Mathematics Reveals New Patterns Of Brain Cell Activity

The work, which appeared in a recent issue of the journal Science, may one day help explain the changes that occur in the brain during normal sleep and reveal the causes of nervous system disorders such as epilepsy.

David Terman, professor of mathematics at Ohio State, and his collaborators developed mathematical equations that describe the patterns with which electrochemical signals bounce back and forth among neurons. They modeled the signals on computer and discovered two patterns that may help advance a new view of how the brain works.

“Traditionally people thought of brain cells as switching either on or off, but that’s much too simple to account for everything brain cells do,” said Terman. “They really have lives of their own.”

Terman continued: “A common way to think about neurons is that one cell fires off a signal that excites its neighbors, and the neighbors fire off a signal and so on, in synchrony with each other, but real communication is more complex than that. One of the questions we’re confronting is how the brain produces smooth, synchronous wave patterns when the cells sometimes fire in an asynchronous way.”

The researchers looked at inhibitory signaling -- when neurons communicate by chemically suppressing activity in other cells and then releasing it. The cells bounce back after they are released and pass the signal along by suppressing other cells. Scientists observed inhibitory signaling among brain cells in the past, but assumed it couldn’t produce the smooth waves that mark synchronous brain activities such as sleep.

“We thought an inhibitory signal would produce a lurching wave, one that wasn’t very smooth. But we discovered that it can produce a very smooth wave that will spread through other cells, just like an excitatory signal,” said Terman. “An inhibitory signal just travels much slower.”

The researchers found that the key to producing a smooth wave was not whether a cell communicates in an excitatory or inhibitory way, but rather which cells it communicates with. A brain cell can talk to its immediate neighbors in what researchers call on-center communication, or it can skip over its immediate neighbors and talk to its neighbors’ neighbors. That kind of communication is called off-center.

Using the computer, the researchers modeled on-center and off-center inhibitory signals, and produced two very different wave patterns.

When the simulated neurons communicated an inhibitory signal to their immediate neighbors, the resulting wave was jerky and disjointed. When they communicated an inhibitory signal to cells beyond their immediate neighbors, the wave flowed smoothly, albeit much slower than a normal excitatory wave. An excitatory wave may travel as fast as 100 meters per second, while the inhibitory wave traveled only 0.6 millimeters per second.

Terman said that the computer simulations may give scientists clues as to how nervous system disorders such as epilepsy jumble communication signals in the brain, and how inhibitory signals can lead to smooth, synchronous waves like those the brain produces during sleep.

“One of our main motivations for studying this is sleep rhythms,” explained Terman. “As someone first drifts off to sleep, the network of neurons in their brain isn’t very synchronized. It breaks up into different groups, each firing in a different pattern. But as the person falls deeper into sleep, the patterns gradually grow more and more synchronized. We’re trying to understand how that happens.”

Terman speculated as to why smooth waves formed by inhibitory signals should travel through neurons so much slower than excitatory signals.

“Whatever message the neurons are sending, it may be that the brain is trying to keep that information around longer,” he said.

If the brain is trying to differentiate between two rapidly consecutive sounds, for example, it may help to retain a record of them, even if only for a few extra milliseconds.

Terman and his collaborators, including John Rinzel of New York University, Xiao-Jing Wang of Brandeis University, and Bard Ermentrout of the University of Pittsburgh, will continue this work, which was sponsored by the Alfred P. Sloan Foundation, National Science Foundation, National Institutes of Health, and the W.M. Keck Foundation.