A biologically motivated and analytically soluble model of collective oscillations in the cortex: I. Theory of weak locking

A model of an associative network of spiking neurons with stationary states, globally locked oscillations, and weakly locked oscillatory states is presented and analyzed. The network is close to biology in the following sense. First, the neurons spike and our model includes an absolute refractory period after each spike. Second, we consider a distribution of axonal delay times. Finally, we describe synaptic signal transmission by excitatory and inhibitory potentials (EPSP and IPSP) with a realistic shape, that is, through a response kernel. During retrieval of a pattern, all active neurons exhibit periodic spike bursts which may or may not be synchronized (‘locked’) into a coherent oscillation. We derive an analytical condition of locking and calculate the period of collective activity during oscillatory retrieval. In a stationary retrieval state, the overlap assumes a constant value proportional to the mean firing rate of the neurons. It is argued that in a biological network an intermediate scenario of “weak locking” is most likely

Lateral Information Processing by Spiking Neurons: A Theoretical Model of the Neural Correlate of Consciousness

Cognitive brain functions, for example, sensory perception, motor control and learning, are understood as computation by axonal-dendritic chemical synapses in networks of integrate-and-fire neurons. Cognitive brain functions may occur either consciously or nonconsciously (on “autopilot”). Conscious cognition is marked by gamma synchrony EEG, mediated largely by dendritic-dendritic gap junctions, sideways connections in input/integration layers. Gap-junction-connected neurons define a sub-network within a larger neural network. A theoretical model (the “conscious pilot”) suggests that as gap junctions open and close, a gamma-synchronized subnetwork, or zone moves through the brain as an executive agent, converting nonconscious “auto-pilot” cognition to consciousness, and enhancing computation by coherent processing and collective integration. In this study we implemented sideways “gap junctions” in a single-layer artificial neural network to perform figure/ground separation. The set of neurons connected through gap junctions form a reconfigurable resistive grid or sub-network zone. In the model, outgoing spikes are temporally integrated and spatially averaged using the fixed resistive grid set up by neurons of similar function which are connected through gap-junctions. This spatial average, essentially a feedback signal from the neuron's output, determines whether particular gap junctions between neurons will open or close. Neurons connected through open gap junctions synchronize their output spikes. We have tested our gap-junction-defined sub-network in a one-layer neural network on artificial retinal inputs using real-world images. Our system is able to perform figure/ground separation where the laterally connected sub-network of neurons represents a perceived object. Even though we only show results for visual stimuli, our approach should generalize to other modalities. The system demonstrates a moving sub-network zone of synchrony, within which the contents of perception are represented and contained. This mobile zone can be viewed as a model of the neural correlate of consciousness in the brain

Gamma Oscillations in a Nonlinear Regime: A Minimal Model Approach Using Heterogeneous Integrate-and-Fire Networks

Fast oscillations and in particular gamma-band oscillation (20-80 Hz) are commonly observed during brain function and are at the center of several neural processing theories. In many cases, mathematical analysis of fast oscillations in neural networks has been focused on the transition between irregular and oscillatory firing viewed as an instability of the asynchronous activity. But in fact, brain slice experiments as well as detailed simulations of biological neural networks have produced a large corpus of results concerning the properties of fully developed oscillations that are far from this transition point. We propose here a mathematical approach to deal with nonlinear oscillations in a network of heterogeneous or noisy integrate-and-fire neurons connected by strong inhibition. This approach involves limited mathematical complexity and gives a good sense of the oscillation mechanism, making it an interesting tool to understand fast rhythmic activity in simulated or biological neural networks. A surprising result of our approach is that under some conditions, a change of the strength of inhibition only weakly influences the period of the oscillation. This is in contrast to standard theoretical and experimental models of interneuron network gamma oscillations (ING), where frequency tightly depends on inhibition strength, but it is similar to observations made in some in vitro preparations in the hippocampus and the olfactory bulb and in some detailed network models. This result is explained by the phenomenon of suppression that is known to occur in strongly coupled oscillating inhibitory networks but had not yet been related to the behavior of oscillation frequency

What matters in neuronal locking?

Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of {\em spiking\/} neurons. Under standard conditions, a necessary and in the limit of a large number of interacting neighbors also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem we present a simple geometric method to verify existence and local stability of a coherent oscillation

