The functional significance of correlations between action potentials of neurons is still a matter of vivid debate. In particular, it is presently unclear how much synchrony is caused by afferent synchronized events and how much is intrinsic due to the connectivity structure of cortex. The available analytical approaches based on the diffusion approximation do not allow to model spike synchrony, preventing a thorough analysis. Here we theoretically investigate to what extent common synaptic afferents and synchronized inputs each contribute to correlated spiking on a fine temporal scale between pairs of neurons. We employ direct simulation and extend earlier analytical methods based on the diffusion approximation to pulse-coupling, allowing us to introduce precisely timed correlations in the spiking activity of the synaptic afferents. We investigate the transmission of correlated synaptic input currents by pairs of integrate-and-fire model neurons, so that the same input covariance can be realized by common inputs or by spiking synchrony. We identify two distinct regimes: In the limit of low correlation linear perturbation theory accurately determines the correlation transmission coefficient, which is typically smaller than unity, but increases sensitively even for weakly synchronous inputs. In the limit of high input correlation, in the presence of synchrony, a qualitatively new picture arises. As the non-linear neuronal response becomes dominant, the output correlation becomes higher than the total correlation in the input. This transmission coefficient larger unity is a direct consequence of non-linear neural processing in the presence of noise, elucidating how synchrony-coded signals benefit from these generic properties present in cortical networks.
Whether spike timing conveys information in cortical networks or whether the firing rate alone is sufficient is a matter of controversial debate, touching the fundamental question of how the brain processes, stores, and conveys information. If the firing rate alone is the decisive signal used in the brain, correlations between action potentials are just an epiphenomenon of cortical connectivity, where pairs of neurons share a considerable fraction of common afferents. Due to membrane leakage, small synaptic amplitudes and the non-linear threshold, nerve cells exhibit lossy transmission of correlation originating from shared synaptic inputs. However, the membrane potential of cortical neurons often displays non-Gaussian fluctuations, caused by synchronized synaptic inputs. Moreover, synchronously active neurons have been found to reflect behavior in primates. In this work we therefore contrast the transmission of correlation due to shared afferents and due to synchronously arriving synaptic impulses for leaky neuron models. We not only find that neurons are highly sensitive to synchronous afferents, but that they can suppress noise on signals transmitted by synchrony, a computational advantage over rate signals.
Recent studies have emphasized the functional role of neuronal activity underlying oscillatory local field potential (LFP) signals during visual processing in natural conditions. While functionally relevant components in multiple frequency bands have been reported, little is known about whether and how these components interact with each other across the dominant frequency bands. We examined this phenomenon in LFP signals obtained from the primary visual cortex of monkeys performing voluntary saccadic eye movements (EMs) on still images of natural-scenes. We identified saccade-related changes in respect to power and phase in four dominant frequency bands: delta-theta (2–4 Hz), alpha-beta (10–13 Hz), low-gamma (20–40 Hz), and high-gamma (>100 Hz). The phase of the delta-theta band component is found to be entrained to the rhythm of the repetitive saccades, while an increment in the power of the alpha-beta and low-gamma bands were locked to the onset of saccades. The degree of the power modulation in these frequency bands is positively correlated with the degree of the phase-locking of the delta-theta oscillations to EMs. These results suggest the presence of cross-frequency interactions in the form of phase-amplitude coupling (PAC) between slow (delta-theta) and faster (alpha-beta and low gamma) oscillations. As shown previously, spikes evoked by visual fixations during free viewing are phase-locked to the fast oscillations. Thus, signals of different types and at different temporal scales are nested to each other during natural viewing. Such cross-frequency interaction may provide a general mechanism to coordinate sensory processing on a fast time scale and motor behavior on a slower time scale during active sensing.
local field potential; oscillation; saccade; natural vision; cross-frequency coupling
Grasping an object involves shaping the hand and fingers in relation to the object’s physical properties. Following object contact, it also requires a fine adjustment of grasp forces for secure manipulation. Earlier studies suggest that the control of hand shaping and grasp force involve partially segregated motor cortical networks. However, it is still unclear how information originating from these networks is processed and integrated. We addressed this issue by analyzing massively parallel signals from population measures (local field potentials, LFPs) and single neuron spiking activities recorded simultaneously during a delayed reach-to-grasp task, by using a 100-electrode array chronically implanted in monkey motor cortex. Motor cortical LFPs exhibit a large multi-component movement-related potential (MRP) around movement onset. Here, we show that the peak amplitude of each MRP component and its latency with respect to movement onset vary along the cortical surface covered by the array. Using a comparative mapping approach, we suggest that the spatio-temporal structure of the MRP reflects the complex physical properties of the reach-to-grasp movement. In addition, we explored how the spatio-temporal structure of the MRP relates to two other measures of neuronal activity: the temporal profile of single neuron spiking activity at each electrode site and the somatosensory receptive field properties of single neuron activities. We observe that the spatial representations of LFP and spiking activities overlap extensively and relate to the spatial distribution of proximal and distal representations of the upper limb. Altogether, these data show that, in motor cortex, a precise spatio-temporal pattern of activation is involved for the control of reach-to-grasp movements and provide some new insight about the functional organization of motor cortex during reaching and object manipulation.
