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Workshop 1: Neuronal Dynamics (October 7-18, 2002)

Organizers: Bard Ermentrout and David Terman

Dynamics plays an important role in neural systems at many levels from the subcellular up to the network levels. The time scales range from the submillisecond to many hours and as a consequence there are many different levels of detail reflected in the models. One of the main interests in systems and cellular neuroscience is to understand how the nonlinear properties of neurons and their connections sculpt inputs and change over time. Recent experiments have shown that the connections between neurons are not static and are influenced by the previous history of the neuron, the relative timing of spikes, and the local firing properties of the neuron. This workshop will focus on the temporal dynamics of neurons at the single cell and network levels.

The dendrites of neurons are often modeled as simple passive delay lines. However, experiments have revealed that there are many nonlinear time-dependent currents which can render the neuron sensitive to both the relative timing of inputs as well as their spatial distribution. Back propagation from the soma through the dendrites has been linked to changes in synaptic efficacy between connected neurons. One of the goals of the workshop is to consider the functional roles of these active processes.

As mentioned above, connections between neurons are dynamic even in relatively short time scales. For example, it has experimentally shown that the strength of connections between two neurons can change depending on the relative firing times of the two connected neurons. These dynamic synapses have been shown to alter the gain control in circuits.

Small networks of neurons have been shown to generate a variety of rhythms. Propagating waves appear to play a role both in development and in sensory processing while synchronous rhythms have been implicated in learning and the separation of inputs. Part of this workshop will be devoted to asking what the possible role of these rhythms is, how they are generated, and how they interact to form spatio-temporal patterns of activity such as transient synchrony and waves.

Large scale modeling of cortical networks requires certain simplifications be made in the characterization of individual neurons. One of the goals of this workshop will be to connect the biophysically detailed models of single neurons and dendrites to the simplified units required in large-scale simulations. Several mathematical approaches to this problems have been quite fruitful. These include mean-field methods (population averages), averaging methods (exploiting differences in time scales), and perturbation methods (weak coupling, neurons near a bifurcation point, etc).

The workshop will bring together computational neuroscientists, mathematicians, and experimental biologists who are all working on questions about the role of temporal dynamics in cells and networks of neurons.

The mathematical areas that are expected to be strongly involved in this workshop include dynamical systems (multiscales, bifurcations, perturbation methods), mean field methods, PDE's, integral differential equations, and stochastic equations.