Using Mathematics to Understand a Species of Bacteria That Can Add Up to Big Trouble: Helicobacter pylori is Sometimes Hard to Stomach

About half of all adult Americans have an intimate companion—one they carry with them everywhere—that usually keeps its presence unknown but can prove to be a most unwelcome guest. Its proper name is Helicobacter pylori—a species of bacteria which usually produces no symptoms in the humans carrying it, but which can cause ulcers and stomach cancer in some individuals.

Though it is an organism widespread in the human population, scientists know very little about H. pylori. To learn how it coexists for long periods of time with people, Medical School scientist Denise Kirschner, Ph.D., created a mathematical model, based on experimental evidence, of the symbiotic relationship between bacterium and host. Results from the model were published in an article by Kirschner and Martin Blaser, M.D., of Vanderbilt University Medical Center in the July 20, 1999, issue of the Proceedings of the National Academy of Sciences.

While several mathematical models have been developed to study HIV, the virus that causes AIDS, this is the first model for Helicobacter pylori, according to Kirschner. “The most important factor in the relationship is the capacity of the host response to the bacteria,” says Kirschner, an assistant professor of microbiology and immunology in the Medical School. “Some people have the ability to flush it from their systems and some don’t. We don’t know why these individual differences exist and we don’t understand exactly how the host responds to the bacteria’s presence. The response may or may not be directly related to the immune system.”

“Everything about the model works and is consistent with indirect experimental data,” Blaser says. “We describe the initial transition from one organism to a bloom of organisms. Then as immunity kicks in, the organisms settle down and reach equilibrium. In essence, bacteria and host are dancing together; each one is signaling the other.”

Helicobacter pylori bacteria live in the thick mucus layer lining the inside of the stomach, which protects epithelial cells from stomach acid, Kirschner explained. When bacteria enter the stomach, probably through fecal-oral transmission, some penetrate the mucus layer and attach to epithelial cells. These bacteria release molecules that irritate and degrade epithelial cells, which creates food for the bacterial colony.

“Our most surprising discovery is the key role played by this small group of adherent bacteria,” Kirschner said. “They only make up one percent of the entire colony, but they must be present or colonization will not take place.” The model also indicates that two competing strains of H. pylori can live together in the stomach at the same time—but not for long. “One strain will always be dominant over the other,” Kirschner says. “But any change in stomach conditions can create advantages for a different strain and allow it to predominate.

“Mathematical models like this one are especially valuable in biomedical research when clinical experiments are difficult or impossible,” Kirschner says. “They help us focus study on areas most likely to produce a positive result and allow us to test experimental treatments quickly and inexpensively to guide human clinical trials.”

Model development was supported by the National Institutes of Health, the Medical Research Service of the Department of Veterans Affairs, and Astra-Merck, Inc.

Kirschner can be reached at kirschne@umich.edu.