For Nickolas Kintos, Ph.D., the popular Jonah crab doesn’t often arrive steamed in white wine and garlic. Instead, it is served across the Internet as a series of neural patterns that dip and climb.
Kintos is a Peter M. Curran Visiting Assistant Professor of Mathematics, a faculty appointment designated for a scholar who is also doing research. When he isn’t teaching subjects like multivariable calculus, linear algebra or complex analysis, Kintos is creating mathematical models of a neural network inside the Jonah crab.
In addition to being tasty, the Jonah crab is particularly suited to neuroscience research. Its digestive system provides an excellent opportunity to study how neural networks control rhythmic movement in the human body, Kintos said. One reason is that the crab’s stomach muscles are striated, which make them very similar to the skeletal muscles in a human.
“The neural activity in the crab’s digestive system is a model system for studying human walking, or breathing, or anything that is a rhythmic motor behavior,” he said. “It would be very difficult to design a neural wiring system of the human being—there are more than a billion neurons. But the crab’s stomatogastric nervous system (STNS), which controls digestion, has about 1,040, so it’s much simpler to study.”
Mathematics, Kintos explained, can be separated basically into two areas: pure mathematics, or math for math’s sake, and applied mathematics, the branch that applies mathematical knowledge to other fields. Kintos is an applied mathematician doing interdisciplinary research with biologists at the New Jersey Institute of Technology and the University of Pennsylvania School of Medicine. Together, they are studying how the oscillations of a central pattern generator network in the crab’s STNS control the muscle movements that enable the animal to chew with its teeth.
Here’s how the research is done:
First, Kintos receives actual biological readings from the team on the voltages of each of the neurons involved. Taking that data, he designs equations that describe the neural system in play.
Biologists, Kintos said, cannot stop an experiment mid-stream to test or weigh the importance of a host of properties. With math, Kintos is able to separate out the most important properties that drive the system, and build a model based on the properties. This, he said, is called a qualitative model.
“In a qualitative model, we don’t know how to solve the system, but we can qualitatively describe it,” Kintos said.
Once Kintos has come up with equations for the qualitative model, he uses the predictions from them to build a quantitative model. Such a model takes into consideration actual biological information—including details about how neurons are connected, or details about their spatial structure—to come up with a finite calculation, i.e., an answer.
Kintos sends his answer back to the biologists, who then test his hypothesis against the real-world behavior of the specimens in the lab.
“Maybe they will work, maybe not. But we go from there,” Kintos said. “I like to see math in action, to use math not only to describe how a system works, but also to predict why it works. [Interdisciplinary research] allows you to take applied mathematics one step further.”
Today, he said, applied mathematics is being used in many areas of interdisciplinary research, including geology, economics, ecology, physics and chemistry.
His research on oscillatory activity, however, is geared specifically toward understanding disorders of human neural activity in patients with spinal cord injuries, Alzheimer’s Disease or Parkinson’s Disease.
Once those disorders are better understood, he said, scientists could build circuits to implant into the brain to reconnect the spinal cord’s severed neurons which generate movement. They could reactivate dead neural connections in people with Alzheimer’s, and they could use deep brain stimulation to correct the misfiring neurons that cause tremors associated with Parkinson’s.
“All of these are long-term hopes,” Kintos said. “My research is just one example of how we can use mathematics to attack real-world problems.”
His research on the crab, “A Modeling Comparison of Projection Neuron- and Neuromodulator-Elicited Oscillations in a Central Pattern Generating Network,” was published last year in the Journal of Computational Neuroscience.
Kintos admitted that he occasionally ponders the different modes of food chewing while he, himself, is eating, and occasionally “mimics some of these modes when I eat crabs myself.”
But never on experimental crabs. Just the ones from the supermarket.
– Janet Sassi