Understanding the principles of network dynamics subserving function in neocortex has received increased attention in neuroscience, as opposed to the classic analysis of single neuron responses to sensory input or internal modalities. However, despite recent advances in recording techniques that allow for the simultaneous measurement of many neurons in parallel, the amount of data involved, and the unsolved fundamental issues in analyzing such massive data sets, have nurtured a revived interest among experimentalists to re-examine the information contained in electric mass signals, such as the local field potential (LFP). The LFP is a spatially slow-changing extracellularly recorded signal composed of low frequencies up to about 300 Hz. It is thought to reflect primarily synaptic currents in a large area around the recording site. Increased oscillation strength of this signal, as has been observed in numerous experimental paradigms, is often believed to be related to synchronized synaptic activity (see, e.g., Elul 1967). However, hitherto little is known about the detailed relationships between neuronal activity, network dynamics and LFP signals in cortex. A deeper understanding of how activity at the neuron level is connected to LFP oscillations might aid in combining simultaneous LFP and single neuron recordings to characterize the network dynamics. Within this project we aim to establish a direct link between the temporal relationships between simultaneously recorded spike trains, and properties of the local field potential. We found that single units in primary motor cortex preferably lock to the LFP if the LFP envelope is large. The preferred phase is the decaying flank of the LFP oscillation [Denker et al, 2007]. In addtion, we search for signatures of synchronous activity between neurons in the LFP signal. To this end, we use advanced techniques to detect epochs of significant synchronous activity (Unitary Events) and methods originating from phase synchronization analysis to disentangle amplitude and phase relationships between spikes and LFP. This enables us to relate three indicators common associated with synchronous activity, namely spike synchrony, strength of oscillations, and the relationship of single neurons to these global oscillations. First results show that there is a link between these three observables acting on different spatial scales, suggesting that neuronal activity of single neurons may be utilized to characterize an underlying common network dynamics.

There has been a long and lively debate, whether rate covariance and temporal coordination of spikes, attributed as potential origins for correlations in cortical spike signals, fulfill different roles in the cortical code. In this context, studies to report spike coordination have often been criticized for ignoring fast non-stationarities, which would result in wrongly assigned spike coordination. The underlying hypothesis of this critique is that spike coordination is the same as rate covariation, only on a faster time scale. To investigate the relevance of this critique, we present a model of correlated doubly stochastic Poisson processes that implements the two concepts of dependence. We derive the cross-correlation function of doubly stochastic point processes and find our implementations to contribute with distinct terms. This allows us to correct the correlation function for rate effects, which shows that spike coordination and rate covariation are distinct concepts of dependence. In particular, this difference does not depend on the respective time scale of dependence. However, exploiting these theoretical differences for data analysis does not always yield satisfactory results. When analyzing data with the cross-correlation function, spike coordination in conjunction with time varying, yet independent rate profiles can not be differentiated from pure rate covariation. This is in sharp contrast to theoretically predicted difference between the concepts. We identify the reason for this effect in our inability to correctly estimate covariation of the firing rates and discuss the validity of our results with respect to different rate estimators, model implementations and analysis methods [Staude et al (2008) Neural Computation 20, 1973–1999].

The cell assembly hypothesis postulates dynamically interacting groups of neurons as building blocks of cortical information processing. Synchronized spikes across large neuronal groups were suggested as a potential signature for active assemblies, resulting in specific higher-order correlations among assembly members. Mathematical concepts for the treatment of higher-order correlations in parallel spike trains have been suggested in the past, but, due to constraints of insufficient sample sizes, estimation of the necessary higher-order parameters from recorded data poses serious problems. As a consequence, most attempts to observe cell-assemblies resort to pairwise interactions. However, existence of pairwise correlations do not imply the presence of higher-order correlations and are not sensitive for sparse synchronous network events. In our opinion, the limited experimental evidence for the existence of active cell assemblies must to a large extend be assigned to the insufficiency of available analysis tools, since massively parallel extracellular recordings are nowadays available. We developed a novel procedure that allows to detect higher-order correlations in massively parallel spike trains based on the statistics of the population histogram, i.e. the distribution of spike counts across the neurons measured in bins of width of a few ms. The shape of this distribution contains information of correlation between the spike trains and can be captured by estimating the cumulants of the distribution. We derived an analytical relation between the cumulants of the distribution of the spike counts and our newly developed model of correlated Poisson spike trains. Based on this relation we devised a statistical test that allows based on estimates of only a few low-order cumulants for the presence of higher-order correlations and to derive its minimal order. The method circumvents the need to estimate large numbers of higher-order parameters and therefore is far less susceptible to the typically very limited data sizes than previously proposed approaches. The method is calibrated for correlated Poisson processes which contained correlations of various orders. The test turned out to be surprisingly sensitive, even for cases where the effect of the higher-order patterns on pairwise correlation coefficients were negligible (in the range of ~ 0.01) [Staude et al, J Comput Neurosci (in press) free]. Currently we explore the stability of the method in more realistic settings, i.e. for data that deviate from Poisson and exhibit non-stationary firing rates.

