Spike Onset Dynamics and Response Speed in Neuronal Populations

Recent studies of cortical neurons driven by fluctuating currents revealed cutoff frequencies for action potential encoding of several hundred Hz. Theoretical studies of biophysical neuron models have predicted a much lower cutoff frequency of the order of average firing rate or the inverse membrane time constant. The biophysical origin of the observed high cutoff frequencies is thus not well understood. Here we introduce a neuron model with dynamical action potential generation, in which the linear response can be analytically calculated for uncorrelated synaptic noise. We find that the cutoff frequencies increase to very large values when the time scale of action potential initiation becomes short.

Figure 1

(a) Illustration of the model. (b) $V(t)$ trajectories for identical noise and three different values of $r$. (c) and (d) show the dependence of stationary firing rate on mean input current and noise strength in the noise driven regime. (${\tau }_m=10\mathrm{ms}$, $v_r=0$, $v_b=10$, ${\tau }_r=0$).

Figure 2

The normalized function ${\nu }_1(\omega )/{\nu }_1(0.1)$ and phase lag for a mean coded signal and noise coded signal with $r=1$, $\mu =0$, and ${\nu }_0=5\mathrm{Hz}$. Other parameters are the same as in Fig. 1. Lines, theory; Symbols, simulation.

Figure 3

(a) and (c) The normalized transmission function ${\nu }_1^{\mathrm{low}}(\omega )/{\nu }_1(0.1)$ for different $r$ with $\mu =0$ and ${\nu }_0=5\mathrm{Hz}$. (b) and (d) The variation of cutoff frequency with $r$ for different firing rates: ${\nu }_0=1$, 5, 10, 20, 30, 40 Hz from lower to upper curves. Other parameters are the same as in Fig. 1.

Figure 4

Variation of the normalized transmission function $|{\nu }_{1c}(\omega )/{\nu }_{1c}(0.1)|$ with increasing correlation time ${\tau }_s$ (with unit ms) of the synaptic noise for $r=10$, 100. Parameter used: $\mu =0$, $v_b=10$, ${\nu }_0=5\mathrm{Hz}$.