Automatic sorting for multi-neuronal activity recorded with tetrodes in the presence of overlapping spikes

Multi-neuronal recording is a powerful electrophysiological technique that has revealed much of what is known about the neuronal interactions in the brain. However, it is difficult to detect precise spike timings, especially synchronized simultaneous firings, among closely neighboring neurons recorded by one common electrode because spike waveforms overlap on the electrode when two or more neurons fire simultaneously. In addition, the non-Gaussian variability (nonstationarity) of spike waveforms, typically seen in the presence of so-called complex spikes, limits the ability to sort multi-neuronal activities into their single-neuron components. Because of these problems, the ordinary spike-sorting techniques often give inaccurate results. Our previous study has shown that independent component analysis (ICA) can solve these problems and separate single-neuron components from multi-neuronal recordings. The ICA has, however, one serious limitation that the number of separated neurons must be less than the number of electrodes. The present study combines the ICA and the efficiency of the ordinary spike-sorting technique (k-means clustering) to solve the spike-overlapping and the nonstationarity problems with no limitation on the number of single neurons to be separated. First, multi-neuronal activities are sorted into an overly large number of clusters by k-means clustering. Second, the sorted clusters are decomposed by ICA. Third, the decomposed clusters are progressively aggregated into a minimal set of putative single neurons based on similarities of basis vectors estimated by ICA. We applied the present procedure to multi-neuronal waveforms recorded with tetrodes composed of four microwires in the prefrontal cortex of awake behaving monkeys. The results demonstrate that there are functional connections among neighboring pyramidal neurons, some of which fire in a precise simultaneous manner and that precisely time-locked monosynaptic connections are working between neighboring pyramidal neurons and interneurons. Detection of these phenomena suggests that the present procedure can sort multi-neuronal activities, which include overlapping spikes and realistic non-Gaussian variability of spike waveforms, into their single-neuron components. We processed several types of synthesized data sets in this procedure and confirmed that the procedure was highly reliable and stable. The present method provides insights into the local circuit bases of excitatory and inhibitory interactions among neighboring neurons.     

Real-time and automatic sorting of multi-neuronal activity for sub-millisecond interactions in vivo

Recent in vitro electrophysiological studies have revealed that neighboring interneurons interact with each other in a sub-millisecond time range via gap junctions and that individual dendritic compartments generate local excitation spikes and back-propagated spikes within a single-neuron. However, most in vivo electrophysiological studies using behaving animals only focus on activity rates of single-neurons and/or large neuronal populations without considering the potential role of such sub-millisecond interactions among neurons. This neglect is due to the limitation of ordinary in vivo multi-neuronal recording and spike sorting techniques applied to behaving animals. Though independent component analysis (ICA) is a powerful method to overcome certain limitations, ICA has a serious problem in that the number of single-electrodes (microwires) must be more than the number of single-neurons to be recorded. Our recently-developed method has solved this limitation of ICA, but a few problems have remained: the computational load is heavy, the method can be used only for off-line, not real-time, processing, and the electrode-neuron drift problem remains unsolved. In this paper, solving all these problems, we introduce a novel system consisting of automatic and real-time spike sorting with ICA in combination with a newly developed multi-electrode, dodecatrode. The system has the potential to answer some important neurobiological questions that have not been explored in in vivo electrophysiological experiments: how sub-millisecond interactions between closely neighboring single-neurons act in freely behaving animals. The system promises to be a bridge connecting electrophysiological studies in vitro and in vivo.     

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.     

基于数学形态学与核主成分分析的峰电位检测与分类方法

目的 为抑制高强度背景噪声及信号叠加的干扰,提高峰电位的检出率和分类的正确性,本文提出一种新的无监督方法.方法 首先,应用数学形态学的复合操作对信号进行降噪,采用定阈值提取峰电位.然后,小波变换和核主成分分析法（kernel principal components analysis,KPCA）相结合,对已提取的峰电位波形进行特征提取.最后,用改进的最小距离法实现峰电位分类.结果 仿真实验结果表明,此方法对于不同噪声强度的信号,峰电位检出率达94%,总分类正确率91%以上,其中大量叠加信号的分类正确率88%以上.结论 本方法能在有效抑制噪声的基础上,准确提取峰电位并有效分类.     

