108.

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Page 202
2.5.6—
Ion Channel Kinetics:
An Interpretation of the Deterministic Model
To breathe some physical life into the abstract mathematics of the deterministic iterative map model, note that the slopes of the lines of the function x(n+l) versus x(n) are greater than 1. This means that increases in the current cause it to increase further and decreases in the current cause it to decrease further. Thus, when the channel is open, a small decrease in the current is soon amplified into further decreases, thus rapidly closing the channel. Similarly, when the channel is closed, a small increase in the current is soon amplified into further increases, thus rapidly opening the channel.
A system that behaved this way, at a larger scale than a channel protein, occurred on Thursday November 7, 1940. It was the failure of the Tacoma Narrows bridge. This failure is often given in college physics courses as an example of simple, forced resonance. This failure was not due to simple, forced resonance. In simple, forced resonance you hit on a structure with a rhythm that excites a natural frequency of the structure into motion. The wind that day did not blow rhythmically. Rather, the bridge acting as a nonlinear, mechanical oscillator organized the nonperiodic motion of the wind into periodic motion of the bridge. The motion of the wind caused the bridge to twist in a way that changed the motion of the wind that caused the bridge to twist even more. The wind supplied the energy, but the bridge used that energy to excite itself.
In the same way, an ion channel protein is also a nonlinear, mechanical oscillator made of sticks and springs, which are sometimes called atoms and atomic forces. Perhaps the ion channel can organize the nonperiodic thermal fluctuations in its structure into coherent motions that change its shape from one that is open to one that is closed to the flow of ions.

 
[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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