Pendulum swings back on 350-year-old mathematical mystery

By | June 11, 2013

A 350-year-old mathematical mystery could lead toward a better understanding of medical conditions like epilepsy or even the behavior of predator-prey systems in the wild, University of Pittsburgh researchers report.

The mystery dates back to 1665, when Dutch mathematician, astronomer, and physicist Christiaan Huygens, inventor of the pendulum clock, first observed that two pendulum clocks mounted together could swing in opposite directions. The cause was tiny vibrations in the beam caused by both clocks, affecting their motions.

The effect, now referred to by scientists as “indirect coupling,” was not mathematically analyzed until nearly 350 years later, and deriving a formula that explains it remains a challenge to mathematicians still. Now, Pitt professors apply this principle to measure the interaction of “units”–such as neurons, for example–that turn “off” and “on” repeatedly. Their findings are highlighted in the latest issue of Physical Review Letters.

… forms of indirect communication that are not typically included in most mathematical studies owing to their complicated elements. In addition to studying neurons, the Pitt researchers applied their methods to a model of artificial gene networks in bacteria, which are used by experimentalists to better understand how genes function.

“In the model we studied, the genes turn off and on rhythmically. While on, they lead to production of proteins and a substance called an autoinducer, which promotes the genes turning on,” said Jonathan E. Rubin. “Past research claimed that this rhythm would occur simultaneously in all the cells. But we show that, depending on the speed of communication, the cells will either go together or become completely out of synch with each another.”

To apply their formula to an epilepsy model, the team assumed that neurons oscillate, or turn off and on in a regular fashion. Ermentrout compares this to Southeast Asian fireflies that flash rhythmically, encouraging synchronization.

“For neurons, we have shown that the slow nature of these interactions encouraged ‘asynchrony,’ or firing at different parts of the cycle,” Ermentrout said. “In these seizure-like states, the slow dynamics that couple the neurons together are such that they encourage the neurons to fire all out of phase with each other.” ….

via Pendulum swings back on 350-year-old mathematical mystery.

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