Fig. 4. Analysis of Nav1.6 experimental trajectories in the soma of hippocampal neurons.

a The time-averaged MSD is different from the ensemble-averaged MSD (gray upper line). The shaded region indicates the 95% confidence interval for the ensemble-averaged MSD. The time-averaged MSD scales with the lag time as τ^0.81±0.05 (dashed lines), while exhibiting aging as it decays with experimental time as $1/t_{\mathrm{m}}^{1-\alpha }$, from which α is estimated to be 0.54 ± 0.02. b Average spectra are presented for three measurement times. The dashed lines show a scaling 1/ω^1.75. Besides the power-law scaling, the spectra exhibit white noise evident at large frequencies, likely due to localization error. The arrow shows the decay in the PSD with measurement time t_m. The inset shows the amplitude of the PSD as a function of measurement time in a log-log plot. It shows that the spectrum exhibits aging with a power law scaling $1/t_{\mathrm{m}}^{1-\alpha }$, from which α is estimated to be 0.50 ± 0.02. The combined measurements provide four different ways to determine the two relevant parameters, indicating the consistency of the model.