Recording spikes from a large fraction of the ganglion cells in a retinal patch

Modelling and Analysis of Electrical Potentials Recorded in Microelectrode Arrays (MEAs)

Microelectrode arrays (MEAs), substrate-integrated planar arrays of up to thousands of closely spaced metal electrode contacts, have long been used to record neuronal activity in in vitro brain slices with high spatial and temporal resolution. However, the analysis of the MEA potentials has generally been mainly qualitative. Here we use a biophysical forward-modelling formalism based on the finite element method (FEM) to establish quantitatively accurate links between neural activity in the slice and potentials recorded in the MEA set-up. Then we develop a simpler approach based on the method of images (MoI) from electrostatics, which allows for computation of MEA potentials by simple formulas similar to what is used for homogeneous volume conductors. As we find MoI to give accurate results in most situations of practical interest, including anisotropic slices covered with highly conductive saline and MEA-electrode contacts of sizable physical extensions, a Python software package (ViMEAPy) has been developed to facilitate forward-modelling of MEA potentials generated by biophysically detailed multicompartmental neurons. We apply our scheme to investigate the influence of the MEA set-up on single-neuron spikes as well as on potentials generated by a cortical network comprising more than 3000 model neurons. The generated MEA potentials are substantially affected by both the saline bath covering the brain slice and a (putative) inadvertent saline layer at the interface between the MEA chip and the brain slice. We further explore methods for estimation of current-source density (CSD) from MEA potentials, and find the results to be much less sensitive to the experimental set-up.

Pharmacological study of direction selectivity in the archer fish retina

Direction selective cells have been found in the retina, the first level of the visual system, in mammals and recently also in the archer fish. These cells are involved in a variety of fast neural computation processes, from the control of eye movements to the detection of prey by the archer fish. The standard model for this mechanism in mammalian retina is well understood and is based on the asymmetry of inhibitory and excitatory inputs to the retinal ganglion cells. However, it remains unclear whether the mechanism that underlies direction selectivity is similar across animal classes. This study reports a pharmacological investigation designed to elucidate the mechanism that underlies motion detection in the archer fish retina. Direction selectivity in the retina was characterized under the influence of specific channel blockers that are known to be present in the different types of neurons of the retina. The results show that the direction-selective mechanism in the archer fish retina is modified only when the inhibitory channels of GABA and Glycine are manipulated. This suggests that the mechanism of direction selectivity in the archer fish retina is fundamentally different from the mechanism of direction selectivity in the mammalian retina.

Spike sorting of synchronous spikes from local neuron ensembles

Synchronous spike discharge of cortical neurons is thought to be a fingerprint of neuronal cooperativity. Because neighboring neurons are more densely connected to one another than neurons that are located further apart, near-synchronous spike discharge can be expected to be prevalent and it might provide an important basis for cortical computations. Using microelectrodes to record local groups of neurons does not allow for the reliable separation of synchronous spikes from different cells, because available spike sorting algorithms cannot correctly resolve the temporally overlapping waveforms. We show that high spike sorting performance of in vivo recordings, including overlapping spikes, can be achieved with a recently developed filter-based template matching procedure. Using tetrodes with a three-dimensional structure, we demonstrate with simulated data and ground truth in vitro data, obtained by dual intracellular recording of two neurons located next to a tetrode, that the spike sorting of synchronous spikes can be as successful as the spike sorting of nonoverlapping spikes and that the spatial information provided by multielectrodes greatly reduces the error rates. We apply the method to tetrode recordings from the prefrontal cortex of behaving primates, and we show that overlapping spikes can be identified and assigned to individual neurons to study synchronous activity in local groups of neurons.

Projection-specific characteristics of retinal input to the brain

The brain receives information about the direction of object motion from several types of retinal ganglion cells (RGCs). On-Off direction-selective (DS) RGCs respond preferentially to stimuli moving quickly in one of four directions and provide a significant (but difficult to quantify) fraction of RGC input to the SC. On DS RGCs, in comparison, respond preferentially to stimuli moving slowly in one of three directions and are thought to only target retinorecipient nuclei comprising the accessory optic system, e.g., the medial terminal nucleus (MTN). To determine the fraction of SC-projecting RGCs that exhibit direction selectivity, and the specificity with which On-Off and On DS RGCs target retinorecipient areas, we performed optical and electrophysiological recordings from RGCs retrogradely labeled from the mouse SC and MTN. We found, surprisingly, that both On-Off and On DS RGCs innervate the SC; collectively they constitute nearly 40% of SC-projecting RGCs. In comparison, only On DS RGCs project to the MTN. Subsequent experiments revealed that individual On DS RGCs innervate either the SC or MTN and exhibit robust projection-specific differences in somatodendritic morphology, cellular excitability, and light-evoked activity; several projection-specific differences in the output of On DS RGCs correspond closely to differences in excitatory synaptic input the cells receive. Our results reveal a robust projection of On DS RGCs to the SC, projection-specific differences in the response properties of On DS RGCs, and biophysical and synaptic mechanisms that underlie these functional differences.

High Accuracy Decoding of Dynamical Motion from a Large Retinal Population

Motion tracking is a challenge the visual system has to solve by reading out the retinal population. It is still unclear how the information from different neurons can be combined together to estimate the position of an object. Here we recorded a large population of ganglion cells in a dense patch of salamander and guinea pig retinas while displaying a bar moving diffusively. We show that the bar's position can be reconstructed from retinal activity with a precision in the hyperacuity regime using a linear decoder acting on 100+ cells. We then took advantage of this unprecedented precision to explore the spatial structure of the retina's population code. The classical view would have suggested that the firing rates of the cells form a moving hill of activity tracking the bar's position. Instead, we found that most ganglion cells in the salamander fired sparsely and idiosyncratically, so that their neural image did not track the bar. Furthermore, ganglion cell activity spanned an area much larger than predicted by their receptive fields, with cells coding for motion far in their surround. As a result, population redundancy was high, and we could find multiple, disjoint subsets of neurons that encoded the trajectory with high precision. This organization allows for diverse collections of ganglion cells to represent high-accuracy motion information in a form easily read out by downstream neural circuits.

