BIOPHYSICAL PROPERTIES OF SUBTHRESHOLD RESONANCE OSCILLATIONS AND SUBTHRESHOLD MEMBRANE OSCILLATIONS IN NEURONS

Abstract

Subthreshold-level activities in neurons play a crucial role in neuronal oscillations. These small-amplitude oscillations have been suggested to be involved in synaptic plasticity and in determining the frequency of network oscillations. Subthreshold membrane oscillations (STOs) and subthreshold resonance oscillations (SROs) are the main constituents of subthreshold-level activities in neurons. In this study, a general theoretical framework for analyzing the mechanisms underlying STOs and SROs in neurons is presented. Results showed that the resting membrane potential and the hyperpolarization-activated potassium channel (h-channel) affect the subthreshold-level activities in stellate cells. The contribution of h-channel on resonance is attributed to its large time constant, which produces the time lag between I_h and the membrane potential. Conversely, the persistent sodium channels (Nap-channels) only play an amplifying role in these neurons.

Keywords: Biophysical Model; Conductance-Based Model; Equivalent RLC Circuit; Stellate Cells; Subthreshold Membrane Oscillation; Subthreshold Resonance Oscillation.

Fig. 1

Biophysical model and its equivalent RLC circuit model for SCs. (a) The biophysical model of SCs is a single compartmental neuronal model with h and NaP channels. V and C are the membrane potential and capacitance, respectively. g_leak, g_h and g_NaP are the maximal conductances for leak, h and NaP channels, respectively. E_L is the reversal potential. E_h and E_Na are equilibrium potentials for h and NaP channels, respectively. I_inp is the synaptic input current. (b) The equivalent RLC electrical circuit model of SCs. The values of resistance and inductance elements for control condition are given in our previous work.

Fig. 2

Comparison between the biophysical model and its equivalent RLC circuit model for SCs. The voltage response (a) and impedance profile (amplitude (b) and phase profile (c)) of biophysical model are similar to the voltage response (d) and impedance profile (amplitude (e) and phase profile (f)) of equivalent RLC circuit model. The results obtained under the control condition.

Fig. 3

The effect of changing resting membrane potential in the resonant properties of biophysical model of SCs. (a) The voltage response for resting membrane potential at the control condition (upper trace), V = −65mV, and hyperpolarized value (lower trace), V = −70mV. (b) Three-dimensional plot of impedance amplitude profile (|Z|) at different resting membrane potentials. (c) Resonance frequency plotted as a function of membrane potential. (d) Q-values (strength of resonance) plotted as a function of membrane potential. For Q = 1, there is no resonance in model.

Fig. 4

The effect of h-channel on impedance profile of the equivalent RLC circuit model of SCs. (a) The impedance amplitude profile shows that increasing of g_h reduces the amplitude of f_res. (b) The impedance phase profiles show that decreasing of g_h reduces the zero-cross frequency (the frequency in which the φ(f) crosses over zero). (c) The total inductive phase (φ_L) in response to changing of g_h. (d) The total inductive phase (φ_L) in response to the changing of resting membrane potential.

Fig. 5

The evolution of SCs dynamics in response to the sinusoidal current. (a) The evolutions of I_NaP and I_h during STO. Noted that I_NaP closely follow the evolution of membrane potential. In contrast, I_h lags the membrane potential. The Increase and decrease in I_h correspond to minimum and maximum peaks of the membrane potential, respectively. The phase-plane of the amplitude of I_h (b) and I_NaP (c) versus the membrane potential. the plot corresponding to I_NaP, demonstrates a straight line. Therefore, the amplitude of I_NaP changes spontaneously. Plot corresponding to I_h shows the hysteresis. It means, during the downswing and upswing of STO, the amplitude of I_h changes with a significant delay.