Automated High-Throughput Characterization of Single Neurons by Means of Simplified Spiking Models

Single-neuron models are useful not only for studying the emergent properties of neural circuits in large-scale simulations, but also for extracting and summarizing in a principled way the information contained in electrophysiological recordings. Here we demonstrate that, using a convex optimization procedure we previously introduced, a Generalized Integrate-and-Fire model can be accurately fitted with a limited amount of data. The model is capable of predicting both the spiking activity and the subthreshold dynamics of different cell types, and can be used for online characterization of neuronal properties. A protocol is proposed that, combined with emergent technologies for automatic patch-clamp recordings, permits automated, in vitro high-throughput characterization of single neurons.

Related papers:

title: High-throughput electrophysiology: an emerging paradigm for ion-channel screening and physiology
abstract: Ion channels represent highly attractive targets for drug discovery and are implicated in a diverse range of disorders, in particular in the central nervous and cardiovascular systems. Moreover, assessment of cardiac ion-channel activity of new chemical entities is now an integral component of drug discovery programmes to assess potential for cardiovascular side effects. Despite their attractiveness as drug discovery targets ion channels remain an under-exploited target class, which is in large part due to the labour-intensive and low-throughput nature of patch-clamp electrophysiology. This Review provides an update on the current state-of-the-art for the various automated electrophysiology platforms that are now available and critically evaluates their impact in terms of ion-channel screening, lead optimization and the assessment of cardiac ion-channel safety liability.

title: A benchmark study with sealchip planar patch-clamp technology.
abstract: Although conventional patch-clamp methods provide high information content, they are labor-intensive and suffer from low throughput and high overall cost. Several approaches for achieving high throughput electrophysiology are under development, among which microchip-based patch-clamp systems uniquely achieve a higher degree of miniaturization, faster perfusion and mixing, and lower reagent cost without losing information content. The goal of this study was to establish a benchmark for our biochip technology with 52 chips tested sequentially. We demonstrate that our microfabrication and processing technology is sufficiently mature to produce a consistent hole size. We further demonstrate high-quality planar whole-cell patch clamping with >75% overall success rate at achieving gigaohm seals, followed by stable whole-cell access lasting at least 15 min with access resistance (Ra) below 15 MOmega and membrane resistance (Rm) above 200 MOmega. These biochips are ideally suited for high throughput compound screening for ion channel targets.

title: Population Patch Clamp Improves Data Consistency and Success Rates in the Measurement of Ionic Currents
abstract: Present whole-cell patch-clamp methodology has only moderate consistency and throughput, rendering impractical functional measurements on large numbers of ion channel ligands or on large numbers of unknown or mutant channel genes. In the population patch clamp (PPC) described herein, a single voltage-clamp amplifier sums the whole-cell currents from multiple cells at once, each sealed to a separate aperture in a planar substrate well. The resulting ensemble currents are more consistent from well to well, and the success rate for each recording attempt is >95%. The PPC was implemented by modifying the PatchPlate substrate and amplifiers in the IonWorks patch-clamp instrument. The increased data consistency and likelihood of a successful recording in each well, combined with 384-well measurements in parallel, allow the direct electrophysiological recording of thousands of ensemble ionic currents per day. Therapeutic groups in drug discovery programs require this order of throughput to screen directed compound libraries against ion channel targets. The potential for studying the function of large numbers of ion channel mutants may be realized with the technique. The procedure incorporates subtraction methods that correct for expected distortions and also reliably produces data that agree with previous patch-clamp studies.

title: Automated whole-cell patch clamp electrophysiology of neurons in vivo
abstract: Whole-cell patch-clamp electrophysiology of neurons is a gold-standard technique for high-fidelity analysis of the biophysical mechanisms of neural computation and pathology, but it requires great skill to perform. We have developed a robot that automatically performs patch clamping in vivo, algorithmically detecting cells by analyzing the temporal sequence of electrode impedance changes. We demonstrate good yield, throughput and quality of automated intracellular recording in mouse cortex and hippocampus.

title: Modeling Single-Neuron Dynamics and Computations: A Balance of Detail and Abstraction
abstract: The fundamental building block of every nervous system is the single neuron. Understanding how these exquisitely structured elements operate is an integral part of the quest to solve the mysteries of the brain. Quantitative mathematical models have proved to be an indispensable tool in pursuing this goal. We review recent advances and examine how single-cell models on five levels of complexity, from black-box approaches to detailed compartmental simulations, address key questions about neural dynamics and signal processing.

title: The Blue Brain Project
abstract: The Blue Brain Project began in July 2005 as a collaboration between Professor Henry Markram from the Brain Mind Institute at the EPFL (Ecole Polytechnique Federale de Lausanne) and IBM (International Business Machines), aimed at modelling the neocortical column. The neocortical column represents the basic functional unit of the cerebral cortex in mammals that underlies nearly all sensory and cognitive processing. These units are repeated millions of times across the cortex, with the basic structure remaining the fundamentally the same from mouse to man. From its origins — IBM's BlueGene/L supercomputer and more than 10 years of experimental data from Professor Markram's laboratory — the project has grown to include an international multidisciplinary team of over 35 experimentalists, modellers and computer scientists. The goal of Phase I was to build a cellular level model of the somatosensory cortex of a 2- week-old rat corresponding to the dimensions of a neocortical column as defined by the dendritic arborizations of the layer 5 pyramidal neurons. We have achieved this goal by developing an entirely new data-driven process for creating, validating and researching the neocortical column. Reverse-engineering a portion of the neocortex involves capturing many levels of detail about microscopic cells and fibers — living, dynamic entities that are invisible to the naked eye. Modelling efforts must examine the experimental design and weigh the potential inconsistencies and relevance of the resulting data to the construction and refinement of the model. A simulation-based research process requires that this consistency check occur in an ongoing fashion. The simulation itself now serves as an essential tool for integrating experimental data and defining new experiments that can precisely gather the information necessary to capture the complete biological detail.

title: Alternative to hand-tuning conductance-based models: construction and analysis of databases of model neurons.
abstract: Conventionally, the parameters of neuronal models are hand-tuned using trial-and-error searches to produce a desired behavior. Here, we present an alternative approach. We have generated a database of about 1.7 million single-compartment model neurons by independently varying 8 maximal membrane conductances based on measurements from lobster stomatogastric neurons. We classified the spontaneous electrical activity of each model neuron and its responsiveness to inputs during runtime with an adaptive algorithm and saved a reduced version of each neuron's activity pattern. Our analysis of the distribution of different activity types (silent, spiking, bursting, irregular) in the 8-dimensional conductance space indicates that the coarse grid of conductance values we chose is sufficient to capture the salient features of the distribution. The database can be searched for different combinations of neuron properties such as activity type, spike or burst frequency, resting potential, frequency-current relation, and phase-response curve. We demonstrate how the database can be screened for models that reproduce the behavior of a specific biological neuron and show that the contents of the database can give insight into the way a neuron's membrane conductances determine its activity pattern and response properties. Similar databases can be constructed to explore parameter spaces in multicompartmental models or small networks, or to examine the effects of changes in the voltage dependence of currents. In all cases, database searches can provide insight into how neuronal and network properties depend on the values of the parameters in the models.

