Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Tuesday, 25.05.2010 17 c.t.

Modeling neuronal activity: stochastic effects on rhythmic firing

by Prof. Dr. Henry C. Tuckwell
from Max Planck Institute for Mathematics in the Sciences, Leipzig

Contact person: Fred Wolf


Seminarraum Haus 2, 4. Stock (Bunsenstr.)


Neural systems usually exhibit both nonlinearity and stochasticity. When these two features are combined the responses to stimulation can be surprising. Noise has most often been associated with the acceleration of neuronal spiking. This is probably generally the case for strong noise, but weak noise can have severe inhibitory effects on rhythmic spiking. This has been demonstrated theoretically in the original Hodgkin-Huxley system of ordinary differential equations (called a point model) as well as experimentally in squid axon. Near the bifurcation to repetitive spiking, weak noise (or any other appropriate stimulus) may easily drive the system from a limit cycle to a stable rest point, leading to a cessation of spiking for a possibly very long time. Transitions back to the limit cycle may occur with small probability with weak noise but with strong noise the system may switch back and forth from rest to spiking with a small first passage time, leading to an apparent overall increase in spiking activity. Several results are presented which indicate that with increasing weak noise a minimum in spike rate versus noise (called "inverse stochastic resonance") can occur for values of the signal (as opposed to noisy component) near the bifurcation value. Spatially distributed systems exhibit more complex patterns of response. With noise over small intervals the spatial model behaviour is similar to the point model but if there is no overlap of signal and noise then weak noise has no effect. With noise on large intervals, there is not only a minimum in the firing rate as the noise level increases but a subsequent maximum. The probability that there was interference with spiking was investigated as a function of the amount of overlap of signal and noise. If signal and noise were on disjoint intervals, then there was no interference, even if the regions of signal and noise were juxtaposed and no matter how large the region of noise (note that this applies only for weak noise). Related results for other neural models of the pacemaker type will also be presented, where the effects of noise depend strongly on the type (Hodgkin 1 or 2) of neuron.

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