Neuron uses the membrane voltage to be the carrier of the electric signals. And the voltage evolving is caused by the changing of membrane conductance to some kinds of ions, which is performed by the gating of individual channels. So, there inevitably exists channel noise (conductance noise). Unlike the current-response--which is directly determined by the conductance under a clamped voltage--to the channel noise, the voltage response is relatively more complex since it needs a relaxation process to approaching its reversal potential. Experimental evidence is shown that the power spectra of current and voltage decrease with different scaling-laws.

In this talk, we will introduce our recent work. We use the piece-wise deterministic Markov process to model the voltage fluctuations driven by a cluster of ligand-gated channels. Firstly, 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 got analytically, and it is proved to has the $1/\omega^4$-form---Its mechanism lies in that the randomness of the voltage fluctuation is weaker than the channel (conductance) noise, which can be approximately described by the Ornstein-Ulenbeck process. 

Jiazeng Wang is an associate professor at School of Mathematical and Statistics, Beijing Technology and Business University. He was a Post-doc at Peking University, from 2009 to 2011. He obtained his PhD degree from Shanghai University in 2008. In these recent years, his primary research interests are in the stochastic dynamics of ion channels, the voltage fluctuations driven by the conductance noise (channel noise), the non-equilibrium properties in membrane-channel systems. He has published 5 papers in this field, in Journals such as ‘Physical Review e’, ‘Chaos’, ‘Journal of Theoretical Biology’.