Correlated neural activity has been observed at various signal levels (e.g., spike count, membrane potential, local field potential, EEG, fMRI BOLD). Most of these signals can be considered as superpositions of spike trains filtered by components of the neural system (synapses, membranes) and the measurement process. It is largely unknown how the spike train correlation structure is altered by this filtering and what the consequences for the dynamics of the system and for the interpretation of measured correlations are. In this study, we focus on linearly filtered spike trains and particularly consider correlations caused by overlapping presynaptic neuron populations. We demonstrate that correlation functions and statistical second-order measures like the variance, the covariance, and the correlation coefficient generally exhibit a complex dependence on the filter properties and the statistics of the presynaptic spike trains. We point out that both contributions can play a significant role in modulating the interaction strength between neurons or neuron populations. In many applications, the coherence allows a filter-independent quantification of correlated activity. In different network models, we discuss the estimation of network connectivity from the high-frequency coherence of simultaneous intracellular recordings of pairs of neurons.

The function of cortical networks depends on the collective interplay between neurons and neuronal populations, which is reflected in the correlation of signals that can be recorded at different levels. To correctly interpret these observations it is important to understand the origin of neuronal correlations. Here we study how cells in large recurrent networks of excitatory and inhibitory neurons interact and how the associated correlations affect stationary states of idle network activity. We demonstrate that the structure of the connectivity matrix of such networks induces considerable correlations between synaptic currents as well as between subthreshold membrane potentials, provided Dale's principle is respected. If, in contrast, synaptic weights are randomly distributed, input correlations can vanish, even for densely connected networks. Although correlations are strongly attenuated when proceeding from membrane potentials to action potentials (spikes), the resulting weak correlations in the spike output can cause substantial fluctuations in the population activity, even in highly diluted networks. We show that simple mean-field models that take the structure of the coupling matrix into account can adequately describe the power spectra of the population activity. The consequences of Dale's principle on correlations and rate fluctuations are discussed in the light of recent experimental findings.

We studied the dynamics of large networks of spiking neurons with conductance-based (nonlinear) synapses and compared them to networks with current-based (linear) synapses. For systems with sparse and inhibition-dominated recurrent connectivity, weak external inputs induced asynchronous irregular firing at low rates. Membrane potentials fluctuated a few millivolts below threshold, and membrane conductances were increased by a factor 2 to 5 with respect to the resting state. This combination of parameters characterizes the ongoing spiking activity typically recorded in the cortex in vivo. Many aspects of the asynchronous irregular state in conductance-based networks could be sufficiently well characterized with a simple numerical mean field approach. In particular, it correctly predicted an intriguing property of conductance-based networks that does not appear to be shared by current-based models: they exhibit states of low-rate asynchronous irregular activity that persist for some period of time even in the absence of external inputs and without cortical pacemakers. Simulations of larger networks (up to 350,000 neurons) demonstrated that the survival time of self-sustained activity increases exponentially with network size.

The balanced random network model attracts considerable interest because it explains the irregular spiking activity at low rates and large membrane potential fluctuations exhibited by cortical neurons in vivo. In this article, we investigate to what extent this model is also compatible with the experimentally observed phenomenon of spike-timing-dependent plasticity (STDP). Confronted with the plethora of theoretical models for STDP available, we reexamine the experimental data. On this basis, we propose a novel STDP update rule, with a multiplicative dependence on the synaptic weight for depression, and a power law dependence for potentiation. We show that this rule, when implemented in large, balanced networks of realistic connectivity and sparseness, is compatible with the asynchronous irregular activity regime. The resultant equilibrium weight distribution is unimodal with fluctuating individual weight trajectories and does not exhibit development of structure. We investigate the robustness of our results with respect to the relative strength of depression. We introduce synchronous stimulation to a group of neurons and demonstrate that the decoupling of this group from the rest of the network is so severe that it cannot effectively control the spiking of other neurons, even those with the highest convergence from this group.

The availability of efficient and reliable simulation tools is one of the mission-critical technologies in the fast-moving field of computational neuroscience. Research indicates that higher brain functions emerge from large and complex cortical networks and their interactions. The large number of elements (neurons) combined with the high connectivity (synapses) of the biological network and the specific type of interactions impose severe constraints on the explorable system size that previously have been hard to overcome. Here we present a collection of new techniques combined to a coherent simulation tool removing the fundamental obstacle in the computational study of biological neural networks: the enormous number of synaptic contacts per neuron. Distributing an individual simulation over multiple computers enables the investigation of networks orders of magnitude larger than previously possible. The software scales excellently on a wide range of tested hardware, so it can be used in an interactive and iterative fashion for the development of ideas, and results can be produced quickly even for very large networks. In con-trast to earlier approaches, a wide class of neuron models and synaptic dynamics can be represented.