Bayes optimal template matching for spike sorting - combining fisher discriminant analysis with optimal filtering

Spike sorting, i.e., the separation of the firing activity of different neurons from extracellular measurements, is a crucial but often error-prone step in the analysis of neuronal responses. Usually, three different problems have to be solved: the detection of spikes in the extracellular recordings, the estimation of the number of neurons and their prototypical (template) spike waveforms, and the assignment of individual spikes to those putative neurons. If the template spike waveforms are known, template matching can be used to solve the detection and classification problem. Here, we show that for the colored Gaussian noise case the optimal template matching is given by a form of linear filtering, which can be derived via linear discriminant analysis. This provides a Bayesian interpretation for the well-known matched filter output. Moreover, with this approach it is possible to compute a spike detection threshold analytically. The method can be implemented by a linear filter bank derived from the templates, and can be used for online spike sorting of multielectrode recordings. It may also be applicable to detection and classification problems of transient signals in general. Its application significantly decreases the error rate on two publicly available spike-sorting benchmark data sets in comparison to state-of-the-art template matching procedures. Finally, we explore the possibility to resolve overlapping spikes using the template matching outputs and show that they can be resolved with high accuracy.

Complexity optimization and high-throughput low-latency hardware implementation of a multi-electrode spike-sorting algorithm

Reliable real-time low-latency spike sorting with large data throughput is essential for studies of neural network dynamics and for brain-machine interfaces (BMIs), in which the stimulation of neural networks is based on the networks' most recent activity. However, the majority of existing multi-electrode spike-sorting algorithms are unsuited for processing high quantities of simultaneously recorded data. Recording from large neuronal networks using large high-density electrode sets (thousands of electrodes) imposes high demands on the data-processing hardware regarding computational complexity and data transmission bandwidth; this, in turn, entails demanding requirements in terms of chip area, memory resources and processing latency. This paper presents computational complexity optimization techniques, which facilitate the use of spike-sorting algorithms in large multi-electrode-based recording systems. The techniques are then applied to a previously published algorithm, on its own, unsuited for large electrode set recordings. Further, a real-time low-latency high-performance VLSI hardware architecture of the modified algorithm is presented, featuring a folded structure capable of processing the activity of hundreds of neurons simultaneously. The hardware is reconfigurable “on-the-fly” and adaptable to the nonstationarities of neuronal recordings. By transmitting exclusively spike time stamps and/or spike waveforms, its real-time processing offers the possibility of data bandwidth and data storage reduction.

Decorrelation of retinal response to natural scenes by fixational eye movements

Under natural viewing conditions the input to the retina is a complex spatiotemporal signal that depends on both the scene and the way the observer moves. It is commonly assumed that the retina processes this input signal efficiently by taking into account the statistics of the natural world. It has recently been argued that incessant microscopic eye movements contribute to this process by decorrelating the input to the retina. Here we tested this theory by measuring the responses of the salamander retina to stimuli replicating the natural input signals experienced by the retina in the presence and absence of fixational eye movements. Contrary to the predictions of classic theories of efficient encoding that do not take behavior into account, we show that the response characteristics of retinal ganglion cells are not sufficient in themselves to disrupt the broad correlations of natural scenes. Specifically, retinal ganglion cells exhibited strong and extensive spatial correlations in the absence of fixational eye movements. However, the levels of correlation in the neural responses dropped in the presence of fixational eye movements, resulting in effective decorrelation of the channels streaming information to the brain. These observations confirm the predictions that microscopic eye movements act to reduce correlations in retinal responses and contribute to visual information processing.

Spatial information in large-scale neural recordings

To record from a given neuron, a recording technology must be able to separate the activity of that neuron from the activity of its neighbors. Here, we develop a Fisher information based framework to determine the conditions under which this is feasible for a given technology. This framework combines measurable point spread functions with measurable noise distributions to produce theoretical bounds on the precision with which a recording technology can localize neural activities. If there is sufficient information to uniquely localize neural activities, then a technology will, from an information theoretic perspective, be able to record from these neurons. We (1) describe this framework, and (2) demonstrate its application in model experiments. This method generalizes to many recording devices that resolve objects in space and should be useful in the design of next-generation scalable neural recording systems.

Revealing neuronal function through microelectrode array recordings

Microelectrode arrays and microprobes have been widely utilized to measure neuronal activity, both in vitro and in vivo. The key advantage is the capability to record and stimulate neurons at multiple sites simultaneously. However, unlike the single-cell or single-channel resolution of intracellular recording, microelectrodes detect signals from all possible sources around every sensor. Here, we review the current understanding of microelectrode signals and the techniques for analyzing them. We introduce the ongoing advancements in microelectrode technology, with focus on achieving higher resolution and quality of recordings by means of monolithic integration with on-chip circuitry. We show how recent advanced microelectrode array measurement methods facilitate the understanding of single neurons as well as network function.

