatic response can be well approximated as the sum of the excitatory postsynaptic potential (EPSP), the inhibitory postsynaptic potential (IPSP), and a nonlinear term proportional to their product (k*EPSP*IPSP), where the coefficient k reflects the strength of shunting effect. The k value shows a pronounced asymmetry in its dependence on E and I locations. For I on the dendritic trunk, k decays rapidly with E-I distance for proximal Es, but remains largely constant for distal Es, indicating a uniformly high shunting efficacy for all distal Es. For I on an oblique branch, the shunting effect is restricted mainly within the branch, with the same proximal/distal asymmetry. This asymmetry can be largely attributed to cable properties of the dendrite. Further modeling studies showed that this rule also applies to the integration of multiple coincident Es and Is. Thus, this arithmetic rule offers a simple analytical tool for studying E-I integration in pyramidal neurons that incorporates the location specificity of GABAergic shunting inhibition.

Multiquantal release underlies the distribution of synaptic efficacies in the neocortex

Inter-pyramidal synaptic connections are characterized by a wide range of EPSP amplitudes. Although repeatedly observed at different brain regions and across layers, little is known about the synaptic characteristics that contribute to this wide range. In particular, the range could potentially be accounted for by differences in all three parameters of the quantal model of synaptic transmission, i.e. the number of release sites, release probability and quantal size. Here, we present a rigorous statistical analysis of the transmission properties of excitatory synaptic connections between layer-5 pyramidal neurons of the somato-sensory cortex. Our central finding is that the EPSP amplitude is strongly correlated with the number of estimated release sites, but not with the release probability or quantal size. In addition, we found that the number of release sites can be more than an order of magnitude higher than the typical number of synaptic contacts for this type of connection. Our findings indicate that transmission at stronger synaptic connections is mediated by multiquantal release from their synaptic contacts. We propose that modulating the number of release sites could be an important mechanism in regulating neocortical synaptic transmission.

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.