Reliability and precision of neural spike timing: simulation of spectrally broadband synaptic inputs

Spectrally broadband stimulation of neurons has been an effective method for studying their dynamic responses to simulated synaptic inputs. Previous studies with such stimulation were mostly based upon the direct intracellular injection of noisy current waveforms. In the present study we analyze and compare the firing output of various identified molluscan neurons to aperiodic, broadband current signals using three types of stimulus paradigms: 1. direct injection in current clamp mode, 2. conductance injection using electrotonic coupling of the input waveform to the neuron, and 3. conductance injection using a simulated chemical excitatory connection. The current waveforms were presented in 15 successive trials and the trial-to-trial variations of the spike responses were analyzed using peri-stimulus spike density functions. Comparing the responses of the neurons to the same type of input waveforms, we found that conductance injection resulted in more reliable and precise spike responses than direct current injection. The statistical parameters of the response spike trains depended on the spectral distribution of the input. The reliability increased with increasing cutoff frequency, while the temporal jitter of spikes changed in the opposite direction. Neurons with endogenous bursting displayed lower reproducibility in their responses to noisy waveforms when injected directly; however, they fired far more reliably and precisely when receiving the same waveforms as conductance inputs. The results show that molluscan neurons are capable of accurately reproducing their responses to synaptic inputs. Conductance injection provides an enhanced experimental technique for assessing the neurons' spike timing reliability and it should be preferred over direct current injection of noisy waveforms.     

Coding movement direction by burst firing in electrosensory neurons

Directional selectivity, in which neurons respond strongly to an object moving in a given direction ("preferred") but respond weakly or not at all to an object moving in the opposite direction ("null"), is a critical computation achieved in brain circuits. Previous measures of direction selectivity have compared the numbers of action potentials elicited by each direction of movement, but most sensory neurons display patterning, such as bursting, in their spike trains. To examine the contribution of patterned responses to direction selectivity, we recorded from midbrain neurons in weakly electric fish and found that most neurons responded with a combination of both bursts and isolated spikes to moving object stimuli. In these neurons, we separated bursts and isolated spikes using an interspike interval (ISI) threshold. The directional bias of bursts was significantly higher than that of either the full spike train or the isolated spike train. To examine the encoding and decoding of bursts, we built biologically plausible models that examine 1) the upstream mechanisms that generate these spiking patterns and 2) downstream decoders of bursts. Our model of upstream mechanisms uses an interaction between afferent input and subthreshold calcium channels to give rise to burst firing that occurs preferentially for one direction of movement. We tested this model in vivo by application of calcium antagonists, which reduced burst firing and eliminated the differences in direction selectivity between bursts, isolated spikes, and the full spike train. Our model of downstream decoders used strong synaptic facilitation to achieve qualitatively similar results to those obtained using the ISI threshold criterion. This model shows that direction selective information carried by bursts can be decoded by downstream neurons using biophysically plausible mechanisms.     

Signal separation of background EEG and spike by using morphological filter

A signal separation method for extracting background electroencephalogram (EEG) from EEG containing spikes was proposed. Morphological filters were designed for extracting spike waveforms, and then the background EEG was obtained by subtracting the detected spike waveforms from the EEG with spike. The proposed method was evaluated by using simulated EEG data, which consisted of a summation of EEG without spike and model waveform of typical spike. The background EEG separated by the method was processed by the automatic background EEG interpretation.     

Quantitative measures of cluster quality for use in extracellular recordings

While the use of multi-channel electrodes (stereotrodes and tetrodes) has allowed for the simultaneous recording and identification of many neurons, quantitative measures of the quality of neurons in such recordings are lacking. In multi-channel recordings, each spike waveform is discriminated in a high-dimensional space, making traditional measures of unit quality inapplicable. We describe two measures of unit isolation quality, Lratio and Isolation Distance, and evaluate their performance using simulations and tetrode recordings. Both measures quantified how well separated the spikes of one cluster (putative neuron) were from other spikes recorded simultaneously on the same multi-channel electrode. In simulations and tetrode recordings, both Lratio and Isolation Distance discriminated well- and poorly-separated clusters. In data sets from the rodent hippocampus in which neurons were simultaneously recorded intracellularly and extracellularly, values of Isolation Distance and Lratio were related to the correct identification of spikes.     

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

To understand a neural circuit completely requires simultaneous recording from most of the neurons in that circuit. Here we report recording and spike sorting techniques that enable us to record from all or nearly all of the ganglion cells in a patch of the retina. With a dense multi-electrode array, each ganglion cell produces a unique pattern of activity on many electrodes when it fires an action potential. Signals from all of the electrodes are combined with an iterative spike sorting algorithm to resolve ambiguities arising from overlapping spike waveforms. We verify that we are recording from a large fraction of ganglion cells over the array by labeling the ganglion cells with a retrogradely transported dye and by comparing the number of labeled and recorded cells. Using these methods, we show that about 60 receptive fields of ganglion cells cover each point in visual space in the salamander, consistent with anatomical findings.     

