Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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BCCN Sonderseminar

Thursday, 31.01.2013 11 s.t.

Fractional neuro-dynamics: from biochemical reactions to spiking activity

by Prof. Dr. Fidel Santamaria
from University of Texas at San Antonio, One UTSA circle, USA

Contact person: Fred Wolf


Ludwig Prandtl lecture hall


Classical theories of reaction-diffusion have been of tremendous use to understand multiple aspects of neuronal activity. Such theories define a given process with a well characterized scale constant and are in thermodynamic equilibrium. However, the cumulative effects of a wide range of heterogeneous components found in cells and networks at multiple scales could give rise to reaction-diffusion processes away from equilibrium. This complex behavior can result in the breakdown of classical laws of reaction diffusion which could give rise to power-law distributions. I will present our combined experimental and computational work that shows the breakdown of classic diffusion at multiple scales in single neurons. I will start by showing that molecular crowding in the post-synaptic density causes anomalous diffusion of glutamate receptors. This process is able to explain the results from single particle tracking experiments and provides a low energy strategy to retained glutamate receptors in the synapse for long periods of time. At a spatial scale two order of magnitude larger than a synapse I will show that the presence of dendritic spines causes anomalous diffusion of soluble cytosolic signals. This type of anomalous diffusion affects the integration of second messengers involved in synaptic plasticity. I will then present our efforts to generalize the analysis of reaction-diffusion systems outside equilibrium by using the fractional reaction diffusion equation. I will explain how we are using fractional dynamics not only to study biochemical integration in dendritic trees but also how this can be used to study other types of power-law dynamics in neuronal activity such as in firing rate correlations.

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