cortical map; high-density recordings; monkey motor cortex; spiking activity; LFP
Cell assemblies, defined as groups of neurons exhibiting precise spike coordination, were proposed as a model of network processing in the cortex. Fortunately, in recent years considerable progress has been made in multi-electrode recordings, which enable recording massively parallel spike trains of hundred(s) of neurons simultaneously. However, due to the challenges inherent in multivariate approaches, most studies in favor of cortical cell assemblies still resorted to analyzing pairwise interactions. However, to recover the underlying correlation structures, higher-order correlations need to be identified directly. Inspired by the Accretion method proposed by Gerstein et al. (1978) we propose a new assembly detection method based on frequent item set mining (FIM). In contrast to Accretion, FIM searches effectively and without redundancy for individual spike patterns that exceed a given support threshold. We study different search methods, with which the space of potential cell assemblies may be explored, as well as different test statistics and subset conditions with which candidate assemblies may be assessed and filtered. It turns out that a core challenge of cell assembly detection is the problem of multiple testing, which causes a large number of false discoveries. Unfortunately, criteria that address individual candidate assemblies and try to assess them with statistical tests and/or subset conditions do not help much to tackle this problem. The core idea of our new method is that in order to cope with the multiple testing problem one has to shift the focus of statistical testing from specific assemblies (consisting of a specific set of neurons) to spike patterns of a certain size (i.e., with a certain number of neurons). This significantly reduces the number of necessary tests, thus alleviating the multiple testing problem. We demonstrate that our method is able to reliably suppress false discoveries, while it is still very sensitive in discovering synchronous activity. Since we exploit high-speed computational techniques from FIM for the tests, our method is also computationally efficient.
massively parallel spike trains; cell assembly; synchronous spike patterns; higher-order correlation; frequent item set mining; surrogate data; multi-variate significance testing
Precise spike coordination between the spiking activities of multiple neurons is suggested as an indication of coordinated network activity in active cell assemblies. Spike correlation analysis aims to identify such cooperative network activity by detecting excess spike synchrony in simultaneously recorded multiple neural spike sequences. Cooperative activity is expected to organize dynamically during behavior and cognition; therefore currently available analysis techniques must be extended to enable the estimation of multiple time-varying spike interactions between neurons simultaneously. In particular, new methods must take advantage of the simultaneous observations of multiple neurons by addressing their higher-order dependencies, which cannot be revealed by pairwise analyses alone. In this paper, we develop a method for estimating time-varying spike interactions by means of a state-space analysis. Discretized parallel spike sequences are modeled as multi-variate binary processes using a log-linear model that provides a well-defined measure of higher-order spike correlation in an information geometry framework. We construct a recursive Bayesian filter/smoother for the extraction of spike interaction parameters. This method can simultaneously estimate the dynamic pairwise spike interactions of multiple single neurons, thereby extending the Ising/spin-glass model analysis of multiple neural spike train data to a nonstationary analysis. Furthermore, the method can estimate dynamic higher-order spike interactions. To validate the inclusion of the higher-order terms in the model, we construct an approximation method to assess the goodness-of-fit to spike data. In addition, we formulate a test method for the presence of higher-order spike correlation even in nonstationary spike data, e.g., data from awake behaving animals. The utility of the proposed methods is tested using simulated spike data with known underlying correlation dynamics. Finally, we apply the methods to neural spike data simultaneously recorded from the motor cortex of an awake monkey and demonstrate that the higher-order spike correlation organizes dynamically in relation to a behavioral demand.
Nearly half a century ago, the Canadian psychologist D. O. Hebb postulated the formation of assemblies of tightly connected cells in cortical recurrent networks because of changes in synaptic weight (Hebb's learning rule) by repetitive sensory stimulation of the network. Consequently, the activation of such an assembly for processing sensory or behavioral information is likely to be expressed by precisely coordinated spiking activities of the participating neurons. However, the available analysis techniques for multiple parallel neural spike data do not allow us to reveal the detailed structure of transiently active assemblies as indicated by their dynamical pairwise and higher-order spike correlations. Here, we construct a state-space model of dynamic spike interactions, and present a recursive Bayesian method that makes it possible to trace multiple neurons exhibiting such precisely coordinated spiking activities in a time-varying manner. We also formulate a hypothesis test of the underlying dynamic spike correlation, which enables us to detect the assemblies activated in association with behavioral events. Therefore, the proposed method can serve as a useful tool to test Hebb's cell assembly hypothesis.