Spike detection methods for polytrodes and high density microelectrode arrays

This paper compares the ability of different methods to detect and resolve spikes recorded extracellularly with polytrode and high-density microelectrode arrays (MEAs). Detecting spikes on such arrays is more complex than with single electrodes or tetrodes since a single spike from a neuron may cause threshold crossings on several adjacent channels, giving rise to multiple events. These initial events have to be recognized as belonging to a single spike. Combining them is, in essence, a clustering problem. A conflicting need is to be able to resolve spike waveforms that occur close together in space and time. We first evaluated three different detection methods, using simulated data in which spike shape waveforms obtained from real recordings were added to noise with an amplitude and temporal structure similar to that found in real recordings. Performance was assessed by calculating the percentage of correctly identified spikes vs. the false positive rate. Using the best of these detection methods, two different methods for avoiding multiple detections per spike were tested: one based on windowing and the other based on clustering. Using parameters that avoided spatial and temporal duplication, the spatiotemporal resolution of the two methods was next evaluated. The method based on clustering gave slightly better results. Both methods could resolve spikes occurring 1 ms or more apart, regardless of their spatial separation. There was no restriction on the temporal resolution of spike pairs for units more than 200 μm apart.

Immunohistochemical and calcium imaging methods in wholemount rat retina

In this paper we describe the tools, reagents, and the practical steps that are needed for: 1) successful preparation of wholemount retinas for immunohistochemistry and, 2) calcium imaging for the study of voltage gated calcium channel (VGCC) mediated calcium signaling in retinal ganglion cells. The calcium imaging method we describe circumvents issues concerning non-specific loading of displaced amacrine cells in the ganglion cell layer.

Step-by-step instructions for retina recordings with perforated multi electrode arrays

Multi-electrode arrays are a state-of-the-art tool in electrophysiology, also in retina research. The output cells of the retina, the retinal ganglion cells, form a monolayer in many species and are well accessible due to their proximity to the inner retinal surface. This structure has allowed the use of multi-electrode arrays for high-throughput, parallel recordings of retinal responses to presented visual stimuli, and has led to significant new insights into retinal organization and function. However, using conventional arrays where electrodes are embedded into a glass or ceramic plate can be associated with three main problems: (1) low signal-to-noise ratio due to poor contact between electrodes and tissue, especially in the case of strongly curved retinas from small animals, e.g. rodents; (2) insufficient oxygen and nutrient supply to cells located on the bottom of the recording chamber; and (3) displacement of the tissue during recordings. Perforated multi-electrode arrays (pMEAs) have been found to alleviate all three issues in brain slice recordings. Over the last years, we have been using such perforated arrays to study light evoked activity in the retinas of various species including mouse, pig, and human. In this article, we provide detailed step-by-step instructions for the use of perforated MEAs to record visual responses from the retina, including spike recordings from retinal ganglion cells and in vitro electroretinograms (ERG). In addition, we provide in-depth technical and methodological troubleshooting information, and show example recordings of good quality as well as examples for the various problems which might be encountered. While our description is based on the specific equipment we use in our own lab, it may also prove useful when establishing retinal MEA recordings with other equipment.

Reconstruction of cell-electrode-adjacencies on multielectrode arrays

The multichannel recordings of signals of many cells cultivated on a multielectrode array (MEA) impose some challenging problems. A meanwhile classic problem is the separation of the recordings of a single electrode into classes of recordings where each class is caused by a single cell. This is the well-known spike sorting. A "dual" problem is the determination of the set of electrodes that record signals of a single cell. This set is called the neighborhood of the cell and has often more than one element if the MEA has a large number of electrodes with high density. A method for the reconstruction of the neighborhoods from the multichannel recordings is presented. Special effort is directed to a precise peak detection. For the evaluation of the algorithm, artificial data, obtained from an appropriate model of MEA recordings, are used. Because the artificial data provide a ground truth, an evaluation of the accuracy of the algorithm is possible. The algorithm works well for realistic parameters.

High-Throughput Hardware for Real-Time Spike Overlap Decomposition in Multi-Electrode Neuronal Recording Systems

Spike overlaps occur frequently in dense neuronal network recordings, creating difficulties for spike sorting. Brainmachine interfaces and in vivo studies of neuronal network dynamics often require that an accurate spike sorting be done in real time, with low execution latency (on the order of milliseconds). Moreover, modern neuronal recording systems that feature thousands of electrodes require processing of several tens or hundreds of neurons in parallel. The existing algorithms capable of performing spike overlap decomposition are generally very complex and unsuitable for real-time implementation, especially for an on-chip implementation. Here we present a hardware device capable of processing pair-wise spike overlaps in real time. A previously-published spike sorting algorithm, which is not suitable for processing data of large neuronal networks with low latency, has been optimized for high-throughput, low-latency hardware implementation. The designed hardware architecture has been verified on an FPGA platform. Low spike sorting error rates (0.05) for overlapping spikes have been achieved with a latency of 2.75 ms, rendering the system particularly suitable for use in closed-loop experiments.

Closed-loop optical neural stimulation based on a 32-channel low-noise recording system with online spike sorting

OBJECTIVE

Closed-loop operation of neuro-electronic systems is desirable for both scientific and clinical (neuroprosthesis) applications. Integrating optical stimulation with recording capability further enhances the selectivity of neural stimulation. We have developed a system enabling the local delivery of optical stimuli and the simultaneous electrical measuring of the neural activities in a closed-loop approach.

APPROACH

The signal analysis is performed online through the implementation of a template matching algorithm. The system performance is demonstrated with the recorded data and in awake rats.

MAIN RESULTS

Specifically, the neural activities are simultaneously recorded, detected, classified online (through spike sorting) from 32 channels, and used to trigger a light emitting diode light source using generated TTL signals.

SIGNIFICANCE

A total processing time of 8 ms is achieved, suitable for optogenetic studies of brain mechanisms online.

Photoreceptor cells with profound structural deficits can support useful vision in mice

PURPOSE

In animal models of degenerative photoreceptor disease, there has been some success in restoring photoreception by transplanting stem cell-derived photoreceptor cells into the subretinal space. However, only a small proportion of transplanted cells develop extended outer segments, considered critical for photoreceptor cell function. The purpose of this study was to determine whether photoreceptor cells that lack a fully formed outer segment could usefully contribute to vision.

