Experiments
in vivo have shown that the reliability in response to fluctuating inputs is high,
whereas constant inputs produced unreliable responses. Simulations using
stochastic Hodgkin-Huxley neuron models confirmed the experimental findings. It
was argued that the fluctuations present in the time-varying inputs become the
main force driving the cell towards a spike, attenuating the influence of the
ion channels stochasticity and increasing reliability. In this work I put
forward an alternative explanation, which is relevant for the neuron models near
a subcritical Hopf bifurcation. Such models, termed resonators, exhibit damped
sub-threshold oscillations, which set the eigenfrequency of the membrane. All resonators,
in particular the Hodgkin-Huxley model, are provably sensitive to those
spectral components of their inputs, which are close to the eigenfrequency. I
suggest that the spectral content around the eigenfrequency is the main factor
leading to high reliability. A signal possessing this spectral content elicits
a relatively reliable response. Constant input is an extreme particular case of
a signal lacking these spectral components, which will lead to low reliability.
To test the hypothesis fluctuating signals constructed as the low-pass Gaussian
white noise are band-pass and band-stop filtered around the eigenfrequency of
the model, which is determined by analyzing the sub-threshold activity. The
band-pass filtered signals elicited responses with high reliability measure
values very close to those produced by the original inputs. In contrast, the
band-stop filtered signals produced very unreliable responses with the reliability
measure values only slightly exceeding those produced by the constant stimuli. These
results confirm the frequency-dependence hypothesis, indicating that the
spectral characteristics of the input signal have a crucial role in determining
the temporal reliability and precision. A new robust measure of reliability is
introduced.
