With gaping, round mouths ringed by sharp, horny teeth, lampreys are among the most primitive of aquatic vertebrates. Lacking bones, they slip through water with a rapid, undulating motion created by flexing their muscles to generate waves that travel from head to tail down their eel-like bodies.
A novel mathematical model of how nerve cells along a lamprey's spinal cord may generate the rhythmic waves of electrical signals that trigger muscle contractions has now provided surprising insights into lamprey locomotion. In particular, the model predicts -- and laboratory experiments confirm -- that the passage of signals from one segment to another along the spinal cord occurs more readily from tail to head than from head to tail.
This finding runs counter to the notion intuitively held by biologists that because the wave travels from head to tail, head-to-tail neutral connections would likely be stronger than tail-to-head connections. It also prompts a variety of previously unasked questions, which require further investigation in the laboratory, concerning the precise characteristics of the signal-carrying fibers that run along the lamprey's spinal cord.
"One wants to understand where these [locomotion] patterns come from," says mathematician Nancy Kopell of Boston University, who, along with G. Bard Ermentrout of the University of Pittsburgh, developed a mathematical model of the neural network responsible for lamprey locomotion. "Mathematics allows one to take a mountain of possibly relevant detail and sort out what's really important."
Kopell described the lamprey work and related research at a joint meeting of the American Mathematical Society and the Mathematical Association of America, held last week in Baltimore.
To help solve the puzzle of how lampreys generate a smoothly coordinated swimming motion, Kopell and Ermentrout started with a set of equations representing a chain of oscillators. Each mathematical oscillator corresponds roughly to a group of cells along the lamprey's signal cord, which collectively generate periodic electrical bursts. "We used as few assumptions and restrictions [in the model] as possible," Kopell says.
The researchers found equations that reproduce the chief characteristics of the electrical signals required to generate the lamprey's distinctive swimming motion. One can picture that motion by imagining the passage of an S-shaped wave along a lamprey's body. As the wave slips off the tail, it simultaneously starts up again at the head so that one full wavelength always spans the length of the lamprey's body. …