Resonance without oscillation?

Roland Mueller ane Andreas V.M. Herz

Humboldt University Berlin

Membrane potentials of single neurons often exhibit subthreshold oscillations, either in the form of spontaneous oscillations or in the form of damped oscillations following a pulse- or step-current input. Similarly, many neurons exhibit subthreshold resonance patterns in response to sine-wave or ZAP-current inputs. Both phenomena are signatures of the same underlying biophysical processes. The specific conditions for resonance and oscillations are, however, not the same. In particular, a neuron may show resonance without exhibiting a spontaneous or damped oscillations. We give a simple mathematical explanation for this counter-intuitive finding and discuss some functional consequences.