title: Efficient estimation of detailed single-neuron models.
abstract: Biophysically accurate multicompartmental models of individual neurons have significantly advanced our understanding of the input-output function of single cells. These models depend on a large number of parameters that are difficult to estimate. In practice, they are often hand-tuned to match measured physiological behaviors, thus raising questions of identifiability and interpretability. We propose a statistical approach to the automatic estimation of various biologically relevant parameters, including 1) the distribution of channel densities, 2) the spatiotemporal pattern of synaptic input, and 3) axial resistances across extended dendrites. Recent experimental advances, notably in voltage-sensitive imaging, motivate us to assume access to: i) the spatiotemporal voltage signal in the dendrite and ii) an approximate description of the channel kinetics of interest. We show here that, given i and ii, parameters 1-3 can be inferred simultaneously by nonnegative linear regression; that this optimization problem possesses a unique solution and is guaranteed to converge despite the large number of parameters and their complex nonlinear interaction; and that standard optimization algorithms efficiently reach this optimum with modest computational and data requirements. We demonstrate that the method leads to accurate estimations on a wide variety of challenging model data sets that include up to about 10(4) parameters (roughly two orders of magnitude more than previously feasible) and describe how the method gives insights into the functional interaction of groups of channels.

title: A Novel Multiple Objective Optimization Framework for Constraining Conductance-Based Neuron Models by Experimental Data
abstract: We present a novel framework for automatically constraining parameters of compartmental models of neurons, given a large set of experimentally measured responses of these neurons. In experiments, intrinsic noise gives rise to a large variability (e.g., in firing pattern) in the voltage responses to repetitions of the exact same input. Thus, the common approach of fitting models by attempting to perfectly replicate, point by point, a single chosen trace out of the spectrum of variable responses does not seem to do justice to the data. In addition, finding a single error function that faithfully characterizes the distance between two spiking traces is not a trivial pursuit. To address these issues, one can adopt a multiple objective optimization approach that allows the use of several error functions jointly. When more than one error function is available, the comparison between experimental voltage traces and model response can be performed on the basis of individual features of interest (e.g., spike rate, spike width). Each feature can be compared between model and experimental mean, in units of its experimental variability, thereby incorporating into the fitting this variability. We demonstrate the success of this approach, when used in conjunction with genetic algorithm optimization, in generating an excellent fit between model behavior and the firing pattern of two distinct electrical classes of cortical interneurons, accommodating and fast-spiking. We argue that the multiple, diverse models generated by this method could serve as the building blocks for the realistic simulation of large neuronal networks.

title: Models of Neocortical Layer 5b Pyramidal Cells Capturing a Wide Range of Dendritic and Perisomatic Active Properties
abstract: The thick-tufted layer 5b pyramidal cell extends its dendritic tree to all six layers of the mammalian neocortex and serves as a major building block for the cortical column. L5b pyramidal cells have been the subject of extensive experimental and modeling studies, yet conductance-based models of these cells that faithfully reproduce both their perisomatic Na+-spiking behavior as well as key dendritic active properties, including Ca2+ spikes and back-propagating action potentials, are still lacking. Based on a large body of experimental recordings from both the soma and dendrites of L5b pyramidal cells in adult rats, we characterized key features of the somatic and dendritic firing and quantified their statistics. We used these features to constrain the density of a set of ion channels over the soma and dendritic surface via multi-objective optimization with an evolutionary algorithm, thus generating a set of detailed conductance-based models that faithfully replicate the back-propagating action potential activated Ca2+ spike firing and the perisomatic firing response to current steps, as well as the experimental variability of the properties. Furthermore, we show a useful way to analyze model parameters with our sets of models, which enabled us to identify some of the mechanisms responsible for the dynamic properties of L5b pyramidal cells as well as mechanisms that are sensitive to morphological changes. This automated framework can be used to develop a database of faithful models for other neuron types. The models we present provide several experimentally-testable predictions and can serve as a powerful tool for theoretical investigations of the contribution of single-cell dynamics to network activity and its computational capabilities.

title: A Self-Organizing State-Space-Model Approach for Parameter Estimation in Hodgkin-Huxley-Type Models of Single Neurons
abstract: Traditional approaches to the problem of parameter estimation in biophysical models of neurons and neural networks usually adopt a global search algorithm (for example, an evolutionary algorithm), often in combination with a local search method (such as gradient descent) in order to minimize the value of a cost function, which measures the discrepancy between various features of the available experimental data and model output. In this study, we approach the problem of parameter estimation in conductance-based models of single neurons from a different perspective. By adopting a hidden-dynamical-systems formalism, we expressed parameter estimation as an inference problem in these systems, which can then be tackled using a range of well-established statistical inference methods. The particular method we used was Kitagawa's self-organizing state-space model, which was applied on a number of Hodgkin-Huxley-type models using simulated or actual electrophysiological data. We showed that the algorithm can be used to estimate a large number of parameters, including maximal conductances, reversal potentials, kinetics of ionic currents, measurement and intrinsic noise, based on low-dimensional experimental data and sufficiently informative priors in the form of pre-defined constraints imposed on model parameters. The algorithm remained operational even when very noisy experimental data were used. Importantly, by combining the self-organizing state-space model with an adaptive sampling algorithm akin to the Covariance Matrix Adaptation Evolution Strategy, we achieved a significant reduction in the variance of parameter estimates. The algorithm did not require the explicit formulation of a cost function and it was straightforward to apply on compartmental models and multiple data sets. Overall, the proposed methodology is particularly suitable for resolving high-dimensional inference problems based on noisy electrophysiological data and, therefore, a potentially useful tool in the construction of biophysical neuron models.

title: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting
abstract: This book explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. "Dynamical Systems in Neuroscience" presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum - or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience.

title: The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs
abstract: How random is the discharge pattern of cortical neurons? We examined recordings from primary visual cortex (V1; Knierim and Van Essen, 1992) and extrastriate cortex (MT; Newsome et al., 1989a) of awake, behaving macaque monkey and compared them to analytical predictions. For nonbursting cells firing at sustained rates up to 300 Hz, we evaluated two indices of firing variability: the ratio of the variance to the mean for the number of action potentials evoked by a constant stimulus, and the rate-normalized coefficient of variation (Cv) of the interspike interval distribution. Firing in virtually all V1 and MT neurons was nearly consistent with a completely random process (e.g., Cv approximately 1). We tried to model this high variability by small, independent, and random EPSPs converging onto a leaky integrate-and- fire neuron (Knight, 1972). Both this and related models predicted very low firing variability (Cv << 1) for realistic EPSP depolarizations and membrane time constants. We also simulated a biophysically very detailed compartmental model of an anatomically reconstructed and physiologically characterized layer V cat pyramidal cell (Douglas et al., 1991) with passive dendrites and active soma. If independent, excitatory synaptic input fired the model cell at the high rates observed in monkey, the Cv and the variability in the number of spikes were both very low, in agreement with the integrate-and-fire models but in strong disagreement with the majority of our monkey data. The simulated cell only produced highly variable firing when Hodgkin-Huxley- like currents (INa and very strong IDR) were placed on distal dendrites. Now the simulated neuron acted more as a millisecond- resolution detector of dendritic spike coincidences than as a temporal integrator. We argue that neurons that act as temporal integrators over many synaptic inputs must fire very regularly. Only in the presence of either fast and strong dendritic nonlinearities or strong synchronization among individual synaptic events will the degree of predicted variability approach that of real cortical neurons.

title: Physiological Gain Leads to High ISI Variability in a Simple Model of a Cortical Regular Spiking Cell
abstract: To understand the interspike interval (ISI) variability displayed by visual cortical neurons (Softky & Koch, 1993), it is critical to examine the dynamics of their neuronal integration, as well as the variability in their synaptic input current. Most previous models have focused on the latter factor. We match a simple integrate-and-fire model to the experimentally measured integrative properties of cortical regular spiking cells (McCormick, Connors, Lighthall, & Prince, 1985). After setting RC parameters, the postspike voltage reset is set to match experimental measurements of neuronal gain (obtained from in vitro plots of firing frequency versus injected current). Examination of the resulting model leads to an intuitive picture of neuronal integration that unifies the seemingly contradictory and random walk pictures that have previously been proposed. When ISIs are dominated by postspike recovery, arguments hold and spiking is regular; after the memory of the last spike becomes negligible, spike threshold crossing is caused by input variance around a steady state and spiking is Poisson. In integrate-and-fire neurons matched to cortical cell physiology, steady-state behavior is predominant, and ISIs are highly variable at all physiological firing rates and for a wide range of inhibitory and excitatory inputs.

