Estimating the contribution of assembly activity to cortical dynamics from spike and population measures

The hypothesis that cortical networks employ the coordinated activity of groups of neurons, termed assemblies, to process information is debated. Results from multiple single-unit recordings are not conclusive because of the dramatic undersampling of the system. However, the local field potential (LFP) is a mesoscopic signal reflecting synchronized network activity. This raises the question whether the LFP can be employed to overcome the problem of undersampling. In a recent study in the motor cortex of the awake behaving monkey based on the locking of coincidences to the LFP we determined a lower bound for the fraction of spike coincidences originating from assembly activation. This quantity together with the locking of single spikes leads to a lower bound for the fraction of spikes originating from any assembly activity. Here we derive a statistical method to estimate the fraction of spike synchrony caused by assemblies—not its lower bound—from the spike data alone. A joint spike and LFP surrogate data model demonstrates consistency of results and the sensitivity of the method. Combining spike and LFP signals, we obtain an estimate of the fraction of spikes resulting from assemblies in the experimental data.     

多通道神经元锋电位检测和分类的新方法

大脑神经元胞外单细胞动作电位(即锋电位)的检测和分类是提取神经元脉冲序列、研究神经系统信息处理机制的关键．为了提高锋电位的检出率和分类的正确性,设计了一种处理多通道锋电位记录信号的算法,用于分析微电极阵列记录的大鼠海马神经元锋电位信号,电极阵列上的测量点排列紧密,4个通道可以同时记录到来自相同神经元的信号．该算法首先利用一种多通道阈值检测法检出四通道记录信号中的锋电位,然后利用一种基于复合锋电位的主成分特征参数分类法将锋电位分类．仿真数据和实验记录信号的检验结果表明：与相应的单通道算法相比,该算法的锋电位检出率和分类的正确性显著提高,并且可以增加单次实验测得的神经元数目．因此,该算法为实现神经元锋电位的自动检测提供了一种简单有效的新 方法．     

An unsupervised automatic method for sorting neuronal spike waveforms in awake and freely moving animals

The present study introduces an approach to automatic classification of extracellularly recorded action potentials of neurons. The classification of spike waveform is considered a pattern recognition problem of special segments of signal that correspond to the appearance of spikes. The spikes generated by one neuron should be recognized as members of the same class. The spike waveforms are described by the nonlinear oscillating model as an ordinary differential equation with perturbation, thus characterizing the signal distortions in both amplitude and phase. It is shown that the use of local variables reduces the problem of spike recognition to the separation of a mixture of normal distributions in the transformed feature space. We have developed an unsupervised iteration-learning algorithm that estimates the number of classes and their centers according to the distance between spike trajectories in phase space. This algorithm scans the learning set to evaluate spike trajectories with maximal probability density in their neighborhood. Following the learning, the procedure of minimal distance is used to perform spike recognition. Estimation of trajectories in phase space requires calculation of the first- and second-order derivatives, and integral operators with piecewise polynomial kernels were used. This provided the computational efficiency of the developed approach for real-time application as required by recordings in behaving animals and in human neurosurgical operations. The new method of spike sorting was tested on simulated and real data and performed better than other approaches currently used in neurophysiology.     

An online spike detection and spike classification algorithm capable of instantaneous resolution of overlapping spikes

For the analysis of neuronal cooperativity, simultaneously recorded extracellular signals from neighboring neurons need to be sorted reliably by a spike sorting method. Many algorithms have been developed to this end, however, to date, none of them manages to fulfill a set of demanding requirements. In particular, it is desirable to have an algorithm that operates online, detects and classifies overlapping spikes in real time, and that adapts to non-stationary data. Here, we present a combined spike detection and classification algorithm, which explicitly addresses these issues. Our approach makes use of linear filters to find a new representation of the data and to optimally enhance the signal-to-noise ratio. We introduce a method called “Deconfusion” which de-correlates the filter outputs and provides source separation. Finally, a set of well-defined thresholds is applied and leads to simultaneous spike detection and spike classification. By incorporating a direct feedback, the algorithm adapts to non-stationary data and is, therefore, well suited for acute recordings. We evaluate our method on simulated and experimental data, including simultaneous intra/extra-cellular recordings made in slices of a rat cortex and recordings from the prefrontal cortex of awake behaving macaques. We compare the results to existing spike detection as well as spike sorting methods. We conclude that our algorithm meets all of the mentioned requirements and outperforms other methods under realistic signal-to-noise ratios and in the presence of overlapping spikes.     