METHODS

Retinal and visual function was tested in wild-type and Rds mice at 90 days of age (Rds(P90)). Photoreceptor cells of mice homozygous for the Rds mutation in peripherin 2 never develop a fully formed outer segment. The electroretinogram and multielectrode recording of retinal ganglion cells were used to test retinal responses to light. Three distinct visual behaviors were used to assess visual capabilities: the optokinetic tracking response, the discrimination-based visual water task, and a measure of the effect of vision on wheel running.

RESULTS

Rds(P90) mice had reduced but measurable electroretinogram responses to light, and exhibited light-evoked responses in multiple types of retinal ganglion cells, the output neurons of the retina. In optokinetic and discrimination-based tests, acuity was measurable but reduced, most notably when contrast was decreased. The wheel running test showed that Rds(P90) mice needed 3 log units brighter luminance than wild type to support useful vision (10 cd/m(2)).

CONCLUSIONS

Photoreceptors that lack fully formed outer segments can support useful vision. This challenges the idea that normal cellular structure needs to be completely reproduced for transplanted cells to contribute to useful vision.

Spike sorting for polytrodes: a divide and conquer approach

In order to determine patterns of neural activity, spike signals recorded by extracellular electrodes have to be clustered (sorted) with the aim of ensuring that each cluster represents all the spikes generated by an individual neuron. Many methods for spike sorting have been proposed but few are easily applicable to recordings from polytrodes which may have 16 or more recording sites. As with tetrodes, these are spaced sufficiently closely that signals from single neurons will usually be recorded on several adjacent sites. Although this offers a better chance of distinguishing neurons with similarly shaped spikes, sorting is difficult in such cases because of the high dimensionality of the space in which the signals must be classified. This report details a method for spike sorting based on a divide and conquer approach. Clusters are initially formed by assigning each event to the channel on which it is largest. Each channel-based cluster is then sub-divided into as many distinct clusters as possible. These are then recombined on the basis of pairwise tests into a final set of clusters. Pairwise tests are also performed to establish how distinct each cluster is from the others. A modified gradient ascent clustering (GAC) algorithm is used to do the clustering. The method can sort spikes with minimal user input in times comparable to real time for recordings lasting up to 45 min. Our results illustrate some of the difficulties inherent in spike sorting, including changes in spike shape over time. We show that some physiologically distinct units may have very similar spike shapes. We show that RMS measures of spike shape similarity are not sensitive enough to discriminate clusters that can otherwise be separated by principal components analysis (PCA). Hence spike sorting based on least-squares matching to templates may be unreliable. Our methods should be applicable to tetrodes and scalable to larger multi-electrode arrays (MEAs).

A unified framework and method for automatic neural spike identification

Automatic identification of action potentials from one or more extracellular electrode recordings is generally achieved by clustering similar segments of the measured voltage trace, a method that fails (or requires substantial human intervention) for spikes whose waveforms overlap. We formulate the problem in terms of a simple probabilistic model, and develop a unified method to identify spike waveforms along with continuous-valued estimates of their arrival times, even in the presence of overlap. Specifically, we make use of a recent algorithm known as Continuous Basis Pursuit for solving linear inverse problems in which the component occurrences are sparse and are at arbitrary continuous-valued times. We demonstrate significant performance improvements over current state-of-the-art clustering methods for four simulated and two real data sets with ground truth, each of which has previously been used as a benchmark for spike sorting. In addition, performance of our method on each of these data sets surpasses that of the best possible clustering method (i.e., one that is specifically optimized to minimize errors on each data set). Finally, the algorithm is almost completely automated, with a computational cost that scales well for multi-electrode arrays.

Adaptation to changes in higher-order stimulus statistics in the salamander retina

Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution.

Searching for collective behavior in a large network of sensory neurons

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such "K-pairwise" models--being systematic extensions of the previously used pairwise Ising models--provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.

Adaptive colour contrast coding in the salamander retina efficiently matches natural scene statistics

The visual system continually adjusts its sensitivity to the statistical properties of the environment through an adaptation process that starts in the retina. Colour perception and processing is commonly thought to occur mainly in high visual areas, and indeed most evidence for chromatic colour contrast adaptation comes from cortical studies. We show that colour contrast adaptation starts in the retina where ganglion cells adjust their responses to the spectral properties of the environment. We demonstrate that the ganglion cells match their responses to red-blue stimulus combinations according to the relative contrast of each of the input channels by rotating their functional response properties in colour space. Using measurements of the chromatic statistics of natural environments, we show that the retina balances inputs from the two (red and blue) stimulated colour channels, as would be expected from theoretical optimal behaviour. Our results suggest that colour is encoded in the retina based on the efficient processing of spectral information that matches spectral combinations in natural scenes on the colour processing level.