title: Predicting Every Spike A Model for the Responses of Visual Neurons
abstract: In the early visual system, neuronal responses can be extremely precise. Under a wide range of stimuli, cells in the retina and thalamus fire spikes very reproducibly, often with millisecond precision on subsequent stimulus repeats. Here we develop a mathematical description of the firing process that, given the recent visual input, accurately predicts the timing of individual spikes. The formalism is successful in matching the spike trains from retinal ganglion cells in salamander, rabbit, and cat, as well as from lateral geniculate nucleus neurons in cat. It adapts to many different response types, from very precise to highly variable. The accuracy of the model allows a compact description of how these neurons encode the visual stimulus.

title: Prediction and Decoding of Retinal Ganglion Cell Responses with a Probabilistic Spiking Model
abstract: Sensory encoding in spiking neurons depends on both the integration of sensory inputs and the intrinsic dynamics and variability of spike generation. We show that the stimulus selectivity, reliability, and timing precision of primate retinal ganglion cell (RGC) light responses can be reproduced accurately with a simple model consisting of a leaky integrate-and-fire spike generator driven by a linearly filtered stimulus, a postspike current, and a Gaussian noise current. We fit model parameters for individual RGCs by maximizing the likelihood of observed spike responses to a stochastic visual stimulus. Although compact, the fitted model predicts the detailed time structure of responses to novel stimuli, accurately capturing the interaction between the spiking history and sensory stimulus selectivity. The model also accounts for the variability in responses to repeated stimuli, even when fit to data from a single (nonrepeating) stimulus sequence. Finally, the model can be used to derive an explicit, maximum-likelihood decoding rule for neural spike trains, thus providing a tool for assessing the limitations that spiking variability imposes on sensory performance.

title: Comparing integrate-and-fire models estimated using intracellular and extracellular data
abstract: We have recently developed a maximum-likelihood (ML) method for estimating integrate-and-fire-based stimulus encoding models that can be used even when only extracellular spike train data is available. Here we derive the ML estimator given the full intracellular voltage trace and apply both the extracellular-only and intracellular method to responses recorded in vitro, allowing a direct comparison of the model fits within a unified statistical framework. Both models are able to capture the behavior of these cells under dynamic stimulus conditions to a high degree of temporal precision, although we observe significant differences in the stochastic behavior of the two models.

title: The quantitative single-neuron modeling competition
abstract: As large-scale, detailed network modeling projects are flourishing in the field of computational neuroscience, it is more and more important to design single neuron models that not only capture qualitative features of real neurons but are quantitatively accurate in silico representations of those. Recent years have seen substantial effort being put in the development of algorithms for the systematic evaluation and optimization of neuron models with respect to electrophysiological data. It is however difficult to compare these methods because of the lack of appropriate benchmark tests. Here, we describe one such effort of providing the community with a standardized set of tests to quantify the performances of single neuron models. Our effort takes the form of a yearly challenge similar to the ones which have been present in the machine learning community for some time. This paper gives an account of the first two challenges which took place in 2007 and 2008 and discusses future directions. The results of the competition suggest that best performance on data obtained from single or double electrode current or conductance injection is achieved by models that combine features of standard leaky integrate-and-fire models with a second variable reflecting adaptation, refractoriness, or a dynamic threshold.

title: Made-to-Order Spiking Neuron Model Equipped with a Multi-Timescale Adaptive Threshold
abstract: Information is transmitted in the brain through various kinds of neurons that respond differently to the same signal. Full characteristics including cognitive functions of the brain should ultimately be comprehended by building simulators capable of precisely mirroring spike responses of a variety of neurons. Neuronal modeling that had remained on a qualitative level has recently advanced to a quantitative level, but is still incapable of accurately predicting biological data and requires high computational cost. In this study, we devised a simple, fast computational model that can be tailored to any cortical neuron not only for reproducing but also for predicting a variety of spike responses to greatly fluctuating currents. The key features of this model are a multi-timescale adaptive threshold predictor and a nonresetting leaky integrator. This model is capable of reproducing a rich variety of neuronal spike responses, including regular spiking, intrinsic bursting, fast spiking, and chattering, by adjusting only three adaptive threshold parameters. This model can express a continuous variety of the firing characteristics in a three-dimensional parameter space rather than just those identified in the conventional discrete categorization. Both high flexibility and low computational cost would help to model the real brain function faithfully and examine how network properties may be influenced by the distributed characteristics of component neurons.

title: A simple model of mechanotransduction in primate glabrous skin.
abstract: Tactile stimulation of the hand evokes highly precise and repeatable patterns of activity in mechanoreceptive afferents; the strength (i.e., firing rate) and timing of these responses have been shown to convey stimulus information. To achieve an understanding of the mechanisms underlying the representation of tactile stimuli in the nerve, we developed a two-stage computational model consisting of a nonlinear mechanical transduction stage followed by a generalized integrate-and-fire mechanism. The model improves upon a recently published counterpart in two important ways. First, complexity is dramatically reduced (at least one order of magnitude fewer parameters). Second, the model comprises a saturating nonlinearity and therefore can be applied to a much wider range of stimuli. We show that both the rate and timing of afferent responses are predicted with remarkable precision and that observed adaptation patterns and threshold behavior are well captured. We conclude that the responses of mechanoreceptive afferents can be understood using a very parsimonious mechanistic model, which can then be used to accurately simulate the responses of afferent populations.

title: Diversity and dynamics of dendritic signaling.
abstract: Communication between neurons in the brain occurs primarily through synapses made onto elaborate treelike structures called dendrites. New electrical and optical recording techniques have led to tremendous advances in our understanding of how dendrites contribute to neuronal computation in the mammalian brain. The varied morphology and electrical and chemical properties of dendrites enable a spectrum of local and long-range signaling, defining the input-output relationship of neurons and the rules for induction of synaptic plasticity. In this way, diversity in dendritic signaling allows individual neurons to carry out specialized functions within their respective networks.

title: Synaptic Integration in Tuft Dendrites of Layer 5 Pyramidal Neurons: A New Unifying Principle
abstract: Fine Dendrites Fire Differently The pyramidal neuron is the basic computational unit in the brain cortex. Its distal tuft dendrite is heavily innervated by horizontal fibers coursing through cortical layer-I providing long-range corticocortical and thalamocortical associational input. Larkum et al. (p. 756) investigated whether the apical tuft dendrites of layer-5 neocortical pyramidal neurons, like basal dendrites, generate n-methyl-d-aspartate (NMDA) spikes using two-photon–guided direct dendritic recording, glutamate uncaging, and modeling. NMDA spikes could be evoked in the distal tuft dendrites, while Ca2+ spikes could be triggered at the bifurcation points. Block of the hyperpolarization-activated current enhanced these NMDA spikes. Thus, the generation of NMDA spikes is a general principle of thin, basal, and tuft dendrites. Thin tuft and basal dendrites of pyramidal neurons use N-methyl-d-aspartate spikes to sum up synaptic inputs in semi-independent compartments. Tuft dendrites are the main target for feedback inputs innervating neocortical layer 5 pyramidal neurons, but their properties remain obscure. We report the existence of N-methyl-d-aspartate (NMDA) spikes in the fine distal tuft dendrites that otherwise did not support the initiation of calcium spikes. Both direct measurements and computer simulations showed that NMDA spikes are the dominant mechanism by which distal synaptic input leads to firing of the neuron and provide the substrate for complex parallel processing of top-down input arriving at the tuft. These data lead to a new unifying view of integration in pyramidal neurons in which all fine dendrites, basal and tuft, integrate inputs locally through the recruitment of NMDA receptor channels relative to the fixed apical calcium and axosomatic sodium integration points.

