Equations Predict Microbe Motions

May 23, 2007

A pair of simple equations with two key variables can predict the varied movements of the disease-causing bacterium Listeria.

This rod-shaped pathogen propels itself by hijacking an infected cell's network of actin fibers. To move forward, it keeps adding protein molecules at its back end, leaving an actin tail (known as a comet) in its wake.

Vivek Shenoy, a professor of engineering at Brown University, and three colleagues developed a mathematical model that mimics the different geometrical paths—a figure-8, a sine curve, a cloverleaf, a circle, a spiral, or a loop-the-loop—that the microorganism follows. With just two variables—an offset distance and an angle relative to its forward motion—the researchers were able to mimic any of its movements.

The key element is a torque that arises from the rotation of the propulsive force about the axis of the bacterium. The "large variety of trajectories with a rich mathematical structure," the researchers report in the Proceedings of the National Academy of Sciences, arises "by varying the rate at which the propulsive force moves about the long axis." Interestingly, mutant strains do not move in ways predicted by the equations.

"If we can understand things in a simpler setting, such as this one," said Shenoy, "then we can use those insights to study more complex phenomena." And, in the end, render dangerous organisms harmless.

Source: PNAS; Brown University, May 11, 2007.