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May 1, 2012 (Vol. 32, No. 9)

Mathematics Transforming Bioresearch

  • Computational Oncology

    Like Dr. Hood, Franziska Michor, Ph.D., from the Harvard School of Public Health and the Dana-Farber Cancer Institute, also takes a computational approach to biology. Her focus is oncology, and as with Dr. Hood, mathematics allows her to see relationships that yield results never before achieved.

    “An exciting example of something we’ve just finished,” she says “is learning to use existing drugs to treat cancer more effectively.”

    Dr. Michor goes on to say that while we do have drugs that are effective in treating cancer, these drugs also exert a powerful selective force on the cancer cells. As with any organism under severe evolutionary pressure, some members of a cancer cell population may acquire molecular changes that strengthen the clan’s chances of survival. The result: drug-resistant cancers.

    Dr. Michor’s research involves learning ways to administer the drugs differently so resistance doesn’t arise.

    “We can make a mathematical model that allows us to study the evolution of resistance cells and then we can use this mathematical model to identify treatment strategies that prevent or delay resistance,” she says, adding that she does this by looking at acquired resistance as a problem in evolution.

    Mathematical modeling works well for modeling evolutionary processes, and such modeling can provide otherwise-invisible insights into the biology of cancer. To study the evolutionary dynamics of resistance under time-varying dosing schedules and pharmacokinetic effects, the populations of sensitive and resistant cells are modeled as multitype nonhomogeneous birth–death processes.

    The drug concentration may affect the birth and death rates of both the sensitive and resistant cell populations in continuous time. This flexible model allows Dr. Michor and her colleagues to consider the effects of generalized treatment strategies as well as detailed pharmacokinetic phenomena such as drug elimination and accumulation over multiple doses.

    Computational tools enable them to develop estimates for the probability of developing resistance and the size of the resistant cell population. With these estimates, they are able to optimize treatment schedules over a subspace of tolerated schedules that minimize the risk of disease progression due to resistance.

    In addition they can locate ideal schedules for controlling the population size of resistant clones in situations where resistance is inevitable.

    This evolutionary mathematical modeling approach in cancer treatment will soon be in clinical trials. Dr. Michor believes that the ability to design optimal treatment strategies for preventing drug resistance may increase the benefits of therapy for many different cancer types.

  • Not Everyone’s Aboard

    Meanwhile, Dr. Michor is surprised by the resistance in the oncology community to mathematical techniques.

    “In physics or economics, it’s key to use math. In cancer research, while using statistics is accepted, it’s not a well-accepted idea to use math to see the underlying framework,” she points out.

    Dr. Michor suspects that oncology has not drawn many mathematicians because there are as yet few examples of successful applications in cancer biology. Odds are that with research like Dr. Michor’s, this will change.

  • Heart of Biology

    “The great book of nature can be read only by those who know the language in which it was written. And this language is mathematics.”

    —Galileo

    Eric Lander, Ph.D., director of the Broad Institute, also takes a highly mathematical approach to investigating biology. “Mathematics is now at the heart of biology,” he states, and his approach is helping pioneer new ways to understand the basis of disease.

    In his view, mathematics has extraordinarily expanded our ability to see patterns and connections. “It seems inconceivable,” he emphasizes, “that we could analyze the trillions of data points that we now collect without mathematics.”

    The trillions of data points he and his colleagues at Broad are developing come from: mapping and sequencing human, and other genomes; understanding the functional elements encoded in genomes through comparative analysis; understanding the genetic variation in the human population and its relationship to disease susceptibility; understanding the distinctive cellular signatures of diseases and of response to drugs; and understanding the mutations underlying cancer.

    “Using mathematics,” according to Dr. Lander, “we can compare the differences across species to show what evolution has conserved and not conserved. We can compare in an unbiased way the similarities and differences among tumors that do and do not respond to a drug. We can do discovery science by taking large datasets and by comparing information; and we can uncover a range of surprising hypotheses from the data that we never would have guessed.”

    Among the surprising discoveries is the fact that “the majority of the functional sequences in the human genome encode regulatory elements that we had been completely blind to. They emerge from cross-species comparisons.” In addition, these discoveries have revealed that thousands of genes don’t code for proteins.

    For Dr. Lander, the ultimate goal is for sequencing to become so simple and inexpensive that it can be routinely deployed as a general-purpose tool throughout biomedicine.

    To fulfill this potential, the cost of whole-genome sequencing will need eventually to approach a few hundred U.S. dollars.

    “With new approaches under development and market-based competition,” he says, “these goals may be feasible within the next decade.”

    Mathematics, with the help of increasingly fast, powerful, and cost-effective technologies is providing us with an ability to see what have up to now been hidden patterns of life. These mathematical insights provide powerful new approaches for understanding disease mechanisms, pioneering new diagnostics techniques, and rethinking how drug targets should be chosen.

    Today’s use of Darwin’s “new sense” is laying the foundation for addressing in ways never before possible many of the serious societal problems involving biologically based systems.


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