Experimental Data Fitting Analysis on Frequency-Current-Temperature Relation

We study experimental data fitting to a frequency gradient curve for current and temperature simulated with the Hodgkin-Huxley (HH) oscillator undergoing saddle-node on invariant cycle bifurcation. In this study, one frequency gradient curve (referred to as the theoretical curve) are constructed by expanding the HH oscillator using small perturbations of the current and temperature while the other gradient curve (referred to as the empirical plot) is obtained with frequency-current relations recorded from hippocampal CA3 pyramidal cells at different environmental temperatures. The empirical plot is best-fitted to the theoretical curve under a certain temperature parameter range using simulations with the HH oscillator. In order to confirm the best-fit, we show that the theoretical curve is overlapped almost of the standard errors for the plot and that a temperature coefficient in the HH oscillator is rescaled to be in a suitable range of the temperature coefficient calculated with the experimental data.