title: Large-scale model of mammalian thalamocortical systems
abstract: The understanding of the structural and dynamic complexity of mammalian brains is greatly facilitated by computer simulations. We present here a detailed large-scale thalamocortical model based on experimental measures in several mammalian species. The model spans three anatomical scales. (i) It is based on global (white-matter) thalamocortical anatomy obtained by means of diffusion tensor imaging (DTI) of a human brain. (ii) It includes multiple thalamic nuclei and six-layered cortical microcircuitry based on in vitro labeling and three-dimensional reconstruction of single neurons of cat visual cortex. (iii) It has 22 basic types of neurons with appropriate laminar distribution of their branching dendritic trees. The model simulates one million multicompartmental spiking neurons calibrated to reproduce known types of responses recorded in vitro in rats. It has almost half a billion synapses with appropriate receptor kinetics, short-term plasticity, and long-term dendritic spike-timing-dependent synaptic plasticity (dendritic STDP). The model exhibits behavioral regimes of normal brain activity that were not explicitly built-in but emerged spontaneously as the result of interactions among anatomical and dynamic processes. We describe spontaneous activity, sensitivity to changes in individual neurons, emergence of waves and rhythms, and functional connectivity on different scales.

title: From Stochastic Nonlinear Integrate-and-Fire to Generalized Linear Models
abstract: Variability in single neuron models is typically implemented either by a stochastic Leaky-Integrate-and-Fire model or by a model of the Generalized Linear Model (GLM) family. We use analytical and numerical methods to relate state-of-the-art models from both schools of thought. First we find the analytical expressions relating the subthreshold voltage from the Adaptive Exponential Integrate-and-Fire model (AdEx) to the Spike-Response Model with escape noise (SRM as an example of a GLM). Then we calculate numerically the link-function that provides the firing probability given a deterministic membrane potential. We find a mathematical expression for this link-function and test the ability of the GLM to predict the firing probability of a neuron receiving complex stimulation. Comparing the prediction performance of various link-functions, we find that a GLM with an exponential link-function provides an excellent approximation to the Adaptive Exponential Integrate-and-Fire with colored-noise input. These results help to understand the relationship between the different approaches to stochastic neuron models.

title: Temporal whitening by power-law adaptation in neocortical neurons
abstract: Spike-frequency adaptation (SFA) is widespread in the CNS, but its function remains unclear. In neocortical pyramidal neurons, adaptation manifests itself by an increase in the firing threshold and by adaptation currents triggered after each spike. Combining electrophysiological recordings in mice with modeling, we found that these adaptation processes lasted for more than 20 s and decayed over multiple timescales according to a power law. The power-law decay associated with adaptation mirrored and canceled the temporal correlations of input current received in vivo at the somata of layer 2/3 somatosensory pyramidal neurons. These findings suggest that, in the cortex, SFA causes temporal decorrelation of output spikes (temporal whitening), an energy-efficient coding procedure that, at high signal-to-noise ratio, improves the information transfer.

title: High-Resolution Intracellular Recordings Using a Real-Time Computational Model of the Electrode
abstract: Intracellular recordings of neuronal membrane potential are a central tool in neurophysiology. In many situations, especially in vivo, the traditional limitation of such recordings is the high electrode resistance and capacitance, which may cause significant measurement errors during current injection. We introduce a computer-aided technique, Active Electrode Compensation (AEC), based on a digital model of the electrode interfaced in real time with the electrophysiological setup. The characteristics of this model are first estimated using white noise current injection. The electrode and membrane contribution are digitally separated, and the recording is then made by online subtraction of the electrode contribution. Tests performed in vitro and in vivo demonstrate that AEC enables high-frequency recordings in demanding conditions, such as injection of conductance noise in dynamic-clamp mode, not feasible with a single high-resistance electrode until now. AEC should be particularly useful to characterize fast neuronal phenomena intracellularly in vivo.

title: Dynamic I-V curves are reliable predictors of naturalistic pyramidal-neuron voltage traces.
abstract: Neuronal response properties are typically probed by intracellular measurements of current-voltage (I-V) relationships during application of current or voltage steps. Here we demonstrate the measurement of a novel I-V curve measured while the neuron exhibits a fluctuating voltage and emits spikes. This dynamic I-V curve requires only a few tens of seconds of experimental time and so lends itself readily to the rapid classification of cell type, quantification of heterogeneities in cell populations, and generation of reduced analytical models. We apply this technique to layer-5 pyramidal cells and show that their dynamic I-V curve comprises linear and exponential components, providing experimental evidence for a recently proposed theoretical model. The approach also allows us to determine the change of neuronal response properties after a spike, millisecond by millisecond, so that postspike refractoriness of pyramidal cells can be quantified. Observations of I-V curves during and in absence of refractoriness are cast into a model that is used to predict both the subthreshold response and spiking activity of the neuron to novel stimuli. The predictions of the resulting model are in excellent agreement with experimental data and close to the intrinsic neuronal reproducibility to repeated stimuli.

title: Improved Similarity Measures for Small Sets of Spike Trains
abstract: Multiple types of measures have been developed to measure the similarity between two spike trains. These were extensively used to classify neuron responses according to stimuli and to validate mathematical models that predict the spike times. Here we analyze the existing similarity measures in the light of trial-to-trial variability. Using a small set of spike train it is often impossible to discriminate correctly between different generative processes. In particular we find that many measures cannot discriminate appropriately for shifts in overall firing intensity or for the amount of jitter in the spike timing. We find that it is possible to modify some of the existing measures by taking into account the variance of the measure across spike trains from the same set. In so doing we remove a sample bias and we find that it is possible to discriminate correctly in all cases. Finally, we demonstrate that without sample bias compensation the similarity of real neurons with spiking neuron models having low stochasticity will be overrated.

title: A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects.
abstract: Multiple factors simultaneously affect the spiking activity of individual neurons. Determining the effects and relative importance of these factors is a challenging problem in neurophysiology. We propose a statistical framework based on the point process likelihood function to relate a neuron's spiking probability to three typical covariates: the neuron's own spiking history, concurrent ensemble activity, and extrinsic covariates such as stimuli or behavior. The framework uses parametric models of the conditional intensity function to define a neuron's spiking probability in terms of the covariates. The discrete time likelihood function for point processes is used to carry out model fitting and model analysis. We show that, by modeling the logarithm of the conditional intensity function as a linear combination of functions of the covariates, the discrete time point process likelihood function is readily analyzed in the generalized linear model (GLM) framework. We illustrate our approach for both GLM and non-GLM likelihood functions using simulated data and multivariate single-unit activity data simultaneously recorded from the motor cortex of a monkey performing a visuomotor pursuit-tracking task. The point process framework provides a flexible, computationally efficient approach for maximum likelihood estimation, goodness-of-fit assessment, residual analysis, model selection, and neural decoding. The framework thus allows for the formulation and analysis of point process models of neural spiking activity that readily capture the simultaneous effects of multiple covariates and enables the assessment of their relative importance.