A Simple Stimulatory Device for Evoking Point-like Tactile Stimuli: A Searchlight for LFP to Spike Transitions

Current neurophysiological research has the aim to develop methodologies to investigate the signal route from neuron to neuron, namely in the transitions from spikes to Local Field Potentials (LFPs) and from LFPs to spikes.LFPs have a complex dependence on spike activity and their relation is still poorly understood¹. The elucidation of these signal relations would be helpful both for clinical diagnostics (e.g. stimulation paradigms for Deep Brain Stimulation) and for a deeper comprehension of neural coding strategies in normal and pathological conditions (e.g. epilepsy, Parkinson disease, chronic pain). To this aim, one has to solve technical issues related to stimulation devices, stimulation paradigms and computational analyses. Therefore, a custom-made stimulation device was developed in order to deliver stimuli well regulated in space and time that does not incur in mechanical resonance. Subsequently, as an exemplification, a set of reliable LFP-spike relationships was extracted.The performance of the device was investigated by extracellular recordings, jointly spikes and LFP responses to the applied stimuli, from the rat Primary Somatosensory cortex. Then, by means of a multi-objective optimization strategy, a predictive model for spike occurrence based on LFPs was estimated.The application of this paradigm shows that the device is adequately suited to deliver high frequency tactile stimulation, outperforming common piezoelectric actuators. As a proof of the efficacy of the device, the following results were presented: 1) the timing and reliability of LFP responses well match the spike responses, 2) LFPs are sensitive to the stimulation history and capture not only the average response but also the trial-to-trial fluctuations in the spike activity and, finally, 3) by using the LFP signal it is possible to estimate a range of predictive models that capture different aspects of the spike activity.     

Comparison of LFP-based and spike-based spectro-temporal receptive fields and cross-correlation in cat primary auditory cortex

Multi-electrode array recordings of spike and local field potential (LFP) activity were made from primary auditory cortex of 12 normal hearing, ketamine-anesthetized cats. We evaluated 259 spectro-temporal receptive fields (STRFs) and 492 frequency-tuning curves (FTCs) based on LFPs and spikes simultaneously recorded on the same electrode. We compared their characteristic frequency (CF) gradients and their cross-correlation distances. The CF gradient for spike-based FTCs was about twice that for 2-40 Hz-filtered LFP-based FTCs, indicating greatly reduced frequency selectivity for LFPs. We also present comparisons for LFPs band-pass filtered between 4-8 Hz, 8-16 Hz and 16-40 Hz, with spike-based STRFs, on the basis of their marginal frequency distributions. We find on average a significantly larger correlation between the spike based marginal frequency distributions and those based on the 16-40 Hz filtered LFP, compared to those based on the 4-8 Hz, 8-16 Hz and 2-40 Hz filtered LFP. This suggests greater frequency specificity for the 16-40 Hz LFPs compared to those of lower frequency content. For spontaneous LFP and spike activity we evaluated 1373 pair correlations for pairs with >200 spikes in 900 s per electrode. Peak correlation-coefficient space constants were similar for the 2-40 Hz filtered LFP (5.5 mm) and the 16-40 Hz LFP (7.4 mm), whereas for spike-pair correlations it was about half that, at 3.2 mm. Comparing spike-pairs with 2-40 Hz (and 16-40 Hz) LFP-pair correlations showed that about 16% (9%) of the variance in the spike-pair correlations could be explained from LFP-pair correlations recorded on the same electrodes within the same electrode array. This larger correlation distance combined with the reduced CF gradient and much broader frequency selectivity suggests that LFPs are not a substitute for spike activity in primary auditory cortex.     

Phase-of-firing coding of natural visual stimuli in primary visual cortex

We investigated the hypothesis that neurons encode rich naturalistic stimuli in terms of their spike times relative to the phase of ongoing network fluctuations rather than only in terms of their spike count. We recorded local field potentials (LFPs) and multiunit spikes from the primary visual cortex of anaesthetized macaques while binocularly presenting a color movie. We found that both the spike counts and the low-frequency LFP phase were reliably modulated by the movie and thus conveyed information about it. Moreover, movie periods eliciting higher firing rates also elicited a higher reliability of LFP phase across trials. To establish whether the LFP phase at which spikes were emitted conveyed visual information that could not be extracted by spike rates alone, we compared the Shannon information about the movie carried by spike counts to that carried by the phase of firing. We found that at low LFP frequencies, the phase of firing conveyed 54% additional information beyond that conveyed by spike counts. The extra information available in the phase of firing was crucial for the disambiguation between stimuli eliciting high spike rates of similar magnitude. Thus, phase coding may allow primary cortical neurons to represent several effective stimuli in an easily decodable format.     