Quantal encoding of information in a retinal ganglion cell

A retinal ganglion cell receives information about a white-noise stimulus as a flickering pattern of glutamate quanta. The ganglion cell reencodes this information as brief bursts of one to six spikes separated by quiescent periods. When the stimulus is repeated, the number of spikes in a burst is highly reproducible (variance < mean) and spike timing is precise to within 10 ms, leading to an estimate that each spike encodes about 2 bits. To understand how the ganglion cell reencodes information, we studied the quantal patterns by repeating a white-noise stimulus and recording excitatory currents from a voltage-clamped, brisk-sustained ganglion cell. Quanta occurred in synchronous bursts of 3 to 65; the resulting postsynaptic currents summed to form excitatory postsynaptic currents (EPSCs). The number of quanta in an EPSC was only moderately reproducible (variance = mean), quantal timing was precise to within 14 ms, and each quantum encoded 0.1-0.4 bit. In conclusion, compared to a spike, a quantum has similar temporal precision, but is less reproducible and encodes less information. Summing multiple quanta into discrete EPSCs improves the reproducibility of the overall quantal pattern and contributes to the reproducibility of the spike train.     

Retinogeniculate synaptic properties controlling spike number and timing in relay neurons

Retinal ganglion cells (RGC) transmit visual signals to thalamocortical relay neurons in the lateral geniculate nucleus via retinogeniculate synapses. Relay neuron spike patterns do not simply reflect those of RGCs, but the mechanisms controlling this transformation are not well understood. We therefore examined synaptic properties controlling the strength and precision of relay neuron firing in mouse (p28-33) brain slices using physiological stimulation patterns and a combination of current clamp and dynamic clamp. In tonic mode (-55 mV), activation of single RGC inputs elicited stereotyped responses in a given neuron. In contrast, responses in different neurons varied from unreliable, to faithfully following, to a gain in the number of spikes. Dynamic clamp experiments indicated these different responses primarily reflected variability in the amplitudes of the N-methyl-d-aspartate (NMDA) and AMPA components. Each of these components played a distinct role in transmission. The AMPA component evoked a single precisely timed, short-latency spike per stimulus, but efficacy decreased during repetitive stimulation due to desensitization and depression. The NMDA component elicited longer-latency spikes and multiple spikes per stimulus and became more effective during repetitive stimuli that led to NMDA current summation. We found that in burst mode (-75 mV), where low-threshold calcium spikes are activated, AMPA and NMDA components and synaptic plasticity influenced spike number, but no combination enabled relay cells to faithfully follow the stimulus. Thus the characteristics of AMPA and NMDA currents, the ratio of these currents and use-dependent plasticity interact to shape how RGC activity is conveyed to relay neurons.     

Bursts and recurrences of bursts in the spike trains of spontaneously active striate cortex neurons

Simultaneous recordings were made from small collections (2-7) of spontaneously active single units in the striate cortex of unanesthetized cats, by means of chronically implanted electrodes. The recorded spike trains were computer scanned for bursts of spikes, and the bursts were catalogued and studied. The firing rates of the neurons ranged from 0.16 to 32 spikes/s; the mean was 8.9 spikes/s, the standard deviation 7.0 spikes/s. Bursts of spikes were assigned a quantitative measure, termed Poisson surprise (S), defined as the negative logarithm of their probability in a random (Poisson) spike train. Only bursts having S greater than 10, corresponding to an occurrence rate of about 0.01 bursts/1,000 spikes in a random spike train, were considered to be of interest. Bursts having S greater than 10 occurred at a rate of about 5-15 bursts/1,000 spikes, or about 1-5 bursts/min. The rate slightly increased with spike rate; averaging about 2 bursts/min for neurons having 3 spikes/s and about 4.5 bursts/min for neurons having 30 spikes/s. About 21% of the recorded units emitted significantly fewer bursts than the rest (below 1 burst/1,000 spikes). The percentage of these neurons was independent of spike rate. The spike rate during bursts was found to be about 3-6 times the average spike rate; about the same for longer as for shorter bursts. Bursts typically contained 10-50 spikes and lasted 0.5-2.0 s. When the number of spikes in the successively emitted bursts was listed, it was found that in some neurons these numbers were not distributed at random but were clustered around one or more preferred values. In this sense, bursts occasionally "recurred" a few times in a few minutes. The finding suggests that neurons are highly reliable. When bursts of two or more simultaneously recorded neurons were compared, the bursts often appeared to be temporally close, especially between pairs of neurons recorded by the same electrode; but bursts seldom started and ended simultaneously on two channels. Recurring bursts emitted by one neuron were occasionally accompanied by time-locked recurring bursts by other neurons.     