When inspecting visual scenes, primates perform on average four saccadic eye movements per second which implies that scene segmentation, feature binding and identification of image components is accomplished is less than 200ms. Thus, individual neurons can contribute only a small number of discharges for these complex computations, suggesting that information is encoded not only in the frequency but also in the timing of action potentials. While monkeys inspected natural scenes, the simultaneous activities of neurons in primary visual cortex was registered with multi-electrodes. Relating these signals to eye movements with Unitary Event Analysis, revealed that discharge rates peaked around 100ms after fixation onset and then decreased to near baseline levels within 200ms. Preceding this increase in firing, there was an episode of enhanced spike synchronization during which discharges of spatially distributed cells coincided within 5ms windows significantly more often than predicted by the discharge rates. This episode started 30ms after fixation onset and ended by the time discharge rates had reached their maximum [Maldonado et al (2008) J Neurophysiol, 100: 1523–1532. (free)].

In a subsequent project, we are interested in the potential mechanisms underlying these results. Therefore we ask the question how the population activity in V1, as measured by the local field potential (LFP), relates to the spiking activity of single units, and how this is related to eye-movement events. Following the hypothesis that saccade triggered LFP oscillations provide the stage for well-timing of incoming spikes that are elicited by sensory input during fixations, we analyze the relation of spike timing to the phase of LFP oscillation. We found that saccades evoke LFP oscillations with a frequency of around 16Hz and that this oscillatory activity persists also during the succeeding fixation. While sensory evoked spikes generally show considerable phase locking to the LFP oscillation, we found that a particular set of spikes of very early spikes, are strongly locked to the oscillation. By use of surrogate methods based on trial shuffling we illustrate that the locking is non-trivial and highly significant. The timing of significant phase locking coincides with the negative peak of the evoked LFP oscillation, and also with the peak of the average firing rate of the neurons, suggesting that these spikes represent the first wave of visually evoked spiking activity [Ito et al, (subm)] .

Eye movements have been extensively studied under experimental conditions where the task required precise eye movements to defined target locations. More recently, attention has been drawn to eye movements during the exploration of complex visual scenes. To identify possible mechanisms underlying the choice of the positions of fixations, we investigated the eye movements of two monkeys freely viewing images of natural scenes [Maldonado, Babul, Singer. Soc. Neurosci. Abstr.: 558.8, 2002; Flores, Berger, Grün, Maldonado. Soc. Neurosci. Abstr.: 165.7, 2005; Maldonado et al, J Neurophysiol (in press)]. We extracted eye movements and fixation positions during respective image presentations. To uncover the image features that relate to fixation positions we derived the distribution of fixation positions on individual images and the saliency maps of the images. Their correlation was quantified by calculating the Kullback-Leibler Distance (KLD). In 75% of the images the KLD was signifcantly smaller than expected assuming random viewing, suggesting a tendency for fixations guided by low-level features. However, for the rest of the images containing primate faces the KLD was significantly larger than expected. In a next step, we additionally explored the scan pathes of the eye movements. Therefore we first identified clusters of fixations positions using mean shift algorithm, resulting typically in 3-5 significant clusters for each individual image. The pathes of eye movements were analyzed by application of a Markov chain analysis where the clusters of fixations were assigned to Markov states. We found that the transition probabilities within clusters were significantly higher than in between clusters suggesting that scan pathes of eye movements are not random, but are comprised of sequences of local explorations.

