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Gabriel Wittum

G-CSC, Universität Frankfurt

Modelling of Signal Processing in Neurons

Abstract:

The crucial feature of neuronal ensembles is their high complexity and variability. This makes modelling and computation very difficult, in particular for detailed models based on first principles. The problem starts with modelling geometry, which has to extract the essential features from those highly complex and variable phenotypes and at the same time has to take in to account the stochastic variability. Moreover, models of the highly complex processes which are living on these geometries are far from being well established, since those are highly complex too and couple on a hierarchy of scales in space and time. Simulating such systems always puts the whole approach to test, including modeling, numerical methods and software implementations. In combination with validation based on experimental data, all components have to be enhanced to reach a reliable solving strategy.

To handle problems of this complexity, new mathematical methods and software tools are required. In recent years, new approaches such as parallel adaptive multigrid methods and corresponding software tools have been developed allowing to treat problems of huge complexity.

In the lecture we present a three dimensional model of signaling in neurons. First we show a method for the reconstruction of the geomety of cells and subcellular structures as three dimensional objects. With this tool, NeuRA, complex geometries of neuron nuclei were reconstructed. We present the results and discuss reasons for the complicated shapes. To that end, we present a model of calcium signaling to the nucleus and show simulation results on reconstructed nuclear geometries. We discuss the implications of these simulations.

We further show reconstructed cell geometries and simulations with a three dimensional active model of signal transduction in the cell which is derived from the Maxwell equations and uses generalized Hodgkin-Huxley fluxes for the description of the ion channels.