Action potential waveform variability limits multi-unit separation in freely behaving rats

Extracellular multi-unit recording is a widely used technique to study spontaneous and evoked neuronal activity in awake behaving animals. These recordings are done using either single-wire or multiwire electrodes such as tetrodes. In this study we have tested the ability of single-wire electrodes to discriminate activity from multiple neurons under conditions of varying noise and neuronal cell density. Using extracellular single-unit recording, coupled with iontophoresis to drive cell activity across a wide dynamic range, we studied spike waveform variability, and explored systematic differences in single-unit spike waveform within and between brain regions as well as the influence of signal-to-noise ratio (SNR) on the similarity of spike waveforms. We also modelled spike misclassification for a range of cell densities based on neuronal recordings obtained at different SNRs. Modelling predictions were confirmed by classifying spike waveforms from multiple cells with various SNRs using a leading commercial spike-sorting system. Our results show that for single-wire recordings, multiple units can only be reliably distinguished under conditions of high recording SNR (≥ 4) and low neuronal density (≈ 20,000/ mm(3)). Physiological and behavioural changes, as well as technical limitations typical of awake animal preparations, reduce the accuracy of single-channel spike classification, resulting in serious classification errors. For SNR <4, the probability of misclassifying spikes approaches 100% in many cases. Our results suggest that in studies where the SNR is low or neuronal density is high, separation of distinct units needs to be evaluated with great caution.     

Direction-selective dendritic action potentials in rabbit retina

Dendritic spikes that propagate toward the soma are well documented, but their physiological role remains uncertain. Our in vitro patch-clamp recordings and two-photon calcium imaging show that direction-selective retinal ganglion cells (DSGCs) utilize orthograde dendritic spikes during physiological activity. DSGCs signal the direction of image motion. Excitatory subthreshold postsynaptic potentials are observed in DSGCs for motion in all directions and provide a weakly tuned directional signal. However, spikes are generated over only a narrow range of motion angles, indicating that spike generation greatly enhances directional tuning. Our results indicate that spikes are initiated at multiple sites within the dendritic arbors of DSGCs and that each dendritic spike initiates a somatic spike. We propose that dendritic spike failure, produced by local inhibitory inputs, might be a critical factor that enhances directional tuning of somatic spikes.     

Conversion of Phase Information into a Spike-Count Code by Bursting Neurons

Single neurons in the cerebral cortex are immersed in a fluctuating electric field, the local field potential (LFP), which mainly originates from synchronous synaptic input into the local neural neighborhood. As shown by recent studies in visual and auditory cortices, the angular phase of the LFP at the time of spike generation adds significant extra information about the external world, beyond the one contained in the firing rate alone. However, no biologically plausible mechanism has yet been suggested that allows downstream neurons to infer the phase of the LFP at the soma of their pre-synaptic afferents. Therefore, so far there is no evidence that the nervous system can process phase information. Here we study a model of a bursting pyramidal neuron, driven by a time-dependent stimulus. We show that the number of spikes per burst varies systematically with the phase of the fluctuating input at the time of burst onset. The mapping between input phase and number of spikes per burst is a robust response feature for a broad range of stimulus statistics. Our results suggest that cortical bursting neurons could play a crucial role in translating LFP phase information into an easily decodable spike count code.     

Explicit-duration hidden Markov model inference of UP-DOWN states from continuous signals

Neocortical neurons show UP-DOWN state (UDS) oscillations under a variety of conditions. These UDS have been extensively studied because of the insight they can yield into the functioning of cortical networks, and their proposed role in putative memory formation. A key element in these studies is determining the precise duration and timing of the UDS. These states are typically determined from the membrane potential of one or a small number of cells, which is often not sufficient to reliably estimate the state of an ensemble of neocortical neurons. The local field potential (LFP) provides an attractive method for determining the state of a patch of cortex with high spatio-temporal resolution; however current methods for inferring UDS from LFP signals lack the robustness and flexibility to be applicable when UDS properties may vary substantially within and across experiments. Here we present an explicit-duration hidden Markov model (EDHMM) framework that is sufficiently general to allow statistically principled inference of UDS from different types of signals (membrane potential, LFP, EEG), combinations of signals (e.g., multichannel LFP recordings) and signal features over long recordings where substantial non-stationarities are present. Using cortical LFPs recorded from urethane-anesthetized mice, we demonstrate that the proposed method allows robust inference of UDS. To illustrate the flexibility of the algorithm we show that it performs well on EEG recordings as well. We then validate these results using simultaneous recordings of the LFP and membrane potential (MP) of nearby cortical neurons, showing that our method offers significant improvements over standard methods. These results could be useful for determining functional connectivity of different brain regions, as well as understanding network dynamics.     

