# BCCN/BFNT AG-Seminar

Tuesday, 25.05.2010 17 c.t.## Modeling neuronal activity: stochastic effects on rhythmic firing

*by Prof. Dr. Henry C. Tuckwell*

Contact person: Fred Wolf

### Location

Seminarraum Haus 2, 4. Stock (Bunsenstr.)### Abstract

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.