Physical principles for scalable neural recording

Simultaneously measuring the activities of all neurons in a mammalian brain at millisecond resolution is a challenge beyond the limits of existing techniques in neuroscience. Entirely new approaches may be required, motivating an analysis of the fundamental physical constraints on the problem. We outline the physical principles governing brain activity mapping using optical, electrical, magnetic resonance, and molecular modalities of neural recording. Focusing on the mouse brain, we analyze the scalability of each method, concentrating on the limitations imposed by spatiotemporal resolution, energy dissipation, and volume displacement. Based on this analysis, all existing approaches require orders of magnitude improvement in key parameters. Electrical recording is limited by the low multiplexing capacity of electrodes and their lack of intrinsic spatial resolution, optical methods are constrained by the scattering of visible light in brain tissue, magnetic resonance is hindered by the diffusion and relaxation timescales of water protons, and the implementation of molecular recording is complicated by the stochastic kinetics of enzymes. Understanding the physical limits of brain activity mapping may provide insight into opportunities for novel solutions. For example, unconventional methods for delivering electrodes may enable unprecedented numbers of recording sites, embedded optical devices could allow optical detectors to be placed within a few scattering lengths of the measured neurons, and new classes of molecularly engineered sensors might obviate cumbersome hardware architectures. We also study the physics of powering and communicating with microscale devices embedded in brain tissue and find that, while radio-frequency electromagnetic data transmission suffers from a severe power-bandwidth tradeoff, communication via infrared light or ultrasound may allow high data rates due to the possibility of spatial multiplexing. The use of embedded local recording and wireless data transmission would only be viable, however, given major improvements to the power efficiency of microelectronic devices.

Spike triggered covariance in strongly correlated gaussian stimuli

Many biological systems perform computations on inputs that have very large dimensionality. Determining the relevant input combinations for a particular computation is often key to understanding its function. A common way to find the relevant input dimensions is to examine the difference in variance between the input distribution and the distribution of inputs associated with certain outputs. In systems neuroscience, the corresponding method is known as spike-triggered covariance (STC). This method has been highly successful in characterizing relevant input dimensions for neurons in a variety of sensory systems. So far, most studies used the STC method with weakly correlated Gaussian inputs. However, it is also important to use this method with inputs that have long range correlations typical of the natural sensory environment. In such cases, the stimulus covariance matrix has one (or more) outstanding eigenvalues that cannot be easily equalized because of sampling variability. Such outstanding modes interfere with analyses of statistical significance of candidate input dimensions that modulate neuronal outputs. In many cases, these modes obscure the significant dimensions. We show that the sensitivity of the STC method in the regime of strongly correlated inputs can be improved by an order of magnitude or more. This can be done by evaluating the significance of dimensions in the subspace orthogonal to the outstanding mode(s). Analyzing the responses of retinal ganglion cells probed with Gaussian noise, we find that taking into account outstanding modes is crucial for recovering relevant input dimensions for these neurons.

In many areas of computational biology, including the analyses of genetic mutations, protein stability and neural coding, as well as in economics, one of the most basic and important steps of data analysis is to find the relevant input dimensions for a particular task. In neural coding problems, the spike-triggered covariance (STC) method identifies relevant input dimensions by comparing the variance of the input distribution along different dimensions to the variance of inputs that elicited a neural response. While in theory the method can be applied to Gaussian stimuli with or without correlations, it has so far been used in studies with only weakly correlated stimuli. Here we show that to use STC with strongly correlated, -type inputs, one has to take into account that the covariance matrix of random samples from this distribution has a complex structure, with one or more outstanding modes. We use simulations on model neurons as well as an analysis of the responses of retinal neurons to demonstrate that taking the presence of these outstanding modes into account improves the sensitivity of the STC method by more than an order of magnitude.

A model-based spike sorting algorithm for removing correlation artifacts in multi-neuron recordings

We examine the problem of estimating the spike trains of multiple neurons from voltage traces recorded on one or more extracellular electrodes. Traditional spike-sorting methods rely on thresholding or clustering of recorded signals to identify spikes. While these methods can detect a large fraction of the spikes from a recording, they generally fail to identify synchronous or near-synchronous spikes: cases in which multiple spikes overlap. Here we investigate the geometry of failures in traditional sorting algorithms, and document the prevalence of such errors in multi-electrode recordings from primate retina. We then develop a method for multi-neuron spike sorting using a model that explicitly accounts for the superposition of spike waveforms. We model the recorded voltage traces as a linear combination of spike waveforms plus a stochastic background component of correlated Gaussian noise. Combining this measurement model with a Bernoulli prior over binary spike trains yields a posterior distribution for spikes given the recorded data. We introduce a greedy algorithm to maximize this posterior that we call "binary pursuit". The algorithm allows modest variability in spike waveforms and recovers spike times with higher precision than the voltage sampling rate. This method substantially corrects cross-correlation artifacts that arise with conventional methods, and substantially outperforms clustering methods on both real and simulated data. Finally, we develop diagnostic tools that can be used to assess errors in spike sorting in the absence of ground truth.

Nanotools for neuroscience and brain activity mapping

Neuroscience is at a crossroads. Great effort is being invested into deciphering specific neural interactions and circuits. At the same time, there exist few general theories or principles that explain brain function. We attribute this disparity, in part, to limitations in current methodologies. Traditional neurophysiological approaches record the activities of one neuron or a few neurons at a time. Neurochemical approaches focus on single neurotransmitters. Yet, there is an increasing realization that neural circuits operate at emergent levels, where the interactions between hundreds or thousands of neurons, utilizing multiple chemical transmitters, generate functional states. Brains function at the nanoscale, so tools to study brains must ultimately operate at this scale, as well. Nanoscience and nanotechnology are poised to provide a rich toolkit of novel methods to explore brain function by enabling simultaneous measurement and manipulation of activity of thousands or even millions of neurons. We and others refer to this goal as the Brain Activity Mapping Project. In this Nano Focus, we discuss how recent developments in nanoscale analysis tools and in the design and synthesis of nanomaterials have generated optical, electrical, and chemical methods that can readily be adapted for use in neuroscience. These approaches represent exciting areas of technical development and research. Moreover, unique opportunities exist for nanoscientists, nanotechnologists, and other physical scientists and engineers to contribute to tackling the challenging problems involved in understanding the fundamentals of brain function.

Stimulus-dependent maximum entropy models of neural population codes

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model-a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population.

