By Moerder D., Pamadi B.
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13 Biological clocks can be exceedingly simple. Some biological clocks simply involve three proteins interacting in a small system. 14 This circadian clock centers on a protein called KaiC. The protein is modified by two other proteins, KaiA and KaiB, that add a small chemical marker onto KaiC or remove that marker. In the test tube as in the cyanobacteria, the percentage of the KaiC protein that is modified oscillates, peaking approximately every 24 hours. The cell watches how much KaiC is marked to know, for example, when the sun is about to rise: this allows the bacterium time to prepare to capture the energy it needs to grow at its maximum potential.
Their equations even foreshadowed some properties of then-hypothetical structures called ion channels—which we now know to be proteins that open and close to let ions pass through the cell membrane—long before these channels were probed by other means. Their mathematical description of this process, known as the Hodgkin-Huxley model, is still in use today, and they won the 1963 Nobel Prize in Physiology or Medicine. Hodgkin and Huxley’s work is an example of what systems biology often aspires to be—a concrete, mathematical understanding of a complicated biological process—but successes like theirs were relatively rare even as recently as the 1990s.
But this mixing process can also sometimes make an otherwise stable system exhibit dynamic behavior. This destabilization, known as the Turing instability, can produce complex patterns. And in some cases, it’s possible that living things use these patterns to define structures, such as the shape of a person’s fingers. Dr. Erwin Frey, the chair of statistical and biological physics at Ludwig-Maximilians-Universität in Munich, uses a simple analogy to explain the Turing instability. It’s a tale of sheep and wolves.
Constrained Minimization of smooth function using a genetic algoritm by Moerder D., Pamadi B.