Bursts of information: coordinating interneurons encode multiple parameters of a periodic motor pattern

The limbs on different segments of the crayfish abdomen that drive forward swimming are directly controlled by modular pattern-generating circuits. These circuits are linked together by axons of identified coordinating interneurons. We described the distributions of these neurons in each abdominal ganglion and monitored their firing during expression of the swimming motor pattern. We analyzed the timing, the numbers of spikes, and the duration of each burst of spikes in these coordinating neurons. To see what information these neurons encoded, we correlated these parameters with the timing, durations, and strengths of bursts of spikes in motor axons from the same modules. During the power-stroke phase of each output cycle, the anterior-projecting neurons fired bursts of spikes that encoded information about the start-time, duration, and strength of each burst of spikes in power-stroke motor neurons from the same module. When the period and intensity of the motor output fluctuated, the bursts of spikes in these neurons tracked these fluctuations accurately. Each additional spike in these neurons signified an increase in the strength of the power-stroke burst. The posterior-projecting neurons that fired during the return-stroke phase encoded similar information about the return-stroke motor neurons. Although homologous neurons from different ganglia were qualitatively similar, neurons from posterior ganglia fired significantly more spikes per burst than those from more anterior ganglia, a segmental gradient that correlates with the normal posterior-to-anterior phase progression of limb movements. We propose that this gradient and a similar gradient in the durations of bursts in power-stroke motor neurons might reflect a hitherto-undetected difference in the excitation or intrinsic excitability of swimmeret modules in different segments.     

Precision of the pacemaker nucleus in a weakly electric fish: network versus cellular influences

We investigated the relative influence of cellular and network properties on the extreme spike timing precision observed in the medullary pacemaker nucleus (Pn) of the weakly electric fish Apteronotus leptorhynchus. Of all known biological rhythms, the electric organ discharge of this and related species is the most temporally precise, with a coefficient of variation (CV = standard deviation/mean period) of 2 x 10(-4) and standard deviation (SD) of 0.12-1.0 micros. The timing of the electric organ discharge is commanded by neurons of the Pn, individual cells of which we show in an in vitro preparation to have only a slightly lesser degree of precision. Among the 100-150 Pn neurons, dye injection into a pacemaker cell resulted in dye coupling in one to five other pacemaker cells and one to three relay cells, consistent with previous results. Relay cell fills, however, showed profuse dendrites and contacts never seen before: relay cell dendrites dye-coupled to one to seven pacemaker and one to seven relay cells. Moderate (0.1-10 nA) intracellular current injection had no effect on a neuron's spiking period, and only slightly modulated its spike amplitude, but could reset the spike phase. In contrast, massive hyperpolarizing current injections (15-25 nA) could force the cell to skip spikes. The relative timing of subthreshold and full spikes suggested that at least some pacemaker cells are likely to be intrinsic oscillators. The relative amplitudes of the subthreshold and full spikes gave a lower bound to the gap junctional coupling coefficient of 0.01-0.08. Three drugs, called gap junction blockers for their mode of action in other preparations, caused immediate and substantial reduction in frequency, altered the phase lag between pairs of neurons, and later caused the spike amplitude to drop, without altering the spike timing precision. Thus we conclude that the high precision of the normal Pn rhythm does not require maximal gap junction conductances between neurons that have ordinary cellular precision. Rather, the spiking precision can be explained as an intrinsic cellular property while the gap junctions act to frequency- and phase-lock the network oscillations.     

Fast and accurate detection of action potentials from somatic calcium fluctuations

Large-scale recording from a population of neurons is a promising strategy for approaching the study of complex brain functions. Taking advantage of the fact that action potentials reliably evoke transient calcium fluctuations in the cell body, functional multineuron calcium imaging (fMCI) monitors the suprathreshold activity of hundreds of neurons. However, a limitation of fMCI is its semi-manual procedure of spike extraction from somatic calcium fluctuations, which is not only time consuming but is also associated with human errors. Here we describe a novel automatic method that combines principal-component analysis and support vector machine. This simple algorithm determines the timings of the spikes in calcium fluorescence traces more rapidly and reliably than human operators.     

