Power spectrum density equation of fluctuating membrane current based on a discrete-time markov chain model: Application to the analysis of ion channels with two and three states
✍ Scribed by Yoshio Ebina; Mamoru Mukuno; Kazuki Nakajima; Ryuzo Shingai; Alan G. Hawkes
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 849 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0882-1666
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✦ Synopsis
Abstract
The measured power spectrum density PWS~EX~ of the fluctuating membrane current of neurons often differs from the well known Lorentz curve. Representing the frequency dependence in the high frequency (f) above the corner frequency as f^−n^, n is less than 2, which indicates that the slope is smaller than in the Lorentz curve f^−2^. The reason for the rise of the high‐frequency side of PWS~EX~ is the aliasing effect produced by application of the FFT to discrete data over a finite interval.
In this study, the theoretical expression PWS~TH~ for the power spectrum density obtained from a discrete‐line Markov model is used in the analysis of the experimental data. In the practical analysis of experimental data, we assume that the number of states of a single kind of channel on the membrane of the neuron is two or three.
Using the discrete‐time Markov model, an expression for PWS~TH~ is derived. When the sampling time approaches zero, this expression approximates the known expression for the power spectrum density under the continuous‐time Markov model. The plot of PWS~TH~ gave a good fit to the experimental data. The open time that we obtained agreed well with existing values. These results confirm the usefulness of this form of PWS~TH~ when it is applied to processing discrete data sampled at finite intervals.