Pairwise correlations among spike trains recorded in vivo have been frequently reported. It has been argued that correlated activity could play an important role in the brain, because it efficiently modulates the response of a postsynaptic neuron. We show here that a neuron's output firing rate critically depends on the higher-order statistics of the input ensemble. We constructed two statistical models of populations of spiking neurons that fired with the same rates and had identical pairwise correlations, but differed with regard to the higher-order interactions within the population. The first ensemble was characterized by clusters of spikes synchronized over the whole population. In the second ensemble, the size of spike clusters was, on average, proportional to the pairwise correlation. For both input models, we assessed the role of the size of the population, the firing rate, and the pairwise correlation on the output rate of two simple model neurons: a continuous firing-rate model and a conductance-based leaky integrate-and-fire neuron. An approximation to the mean output rate of the firing-rate neuron could be derived analytically with the help of shot noise theory. Interestingly, the essential features of the mean response of the two neuron models were similar. For both neuron models, the three input parameters played radically different roles with respect to the postsynaptic firing rate, depending on the interaction structure of the input. For instance, in the case of an ensemble with small and distributed spike clusters, the output firing rate was efficiently controlled by the size of the input population. In addition to the interaction structure, the ratio of inhibition to excitation was found to strongly modulate the effect of correlation on the postsynaptic firing rate.

It has been proposed that cortical neurons organize dynamically into functional groups (cell assemblies) by the temporal structure of their joint spiking activity. Here, we describe a novel method to detect conspicuous patterns of coincident joint spike activity among simultaneously recorded single neurons. The statistical significance of these unitary events of coincident joint spike activity is evaluated by the joint-surprise. The method is tested and calibrated on the basis of simulated, stationary spike trains of independently firing neurons, into which coincident joint spike events were inserted under controlled conditions. The sensitivity and specificity of the method are investigated for their dependence on physiological parameters (firing rate, coincidence precision, coincidence pattern complexity) and temporal resolution of the analysis. In the companion article in this issue, we describe an extension of the method, designed to deal with nonstationary firing rates.

In order to detect members of a functional group (cell assembly) in simultaneously recorded neuronal spiking activity, we adopted the widely used operational definition that membership in a common assembly is expressed in near-simultaneous spike activity. Unitary event analysis, a statistical method to detect the significant occurrence of coincident spiking activity in stationary data, was recently developed (see the companion article in this issue). The technique for the detection of unitary events is based on the assumption that the underlying processes are stationary in time. This requirement, however, is usually not fulfilled in neuronal data. Here we describe a method that properly normalizes for changes of rate: the unitary events by moving window analysis (UEMWA). Analysis for unitary events is performed separately in overlapping time segments by sliding a window of constant width along the data. In each window, stationarity is assumed. Performance and sensitivity are demonstrated by use of simulated spike trains of independently firing neurons, into which coincident events are inserted. If cortical neurons organize dynamically into functional groups, the occurrence of near-simultaneous spike activity should be time varying and related to behavior and stimuli. UEMWA also accounts for these potentially interesting nonstationarities and allows locating them in time. The potential of the new method is illustrated by results from multiple single-unit recordings from frontal and motor cortical areas in awake, behaving monkey.

Inspired by different conceptualizations of temporal neural coding schemes, there has been recent interest in the search for signs of precisely synchronized neural activity in the cortex. One method developed for this task is unitary-event analysis. This method tests multiple single-neuron recordings for short epochs with significantly more coincident spikes than expected from independent neurons. We reformulated the statistical test underlying this method using a coincidence count distribution based on empirical spike counts rather than on estimated spike probabilities. In the case of two neurons, the requirement of stationary firing rates, originally imposed on both neurons, can be relaxed; only the rate of one neuron needs to be stationary, while the other may follow an arbitrary time course. By analytical calculations of the test power curves of the original and the revised method, we demonstrate that the test power can be increased by a factor of two or more in physiologically realistic regimes. In addition, we analyze the effective significance levels of both methods for neural firing rates ranging between 0.2 Hz and 30 Hz.