UA researchers have generated a mathematical model that can track the movement of the bacteria that causes Lyme disease, allowing them to explain the appearance of the “bull’s-eye” rash on the skin.

The study, led by Charles Wolgemuth, an associate professor of physics at the UA, and Dhruv Vig, a molecular and cellular biology graduate student, was published in the Biophysical Journal earlier this month.

Lyme disease is a caused by the infection of a bacteria known as Borrelia burgdorferi that is transmitted to humans primarily by deer ticks, said Eric Price, a lecturer in the department of physiology at the UA.

The bacteria starts out in the gut of the tick, where it then mobilizes and makes its way to the salivary glands. Once a human host is bitten by a tick, the bacteria can enter the skin and spread to other locations in the body, Price said.

“The model was actually able to tell us what parameters were controlling that spreading rate of 1 to 3 centimeter movement per day,” Vig said. “What it actually ended up being were the bacteria parameters.”

What interested researchers in the development of the mathematical model was the bacteria’s replication rate, the speed at which the bacteria moved throughout the body and the length of time they got “stuck” on the skin, Vig said.

“We are interested in figuring out how the bacterium is able to move through things like our skin or connective tissue or things that these bacteria are able to invade,” Wolgemuth said. “They are much better than a lot of other bacteria at going through our bodies.”

The spiral shape of the bacterium facilitates its movement, which is similar to that of a snake, according to Vig and Wolgemuth. This allows the bacteria to move through different tissues in the body.

The researchers hypothesized it was this unique movement that caused the characteristic bull’s-eye rash, which is due to the immune system trying to fight off the bacterium, Wolgemuth said.

The immune response causes skin inflammation that leads to the hyperemia, an increase in blood flow in the capillaries that causes the rash to appear, according to the published article.

Because the immune cells aren’t fast enough to catch them, the bacteria are able to disperse and create the outer ring of the rash. After a period of time, the bacteria then regroup at the center of the rash, which creates a red spot in the center, according to the article.

Once the researchers understood how the bacteria moved throughout the body and the role this movement played in the bull’s-eye rash, the team began to look at how their model could be applied to treating Lyme disease and how it could optimize antibiotic treatment, Vig said.

Treatment for Lyme disease typically involves taking antibiotics for 30 days. Vig and Wolgemuth found that within about seven days to two weeks of taking these antibiotics, the bacteria are cleared from the body.

However, because the rash sometimes lingers even after the bacteria has been cleared from the
body, people continue to take antibiotics unnecessarily, Vig said.

The hope is that the model will be used for more objective clinical trials tracking the effect of antibiotics and the subsequent disappearance of the bacteria from the body; this is in order to avoid excessive antibiotic ingestion, Vig added.

Both Vig and Wolgemuth said they are optimistic about the future use of the mathematical model in tracking bacteria in other diseases and rashes.

“One of the great beauties of [mathematical modeling] is that the thought process of the systems of equations that you can come up with can also be applied to other diseases,” Vig said.