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Workshop 1 Summary by David Terman and Bard Ermentrout:
Workshop 1: Neuronal Dynamics The workshop attracted mathematicians, biologists and other scientists to discuss the role of nonlinear dynamics in neural systems. The two week workshop consisted of four major themes. These were: (1) oscillations, (2) waves, (3) synaptic plasticity and (4) vision. There were, typically, two one-hour lectures each morning and one or two one- hour lectures each afternoon. There were also a small number of half hour lectures each afternoon. The speakers included neuroscientists who could discuss recent experiments in which nonlinear properties of neural systems play an important role in the system's behavior and theoreticians who could discuss recent modeling efforts and theoretical tools to analyze the models. The speakers were chosen for both their expertise in a particular area and their ability to speak to a multidisciplinary audience. There was significant free time in which no lectures were scheduled. The provided opportunities for the participants to have informal discussions. There was a formally scheduled meeting in which the participants discussed past successes of computational neuroscience and what are the major challenges for future research. Some of the experimentalists who spoke during the oscillations
portion of the workshop were Barry Connors, Roger Traub and Jeffery
Smith. Connors described recent experiments that suggest electrical
synapses are far more widespread in the nervous system than suspected
just a few years ago. He presented evidence that electrical synapses
now seem to play a major feature of the neural circuitry in the
neocortex, hippocampus, thalamus, striatum, and many other brain
structures. Traub also discussed electrical synapses. He emphasized
the role of gap junctions between the axons of principal neurons
and the generation of fast oscillations in neuronal populations.
He also described modeling projects related to these issues. Smith
described experimental and modeling studies Theoreticians who spoke during the oscillators portion of the program were Tim Lewis, XJ Wang and Carl van Vreeswijk. Lewis discussed modeling and analytic work to understand the possible roles of electrical coupling in generating synchronous and asynchronous rhythms. This was very closely related to the experimental studies of Connors. XJ Wang described recent results related to the role of noise in generating network oscillations and van Vreeswijk presented interesting techniques for studying large populations of reduced neuronal models. Experimentalists who spoke during the waves portion of the program included Philip Ulinski, David Kleinfeld and Marla Feller. Ulinski described experiments on waves of activity that propagate throughout the visual cortex of freshwater turtles. He went on to describe recent mathematical models of turtle visual cortex used to study the cellular mechanisms underlying the propagation of waves and to suggest that information about visual stimuli is encoded in the temporal dynamics of the waves. Feller described her work on the mechanisms underlying spontaneous propagating activity in the developing mammalian retina. Theoreticians speaking during the wave portion of the program included David Hansel and David Golomb. Both described mathematical techniques to analyze large populations of model neurons. These techniques were used to understand mechanisms underlying propagating waves and other patterns in a variety of neural systems. Speakers during the synaptic plasticity portion included Larry Abbott, Guoqiang Bi, Dan Johnston and Carson Chow. Bi summarized experimental studies on so-called spike timing-dependent plasticity. This represents a quantitative extension of the famous Hebb's rule and may have profound implications in the development and function of neuronal circuits. Johnston described experiments and modeling studies on information processing and storage by neuronal dendrites. Abbott and Chow presented the results of theoretical and modeling studies on issues related to synaptic plasticity. Chow presented a model of neuronal ionic and molecular dynamics that seems to account for the experimental results described by Bi. Some the speakers during the vision portion were Robert Shapley, David McLaughlin and Paul Bressloff. Shapley is an experimentalist and McLaughlin a mathematician who are working together on constructing a computational model for neurons within the primary visual cortex. These speakers described their model, the relevant experiments and recent results on how the model can be used to better understand time-dependent sensitivity and selectivity for orientation and spatial frequency in the visual cortex. Bressloff presented another approach for modeling dynamics within the visual cortex. He presented recent analytical results regarding the large-scale dynamics of cortex in the presence of periodically modulated long-range interactions. There was a very interesting discussion at the end of the first week. The discussion began with listing major successes of mathematical methods to neuroscience. This list included the Hodgkin-Huxley model for the action potential and the works of Donald Hebb, David Marr, and William Rall. The discussion then turned to listing major developments within mathematics that were motivated by problems originating in neuroscience. This list included the development of the Evans function for determining the stability of propagating waves, many aspects of geometric singular perturbation theory and biologically inspired machine learning. Major new challenges and open problems were then discussed. This included discussion of dynamic reorganization and homeostasis, modeling of diseases and degenerative disorders and issues related to the spanning of many scales, from the molecular to behavior. Some participants questioned whether genetics or molecular research could help address this issue. Finally, there was a long discussion of how to get mathematicians more involved in neuroscience research. What was remarkable about this workshop was that scientists from numerous disciplines were speaking a common language. These disciplines include mathematics, biology, neuroscience, physics and computer science. We expect that this development of multidisciplinary communication will allow for significant advances in our understanding of neuronal processes and the development of new and exciting mathematical theories to address these issues.
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