Bringing Anatomical Information into Neuronal Network Models.

For constructing neuronal network models computational neuroscientists have access to wide-ranging anatomical data that nevertheless tend to cover only a fraction of the parameters to be determined. Finding and interpreting the most relevant data, estimating missing values, and combining the data and estimates from various sources into a coherent whole is a daunting task. With this chapter we aim to provide guidance to modelers by describing the main types of anatomical data that may be useful for informing neuronal network models. We further discuss aspects of the underlying experimental techniques relevant to the interpretation of the data, list particularly comprehensive data sets, and describe methods for filling in the gaps in the experimental data. Such methods of "predictive connectomics" estimate connectivity where the data are lacking based on statistical relationships with known quantities. Exploiting organizational principles that link the plethora of data in a unifying framework can be useful for informing computational models. Besides overarching principles, we touch upon the most prominent features of brain organization that are likely to influence predicted neuronal network dynamics, with a focus on the mammalian cerebral cortex. Given the still existing need for modelers to navigate a complex data landscape full of holes and stumbling blocks, it is vital that the field of neuroanatomy is moving toward increasingly systematic data collection, representation, and publication.

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

Common 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.

MEA-Tools: an open source toolbox for the analysis of multi-electrode data with MATLAB.

Recent advances in electrophysiological techniques have created new tools for the acquisition and storage of neuronal activity recorded simultaneously with numerous electrodes. These techniques support the analysis of the function as well as the structure of individual electrogenic cells in the context of surrounding neuronal or cardiac network. Commercially available tools for the analysis of such data, however, cannot be easily adapted to newly emerging requirements for data analysis and visualization, and cross compatibility between them is limited. In this report we introduce a free open source toolbox called microelectrode array tools (MEA-Tools) for the analysis of multi-electrode data based on the common data analysis environment MATLAB (version 5.3-6.1, The Mathworks, Natick, MA). The toolbox itself is platform independent. The file interface currently supports files recorded with MCRack (Multi Channel Systems, Reutlingen, Germany) under Microsoft Windows 95, 98, NT, and 2000, but can be adapted to other data acquisition systems. Functions are controlled via command line input and graphical user interfaces, and support common requirements for the analysis of local field potentials, extracellular spike activity, and continuous recordings, in addition to supplementary data acquired by additional instruments, e.g. intracellular amplifiers. Data may be processed as continuous recordings or time windows triggered to some event.

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].

Neural dynamics in cortical networks--precision of joint-spiking events.

Electrophysiological studies of cortical function on the basis of multiple single-neuron recordings reveal neuronal interactions which depend on stimulus context and behavioural events. These interactions exhibit dynamics on different time scales, with time constants down to the millisecond range. Mechanisms underlying such dynamic organization of the cortical network were investigated by experimental and theoretical approaches. We review some recent results from these studies, concentrating on the occurrence of precise joint-spiking events in cortical activity, both in physiological and in model neural networks. These findings suggest that a combinatorial neural code, based on rapid associations of groups of neurons co-ordinating their activity at the single spike level, is biologically feasible.

Dynamical changes and temporal precision of synchronized spiking activity in monkey motor cortex during movement preparation.

Movement preparation is considered to be based on central processes which are responsible for improving motor performance. For instance, it has been shown that motor cortical neurones change their activity selectively in relation to prior information about movement parameters. However, it is not clear how groups of neurones dynamically organize their activity to cope with computational demands. The aim of the study was to compare the firing rate of multiple simultaneously recorded neurones with the interaction between them by describing not only the frequency of occurrence of epochs of significant synchronization, but also its modulation in time and its changes in temporal precision during an instructed delay. Multiple single-neurone activity was thus recorded in monkey motor cortex during the performance of two different delayed multi-directional pointing tasks. In order to detect conspicuous spike coincidences in simultaneously recorded spike trains by tolerating temporal jitter ranging from 0 to 20 ms and to calculate their statistical significance, a modified method of the 'Unitary Events' analysis was used. Two main results were obtained. First, simultaneously recorded neurones synchronize their spiking activity in a highly dynamic way. Synchronization becomes significant only during short periods (about 100 to 200 ms). Several such periods occurred during a behavioural trial more or less regularly. Second, in many pairs of neurones, the temporal precision of synchronous activity was highest at the end of the preparatory period. As a matter of fact, at the beginning of this period, after the presentation of the preparatory signal, neurones significantly synchronize their spiking activity, but with low temporal precision. As time advances, significant synchronization becomes more precise. Data indicate that not only the discharge rate is involved in preparatory processes, but also temporal aspects of neuronal activity as expressed in the precise synchronization of individual action potentials.