Multiple electrode recordings offer the chance to detect assembly activities, and to identify the network composition and functions. In order to extract the single unit spiking activities from such extra-cellular multi-unit signals, spike sorting is performed on the data. This is a crucial step of data pre-processing in preparation for further analyses. However, due to noise and large variability in recordings of neuronal signals the improvement of spike sorting techniques is still open field of research. Indeed, spike sorting is subject to errors, and the consequences of it on subsequent analyses are poorly understood. Here we present work on the impact of imperfect sorting on different spike correlation analysis methods, such as Unitary Event analysis [Grün et al, 2002a,b] and cross-correlation function. We modeled the effect of spike sorting errors by "polluting" parallel spike trains with typical failures of spike sorting procedures: falsely assigned spikes (false positives, FP), and/or erroneously missed spikes (false negatives, FN). We have shown that for pairs of parallel spike trains the significance of the correlation is reduced for FNs as well as for FPs [Pazienti & Grün, 2006]. Furthermore, FNs have a stronger effect and therefore a tolerant sorting strategy seems in those cases preferable. Interestingly, inserted FPs do not introduce false positive correlation. Similar effects can be observed for cross-correlation analysis. However, for larger numbers of simultaneous spike trains, considerations on higher-order correlations come into play. Thus, in the analysis of these effects we have to differentiate the order of the underlying, inserted correlation patterns (order w) from the number of spikes (complexity x) in the measured coincidences. We derived an analytical description of the effects of spike sorting errors on the measures that underly the significance estimation of the Unitary Events method: the number of coincidences measured and expected, given the rates. We find for 'direct' cases, in which we compare occurrence counts of patterns of the same complexity as order was inserted (i.e. w=x), FP and FN errors lead to an underestimation of the significance of synchronous events. However, in the case of particular 'cross' cases (w larger than x), sorting errors on original patterns may lead to an increase of patterns of lower complexity and thus to an increase of their significance [Pazienti & Grün, to be submitted]. Thus, an understanding of data manipulation by pre-processing procedures, and their impact on subsequent data analysis is an important step to rule out inconsistencies in the interpretation of results.

Common to correlation analysis techniques for neuronal spiking activity are assumptions regarding the statistics of the considered spike trains. However, experimental data may fail to be compatible with these assumptions and this failure can lead to falsely assigned significant outcomes. Most typical features of experimental data are that firing rates are non-stationary in time, but also across trials, or that internal structure of the spike trains does not follow the Poisson assumption. In a number of studies during the last years we studied the effect of such violations on the Unitary Event analysis method [Grün et al, 2002a] and suggested alternative approaches for solutions [Grün et al, 2002b; Grün et al, 2003; Pipa et al, 2003a,b; Pipa et al, 2007]. In this project we focus on the aspect if the autostructure of the spike trains deviates from Poisson. In particular we concentrate on renewal processes that follow a Gamma-distribution and a log-normal distribution. The internal structure of the spike trains, as well as other manipulations such as dithering or clipping, influence the shape of the distribution of coincident spike events occurring between such processes [see also Pipa, 2001 (Diploma thesis)]. Thus if we assume a Poission distribution for the evaluation of the significance of coincidences we may risk detection of false positives. In this study we compare coincidence distributions from simultaneous Gamma-, and log-normal processes with the one resulting from Poisson processes for a wide range of parameters (coefficient of variation, rate, bin-size, duration). For a large range of parameters, in particular for CVs compatible with experimental data, the Poisson assumption does not lead to false positive results [Pipa et al, submitted].

A major endeavor in neuroscience is to resolve the paradox between the apparent random cortical connectivity and the unparalleled complex computations the brain performs. A potential solution to this problem is the synfire hypothesis: the cortical tissue is composed of a superposition of feed-forward subnetworks each capable of transmitting packets of synchronized spikes with high reliability and computations are carried out by interactions of these chains. Indeed, advanced statistical techniques have demonstrated the task related occurence of spatio-temporal spike patterns in limited data sets. However, the number of parallel recordings has been too low to unambiguously identify the signature of synfire chains and these tools do not scale to massively parallel spike trains. Here we present a new method that visualizes the repetitive occurence of synfire activity in large data sets. In contrast to earlier approaches we achieve reliability by appropriately averaging over neuron space and time. We test the method with data from a large-scale balanced recurrent network in the asynchronous irregular regime containing fifty randomly activated synfire chains. The sensitivity is high enough to detect synfire chain activity in simultaneous single-unit recordings of 200 neurons, enabling application to experimental data in the near future [Schrader et al (2008) J Neurophysiol. 100(4):2165-2176 (free)].