title: Spatio-temporal correlations and visual signalling in a complete neuronal population
abstract: Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies, their origin and importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses. The model, with parameters fit directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal linear decoding. This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and provides a general framework for understanding the importance of correlated activity in populations of neurons.

title: Parameter extraction and classification of three cortical neuron types reveals two distinct adaptation mechanisms.
abstract: Cortical information processing originates from the exchange of action potentials between many cell types. To capture the essence of these interactions, it is of critical importance to build mathematical models that reflect the characteristic features of spike generation in individual neurons. We propose a framework to automatically extract such features from current-clamp experiments, in particular the passive properties of a neuron (i.e., membrane time constant, reversal potential, and capacitance), the spike-triggered adaptation currents, as well as the dynamics of the action potential threshold. The stochastic model that results from our maximum likelihood approach accurately predicts the spike times, the subthreshold voltage, the firing patterns, and the type of frequency-current curve. Extracting the model parameters for three cortical cell types revealed that cell types show highly significant differences in the time course of the spike-triggered currents and moving threshold, that is, in their adaptation and refractory properties but not in their passive properties. In particular, GABAergic fast-spiking neurons mediate weak adaptation through spike-triggered currents only, whereas regular spiking excitatory neurons mediate adaptation with both moving threshold and spike-triggered currents. GABAergic nonfast-spiking neurons combine the two distinct adaptation mechanisms with reduced strength. Differences between cell types are large enough to enable automatic classification of neurons into three different classes. Parameter extraction is performed for individual neurons so that we find not only the mean parameter values for each neuron type but also the spread of parameters within a group of neurons, which will be useful for future large-scale computer simulations.

title: Predicting spike timing of neocortical pyramidal neurons by simple threshold models
abstract: Neurons generate spikes reliably with millisecond precision if driven by a fluctuating current—is it then possible to predict the spike timing knowing the input? We determined parameters of an adapting threshold model using data recorded in vitro from 24 layer 5 pyramidal neurons from rat somatosensory cortex, stimulated intracellularly by a fluctuating current simulating synaptic bombardment in vivo. The model generates output spikes whenever the membrane voltage (a filtered version of the input current) reaches a dynamic threshold. We find that for input currents with large fluctuation amplitude, up to 75% of the spike times can be predicted with a precision of ±2 ms. Some of the intrinsic neuronal unreliability can be accounted for by a noisy threshold mechanism. Our results suggest that, under random current injection into the soma, (i) neuronal behavior in the subthreshold regime can be well approximated by a simple linear filter; and (ii) most of the nonlinearities are captured by a simple threshold process.

title: Associative memory in a network of ‘spiking’ neurons
abstract: The Hopfield network provides a simple model of an associative memory in a neuronal structure. It is, however, based on highly artificial assumptions, especially the use of formal two-state neurons or graded-response neurons. The authors address the question of what happens if formal neurons are replaced by a model of ‘spiking’ neurons. They do so in two steps. First, they show how to include refractoriness and noise into a simple threshold model of neuronal spiking. The spike trains resulting from such a model reproduce the distribution of interspike intervals and gain functions found in real neurons. In a second step they connect the model neurons so as to form a large associative memory system. The spike transmission is described by a synaptic kernel which includes axonal delays, ‘Hebbian’ synaptic efficacies, and a realistic postsynaptic response. The collective behaviour of the system is predicted by a set of dynamical equations which are exact in the limit of a large and fully connected network that...

title: Maximum likelihood estimation of cascade point-process neural encoding models
abstract: Recent work has examined the estimation of models of stimulus-driven neural activity in which some linear filtering process is followed by a nonlinear, probabilistic spiking stage. We analyze the estimation of one such model for which this nonlinear step is implemented by a known parametric function; the assumption that this function is known speeds the estimation process considerably. We investigate the shape of the likelihood function for this type of model, give a simple condition on the nonlinearity ensuring that no non-global local maxima exist in the likelihood—leading, in turn, to efficient algorithms for the computation of the maximum likelihood estimator—and discuss the implications for the form of the allowed nonlinearities. Finally, we note some interesting connections between the likelihood-based estimators and the classical spike-triggered average estimator, discuss some useful extensions of the basic model structure, and provide two novel applications to physiological data.

title: Reliability of spike timing in neocortical neurons.
abstract: It is not known whether the variability of neural activity in the cerebral cortex carries information or reflects noisy underlying mechanisms. In an examination of the reliability of spike generation using recordings from neurons in rat neocortical slices, the precision of spike timing was found to depend on stimulus transients. Constant stimuli led to imprecise spike trains, whereas stimuli with fluctuations resembling synaptic activity produced spike trains with timing reproducible to less than 1 millisecond. These data suggest a low intrinsic noise level in spike generation, which could allow cortical neurons to accurately transform synaptic input into spike sequences, supporting a possible role for spike timing in the processing of cortical information by the neocortex.

title: Fractional differentiation by neocortical pyramidal neurons
abstract: Neural systems adapt to changes in stimulus statistics. However, it is not known how stimuli with complex temporal dynamics drive the dynamics of adaptation and the resulting firing rate. For single neurons, it has often been assumed that adaptation has a single time scale. We found that single rat neocortical pyramidal neurons adapt with a time scale that depends on the time scale of changes in stimulus statistics. This multiple time scale adaptation is consistent with fractional order differentiation, such that the neuron's firing rate is a fractional derivative of slowly varying stimulus parameters. Biophysically, even though neuronal fractional differentiation effectively yields adaptation with many time scales, we found that its implementation required only a few properly balanced known adaptive mechanisms. Fractional differentiation provides single neurons with a fundamental and general computation that can contribute to efficient information processing, stimulus anticipation and frequency-independent phase shifts of oscillatory neuronal firing.

title: Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo.
abstract: During wakefulness, neocortical neurons are subjected to an intense synaptic bombardment. To assess the consequences of this background activity for the integrative properties of pyramidal neurons, we constrained biophysical models with in vivo intracellular data obtained in anesthetized cats during periods of intense network activity similar to that observed in the waking state. In pyramidal cells of the parietal cortex (area 5-7), synaptic activity was responsible for an approximately fivefold decrease in input resistance (Rin), a more depolarized membrane potential (Vm), and a marked increase in the amplitude of Vm fluctuations, as determined by comparing the same cells before and after microperfusion of tetrodotoxin (TTX). The model was constrained by measurements of Rin, by the average value and standard deviation of the Vm measured from epochs of intense synaptic activity recorded with KAc or KCl-filled pipettes as well as the values measured in the same cells after TTX. To reproduce all experimental results, the simulated synaptic activity had to be of relatively high frequency (1-5 Hz) at excitatory and inhibitory synapses. In addition, synaptic inputs had to be significantly correlated (correlation coefficient approximately 0.1) to reproduce the amplitude of Vm fluctuations recorded experimentally. The presence of voltage-dependent K+ currents, estimated from current-voltage relations after TTX, affected these parameters by <10%. The model predicts that the conductance due to synaptic activity is 7-30 times larger than the somatic leak conductance to be consistent with the approximately fivefold change in Rin. The impact of this massive increase in conductance on dendritic attenuation was investigated for passive neurons and neurons with voltage-dependent Na+/K+ currents in soma and dendrites. In passive neurons, correlated synaptic bombardment had a major influence on dendritic attenuation. The electrotonic attenuation of simulated synaptic inputs was enhanced greatly in the presence of synaptic bombardment, with distal synapses having minimal effects at the soma. Similarly, in the presence of dendritic voltage-dependent currents, the convergence of hundreds of synaptic inputs was required to evoke action potentials reliably. In this case, however, dendritic voltage-dependent currents minimized the variability due to input location, with distal apical synapses being as effective as synapses on basal dendrites. In conclusion, this combination of intracellular and computational data suggests that, during low-amplitude fast electroencephalographic activity, neocortical neurons are bombarded continuously by correlated synaptic inputs at high frequency, which significantly affect their integrative properties. A series of predictions are suggested to test this model.

