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From dynamics to structure of neuronal networks
Max-Planck-Scientists in Göttingen have developed a method to identify possible wiring diagrams of a network based on its dynamics
The nerve cells of the brain are inter-connected to a complex network. All brain activities are the result of the "firing" of nerve cells, when they send electrical pulses - like a Morse code - to other cells of the brain. This process depends on the exact dynamics of the neuronal activity. When the brain receives sensory input, calculates or remembers, it processes information encoded in a series of neuronal impulses in different nerve cells. Although no two people have the same brain, they can still share the same thought. Thus, only to a certain extent is the dynamics of neuronal activity dependent on the structure of neuronal networks. Also for networks far simpler than that of the human brain this idea applies: different structures can display the same functionality. Raoul-Martin Memmesheimer and Marc Timme, researchers at the Max Planck Institute for Dynamics and Self-Organization and the Bernstein Center for Computational Neuroscience Göttingen, have developed a mathematical method to describe the set of all networks that exhibit a given dynamics. With this, they provide researchers with a tool which can be used to investigate the correlation between structure and function of a neuronal network.
A common approach in scientific research is to investigate the structure of a system in order to then draw conclusions about its function. Memmesheimer and Timme now took the reverse perspective. "For some simple networks we know the activity dynamics, that is, their function, but not their exact structure", explains Memmesheimer. "Any given dynamics can normally be created by a variety of different networks. We have developed a method to mathematically pin down this diversity". This procedure resembles juggling with many unknown quantities and requires high computational power. Already in a network of 1000 neurons (where each neuron can be connected to any other) there are a million possible contacts between any two neurons and consequently an unimaginably large number of possible networks. Each combination can have either an inhibiting or an activating effect on the downstream neuron and, in addition to this, can differ in its intensity and reaction time. The entirety of all possible networks of a defined dynamics resembles a complex figure in a multidimensional space. Here, every point on the surface specifies the data required to determine a network with the desired dynamics. Memmesheimer and Timme have now worked out a mathematical description for this figure.
The researchers examined the applicability of their model on the basis of a concrete question. They calculated all possible networks that generate a given dynamics and simultaneously fulfil a further condition: the structure of the network should be as simple as possible, that is, the number of connections and the strength of the synapses should be minimal. "Applied to a real network, one could for example analyze which structural optimization principles function in evolution", says Timme. The dynamics of a number of very simple networks that generate repetitive patterns - like the insect walking pattern - are already well-understood. Has evolutionary pressure kept the structural complexity of such networks to a minimum - or could there have been other networks with an even simpler structure, yet possessing the same dynamics? Is it possible that many more networks fulfilling the same functional and structural conditions could have evolved? There is still no definite answer to these puzzles, however, with the help of the new methods developed by Memmesheimer and Timme, we have come a step closer towards understanding them.
Original publications:
Memmesheimer, R.-M. and Timme, M (2006). Designing the Dynamics of Spiking Neural Networks. Physical Review Letters 97 (18), 188101
Memmesheimer, R.-M. and Timme, M. (2006). Designing complex networks. Physica D: Nonlinear Phenomena 224 (1-2), 182-201.
Contact:
Dr. Marc Timme
Network Dynamics Group
Max Planck Institute for Dynamics and Self-Organization
Bunsenstr. 10
37073 Göttingen
timme@nld.ds.mpg.de
http://www.chaos.gwdg.de/~timme
The Federal Ministry of Education and Science (BMBF) has founded four Bernstein Centers for Computational Neuroscience (BCCN) in Berlin, Freiburg, Göttingen, and Munich. The interdisciplinary field of research combines experiments with data analysis and computer simulation on the basis of well-defined theoretical concepts. The central aim of Computational Neuroscience is to identify the neuronal basis of brain performance.
The BCCN Göttingen is a joint center of the Georg-August-University Göttingen, the Max Planck Institute for Dynamics and Self-Organization, the Max Planck Institute for biophysical Chemistry, the German Primate Center, and Otto Bock HealthCare GmbH.
http://www.chaos.gwdg.de/~timme
http://www.bccn-goettingen.de
http://www.bernstein-zentren.de
Different neuronal networks can bear the same pattern of activity - as shown in this example of a ne ...
Max Planck Institute for Dynamics and Self-Organization
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Different neuronal networks can bear the same pattern of activity - as shown in this example of a ne ...
Max Planck Institute for Dynamics and Self-Organization
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