Markus Diesmann

Stable propagation of synchronous spiking in cortical neural networks.

The classical view of neural coding has emphasized the importance of information carried by the rate at which neurons discharge action potentials. More recent proposals that information may be carried by precise spike timing have been challenged by the assumption that these neurons operate in a noisy fashion—presumably reflecting fluctuations in synaptic input—and, thus, incapable of transmitting signals with millisecond fidelity. Here we show that precisely synchronized action potentials can propagate within a model of cortical network activity that recapitulates many of the features of biological systems. An attractor, yielding a stable spiking precision in the (sub)millisecond range, governs the dynamics of synchronization. Our results indicate that a combinatorial neural code, based on rapid associations of groups of neurons co-ordinating their activity at the single spike level, is possible within a cortical-like network.

Unitary events in multiple single-neuron spiking activity: I. detection and significance

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.

Activity dynamics and propagation of synchronous spiking in locally connected random networks

Abstract.u2002Random network models have been a popular tool for investigating cortical network dynamics. On the scale of roughly a cubic millimeter of cortex, containing about 100,000 neurons, cortical anatomy suggests a more realistic architecture. In this locally connected random network, the connection probability decreases in a Gaussian fashion with the distance between neurons. Here we present three main results from a simulation study of the activity dynamics in such networks. First, for a broad range of parameters these dynamics exhibit a stationary state of asynchronous network activity with irregular single-neuron spiking. This state can be used as a realistic model of ongoing network activity. Parametric dependence of this state and the nature of the network dynamics in other regimes are described. Second, a synchronous excitatory stimulus to a fraction of the neurons results in a strong activity response that easily dominates the network dynamics. And third, due to that activity response an embedding of a divergent-convergent feed-forward subnetwork (as in synfire chains) does not naturally lead to a stable propagation of synchronous activity in the subnetwork; this is in contrast to our earlier findings in isolated subnetworks of that type. Possible mechanisms for stabilizing the interplay of volleys of synchronous spikes and network dynamics by specific learning rules or generalizations of the subnetworks are discussed.

Unitary events in multiple single-neuron spiking activity: II. nonstationary data

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.

Propagation of cortical synfire activity: survival probability in single trials and stability in the mean.

The synfire hypothesis states that under appropriate conditions volleys of synchronized spikes (pulse packets) can propagate through the cortical network by traveling along chains of groups of cortical neurons. Here, we present results from network simulations, taking full account of the variability in pulse packet realizations. We repeatedly stimulated a synfire chain of model neurons and estimated activity (a) and temporal jitter (sigma) of the spike response for each neuron group in the chain in many trials. The survival probability of the activity was assessed for each point in (a, sigma)-space. The results confirm and extend our earlier predictions based on single neuron properties and a deterministic state-space analysis [Diesmann, M., Gewaltig, M.-O., & Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature, 402, 529-533].

Breaking synchrony by heterogeneity in complex networks

For networks of pulse-coupled oscillators with complex connectivity, we demonstrate that in the presence of coupling heterogeneity precisely timed periodic firing patterns replace the state of global synchrony that exists in homogenous networks only. With increasing disorder, these firing patterns persist until a critical temporal extent is reached that is of the order of the interaction delay. For stronger disorder the periodic firing patterns cease to exist and only asynchronous, aperiodic states are observed. We derive self-consistency equations to predict the precise temporal structure of a pattern from a network of given connectivity and heterogeneity. Moreover, we show how to design heterogeneous coupling architectures to create an arbitrary prescribed pattern.

Effect of cross-trial nonstationarity on joint-spike events.

Abstract.u2002Common to most correlation analysis techniques for neuronal spiking activity are assumptions of stationarity with respect to various parameters. However, experimental data may fail to be compatible with these assumptions. This failure can lead to falsely assigned significant outcomes. Here we study the effect of nonstationarity of spike rate across trials in a model-based approach. Using a two-rate-state model, where rates are drawn independently for trials and neurons, we show in detail that nonstationarity across trials induces apparent covariation of spike rates identified as the generator of false positives. This finding has specific implications for the ``shuffle predictor. Within the framework developed for our model, covariation of spike rates and the mechanism by which the shuffle predictor leads to wrong interpretation of the data can be discussed. Corrections for the influence of nonstationarity across trials by improvements of the predictor are presented.

The spread of rate and correlation in stationary cortical networks

Abstract The analysis of the spatial and temporal structure of spike cross-correlation in experimental data is an important tool in the exploration of cortical processing. Recent theoretical studies investigated the impact of correlation between afferents on the spike rate of single neurons and the effect of input correlation on the output correlation of pairs of neurons. Here, this knowledge is combined to a model simultaneously describing the spatial propagation of rate and correlation, allowing for an interpretation of its constituents in terms of network activity. The application to an embedded feed-forward network provides insight into the mechanisms stabilizing its asynchronous mode.

State space analysis of synchronous spiking in cortical neural networks

Abstract Recent proposals that information in cortical neurons may be encoded by precise spike timing have been challenged by the assumption that neurons in vivo can only operate in a noisy fashion, due to large fluctuations in synaptic input activity. Here, we show that despite the background, volleys of precisely synchronized action potentials can stably propagate within a model network of basic integrate-and-fire neurons. The construction of an iterative mapping for the transmission of synchronized spikes between groups of neurons allows for a two-dimensional state space analysis. An attractor, yielding stable spiking precision in the (sub-)millisecond range, governs the synchronization dynamics.

The ground state of cortical feed-forward networks

Abstract The occurrence of spatio-temporal spike patterns in the cortex is explained by models of divergent/convergent feed-forward subnetworks—synfire chains. Their excited mode is characterized by spike volleys propagating from one neuron group to the next. We demonstrate the existence of an upper bound for group size: above a critical value synchronous activity develops spontaneously from random fluctuations. Stability of the ground state, in which neurons independently fire at low rates, is lost. Comparison of an analytic rate model with network simulations shows that the transition from the asynchronous into the synchronous regime is driven by an instability in rate dynamics.