Functional Role of Critical Dynamics in Flexible Visual Information Processing

Recent experimental and theoretical work has established the hypothesis that cortical neurons operate close to a critical state which signifies a phase transition from chaotic to ordered dynamics. Critical dynamics are suggested to optimize several aspects of neuronal information processing. However, although signatures of critical dynamics have been demonstrated in recordings of spontaneously active cortical neurons, little is known about how these dynamics are affected by task-dependent changes in neuronal activity when the cortex is engaged in stimulus processing. In fact, some in vivo investigations of the awake and active cortex report either an absence of signatures of criticality or relatively weak ones. In addition, the functional role of criticality in optimizing computation is often reported in abstract theoretical studies, adopting minimalistic models with homogeneous topology and slowly-driven networks. Consequently, there is a lack of concrete links between information theoretical benefits of the critical state and neuronal networks performing a behaviourally relevant task. In this thesis we explore such concrete links by focusing on the visual system, which needs to meet major computational challenges on a daily basis. Among others, the visual system is responsible for the rapid integration of relevant information from a large number of single channels, and in a flexible manner depending on the behavioral and environmental contexts. We postulate that critical neuronal dynamics in the form of cascades of activity spanning large populations of neurons may support such quick and complex computations. Specifically, we consider two notable examples of well-known phenomena in visual information processing: First the enhancement of object discriminability under selective attention, and second, a feature integration and figure-ground segregation scenario. In the first example, we model the top-down modulation of the activity of visuocortical neurons in order to selectively improve the processing of an attended region in a visual scene. In the second example, we model how neuronal activity may be modulated in a bottom-up fashion by the properties of the visual stimulus itself, which makes it possible to perceive different shapes and objects. We find in both scenarios that the task performance may be improved by employing critical networks. In addition, we suggest that the specific task- or stimulus-dependent modulations of information processing may be optimally supported by the tuning of relevant local neuronal networks towards or away from the critical point. Thus, the relevance of this dissertation is summarized by the following points: We formally extend the existing models of criticality to inhomogeneous systems subject to a strong external drive. We present concrete functional benefits for networks operating near the critical point in well-known experimental paradigms. Importantly, we find emergent critical dynamics only in the parts of the network which are processing the behaviourally relevant information. We suggest that the implied locality of critical dynamics in space and time may help explain why some studies report no signatures of criticality in the active cortex

Neural models of learning and visual grouping in the presence of finite conduction velocities

The hypothesis of object binding-by-synchronization in the visual cortex has been supported by recent experiments in awake monkeys. They demonstrated coherence among gamma-activities (30–90 Hz) of local neural groups and its perceptual modulation according to the rules of figure-ground segregation. Interactions within and between these neural groups are based on axonal spike conduction with finite velocities. Physiological studies confirmed that the majority of transmission delays is comparable to the temporal scale defined by gamma-activity (11–33 ms). How do these finite velocities influence the development of synaptic connections within and between visual areas? What is the relationship between the range of gamma-coherence and the velocity of signal transmission? Are these large temporal delays compatible with recently discovered phenomenon of gamma-waves traveling across larger parts of the primary visual cortex? The refinement of connections in the immature visual cortex depends on temporal Hebbian learning to adjust synaptic efficacies between spiking neurons. The impact of constant, finite, axonal spike conduction velocities on this process was investigated using a set of topographic network models. Random spike trains with a confined temporal correlation width mimicked cortical activity before visual experience. After learning, the lateral connectivity within one network layer became spatially restricted, the width of the connection profile being directly proportional to the lateral conduction velocity. Furthermore, restricted feedforward divergence developed between neurons of two successive layers. The size of this connection profile matched the lateral connection profile of the lower layer neuron. The mechanism in this network model is suitable to explain the emergence of larger receptive fields at higher visual areas while preserving a retinotopic mapping. The influence of finite conduction velocities on the local generation of gamma-activities and their spatial synchronization was investigated in a model of a mature visual area. Sustained input and local inhibitory feedback was sufficient for the emergence of coherent gamma-activity that extended across few millimeters. Conduction velocities had a direct impact on the frequency of gamma-oscillations, but did neither affect gamma-power nor the spatial extent of gamma-coherence. Adding long-range horizontal connections between excitatory neurons, as found in layer 2/3 of the primary visual cortex, increased the spatial range of gamma-coherence. The range was maximal for zero transmission delays, and for all distances attenuated with finite, decreasing lateral conduction velocities. Below a velocity of 0.5 m/s, gamma-power and gamma-coherence were even smaller than without these connections at all, i.e., slow horizontal connections actively desynchronized neural populations. In conclusion, the enhancement of gamma-coherence by horizontal excitatory connections critically depends on fast conduction velocities. Coherent gamma-activity in the primary visual cortex and the accompanying models was found to only cover small regions of the visual field. This challenges the role of gamma-synchronization to solve the binding problem for larger object representations. Further analysis of the previous model revealed that the patches of coherent gamma-activity (1.8 mm half-height decline) were part of more globally occurring gamma-waves, which coupled over much larger distances (6.3 mm half-height decline). The model gamma-waves observed here are very similar to those found in the primary visual cortex of awake monkeys, indicating that local recurrent inhibition and restricted horizontal connections with finite axonal velocities are sufficient requirements for their emergence. In conclusion, since the model is in accordance with the connectivity and gamma-processes in the primary visual cortex, the results support the hypothesis that gamma-waves provide a generalized concept for object binding in the visual cortex