Mathematicians from the University of Pittsburgh have now devised a formula that may help unveil the dynamics between predator and prey, analyze epilepsy and other medical conditions.
For over 350 years, scientists have been unable to derive a formula to explain Christiaan Huygens pendulum clock.
It was in the year 1665 that the Dutch astronomer, mathematician and physicist Christiaan Huygens discovered the pendulum, and observed that when two pendulum clocks were mounted together, they swung in opposite directions. This effect, now known as 'indirect coupling' was not actually analyzed mathematically until now.
Mathematicians at the University of Pittsburg have now put forth their formula to analyze medical conditions too.
"We have developed a mathematical approach to better understanding the 'ingredients' in a system that affect synchrony in a number of medical and ecological conditions," coauthor of the study and professor in Pitt's Department of Mathematics within the Kenneth P. Dietrich School of Arts and Sciences, Jonathan E. Rubin, said. "Researchers can use our ideas to generate predictions that can be tested through experiments."
This new formula is expected to help researchers better understand conditions like epilepsy wherein the neurons become overly active and don't turn off, leading to seizures.
The formula may also help understand how bacteria may use external cues to synchronize their growth.
Apart from studying neurons, the mathematicians from Pitt also applied their formula to a model of artificial gene networks in bacteria to better understand how their genes functioned.
"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," Jonathan E. Rubin said. "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."
When they applied their formula to an epilepsy model, they assumed that the neurons oscillate in a rhythmic way, just like the pendulum. "For neurons, we have shown that the slow nature of these interactions encouraged 'asynchrony,' or firing at different parts of the cycle," G Bard Ermentrout, University Professor of Computational Biology explained. "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."
The National Science Foundation Grant supported this work, and the study is now available online in Physical Review Letters.