title: The role of single neurons in information processing
abstract: Neurons carry out the many operations that extract meaningful information from sensory receptor arrays at the organism's periphery and translate these into action, imagery and memory. Within today's dominant computational paradigm, these operations, involving synapses, membrane ionic channels and changes in membrane potential, are thought of as steps in an algorithm or as computations. The role of neurons in these computations has evolved conceptually from that of a simple integrator of synaptic inputs until a threshold is reached and an output pulse is initiated, to a much more sophisticated processor with mixed analog-digital logic and highly adaptive synaptic elements.

title: Core Conductor Theory and Cable Properties of Neurons
abstract: The sections in this article are: 
 
 
1 
 
1.1 
Core Conductor Concept 
 
1.2 
Perspective 
 
1.3 
Comment 
 
1.4 
Reviews and Monographs 
 
 
 
 
2 
Brief Historical Notes 
2.1 
Early Electrophysiology 
 
2.2 
Electrotonus 
 
2.3 
Passive Membrane Electrotonus 
 
2.4 
Passive Versus Active Membrane 
 
2.5 
Cable Theory 
 
2.6 
Core Conductor Concept 
 
2.7 
Core Conductor Theory 
 
2.8 
Estimation of Membrane Capacitance 
 
2.9 
Resting Membrane Resistivitiy 
 
2.10 
Passive Cable Parameters of Invertebrate Axons 
 
2.11 
Importance of Single Axon Preparations 
 
2.12 
Estimation of Parameters for Myelinated Axons 
 
2.13 
Space and Voltage Clamp 
 
 
 
 
3 
Dendritic Aspects of Neurons 
3.1 
Axon-Dendrite Contrast 
 
3.2 
Microelectrodes in Motoneurons 
 
3.3 
Theoretical Neuron Models and Parameters 
 
3.4 
Class of Trees Equivalent to Cylinders 
 
3.5 
Motoneuron Membrane Resistivity and Dendritic Dominance 
 
3.6 
Dendritic Electrotonic Length 
 
3.7 
Membrane Potential Transients and Time Constants 
 
3.8 
Spatiotemporal Effects with Dendritic Synapses 
 
3.9 
Excitatory Postsynaptic Potential Shape Index Loci 
 
3.10 
Comments on Extracellular Potentials 
 
3.11 
Additional Comments and References 
 
 
 
 
4 
Cable Equations Defined 
4.1 
Usual Cable Equation 
 
4.2 
Steady-state Cable Equations 
 
 
General Solution of Steady-state Cable Equation 
 
4.7 
Basic Transient Solutions of Cable Equation 
 
4.8 
Solutions Using Separation of Variables 
 
4.9 
Fundamental Solution for Instantaneous Point Charge 
 
 
 
 
5 
List of Symbols 
 
6 
Assumptions and Derivation of Cable Theory 
6.1 
One Dimensional in Space 
 
6.2 
Intracellular Core Resistance 
 
6.3 
Ohm's Law for Core Current 
 
6.4 
Conservation of Current 
 
6.5 
Relation of Membrane Current to Vi 
 
6.6 
Effect of Assuming Extracellular Isopotentiality 
 
6.7 
Passive Membrane Model 
 
6.8 
Resulting Cable Equation for Simple Case 
 
6.9 
Physical Meaning of Cable Equation Terms 
 
6.10 
Physical Meaning of τ 
 
6.11 
Physical Meaning of λ 
 
6.12 
Electrotonic Distance, Length, and Decrement 
 
6.13 
Effect of Placing Axon in Oil 
 
6.14 
Effect of Applied Current 
 
6.15 
Comment on Sign Conventions 
 
6.16 
Effect of Synaptic Membrane Conductance 
 
6.17 
Effect of Active Membrane Properties 
 
 
 
 
7 
Input Resistance and Steady Decrement with Distance 
7.1 
Note on Correspondence with Experiment 
 
7.2 
Cable of Semi-infinite Length 
 
7.3 
Comments about R∞, G∞, Core Current, and Input Current 
 
7.4 
Doubly Infinite Length 
 
7.5 
Case of Voltage Clamps at X1 and X2 
 
7.6 
Relations Between Axon Parameters 
 
7.7 
Finite Length: Effect of Boundary Condition at X= X1 
 
7.8 
Sealed End at X= X1: Case of B1 = 0 
 
7.9 
Voltage Clamp(V1 = 0) at X = X1: Case of B1 = ∞ 
 
7.10 
Semi-infinite Extension at X = X1: Case of B1 = 1 
 
7.11 
Input Conductance for Finite Length General Case 
 
7.12 
Branches at X = X1 
 
7.13 
Comment on Branching Equivalent to a Cylinder 
 
7.14 
Comment on Membrane Injury at X = X1 
 
7.15 
Comment on Steady Synaptic Input at X= X1 
 
7.16 
Case of Input to One Branch of Dendritic Neuron Model 
 
 
 
 
8 
Passive Membrane Potential Transients and Time Constants 
8.1 
Passive Decay Transients 
 
8.2 
Time Constant Ratios and Electrotonic Length 
 
8.3 
Effect of Large L and Infinite L 
 
8.4 
Transient Response to Applied Current Step, for Finite Length 
 
8.5 
Applied Current Step with L Large or Infinite 
 
8.6 
Voltage Clamp at X = 0, with Infinite L 
 
8.7 
Voltage Clamp with Finite Length 
 
8.8 
Transient Response to Current Injected at One Branch of Model 
 
 
 
 
9 
Relations Between Neuron Model Parameters 
9.1 
Input Resistance and Membrane Resistivity 
 
9.2 
Dendritic Tree Input Resistance and Membrane Resistivity 
 
9.3 
Results for Trees Equivalent to Cylinders 
 
9.4 
Result for Neuron Equivalent to Cylinder 
 
9.5 
Estimation of Motoneuron Parameters

title: layer 2 / 3 of mouse barrel cortex Microcircuits of excitatory and inhibitory neurons in
abstract: layer 2/3 of mouse barrel cortex Microcircuits of excitatory and inhibitory neurons in You might find this additional info useful...

title: Ca2+-activated K+ currents in neurones: types, physiological roles and modulation
abstract: Action potentials in neurones are followed by a hyperpolarization, which can last up to several seconds. This hyperpolarization has several phases that are mediated by the activation of different types of Ca(2+)-activated K+ currents. Patch-clamp studies have revealed two families of Ca(2+)-activated K+ channels of small (SKCa) and high (BKCa) conductance. Activation of BKCa channels contributes to action-potential repolarization, while SKCa channels are thought to underlie the afterhyperpolarization (AHP). In addition, AHPs in neurones can be divided into two distinct types that are easily separated by kinetic and pharmacological criteria. It is now clear that only one type of AHP can be explained by activation of SKCa channels while a new type of Ca(2+)-activated K+ channel underlies the other. Modulation of this channel by a range of transmitters is a key determinant of the excitability of many neurones.