Context matters: the illusive simplicity of macaque V1 receptive fields

Even in V1, where neurons have well characterized classical receptive fields (CRFs), it has been difficult to deduce which features of natural scenes stimuli they actually respond to. Forward models based upon CRF stimuli have had limited success in predicting the response of V1 neurons to natural scenes. As natural scenes exhibit complex spatial and temporal correlations, this could be due to surround effects that modulate the sensitivity of the CRF. Here, instead of attempting a forward model, we quantify the importance of the natural scenes surround for awake macaque monkeys by modeling it non-parametrically. We also quantify the influence of two forms of trial to trial variability. The first is related to the neuron's own spike history. The second is related to ongoing mean field population activity reflected by the local field potential (LFP). We find that the surround produces strong temporal modulations in the firing rate that can be both suppressive and facilitative. Further, the LFP is found to induce a precise timing in spikes, which tend to be temporally localized on sharp LFP transients in the gamma frequency range. Using the pseudo R(2) as a measure of model fit, we find that during natural scene viewing the CRF dominates, accounting for 60% of the fit, but that taken collectively the surround, spike history and LFP are almost as important, accounting for 40%. However, overall only a small proportion of V1 spiking statistics could be explained (R(2)～5%), even when the full stimulus, spike history and LFP were taken into account. This suggests that under natural scene conditions, the dominant influence on V1 neurons is not the stimulus, nor the mean field dynamics of the LFP, but the complex, incoherent dynamics of the network in which neurons are embedded.     

Predicting stimulus-locked single unit spiking from cortical local field potentials

The rapidly increasing use of the local field potential (LFP) has motivated research to better understand its relation to the gold standard of neural activity, single unit (SU) spiking. We addressed this in an in vivo, awake, restrained mouse auditory cortical electrophysiology preparation by asking whether the LFP could actually be used to predict stimulus-evoked SU spiking. Implementing a Bayesian algorithm to predict the likelihood of spiking on a trial by trial basis from different representations of the despiked LFP signal, we were able to predict, with high quality and fine temporal resolution (2 ms), the time course of a SU’s excitatory or inhibitory firing rate response to natural species-specific vocalizations. Our best predictions were achieved by representing the LFP by its wide-band Hilbert phase signal, and approximating the statistical structure of this signal at different time points as independent. Our results show that each SU’s action potential has a unique relationship with the LFP that can be reliably used to predict the occurrence of spikes. This “signature” interaction can reflect both pre- and post-spike neural activity that is intrinsic to the local circuit rather than just dictated by the stimulus. Finally, the time course of this “signature” may be most faithful when the full bandwidth of the LFP, rather than specific narrow-band components, is used for representation.     

Predicting spike occurrence and neuronal responsiveness from LFPs in primary somatosensory cortex

Local Field Potentials (LFPs) integrate multiple neuronal events like synaptic inputs and intracellular potentials. LFP spatiotemporal features are particularly relevant in view of their applications both in research (e.g. for understanding brain rhythms, inter-areal neural communication and neuronal coding) and in the clinics (e.g. for improving invasive Brain-Machine Interface devices). However the relation between LFPs and spikes is complex and not fully understood. As spikes represent the fundamental currency of neuronal communication this gap in knowledge strongly limits our comprehension of neuronal phenomena underlying LFPs. We investigated the LFP-spike relation during tactile stimulation in primary somatosensory (S-I) cortex in the rat. First we quantified how reliably LFPs and spikes code for a stimulus occurrence. Then we used the information obtained from our analyses to design a predictive model for spike occurrence based on LFP inputs. The model was endowed with a flexible meta-structure whose exact form, both in parameters and structure, was estimated by using a multi-objective optimization strategy. Our method provided a set of nonlinear simple equations that maximized the match between models and true neurons in terms of spike timings and Peri Stimulus Time Histograms. We found that both LFPs and spikes can code for stimulus occurrence with millisecond precision, showing, however, high variability. Spike patterns were predicted significantly above chance for 75% of the neurons analysed. Crucially, the level of prediction accuracy depended on the reliability in coding for the stimulus occurrence. The best predictions were obtained when both spikes and LFPs were highly responsive to the stimuli. Spike reliability is known to depend on neuron intrinsic properties (i.e. on channel noise) and on spontaneous local network fluctuations. Our results suggest that the latter, measured through the LFP response variability, play a dominant role.     

