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Page 36
1.3.5—
Example of a Power Law Scaling of a Process in Time:
Ion Channel Kinetics
We wanted to find out if there is a scaling relationship present in the open and closed times that we recorded from a potassium ion channel in the cells that line the inside of the cornea in the eye.
We needed to determine how the probability to change from closed to open depends on the time resolution used to measure it. The channel must be closed long enough for us to see it as closed. Thus, from our data, we determined the conditional probability that a closed channel will open, given that it has already remained closed for a certain amount of time. That certain amount of time then sets the time resolution at which the measurement is done.
We called this conditional probability the effective kinetic rate constant, keff and the time resolution at which it was measured the effective time scale, teff. We plotted the logarithm of the effective kinetic rate constant Log [keff]versus the logarithm of the effective time scale Log [teff] at which it was measured. The data were a straight line on this plot. That tells us that the ion channel kinetics has a power law scaling characteristic of a fractal, where keff is proportional to teffb.

 
[Cover] [Abbreviated Contents] [Contents] [Index]


Fractals and Chaos Simplified for the Life Sciences
Fractals and Chaos Simplified for the Life Sciences
ISBN: 0195120248
EAN: 2147483647
Year: 2005
Pages: 261

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