A detailed and fast model of extracellular recordings

We present a novel method to generate realistic simulations of extracellular recordings. The simulations were obtained by superimposing the activity of neurons placed randomly in a cube of brain tissue. Detailed models of individual neurons were used to reproduce the extracellular action potentials of close-by neurons. To reduce the computational load, the contributions of neurons further away were simulated using previously recorded spikes with their amplitude normalized by the distance to the recording electrode. For making the simulations more realistic, we also considered a model of a finite-size electrode by averaging the potential along the electrode surface and modeling the electrode-tissue interface with a capacitive filter. This model allowed studying the effect of the electrode diameter on the quality of the recordings and how it affects the number of identified neurons after spike sorting. Given that not all neurons are active at a time, we also generated simulations with different ratios of active neurons and estimated the ratio that matches the signal-to-noise values observed in real data. Finally, we used the model to simulate tetrode recordings.

Retinal metric: a stimulus distance measure derived from population neural responses

The ability of an organism to distinguish between various stimuli is limited by the structure and noise in the population code of its sensory neurons. Here we infer a distance measure on the stimulus space directly from the recorded activity of 100 neurons in the salamander retina. In contrast to previously used measures of stimulus similarity, this "neural metric" tells us how distinguishable a pair of stimulus clips is to the retina, based on the similarity between the induced distributions of population responses. We show that the retinal distance strongly deviates from Euclidean, or any static metric, yet has a simple structure: we identify the stimulus features that the neural population is jointly sensitive to, and show the support-vector-machine-like kernel function relating the stimulus and neural response spaces. We show that the non-Euclidean nature of the retinal distance has important consequences for neural decoding.

Imaging the response of the retina to electrical stimulation with genetically encoded calcium indicators

Epiretinal implants for the blind are designed to stimulate surviving retinal neurons, thus bypassing the diseased photoreceptor layer. Single-unit or multielectrode recordings from isolated animal retina are commonly used to inform the design of these implants. However, such electrical recordings provide limited information about the spatial patterns of retinal activation. Calcium imaging overcomes this limitation, as imaging enables high spatial resolution mapping of retinal ganglion cell (RGC) activity as well as simultaneous recording from hundreds of RGCs. Prior experiments in amphibian retina have demonstrated proof of principle, yet experiments in mammalian retina have been hindered by the inability to load calcium indicators into mature mammalian RGCs. Here, we report a method for labeling the majority of ganglion cells in adult rat retina with genetically encoded calcium indicators, specifically GCaMP3 and GCaMP5G. Intravitreal injection of an adeno-associated viral vector targets ∼85% of ganglion cells with high specificity. Because of the large fluorescence signals provided by the GCaMP sensors, we can now for the first time visualize the response of the retina to electrical stimulation in real-time. Imaging transduced retinas mounted on multielectrode arrays reveals how stimulus pulse shape can dramatically affect the spatial extent of RGC activation, which has clear implications in prosthetic applications. Our method can be easily adapted to work with other fluorescent indicator proteins in both wild-type and transgenic mammals.

Mapping a complete neural population in the retina

Recording simultaneously from essentially all of the relevant neurons in a local circuit is crucial to understand how they collectively represent information. Here we show that the combination of a large, dense multielectrode array and a novel, mostly automated spike-sorting algorithm allowed us to record simultaneously from a highly overlapping population of >200 ganglion cells in the salamander retina. By combining these methods with labeling and imaging, we showed that up to 95% of the ganglion cells over the area of the array were recorded. By measuring the coverage of visual space by the receptive fields of the recorded cells, we concluded that our technique captured a neural population that forms an essentially complete representation of a region of visual space. This completeness allowed us to determine the spatial layout of different cell types as well as identify a novel group of ganglion cells that responded reliably to a set of naturalistic and artificial stimuli but had no measurable receptive field. Thus, our method allows unprecedented access to the complete neural representation of visual information, a crucial step for the understanding of population coding in sensory systems.

Divergence of visual channels in the inner retina

Bipolar cells form parallel channels that carry visual signals from the outer to the inner retina. Each type of bipolar cell is thought to carry a distinct visual message to select types of amacrine cells and ganglion cells. However, the number of ganglion cell types exceeds that of the bipolar cells providing their input, suggesting that bipolar cell signals diversify on transmission to ganglion cells. We explored in the salamander retina how signals from individual bipolar cells feed into multiple ganglion cells and found that each bipolar cell was able to evoke distinct responses among ganglion cells, differing in kinetics, adaptation and rectification properties. This signal divergence resulted primarily from interactions with amacrine cells that allowed each bipolar cell to send distinct signals to its target ganglion cells. Our findings indicate that individual bipolar cell-ganglion cell connections have distinct transfer functions. This expands the number of visual channels in the inner retina and enhances the computational power and feature selectivity of early visual processing.

Recording from defined populations of retinal ganglion cells using a high-density CMOS-integrated microelectrode array with real-time switchable electrode selection

In order to understand how retinal circuits encode visual scenes, the neural activity of defined populations of retinal ganglion cells (RGCs) has to be investigated. Here we report on a method for stimulating, detecting, and subsequently targeting defined populations of RGCs. The possibility to select a distinct population of RGCs for extracellular recording enables the design of experiments that can increase our understanding of how these neurons extract precise spatio-temporal features from the visual scene, and how the brain interprets retinal signals. We used light stimulation to elicit a response from physiologically distinct types of RGCs and then utilized the dynamic-configurability capabilities of a microelectronics-based high-density microelectrode array (MEA) to record their synchronous action potentials. The layout characteristics of the MEA made it possible to stimulate and record from multiple, highly overlapping RGCs simultaneously without light-induced artifacts. The high-density of electrodes and the high signal-to-noise ratio of the MEA circuitry allowed for recording of the activity of each RGC on 14±7 electrodes. The spatial features of the electrical activity of each RGC greatly facilitated spike sorting. We were thus able to localize, identify and record from defined RGCs within a region of mouse retina. In addition, we stimulated and recorded from genetically modified RGCs to demonstrate the applicability of optogenetic methods, which introduces an additional feature to target a defined cell type. The developed methodologies can likewise be applied to other neuronal preparations including brain slices or cultured neurons.