title: Multiple potassium conductances and their functions in neurons from cat sensorimotor cortex in vitro.
abstract: 1. Potassium conductances were studied in large layer V neurons using an in vitro slice preparation of cat sensorimotor cortex. The kinetics and pharmacological sensitivity of K+ currents were studied directly using single microelectrode voltage clamp and indirectly by evoking single or multiple spikes and recording the spike repolarization and subsequent afterhyperpolarizations (AHPs). 2. A fast-decaying afterhyperpolarization (fAHP) and a subsequent medium-duration afterhyperpolarization (mAHP) followed a single spike. The amplitude and duration of the mAHP increased when multiple spikes were evoked at a fast rate (e.g., 100 Hz), and a slower afterhyperpolarization (sAHP) appeared only after sustained repetitive firing. 3. All AHPs were reduced by membrane potential hyperpolarization and raised extracellular K+ concentration, suggesting they were caused by an increased K+ conductance. Only the mAHP and sAHP reversed at the estimated value of potassium equilibrium potential (-100 mV), whereas the mean reversal potential of the fAHP was nearly identical to the mean value of resting potential (-71 mV). 4. Mechanisms underlying spike repolarization, the fAHP, and the mAHP were investigated. Two rapidly activating outward currents, a fast-inactivating current and a slowly inactivating delayed rectifier, were detected by voltage clamp. Both currents were reduced rapidly by tetraethylammonium (TEA). The fast transient current was reduced slowly after divalent cations were substituted for Ca2+ (through a mechanism unrelated to blockade of Ca2+ channels), whereas the delayed rectifier was unaffected. 5. Spike duration was increased and the fAHP was abolished only by blocking agents that reduced the fast outward currents. Effects of extracellular and intracellular TEA were similar. Effects of TEA and Ca2+-free perfusate were additive and resembled the effects of intracellular Cs+. The addition of apamin, d-tubocurare, or Cd2+ was ineffective. We conclude that the two fast outward currents reflect pharmacologically and kinetically separate K+ conductances that are primarily responsible for spike repolarization and the fAHP. 6. Voltage-clamp studies revealed two additional outward currents, which were persistent and Ca2+-mediated. Each current activated and deactivated slowly, but the kinetics of one component were approximately 10 times slower than the other. The decay of these currents gave rise to AHPs resembling the mAHP and the early sAHP. 7. Neither the mAHP nor the sAHP was reduced by TEA. The mAHP was reduced when divalent cations were substituted for Ca2+ or when Cd2+, apamin, or d-tubocurare were added.(ABSTRACT TRUNCATED AT 400

title: Dynamic spike threshold reveals a mechanism for synaptic coincidence detection in cortical neurons in vivo.
abstract: Cortical neurons are sensitive to the timing of their synaptic inputs. They can synchronize their firing on a millisecond time scale and follow rapid stimulus fluctuations with high temporal precision. These findings suggest that cortical neurons have an enhanced sensitivity to synchronous synaptic inputs that lead to rapid rates of depolarization. The voltage-gated currents underlying action potential generation may provide one mechanism to amplify rapid depolarizations. We have tested this hypothesis by analyzing the relations between membrane potential fluctuations and spike threshold in cat visual cortical neurons recorded intracellularly in vivo. We find that visual stimuli evoke broad variations in spike threshold that are caused in large part by an inverse relation between spike threshold and the rate of membrane depolarization preceding a spike. We also find that spike threshold is inversely related to the rate of rise of the action potential upstroke, suggesting that increases in spike threshold result from a decrease in the availability of Na(+) channels. By using a simple neuronal model, we show that voltage-gated Na(+) and K(+) conductances endow cortical neurons with an enhanced sensitivity to rapid depolarizations that arise from synchronous excitatory synaptic inputs. Thus, the basic mechanism responsible for action potential generation also enhances the sensitivity of cortical neurons to coincident synaptic inputs.

title: Adaptive Coincidence Detection and Dynamic Gain Control in Visual Cortical Neurons In Vivo
abstract: Several theories have proposed a functional role for response synchronization in sensory perception. Critics of these theories have argued that selective synchronization is physiologically implausible when cortical networks operate at high levels of activity. Using intracellular recordings from visual cortex in vivo, in combination with numerical simulations, we find dynamic changes in spike threshold that reduce cellular sensitivity to slow depolarizations and concurrently increase the relative sensitivity to rapid depolarizations. Consistent with this, we find that spike activity and high-frequency fluctuations in membrane potential are closely correlated and that both are more tightly tuned for stimulus orientation than the mean membrane potential. These findings suggest that under high-input conditions the spike-generating mechanism adaptively enhances the sensitivity to synchronous inputs while simultaneously decreasing the sensitivity to temporally uncorrelated inputs.

title: Interneurons of the neocortical inhibitory system
abstract: Mammals adapt to a rapidly changing world because of the sophisticated cognitive functions that are supported by the neocortex. The neocortex, which forms almost 80% of the human brain, seems to have arisen from repeated duplication of a stereotypical microcircuit template with subtle specializations for different brain regions and species. The quest to unravel the blueprint of this template started more than a century ago and has revealed an immensely intricate design. The largest obstacle is the daunting variety of inhibitory interneurons that are found in the circuit. This review focuses on the organizing principles that govern the diversity of inhibitory interneurons and their circuits.

title: Intrinsic biophysical diversity decorrelates neuronal firing while increasing information content
abstract: Although examples of variation and diversity exist throughout the nervous system, their importance remains a source of debate. Even neurons of the same molecular type have notable intrinsic differences. Largely unknown, however, is the degree to which these differences impair or assist neural coding. We examined the outputs from a single type of neuron, the mitral cells of the mouse olfactory bulb, to identical stimuli and found that each cell's spiking response was dictated by its unique biophysical fingerprint. Using this intrinsic heterogeneity, diverse populations were able to code for twofold more information than their homogeneous counterparts. In addition, biophysical variability alone reduced pair-wise output spike correlations to low levels. Our results indicate that intrinsic neuronal diversity is important for neural coding and is not simply the result of biological imprecision.

title: Intermediate intrinsic diversity enhances neural population coding
abstract: Cell-to-cell variability in molecular, genetic, and physiological features is increasingly recognized as a critical feature of complex biological systems, including the brain. Although such variability has potential advantages in robustness and reliability, how and why biological circuits assemble heterogeneous cells into functional groups is poorly understood. Here, we develop analytic approaches toward answering how neuron-level variation in intrinsic biophysical properties of olfactory bulb mitral cells influences population coding of fluctuating stimuli. We capture the intrinsic diversity of recorded populations of neurons through a statistical approach based on generalized linear models. These models are flexible enough to predict the diverse responses of individual neurons yet provide a common reference frame for comparing one neuron to the next. We then use Bayesian stimulus decoding to ask how effectively different populations of mitral cells, varying in their diversity, encode a common stimulus. We show that a key advantage provided by physiological levels of intrinsic diversity is more efficient and more robust encoding of stimuli by the population as a whole. However, we find that the populations that best encode stimulus features are not simply the most heterogeneous, but those that balance diversity with the benefits of neural similarity.

title: Spike-timing prediction in cortical neurons with active dendrites
abstract: A complete single-neuron model must correctly reproduce the firing of spikes and bursts. We present a study of a simplified model of deep pyramidal cells of the cortex with active dendrites. We hypothesized that we can model the soma and its apical dendrite with only two compartments, without significant loss in the accuracy of spike-timing predictions. The model is based on experimentally measurable impulse-response functions, which transfer the effect of current injected in one compartment to current reaching the other. Each compartment was modeled with a pair of non-linear differential equations and a small number of parameters that approximate the Hodgkin-and-Huxley equations. The predictive power of this model was tested on electrophysiological experiments where noisy current was injected in both the soma and the apical dendrite simultaneously. We conclude that a simple two-compartment model can predict spike times of pyramidal cells stimulated in the soma and dendrites simultaneously. Our results support that regenerating activity in the apical dendritic is required to properly account for the dynamics of layer 5 pyramidal cells under in-vivo-like conditions.