Object selectivity of local field potentials and spikes in the macaque inferior temporal cortex

Local field potentials (LFPs) arise largely from dendritic activity over large brain regions and thus provide a measure of the input to and local processing within an area. We characterized LFPs and their relationship to spikes (multi and single unit) in monkey inferior temporal cortex (IT). LFP responses in IT to complex objects showed strong selectivity at 44% of the sites and tolerance to retinal position and size. The LFP preferences were poorly predicted by the spike preferences at the same site but were better explained by averaging spikes within approximately 3 mm. A comparison of separate sites suggests that selectivity is similar on a scale of approximately 800 microm for spikes and approximately 5 mm for LFPs. These observations imply that inputs to IT neurons convey selectivity for complex shapes and that such input may have an underlying organization spanning several millimeters.     

Optical Recording of Suprathreshold Neural Activity with Single-cell and Single-spike Resolution

Signaling of information in the vertebrate central nervous system is often carried by populations of neurons rather than individual neurons. Also propagation of suprathreshold spiking activity involves populations of neurons. Empirical studies addressing cortical function directly thus require recordings from populations of neurons with high resolution. Here we describe an optical method and a deconvolution algorithm to record neural activity from up to 100 neurons with single-cell and single-spike resolution. This method relies on detection of the transient increases in intracellular somatic calcium concentration associated with suprathreshold electrical spikes (action potentials) in cortical neurons. High temporal resolution of the optical recordings is achieved by a fast random-access scanning technique using acousto-optical deflectors (AODs)¹. Two-photon excitation of the calcium-sensitive dye results in high spatial resolution in opaque brain tissue². Reconstruction of spikes from the fluorescence calcium recordings is achieved by a maximum-likelihood method. Simultaneous electrophysiological and optical recordings indicate that our method reliably detects spikes (>97% spike detection efficiency), has a low rate of false positive spike detection (< 0.003 spikes/sec), and a high temporal precision (about 3 msec) ³. This optical method of spike detection can be used to record neural activity in vitro and in anesthetized animals in vivo^3,4.     

Measuring activity in olfactory receptor neurons in Drosophila: Focus on spike amplitude

Olfactory responses at the receptor level have been thoroughly described in Drosophila melanogaster by electrophysiological methods. Single sensilla recordings (SSRs) measure neuronal activity in intact individuals in response to odors. For sensilla that contain more than one olfactory receptor neuron (ORN), their different spontaneous spike amplitudes can distinguish each signal under resting conditions. However, activity is mainly described by spike frequency.Some reports on ORN response dynamics studied two components in the olfactory responses of ORNs: a fast component that is reflected by the spike frequency and a slow component that is observed in the LFP (local field potential, the single sensillum counterpart of the electroantennogram, EAG). However, no apparent correlation was found between the two elements.In this report, we show that odorant stimulation produces two different effects in the fast component, affecting spike frequency and spike amplitude. Spike amplitude clearly diminishes at the beginning of a response, but it recovers more slowly than spike frequency after stimulus cessation, suggesting that ORNs return to resting conditions long after they recover a normal spontaneous spike frequency. Moreover, spike amplitude recovery follows the same kinetics as the slow voltage component measured by the LFP, suggesting that both measures are connected.These results were obtained in ab2 and ab3 sensilla in response to two odors at different concentrations. Both spike amplitude and LFP kinetics depend on odorant, concentration and neuron, suggesting that like the EAG they may reflect olfactory information.     

Computing the Local Field Potential (LFP) from Integrate-and-Fire Network Models

Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best “LFP proxy”, we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with “ground-truth” LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo.     

An identification technique for the spike artefact of saccadic eye movements

Many subjects have a negative spike in the beginning of a saccade in electro-oculographic signals. The amplitude of the spike depends on the location of the electrodes. The spike distorts the saccades and causes errors in the parameters. The saccade spike can assist in the identification of small saccades. A syntactic technique, based on formal languages and parsing is presented which looks for spikes from the electro-oculographic signal. For calculation of the algorithm, saccades from the photoelectric signal have been concurrently recorded and compared with the electro-oculographic signal.     

Selecting the signals for a brain-machine interface

Brain-machine interfaces are being developed to assist paralyzed patients by enabling them to operate machines with recordings of their own neural activity. Recent studies show that motor parameters, such as hand trajectory, and cognitive parameters, such as the goal and predicted value of an action, can be decoded from the recorded activity to provide control signals. Neural prosthetics that use simultaneously a variety of cognitive and motor signals can maximize the ability of patients to communicate and interact with the outside world. Although most studies have recorded electroencephalograms or spike activity, recent research shows that local field potentials (LFPs) offer a promising additional signal. The decode performances of LFPs and spike signals are comparable and, because LFP recordings are more long lasting, they might help to increase the lifetime of the prosthetics.