Abstracts of Invited Talks

There is a close correspondence between the dynamics and properties of large networks of spiking neurons and that of forest fires. Consider first a network of integrate-and-fire neurons. Each neuron is either hyperpolarized or refractory, depolarized or sensitive, or else activated. Now consider a forest fire comprising burned, green, or burning trees. Lattice models of such forest fires have recently been shown to exhibit a form of self-organized critical behavior. We show that integrate-and-fire neural networks exhibit similar behavior and describe a number of new features associated with the dynamics of such networks. In particular we show how power law distributions for interspike intervals appear, and how stochastic resonance effects underlie the formation of coherent activity.

I will discuss the behavior of arrays of weakly coupled oscillators in one, two, and three dimensions. Here I focus more on the behavior due to the topology of the connectivity than on the details of the individual oscillators. I describe patterns driven by bondary heterogeneities in one-dimension and show that the patterns in two- and three-dimensions are in a sense a product of the one-dimensional cases. I also demonstrate non-trivial two- and three-dimensional patterns that do not naturally reduce to the lower-dimensional patterns.

Synchronous activity is currently an intensely studied subject in neurophysiology. In vision, where it remains controversial, it has been attributed to a variety of functions ranging from scene segmentation to visual awareness. Prior to 1980, synchronous activity wasn't even on the radar screen of most visual neuro- scientists. It was relegated to theories of olfactory processing and synaptic plasticity. Studies of visual processing were dominated by the analysis of receptive field properties and the mapping of cortical areas. This began to change, however, with the gradual realization that visual perception is fundamentally a distributed, combinatorial process. A theory was needed to incorporate distributed processing, combinatorial flexibility and temporal dynamics. This theory, preceded by concepts introduced by Hebb and others, emerged in the form of two largely ignored papers by Milner (1974) and von der Malsburg (1981). They proposed that perceptual grouping is mediated dynamically by distributed assemblies of synchronously firing neurons. Later, this model captured widespread attention with the discovery of stimulus dependent synchronous firing in visual cortex. Subsequent work has revealed that synchronous activity is a robust and general feature of neuronal networks. We have a much better understanding of how it is generated, and there are many interesting correlates with perceptual, motor and cognitive functions. The jury is still out, however, regarding the functions of synchronous activity, and critics abound. I will briefly review the history of synchronous activity, discuss the pros and cons of the correlation model, and lay out some arguments for why I think synchronous activity is fundamentally important for many brain processes.

Much of the data for the ocean is Lagrangian in that it is derived from subsurface floats drifting with the flow. At the same time, many questions about the ocean involve transport and mixing, and therefore concern Lagrangian dynamics. Dynamical systems offers significant insight into Lagrangian dynamics based on invariant manifolds of stagnation points. A strategy for model analysis, based on these ideas, at both model input and output will be described. This will include Lagrangian data assimilation, optimal float placement design and an approach to model evaluation.

Properties and function of two classes of cells -- simple (linear) and complex (nonlinear) -- will be summarized. A large scale computational model containing both simple and complex cells will be described. Within this model, the mechanisms which result from the neuronal architecture and which produce both types of cells will be unveiled. This work is joint with Jim Wielaard, Louis Tao, Mike Shelley and Bob Shapley.

Oscillatory behavior is a ubiquitous, but yet not fully understood, feature of motor control networks. One of the behavioral manifestations of such oscillatory activity is the presence of tremors, which occur both in the normally functioning motor system and in a number of motor disorders, one of the best examples being the tremor associated with Parkinson's disease. The resurgence in recent years of microelectrode-guided surgical treatment of the motor symptoms of the disease has provided an opportunity to study the characteristics of neural activity within the basal ganglia and thalamus of parkinsonian patients. Our studies of the spatiotemporal dynamics of oscillatory activity in the basal ganglia and its relationship to tremor have provided insights into the types of networks in the brain that can support the dynamical features of the observed activity.

