Characterizing the voltage fluctuations driven by a cluster of ligand-gated channels

In this paper we present the properties of the voltage fluctuations driven by a cluster of ligand-gated channels. First, the second-order moment of the voltage is expressed in form of the integrated resistance and the random force. Then the power spectrum of the voltage noise is obtained analytically, and it is proved to have the $1/{\omega }^4$-form. Its mechanism lies in that the randomness of the voltage fluctuation is weaker than channel (conductance) noise, which can be approximately described by the Ornstein-Ulenbeck process.

Figure 1

The equivalent electric circuit of the system. Especially note that the reversal potentials $V_{Ch}$ of the postsynaptic currents may be positive or negative, depending on the type of the synapse, so the battery $V_{Ch}$ (accordingly the current $I_{Ch}$) may has different directions.

Figure 2

The three kinds of power spectra calculated from three methods respectively. The values of other parameters are $C_m=0.01\text{pF}/\mu {\text{m}}^2\times 6\mu {\text{m}}^2$, $V_L=-54.4\text{mV}$, $V_{Ch}=0\text{mV}$, $k^{+}=0.01$, $k^{-}=1$, and $N=30$.