Channel noise effects on first spike latency of a stochastic Hodgkin-Huxley neuron

While it is widely accepted that information is encoded in neurons via action potentials or spikes, it is far less understood what specific features of spiking contain encoded information. Experimental evidence has suggested that the timing of the first spike may be an energy-efficient coding mechanism that contains more neural information than subsequent spikes. Therefore, the biophysical features of neurons that underlie response latency are of considerable interest. Here we examine the effects of channel noise on the first spike latency of a Hodgkin-Huxley neuron receiving random input from many other neurons. Because the principal feature of a Hodgkin-Huxley neuron is the stochastic opening and closing of channels, the fluctuations in the number of open channels lead to fluctuations in the membrane voltage and modify the timing of the first spike. Our results show that when a neuron has a larger number of channels, (i) the occurrence of the first spike is delayed and (ii) the variation in the first spike timing is greater. We also show that the mean, median, and interquartile range of first spike latency can be accurately predicted from a simple linear regression by knowing only the number of channels in the neuron and the rate at which presynaptic neurons fire, but the standard deviation (i.e., neuronal jitter) cannot be predicted using only this information. We then compare our results to another commonly used stochastic Hodgkin-Huxley model and show that the more commonly used model overstates the first spike latency but can predict the standard deviation of first spike latencies accurately. We end by suggesting a more suitable definition for the neuronal jitter based upon our simulations and comparison of the two models.

Figure 1

Examples of the distribution of first spiking times obtained from the set of equations Eq. (3) showing positive skewness. Parameters used for low-noise plots [panels (a) and (c)] were $N_{\text{Na}}=1800$ and $N_{\text{K}}=540$, while for high-noise plots [panels (b) and (d)], they were $N_{\text{Na}}=600$ and $N_{\text{K}}=180$. For low-rate plots [panels (a) and (b)], the parameters for the synaptic input current were $\lambda =25$ Hz and $p=0.10$, while for high-rate plots [panels (c) and (d)], the parameters were $\lambda =100$ Hz and $p=0.30$. Panel (e) shows no channel noise with high synaptic input.

Figure 2

Plots of the mean, median, IQR, and standard deviation (STD) of the result of 1000 simulations of the set of equations Eq. (3) for each value of effective rate for two channel areas (10 and $30\mu {\text{m}}^2$). The plots show that the mean, median, and IQR are modeled exceptionally well by a linear function, whereas the standard deviation is not.

Figure 3

Median first spike latency and IQR for various effective firing rates as a function of the change in the number of channels in the Hodgkin-Huxley neuron. Lines show best fit linear regression for various effective rates. Top line to bottom line show best linear fits for circles, triangles, pluses, and stars, respectively.

Figure 4

Plots of the subunit noise model Eq. (5) comparing the median (top plot), IQR (second plot), mean (third plot), and the standard deviation (bottom plot) for different values of the effective rates $\lambda p$ for the case when noise perturbs subunit fractions. The parameter for the area of the neuron is $A=30\mu {\text{m}}^2$.