title: Connectivity reflects coding: a model of voltage-based STDP with homeostasis
abstract: Electrophysiological connectivity patterns in cortex often have a few strong connections, which are sometimes bidirectional, among a lot of weak connections. To explain these connectivity patterns, we created a model of spike timing–dependent plasticity (STDP) in which synaptic changes depend on presynaptic spike arrival and the postsynaptic membrane potential, filtered with two different time constants. Our model describes several nonlinear effects that are observed in STDP experiments, as well as the voltage dependence of plasticity. We found that, in a simulated recurrent network of spiking neurons, our plasticity rule led not only to development of localized receptive fields but also to connectivity patterns that reflect the neural code. For temporal coding procedures with spatio-temporal input correlations, strong connections were predominantly unidirectional, whereas they were bidirectional under rate-coded input with spatial correlations only. Thus, variable connectivity patterns in the brain could reflect different coding principles across brain areas; moreover, our simulations suggested that plasticity is fast.

title: A Generalized Linear Integrate-and-Fire Neural Model Produces Diverse Spiking Behaviors
abstract: For simulations of neural networks, there is a trade-off between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrate-and-fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firing-induced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model's rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This single-neuron model can be implemented using algorithms similar to the standard integrate-and-fire model. It is a natural match with event-driven algorithms for which the firing times are obtained as a solution of a polynomial equation.

title: A Threshold Equation for Action Potential Initiation
abstract: In central neurons, the threshold for spike initiation can depend on the stimulus and varies between cells and between recording sites in a given cell, but it is unclear what mechanisms underlie this variability. Properties of ionic channels are likely to play a role in threshold modulation. We examined in models the influence of Na channel activation, inactivation, slow voltage-gated channels and synaptic conductances on spike threshold. We propose a threshold equation which quantifies the contribution of all these mechanisms. It provides an instantaneous time-varying value of the threshold, which applies to neurons with fluctuating inputs. We deduce a differential equation for the threshold, similar to the equations of gating variables in the Hodgkin-Huxley formalism, which describes how the spike threshold varies with the membrane potential, depending on channel properties. We find that spike threshold depends logarithmically on Na channel density, and that Na channel inactivation and K channels can dynamically modulate it in an adaptive way: the threshold increases with membrane potential and after every action potential. Our equation was validated with simulations of a previously published multicompartemental model of spike initiation. Finally, we observed that threshold variability in models depends crucially on the shape of the Na activation function near spike initiation (about −55 mV), while its parameters are adjusted near half-activation voltage (about −30 mV), which might explain why many models exhibit little threshold variability, contrary to experimental observations. We conclude that ionic channels can account for large variations in spike threshold.

title: Kv1 channels control spike threshold dynamics and spike timing in cortical pyramidal neurones
abstract: Spiking neurones generate action potentials when the transmembrane voltage difference near the spike generating zone reaches a threshold level. Above the threshold, the inward sodium current exceeds the outward potassium current, causing the rapid upstroke of the action potential. In many neurones, including cortical pyramidal cells, the threshold is not constant but responds to a change in voltage with a short delay. The functional effect is equivalent to high‐pass filtering of the voltage response, and a major benefit is enhanced spike timing precision. Two mechanisms that may contribute to a dynamic spike threshold are sodium channel inactivation and potassium channel activation, both caused by a rise in voltage. We found that blocking low‐threshold Kv1 potassium channels greatly reduced threshold changes in pyramidal neurones located in layer 2–3 of the rat motor cortex. Studies using noise stimulation showed that blocking Kv1 impaired the ability of these cells to encode fast components of the input signal with precisely timed spikes. These results demonstrate a key role of Kv1 in cortical spike timing, with possible implications for information coding as well as pathological hypersynchronous discharges in epilepsy.

title: Adaptive exponential integrate-and-fire model as an effective description of neuronal activity.
abstract: We introduce a two-dimensional integrate-and-fire model that combines an exponential spike mechanism with an adaptation equation, based on recent theoretical findings. We describe a systematic method to estimate its parameters with simple electrophysiological protocols (current-clamp injection of pulses and ramps) and apply it to a detailed conductance-based model of a regular spiking neuron. Our simple model predicts correctly the timing of 96% of the spikes (+/-2 ms) of the detailed model in response to injection of noisy synaptic conductances. The model is especially reliable in high-conductance states, typical of cortical activity in vivo, in which intrinsic conductances were found to have a reduced role in shaping spike trains. These results are promising because this simple model has enough expressive power to reproduce qualitatively several electrophysiological classes described in vitro.

title: Simple model of spiking neurons
abstract: A model is presented that reproduces spiking and bursting behavior of known types of cortical neurons. The model combines the biologically plausibility of Hodgkin-Huxley-type dynamics and the computational efficiency of integrate-and-fire neurons. Using this model, one can simulate tens of thousands of spiking cortical neurons in real time (1 ms resolution) using a desktop PC.

title: Firing patterns in the adaptive exponential integrate-and-fire model
abstract: For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations.

title: Dynamics and bifurcations of the adaptive exponential integrate-and-fire model
abstract: Recently, several two-dimensional spiking neuron models have been introduced, with the aim of reproducing the diversity of electrophysiological features displayed by real neurons while keeping a simple model, for simulation and analysis purposes. Among these models, the adaptive integrate-and-fire model is physiologically relevant in that its parameters can be easily related to physiological quantities. The interaction of the differential equations with the reset results in a rich and complex dynamical structure. We relate the subthreshold features of the model to the dynamical properties of the differential system and the spike patterns to the properties of a Poincaré map defined by the sequence of spikes. We find a complex bifurcation structure which has a direct interpretation in terms of spike trains. For some parameter values, spike patterns are chaotic.

title: Neuroscience thinks big (and collaboratively)
abstract: Despite cash-strapped times for research, several ambitious collaborative neuroscience projects have attracted large amounts of funding and media attention. In Europe, the Human Brain Project aims to develop a large-scale computer simulation of the brain, whereas in the United States, the Brain Activity Map is working towards establishing a functional connectome of the entire brain, and the Allen Institute for Brain Science has embarked upon a 10-year project to understand the mouse visual cortex (the MindScope project). US President Barack Obama's announcement of the BRAIN Initiative (Brain Research through Advancing Innovative Neurotechnologies Initiative) in April 2013 highlights the political commitment to neuroscience and is expected to further foster interdisciplinary collaborations, accelerate the development of new technologies and thus fuel much needed medical advances. In this Viewpoint article, five prominent neuroscientists explain the aims of the projects and how they are addressing some of the questions (and criticisms) that have arisen.

title: The NEURON Book
abstract: Assuming no previous knowledge of computer programming or numerical methods, The NEURON Book provides practical advice on how to get the most out of the NEURON software program. Although written primarily for neuroscientists, teachers and students, readers with a background in the physical sciences or mathematics and some knowledge about brain cells and circuits, will also find it helpful. Covering details of NEURON's inner workings, and practical considerations specifying anatomical and biophysical properties to be represented in models, this book uses a problem-solving approach that includes many examples to challenge readers.

title: A benchmark test for a quantitative assessment of simple neuron models
abstract: Several methods and algorithms have recently been proposed that allow for the systematic evaluation of simple neuron models from intracellular or extracellular recordings. Models built in this way generate good quantitative predictions of the future activity of neurons under temporally structured current injection. It is, however, difficult to compare the advantages of various models and algorithms since each model is designed for a different set of data. Here, we report about one of the first attempts to establish a benchmark test that permits a systematic comparison of methods and performances in predicting the activity of rat cortical pyramidal neurons. We present early submissions to the benchmark test and discuss implications for the design of future tests and simple neurons models.