Exact digital simulation of time-invariant linear systems with applications to neuronal modeling.

An efficient new method for the exact digital simulation of time-invariant linear systems is presented. Such systems are frequently encountered as models for neuronal systems, or as submodules of such systems. The matrix exponential is used to construct a matrix iteration, which propagates the dynamic state of the system step by step on a regular time grid. A large and general class of dynamic inputs to the system, including trains of delta-pulses, can be incorporated into the exact simulation scheme. An extension of the proposed scheme presents an attractive alternative for the approximate simulation of networks of integrate-and-fire neurons with linear sub-threshold integration and non-linear spike generation. The performance of the proposed method is analyzed in comparison with a number of multi-purpose solvers. In simulations of integrate-and-fire neurons, Exact Integration systematically generates the smallest error with respect to both sub-threshold dynamics and spike timing. For the simulation of systems where precise spike timing is important, this results in a practical advantage in particular at moderate integration step sizes.

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.

Detecting unitary events without discretization of time.

In earlier studies we developed the 'Unitary Events' analysis (Grün S. Unitary Joint-Events in Multiple-Neuron Spiking Activity: Detection, Significance and Interpretation. Reihe Physik, Band 60. Thun, Frankfurt/Main: Verlag Harri Deutsch, 1996.) to detect the presence of conspicuous spike coincidences in multiple single unit recordings and to evaluate their statistical significance. The method enabled us to study the relation between spike synchronization and behavioral events (Riehle A, Grün S, Diesmann M, Aertsen A. Spike synchronization and rate modulation differentially involved in motor cortical function. Science 1997;278:1950-1953.). There is recent experimental evidence that the timing accuracy of coincident spiking events, which might be relevant for higher brain function, may be in the range of 1-5 ms. To detect coincidences on that time scale, we sectioned the observation interval into short disjunct time slices ('bins'). Unitary Events analysis of this discretized process demonstrated that coincident events can indeed be reliably detected. However, the method looses sensitivity for higher temporal jitter of the events constituting the coincidences (Grün S. Unitary Joint-Events in Multiple-Neuron Spiking Activity: Detection, Significance and Interpretation. Reihe Physik, Band 60. Thun, Frankfurt/Main: Verlag Harri Deutsch, 1996.). Here we present a new approach, the 'multiple shift' method (MS), which overcomes the need for binning and treats the data in their (original) high time resolution (typically 1 ms, or better). Technically, coincidences are detected by shifting the spike trains against each other over the range of allowed coincidence width and integrating the number of exact coincidences (on the time resolution of the data) over all shifts. We found that the new method enhances the sensitivity for coincidences with temporal jitter. Both methods are outlined and compared on the basis of their analytical description and their application on simulated data. The performance on experimental data is illustrated.

Spike synchronization and rate modulation differentially involved in motor cortical function.

It is now commonly accepted that planning and execution of movements are based on distributed processing by neuronal populations in motor cortical areas. It is less clear, though, how these populations organize dynamically to cope with the momentary computational demands. Simultaneously recorded activities of neurons in the primary motor cortex of monkeys during performance of a delayed-pointing task exhibited context-dependent, rapid changes in the patterns of coincident action potentials. Accurate spike synchronization occurred in relation to external events (stimuli, movements) and was commonly accompanied by discharge rate modulations but without precise time locking of the spikes to these external events. Spike synchronization also occurred in relation to purely internal events (stimulus expectancy), where firing rate modulations were distinctly absent. These findings indicate that internally generated synchronization of individual spike discharges may subserve the cortical organization of cognitive motor processes.

Propagation of synchronous spiking activity in feedforward neural networks.

'Synfire' activity has been proposed as a model for the experimentally observed accurate spike patterns in cortical activity. We investigated the structural and dynamical aspects of this theory. To quantify the degree of synchrony in neural activity, we introduced the concept of 'pulse packets'. This enabled us to derive a novel neural transmission function which was used to assess the role of the single neuron dynamics and to characterize the stability conditions for propagating synfire activity. Thus, we could demonstrate that the cortical network is able to sustain synchronous spiking activity using local feedforward (synfire) connections. This new approach opens the way for a quantitative description of neural network dynamics, and enables us to test the synfire hypothesis on physiological data.