Active dendrites support efficient initiation of dendritic spikes in hippocampal CA3 pyramidal neurons

CA3 pyramidal neurons are important for memory formation and pattern completion in the hippocampal network. It is generally thought that proximal synapses from the mossy fibers activate these neurons most efficiently, whereas distal inputs from the perforant path have a weaker modulatory influence. We used confocally targeted patch-clamp recording from dendrites and axons to map the activation of rat CA3 pyramidal neurons at the subcellular level. Our results reveal two distinct dendritic domains. In the proximal domain, action potentials initiated in the axon backpropagate actively with large amplitude and fast time course. In the distal domain, Na(+) channel-mediated dendritic spikes are efficiently initiated by waveforms mimicking synaptic events. CA3 pyramidal neuron dendrites showed a high Na(+)-to-K(+) conductance density ratio, providing ideal conditions for active backpropagation and dendritic spike initiation. Dendritic spikes may enhance the computational power of CA3 pyramidal neurons in the hippocampal network.     

Spike coding during locomotor network activity in ventrally located neurons in the isolated spinal cord from neonatal rat

To characterize spike coding in spinal neurons during rhythmic locomotor activity, we recorded from individual cells in the lumbar spinal cord of neonatal rats by using the on-cell patch-clamp technique. Locomotor activity was induced by N-methyl-D aspartate (NMDA) and 5-hydroxytryptamine (5-HT) and monitored by ventral root recording. We made an estimator based on the assumption that the number of spikes arriving during two halves of the locomotor cycle could be a code used by the neuronal network to distinguish between the halves. This estimator, termed the spike contrast, was calculated as the difference between the number of spikes in the most and least active half of an average cycle. The root activity defined the individual cycles and the positions of the spikes were calculated relative to these cycles. By comparing the average spike contrast to the spike contrast in noncyclic, randomized spike trains we found that approximately one half the cells (19 of 42) contained a significant spike contrast, averaging 1.25 +/- 0.23 (SE) spikes/cycle. The distribution of spike contrasts in the total population of cells was exponential, showing that weak modulation was more typical than strong modulation. To investigate if this low spike contrast was misleading because a higher spike contrast averaged out by occurring at different positions in the individual cycles we compared the spike contrast obtained from the average cycle to its maximal value in the individual cycles. The value was larger (3.13 +/- 0.25 spikes) than the spike contrast in the average cycle but not larger than the spike contrast in the individual cycles of a random, noncyclic spike trains (3.21 +/- 0.21 spikes). This result suggested that the important distinction between cyclic and noncyclic cells was only the repeated cycle position of the spike contrast and not its magnitude. Low spike frequencies (5.2 +/- 0.82 spikes/cycle, that were on average 3.5 s long) and a minimal spike interval of 100-200 ms limited the spike contrast. The standard deviation (SD) of the spike contrast in the individual neurons was similar to the average spike contrasts and was probably stochastic because the SDs of the simulated, noncyclic spike trains were also similar. In conclusion we find a highly distributed and variable locomotor related cyclic signal that is represented in the individual neurons by very few spikes and that becomes significant only because the spike contrast is repeated at a preferred phase of the locomotor cycle.     

Intracellular features predicted by extracellular recordings in the hippocampus in vivo

Multichannel tetrode array recording in awake behaving animals provides a powerful method to record the activity of large numbers of neurons. The power of this method could be extended if further information concerning the intracellular state of the neurons could be extracted from the extracellularly recorded signals. Toward this end, we have simultaneously recorded intracellular and extracellular signals from hippocampal CA1 pyramidal cells and interneurons in the anesthetized rat. We found that several intracellular parameters can be deduced from extracellular spike waveforms. The width of the intracellular action potential is defined precisely by distinct points on the extracellular spike. Amplitude changes of the intracellular action potential are reflected by changes in the amplitude of the initial negative phase of the extracellular spike, and these amplitude changes are dependent on the state of the network. In addition, intracellular recordings from dendrites with simultaneous extracellular recordings from the soma indicate that, on average, action potentials are initiated in the perisomatic region and propagate to the dendrites at 1.68 m/s. Finally we determined that a tetrode in hippocampal area CA1 theoretically should be able to record electrical signals from approximately 1, 000 neurons. Of these, 60-100 neurons should generate spikes of sufficient amplitude to be detectable from the noise and to allow for their separation using current spatial clustering methods. This theoretical maximum is in contrast to the approximately six units that are usually detected per tetrode. From this, we conclude that a large percentage of hippocampal CA1 pyramidal cells are silent in any given behavioral condition.