Predicting single-neuron activity in locally connected networks

The characterization of coordinated activity in neuronal populations has received renewed interest in the light of advancing experimental techniques that allow recordings from multiple units simultaneously. Across both in vitro and in vivo preparations, nearby neurons show coordinated responses when spontaneously active and when subject to external stimuli. Recent work (Truccolo, Hochberg, & Donoghue, 2010 ) has connected these coordinated responses to behavior, showing that small ensembles of neurons in arm-related areas of sensorimotor cortex can reliably predict single-neuron spikes in behaving monkeys and humans. We investigate this phenomenon using an analogous point process model, showing that in the case of a computational model of cortex responding to random background inputs, one is similarly able to predict the future state of a single neuron by considering its own spiking history, together with the spiking histories of randomly sampled ensembles of nearby neurons. This model exhibits realistic cortical architecture and displays bursting episodes in the two distinct connectivity schemes studied. We conjecture that the baseline predictability we find in these instances is characteristic of locally connected networks more broadly considered.

Archer fish fast hunting maneuver may be guided by directionally selective retinal ganglion cells

Archer fish are known for their unique hunting method, where one fish in a group shoots down an insect with a jet of water while all the other fish are observing the prey's motion. To reap its reward, the archer fish must reach the prey before its competitors. This requires fast computation of the direction of motion of the prey, which enables the fish to initiate a turn towards the prey with an accuracy of 99%, at about 100 ms after the prey is shot. We explored the hypothesis that direction-selective retinal ganglion cells may underlie this rapid processing. We quantified the degree of directional selectivity of ganglion cells in the archer fish retina. The cells could be categorized into three groups: sharply (5%), broadly (37%) and non-tuned (58%) directionally selective cells. To relate the electrophysiological data to the behavioral results we studied a computational model and estimated the time required to accumulate sufficient directional information to match the decision accuracy of the fish. The computational model is based on two direction-selective populations that race against each other until one reaches the threshold and drives the decision. We found that this competition model can account for the observed response time at the required accuracy. Thus, our results are consistent with the hypothesis that the fast response behavior of the archer fish relies on retinal identification of movement direction.

Gibbs distribution analysis of temporal correlations structure in retina ganglion cells

We present a method to estimate Gibbs distributions with spatio-temporal constraints on spike trains statistics. We apply this method to spike trains recorded from ganglion cells of the salamander retina, in response to natural movies. Our analysis, restricted to a few neurons, performs more accurately than pairwise synchronization models (Ising) or the 1-time step Markov models (Marre et al., 2009) to describe the statistics of spatio-temporal spike patterns and emphasizes the role of higher order spatio-temporal interactions.

Low error discrimination using a correlated population code

We explored the manner in which spatial information is encoded by retinal ganglion cell populations. We flashed a set of 36 shape stimuli onto the tiger salamander retina and used different decoding algorithms to read out information from a population of 162 ganglion cells. We compared the discrimination performance of linear decoders, which ignore correlation induced by common stimulation, with nonlinear decoders, which can accurately model these correlations. Similar to previous studies, decoders that ignored correlation suffered only a modest drop in discrimination performance for groups of up to ∼30 cells. However, for more realistic groups of 100+ cells, we found order-of-magnitude differences in the error rate. We also compared decoders that used only the presence of a single spike from each cell with more complex decoders that included information from multiple spike counts and multiple time bins. More complex decoders substantially outperformed simpler decoders, showing the importance of spike timing information. Particularly effective was the first spike latency representation, which allowed zero discrimination errors for the majority of shape stimuli. Furthermore, the performance of nonlinear decoders showed even greater enhancement compared with linear decoders for these complex representations. Finally, decoders that approximated the correlation structure in the population by matching all pairwise correlations with a maximum entropy model fit to all 162 neurons were quite successful, especially for the spike latency representation. Together, these results suggest a picture in which linear decoders allow a coarse categorization of shape stimuli, whereas nonlinear decoders, which take advantage of both correlation and spike timing, are needed to achieve high-fidelity discrimination.

Applicability of independent component analysis on high-density microelectrode array recordings

Emerging complementary metal oxide semiconductor (CMOS)-based, high-density microelectrode array (HD-MEA) devices provide high spatial resolution at subcellular level and a large number of readout channels. These devices allow for simultaneous recording of extracellular activity of a large number of neurons with every neuron being detected by multiple electrodes. To analyze the recorded signals, spiking events have to be assigned to individual neurons, a process referred to as "spike sorting." For a set of observed signals, which constitute a linear mixture of a set of source signals, independent component (IC) analysis (ICA) can be used to demix blindly the data and extract the individual source signals. This technique offers great potential to alleviate the problem of spike sorting in HD-MEA recordings, as it represents an unsupervised method to separate the neuronal sources. The separated sources or ICs then constitute estimates of single-neuron signals, and threshold detection on the ICs yields the sorted spike times. However, it is unknown to what extent extracellular neuronal recordings meet the requirements of ICA. In this paper, we evaluate the applicability of ICA to spike sorting of HD-MEA recordings. The analysis of extracellular neuronal signals, recorded at high spatiotemporal resolution, reveals that the recorded data cannot be modeled as a purely linear mixture. As a consequence, ICA fails to separate completely the neuronal signals and cannot be used as a stand-alone method for spike sorting in HD-MEA recordings. We assessed the demixing performance of ICA using simulated data sets and found that the performance strongly depends on neuronal density and spike amplitude. Furthermore, we show how postprocessing techniques can be used to overcome the most severe limitations of ICA. In combination with these postprocessing techniques, ICA represents a viable method to facilitate rapid spike sorting of multidimensional neuronal recordings.

