# The Art of Mathematical Modeling

This ScienceLives article was provided to LiveScience in partnership with the National Science Foundation.

Not everything we wish to know in biology can be measured directly, either because doing so is too costly or simply impossible. In some cases, scientists can look to biological "signposts," called biomarkers, to infer information. Medical practitioners, for example, can use the presence of certain molecules in blood or tissue to diagnose or predict disease. The proteins known as antibodies are examples of biomarkers indicating possible infection.

Chris Remien, a postdoctoral fellow at the National Institute for Mathematical and Biological Synthesis, uses math to better understand how biological markers relate to the diets of animals and how they metabolize nutrients and toxins. The food and water animals consume leave chemical signatures (biomarkers) in their tissues; however, metabolism sometimes alters these signatures. Remien develops mathematical models to understand how metabolism can change the biomarkers.

Remien's models also help doctors estimate the extent of liver damage following overdose of acetaminophen (the active ingredient in some pain medicines), which is crucial for determining patient survival.

Name: Chris Remien Age: 30 Institution: National Institute for Mathematical and Biological Synthesis Hometown: Ishpeming, Mich. Field of Study: Mathematical biology

What inspired you to choose this field of study?

I have always enjoyed problem solving, which is what initially drew me to mathematics. Over time, I became more drawn to problems rooted in the real world, in data. Biology asks perhaps the biggest and most exciting questions of the real world, those related to life. The complexity of life means that intuition alone is often not enough and mathematics and simulation can sometimes come to the rescue. It is an exciting time to be a quantitative person asking biological questions.

Trust your gut. A huge part of the art of modeling is simply figuring out exactly what to model, what is important to the question at hand. For the best problems, you have a deep feeling that more information can be uncovered through modeling, even if you don't yet see exactly how it should be done.

What was your first scientific experiment as a child?

I spent a lot of time playing outside as a child, which led me to wonder why things were as they were. Why do these trees grow here, and others grow elsewhere? We would catch tadpoles, put them in our backyard pond, and watch them turn into frogs. Spending time outside has led to a fascination with the natural world that continues to this day.

I love how mathematics allows us to see the unseeable. If we are clever enough, mathematical models can be used to gain information on things that are impossible to measure directly, which is very exciting. I have been fortunate to work with a range of people, from ecologists to medical doctors, asking very different questions. Mathematics highlights similarities between them.

What is the most important characteristic a scientist must demonstrate in order to be an effective scientist?

Creativity. The most interesting questions require completely novel approaches. The most creative people are usually the ones driving a field in new and exciting directions.

What are the societal benefits of your research?

Research on stable isotope ratios has already seen a number of interesting results. In one case, understanding the stable isotope ratios of hair led to the identification of a murder victim by determining her travel history. It turns out that stable isotope ratios of oxygen and hydrogen in water vary with geography on a continental scale, and so because the stable isotope ratios in drinking water get incorporated into hair, a record of travel history is revealed by looking at the isotope composition of scalp hair.

Another example of the usefulness of stable isotope ratios can be found in the tropics where woody plants and grasses, which use different types of photosynthesis, have very different carbon isotope ratios. We have used stable isotopes to quantify African elephant diet over time as it relates to rainfall history, which is useful information for elephant conservation. Typically, after rainfall, grasses become more abundant and constitute a greater portion of an elephant's diet. Using carbon isotopes in hair, we can see exactly how much grass these animals are eating and how their diet changes with changes in rainfall.

Similarly, we have used carbon isotopes in fossil soils to determine the fraction of woody cover sites that bear hominin fossils, a problem that has implications for the history of our species. Because woody plants and grasses have very different carbon isotope ratios, there is a strong relationship between carbon isotope ratios of soil and fraction of woody cover.

In other research, my work on acetaminophen overdose will hopefully have a direct impact in how medical doctors view acetaminophen overdose patients. Our modeling efforts offer insight into the nature of the dynamics of an overdose and hopefully will be able to better guide physicians in determining whether a patient will require a liver transplant for survival.

Who has had the most influence on your thinking as a researcher?

I am greatly indebted to my graduate school mentors Fred Adler and Thure Cerling, who taught me the art of creative problem solving.

What about your field or being a scientist do you think would surprise people first?

I think it's not often appreciated that mathematical modeling is an art. A good model is predictive and useful, but also offers insight into the underlying processes.

If you could only rescue one thing from your burning office, what would it be?

My trusty Macbook and a full cup of coffee.

What music do you play most often in your office or car?

Anything from Modest Mouse to Johnny Cash to classical, depending on the mood of the day.

Editor's Note: The researchers depicted in ScienceLives articles have been supported by the National Science Foundation, the federal agency charged with funding basic research and education across all fields of science and engineering. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. See the ScienceLives archive.