While oscillations of the local field potential (LFP) are commonly attributed to the synchronization of neuronal firing rate on the same time scale, their relationship to coincident spiking in the millisecond range is unknown. Here, we present experimental evidence to reconcile the notions of synchrony at the level of spiking and at the mesoscopic scale. We demonstrate that only in time intervals of significant spike synchrony that cannot be explained on the basis of firing rates, coincident spikes are better phase locked to the LFP than predicted by the locking of the individual spikes. This effect is enhanced in periods of large LFP amplitudes. A quantitative model explains the LFP dynamics by the orchestrated spiking activity in neuronal groups that contribute the observed surplus synchrony. From the correlation analysis, we infer that neurons participate in different constellations but contribute only a fraction of their spikes to temporally precise spike configurations. This finding provides direct evidence for the hypothesized relation that precise spike synchrony constitutes a major temporally and spatially organized component of the LFP.
motor cortex; oscillation; population signals; synchrony
During natural vision, primates perform frequent saccadic eye movements, allowing only a narrow time window for processing the visual information at each location. Individual neurons may contribute only with a few spikes to the visual processing during each fixation, suggesting precise spike timing as a relevant mechanism for information processing. We recently found in V1 of monkeys freely viewing natural images, that fixation-related spike synchronization occurs at the early phase of the rate response after fixation-onset, suggesting a specific role of the first response spikes in V1. Here, we show that there are strong local field potential (LFP) modulations locked to the onset of saccades, which continue into the successive fixation periods. Visually induced spikes, in particular the first spikes after the onset of a fixation, are locked to a specific epoch of the LFP modulation. We suggest that the modulation of neural excitability, which is reflected by the saccade-related LFP changes, serves as a corollary signal enabling precise timing of spikes in V1 and thereby providing a mechanism for spike synchronization.
free viewing; local field potential; phase locking; primary visual cortex; spike synchrony
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.
LFP; Synchrony; Oscillations; Network dynamics; Motor cortex
The extent to which groups of neurons exhibit higher-order correlations in their spiking activity is a controversial issue in current brain research. A major difficulty is that currently available tools for the analysis of massively parallel spike trains (N >10) for higher-order correlations typically require vast sample sizes. While multiple single-cell recordings become increasingly available, experimental approaches to investigate the role of higher-order correlations suffer from the limitations of available analysis techniques. We have recently presented a novel method for cumulant-based inference of higher-order correlations (CuBIC) that detects correlations of higher order even from relatively short data stretches of length T = 10–100 s. CuBIC employs the compound Poisson process (CPP) as a statistical model for the population spike counts, and assumes spike trains to be stationary in the analyzed data stretch. In the present study, we describe a non-stationary version of the CPP by decoupling the correlation structure from the spiking intensity of the population. This allows us to adapt CuBIC to time-varying firing rates. Numerical simulations reveal that the adaptation corrects for false positive inference of correlations in data with pure rate co-variation, while allowing for temporal variations of the firing rates has a surprisingly small effect on CuBICs sensitivity for correlations.
multiple unit activity; higher-order correlations; non-stationarity; statistical population model
Detecting the excess of spike synchrony and testing its significance can not be done analytically for many types of spike trains and relies on adequate surrogate methods. The main challenge for these methods is to conserve certain features of the spike trains, the two most important being the firing rate and the inter-spike interval statistics. In this study we make use of operational time to introduce generalizations to spike dithering and propose two novel surrogate methods which conserve both features with high accuracy. Compared to earlier approaches, the methods show an improved robustness in detecting excess synchrony between spike trains.
surrogate data; dithering; operational time; spike synchrony
Recent developments in electrophysiological and optical recording techniques enable the simultaneous observation of large numbers of neurons. A meaningful interpretation of the resulting multivariate data, however, presents a serious challenge. In particular, the estimation of higher-order correlations that characterize the cooperative dynamics of groups of neurons is impeded by the combinatorial explosion of the parameter space. The resulting requirements with respect to sample size and recording time has rendered the detection of coordinated neuronal groups exceedingly difficult. Here we describe a novel approach to infer higher-order correlations in massively parallel spike trains that is less susceptible to these problems. Based on the superimposed activity of all recorded neurons, the cumulant-based inference of higher-order correlations (CuBIC) presented here exploits the fact that the absence of higher-order correlations imposes also strong constraints on correlations of lower order. Thus, estimates of only few lower-order cumulants suffice to infer higher-order correlations in the population. As a consequence, CuBIC is much better compatible with the constraints of in vivo recordings than previous approaches, which is shown by a systematic analysis of its parameter dependence.
Multichannel recordings; Spike train analysis; Higher-order correlations; Cell assembly hypothesis
The chance of detecting assembly activity is expected to increase if the spiking activities of large numbers of neurons are recorded simultaneously. Although such massively parallel recordings are now becoming available, methods able to analyze such data for spike correlation are still rare, as a combinatorial explosion often makes it infeasible to extend methods developed for smaller data sets. By evaluating pattern complexity distributions the existence of correlated groups can be detected, but their member neurons cannot be identified. In this contribution, we present approaches to actually identify the individual neurons involved in assemblies. Our results may complement other methods and also provide a way to reduce data sets to the “relevant” neurons, thus allowing us to carry out a refined analysis of the detailed correlation structure due to reduced computation time.