Test tubes, pipets and microscopes are familiar workhorses in a cancer biologist's inventory of tools.
Just as useful, says Dr. Georg Luebeck, a mathematical modeler in the Public Health Sciences Division, are sound mathematical and statistical concepts that allow scientists to manipulate their results into interpretable data. The tools of the "dry lab" are differential equations, integrations and algorithms to derive expressions for the likelihood of experimental outcomes.
Math serves an equally critical role in the design of experiments, allowing researchers to develop models for testing new ideas. What's more, numerical and statistical analysis often can provide a picture of the steps in a biological process that can't be seen easily with lab manipulations.
"Really, all scientists are modelers. We all have an idea in mind when we want to test something new," said Luebeck, a newly appointed faculty member in the Biostatistics Program. "Many scientists do this by making logical associations, but often it can be helpful to put a math perspective on a problem. That gives you an anchor, a marker to go by as you do your experiment."
Theoretical physics
Born and raised Germany, Luebeck joined PHS in 1988 as a staff scientist to work with Dr. Suresh Moolgavkar. Prior to his arrival at the center, Luebeck completed postdoctoral work at the Neils Bohr Institute for Astronomy, Physics and Geophysics in Copenhagen after earning a doctorate in theoretical physics at the University of Washington.
"As a physicist, you're trained to model complex systems, such as the properties and the interactions of elementary particles," he said. "But the entire world of biology, genetics and biostatistics was totally new to me. It took a few years to catch up and learn the language, and I am still learning."
Since that time, Luebeck and colleagues have devised formulas, equations and computer programs that simulate and predict biological processes, such as how tumors form in people or animals exposed to a variety of carcinogens. Using this approach, the PHS group has modeled successfully how exposure to radon (an alpha-particle emitter) causes lung cancer in uranium miners and how liver cancer develops in rats exposed to cancer-causing chemicals.
Such studies contribute to the understanding of cancer risks associated with exposures to toxic chemicals or radiation. Modeling carcinogenesis also has made it possible to assess risks from complex individual exposures, a considerable advantage over tried empirical methods.
Recently established collaborations with experimental biologists in the PHS and Human Biology divisions will let the modeling group apply its techniques to the multi-step development of Barrett's esophagus, a pre-cancerous condition studied by Dr. Brian Reid's research team, and colon cancer, a focus of Dr. John Potter's group.
The relationship between mathematical modelers and experimentalists is synergistic: Just as mathematics helps to guide the interpretation of physical observations, a model's success hinges on incorporation of observations and measurements made at the lab bench.
Luebeck's modeling interests are focused on understanding the rate-limiting events involved in the cancellation of growth controls in normal cells on the pathway to cancer.
"The basic concept of multistage carcinogenesis has been around for many years," he said. "Scientists have long observed that the incidence of many solid tumors rises with age in a peculiar way. That suggests that there are rate-limiting steps in the pathway to cancer, although an exact number of steps is hard to come by from analyses of cancer incidence alone."
About 30 years ago, Dr. Alfred Knudson of Fox Chase Cancer Center in Philadelphia developed what is known as the "two-hit" model of carcinogenesis to explain both hereditary and non-hereditary forms of cancer. The model dictates that some cancers arise when mutations occur in both copies of a gene essential for keeping normal cell growth in check.
Such cancers arise with increased probability in individuals born with one of the two copies already defective, because only one additional mutation (in the healthy copy) needs to take place over the course of their lifetime for cancer to develop. Those born with two healthy copies of the gene must incur two mutations, which explains why non-hereditary forms of many cancers arise with lower frequency - and later in life - than inherited forms.
Mathematical framework
Over the last 10 years, Luebeck and PHS colleague Moolgavkar continued to build upon Knudson's ideas and helped develop the mathematical framework of what is now known as the two-stage clonal-expansion model.
Luebeck said the human body constantly produces abnormal cells, yet most of the time, such potentially cancer-causing cells are killed via a process called apoptosis.
"In normal adult tissue, cell birth and cell death or differentiation are well balanced," he said. "But if abnormal cells escape apoptosis, a tumor can develop."
With collaborators in Austria and Germany, Luebeck has successfully modeled the formation and the development of premalignant lesions in rat liver. A powerful aspect of the mathematical approach, he said, is that it can provide numerical estimates of the rate of initiation of such lesions and of their cell kinetics, in particular the incidence of apoptosis - which can be difficult to measure experimentally.
The group plans to use similar strategies to analyze data on tissue in people with Barrett's esophagus, a condition in which abnormal cells build up in the lining of the esophagus, putting those individuals at high risk for developing esophageal cancer. In addition, they will use mathematical modeling to predict the number and sizes of polyps, potentially cancerous precursors in the colon, that form during the course of cancer development.
"The ability to come up with quantitative predictions based on our current understanding of the biology of colorectal cancer is of substantial value for the design of intervention and prevention strategies," Luebeck said.