Towards reliable spike-train recordings from thousands of neurons with multielectrodes

The new generation of silicon-based multielectrodes comprising hundreds or more electrode contacts offers unprecedented possibilities for simultaneous recordings of spike trains from thousands of neurons. Such data will not only be invaluable for finding out how neural networks in the brain work, but will likely be important also for neural prosthesis applications. This opportunity can only be realized if efficient, accurate and validated methods for automatic spike sorting are provided. In this review we describe some of the challenges that must be met to achieve this goal, and in particular argue for the critical need of realistic model data to be used as ground truth in the validation of spike-sorting algorithms.

Modeling the impact of common noise inputs on the network activity of retinal ganglion cells

Synchronized spontaneous firing among retinal ganglion cells (RGCs), on timescales faster than visual responses, has been reported in many studies. Two candidate mechanisms of synchronized firing include direct coupling and shared noisy inputs. In neighboring parasol cells of primate retina, which exhibit rapid synchronized firing that has been studied extensively, recent experimental work indicates that direct electrical or synaptic coupling is weak, but shared synaptic input in the absence of modulated stimuli is strong. However, previous modeling efforts have not accounted for this aspect of firing in the parasol cell population. Here we develop a new model that incorporates the effects of common noise, and apply it to analyze the light responses and synchronized firing of a large, densely-sampled network of over 250 simultaneously recorded parasol cells. We use a generalized linear model in which the spike rate in each cell is determined by the linear combination of the spatio-temporally filtered visual input, the temporally filtered prior spikes of that cell, and unobserved sources representing common noise. The model accurately captures the statistical structure of the spike trains and the encoding of the visual stimulus, without the direct coupling assumption present in previous modeling work. Finally, we examined the problem of decoding the visual stimulus from the spike train given the estimated parameters. The common-noise model produces Bayesian decoding performance as accurate as that of a model with direct coupling, but with significantly more robustness to spike timing perturbations.

Synergy from silence in a combinatorial neural code

The manner in which groups of neurons represent events in the external world is a central question in neuroscience. Estimation of the information encoded by small groups of neurons has shown that in many neural systems, cells carry mildly redundant information. These measures average over all the activity patterns of a neural population. Here, we analyze the population code of the salamander and guinea pig retinas by quantifying the information conveyed by specific multicell activity patterns. Synchronous spikes, even though they are relatively rare and highly informative, convey less information than the sum of either spike alone, making them redundant coding symbols. Instead, patterns of spiking in one cell and silence in others, which are relatively common and often overlooked as special coding symbols, were found to be mostly synergistic. Our results reflect that the mild average redundancy between ganglion cells that was previously reported is actually the result of redundant and synergistic multicell patterns, whose contributions partially cancel each other when taking the average over all patterns. We further show that similar coding properties emerge in a generic model of neural responses, suggesting that this form of combinatorial coding, in which specific compound patterns carry synergistic or redundant information, may exist in other neural circuits.

MULTIPLE TESTING OF LOCAL MAXIMA FOR DETECTION OF PEAKS IN 1D

A topological multiple testing scheme for one-dimensional domains is proposed where, rather than testing every spatial or temporal location for the presence of a signal, tests are performed only at the local maxima of the smoothed observed sequence. Assuming unimodal true peaks with finite support and Gaussian stationary ergodic noise, it is shown that the algorithm with Bonferroni or Benjamini-Hochberg correction provides asymptotic strong control of the family wise error rate and false discovery rate, and is power consistent, as the search space and the signal strength get large, where the search space may grow exponentially faster than the signal strength. Simulations show that error levels are maintained for nonasymptotic conditions, and that power is maximized when the smoothing kernel is close in shape and bandwidth to the signal peaks, akin to the matched filter theorem in signal processing. The methods are illustrated in an analysis of electrical recordings of neuronal cell activity.

Far from equilibrium percolation, stochastic and shape resonances in the physics of life

Key physical concepts, relevant for the cross-fertilization between condensed matter physics and the physics of life seen as a collective phenomenon in a system out-of-equilibrium, are discussed. The onset of life can be driven by: (a) the critical fluctuations at the protonic percolation threshold in membrane transport; (b) the stochastic resonance in biological systems, a mechanism that can exploit external and self-generated noise in order to gain efficiency in signal processing; and (c) the shape resonance (or Fano resonance or Feshbach resonance) in the association and dissociation processes of bio-molecules (a quantum mechanism that could play a key role to establish a macroscopic quantum coherence in the cell).

Multiplexed, high density electrophysiology with nanofabricated neural probes

Extracellular electrode arrays can reveal the neuronal network correlates of behavior with single-cell, single-spike, and sub-millisecond resolution. However, implantable electrodes are inherently invasive, and efforts to scale up the number and density of recording sites must compromise on device size in order to connect the electrodes. Here, we report on silicon-based neural probes employing nanofabricated, high-density electrical leads. Furthermore, we address the challenge of reading out multichannel data with an application-specific integrated circuit (ASIC) performing signal amplification, band-pass filtering, and multiplexing functions. We demonstrate high spatial resolution extracellular measurements with a fully integrated, low noise 64-channel system weighing just 330 mg. The on-chip multiplexers make possible recordings with substantially fewer external wires than the number of input channels. By combining nanofabricated probes with ASICs we have implemented a system for performing large-scale, high-density electrophysiology in small, freely behaving animals that is both minimally invasive and highly scalable.