The evaluation and encoding of relations among distributed neuronal responses are essential components of neuronal processes underlying cognition, memory formation and sensory-motor coordination. In complex brains multiple and rapidly changing relations need to be defined in parallel, which requires highly flexible dynamic binding mechanisms. One option for the encoding of relations is the formation of conjunction-specific neurons that respond selectively to particular constellations of activity in converging afferents. Another option is to label responses as related by synchronizing the respective discharges with a precision in the millisecond range. Synchronization enhances with high temporal resolution the saliency of the synchronized discharges and hence can be exploited for the selection and binding of responses. Experimental results suggest the following conclusions. (1) Precise synchronization is often associated with an oscillatory patterning of neuronal responses in the β and γ frequency range. (2) Both phenomena exhibit a marked state dependency and occur only when the cortex is in an activated state characterized by a desynchronized EEG. (3) Maintenance of this state requires release of acetylcholine acting on muscarinic receptors. (4) In sensory processing precise synchronization is likely to serve the selection and grouping of short response segments for further joint processing. (5) When neurons engage in oscillatory activity Hebbian modifications exhibit a marked phase sensitivity. Synaptic gain increases (decreases) when pre- and postsynaptic elements oscillate in phase (in counterphase) whereby phase offsets as small as 15 ms suffice to reverse the polarity of the synaptic modifications. (6) Synchronization of oscillatory activity occurs also in the absence of sensory stimulation and then appears to serve coordination of activity across cortical areas in the context of attention-dependent processes such as task anticipation and short-term memory. It is suggested that these properties of synchronization are compatible with the hypothesis that it serves as a relation defining mechanism.

Further reading:

Singer, W. (1999) Neuronal synchrony: a versatile code for the definition of relations? Neuron 24: 49-65

Engel, A.K., P. Fries, and W. Singer (2001) Dynamic predictions: oscillations and synchrony in top-down processing. Nature Rev. Neurosci. 2: 704-716

The basal ganglia are a group of nuclei that play an important role in the generation of movement. Dysfunction of the basal ganglia is associated with movement disorders such as Parkinson's disease and Huntington's chorea. Structures within the basal ganglia have in fact been the target of recent therapeutic surgical procedures including deep brain stimulation. We develop a computational model, based on recent experiments, in order to test hypotheses on the role of neuronal activity within the basal ganglia in both normal and pathological states. We further use the model to formulate hypotheses on possible mechanisms underlying DBS.

Nanomolar concentrations of kainate are able to induce "persistent" gamma frequency (about 25-70 Hz) oscillations in hippocampus in vitro.  Such oscillations depend upon chemically gated synaptic transmission, specifically via AMPA and GABA-A receptors.  In addition, the oscillations depend upon electrical coupling between neuronal elements of two fundamentally different sorts: between axons of pyramidal cells, and between the dendrites of interneurons.  Experiments and simulations indicate that the roles played by the two sorts of electrical coupling are distinct.  Axonal coupling is necessary for the oscillation to occur at all (unless the axons are spontaneously hyperactive); whereas, interneuronal dendritic coupling modulates the coherence of the oscillations.

In collaboration with I. Pais, S. Hormuzdi, A. Bibbig, F.E.N. LeBeau, H. Monyer, the late E.H. Buhl, and M.A. Whittington. Supported by NINDS and Volkswagen Stiftung.

Depth EEG recordings from the hippocampus reveal two predominant oscillatory components in the gamma band (30 - 80 Hz) and theta band (4 - 12 Hz). In vitro hippocampla slice experiments have revealed may clues as to the mechanism of gamma band oscillations but the origin of theta frequency activity is only just becoming clear. The talk will review the mechanism of generation of gamma frequency oscillations from a cellular and network level and use this as a platform to demonstrate the differences in comparison with a new model of theta rhythms. Both rhythms are dependent on inhibitory interneurons but the types of interneuron differ in the following ways: gamma-generating interneurons are predominantly fast spiking, perisomatically targeting neurons producing large, brief inhibitory postsynaptic events in principal cells. Theta generating neurons are relatively slow spiking, distal dendrite targeting neurons producing small, prolonged inhibitory postsynaptic events. In addition a number of intrinsic conductances in both theta generating interneurons and principal cells are involved in theta generation. The interplay between these two rhythms is critically dependent on the degree of fast excitatory synaptic activity in the hippocampus. The possible consequences of this for hippocampal function will be discussed.