# Living Proof: MBI Celebrates the Future of Biomathematics

The Mathematical Biosciences Institute is ten years old. To mark the milestone, it did what institutes do: It held a meeting. Rather than a self-laudatory review of past accomplishments, MBI set its sights on the *future *of mathematical biology.

“This century *is* the century of biology,” Friedman said at the banquet. Much as math and physics partnered in the past, math and biology will partner well into the future. The burgeoning relationship is driven by the complexity of biological problems and by recent stunning technological developments in experimental and computational capabilities. Researchers are able to probe increasingly fine detail with increasing accuracy, presenting mathematical modelers and analysts with a firehose of data from which they can slake their simulated and theoretic thirst. The challenge for mathematical scientists will be to seize the opportunities presented by the partnership. “New math will not only advance biology,” Friedman says, “but new math will come out of it.”

### Slicing and Dicing the Data

Nicholas Jewell, a biostatistician at UC Berkeley, gave a glimpse of what lies ahead in the age of big data. “When I arrived in the school of public health at Berkeley [in 1981], there wasn’t a single computer anywhere in the department,” he recalls. Statisticians for the most part dealt with problems having a relatively small number of observations and variables. Nowadays, the pressing problems bristle with huge numbers of observations comprising ultra-high-dimensional data sets that often feature non-standard data (such as video or Tweets), giving rise to non-standard questions (e.g., Can you recognize an incipient flu epidemic based on Google searches?).

“Statisticians are at the fundamental core of every endeavor,” Jewell says. Of all the data currently stored, he points out, an estimated 90% was created in the last two years. It’s sometimes proposed that science can now dispense with theory and “just let the data speak.” Nothing could miss the mark more widely, Jewell says: “The more data we have, the more mistakes we seem to make.”

The core tasks haven’t changed. Statistics is vital in obtaining data, and cleaning and exploring it, as well as in modeling data, and drawing inferences in the presence of variation. Jewell described an analysis he and colleagues have done of an AIDS study known as the MIRA trial (Methods for Improving Reproductive Health in Africa). The trial, conducted in 2003–2006, assigned initially healthy women at random to a “control arm,” in which subjects were given only condoms and intensive condom counseling (the “gold standard” for HIV prevention), or an “intervention arm,” in which subjects received a diaphragm and contraceptive gel in addition to condoms and condom counseling.

From an “intention to treat” standpoint, the study was a wash: 158 of the 2472 women in the intervention arm were infected with HIV by the end of the trial, versus 151 of the 2476 women in the control arm. The researchers noted, however, that the intervention arm reported significantly less condom use (53.5%) than the control arm (85.1%), which might have cancelled a protective effect of the intervention. Indeed, a crude analysis adjusting for condom use suggests exactly that. But the Berkeley group found that a more detailed look at the data did not support such a conclusion. Their “direct effects” analysis, which took into account confounding factors and the time-dependent nature of the data, showed that the information in the study was not sufficient to tell whether the differential condom use was masking a benefit from the diaphragm.

New, sophisticated methods, such as direct effects analysis, will help wring the most out of the welter of data facing public health officials and better establish the limits on how the data can be interpreted. If you want to solve 21st-century problems, Jewell says, “you can’t use 20th-century statistics.”

### This Is Your Brain on Math

If public health is beset by confounding factors, the human brain is a tangle of differential equations. Nancy Kopell of Boston University and Emery Brown of MIT and Harvard Medical School gave talks on mathematical aspects of neuroscience, the subject of MBI’s current annual program. Kopell has spent decades studying the rhythms of thought; Brown has spent recent years trying to understand exactly what happens when he makes people *stop *thinking.

Somewhat more precisely, Kopell and colleagues are trying to understand the brain as a huge system of coupled oscillators. Some aspects of its dynamics are clarified with simple models based on a handful of excitatory and inhibitory cells, while other aspects demand large-scale computer simulations. Kopell described an ambitious project spearheaded by Michelle McCarthy of BU to establish the origin of pathological “beta” oscillations associated with Parkinson’s disease. Beta waves span a range of frequencies between 12 and 30 Hertz; everybody has them, but they are pronounced in people with Parkinson’s. One theory is that the abnormal oscillations are caused by structural changes in the network connecting fast-spiking interneurons and a class of inhibitory cells called medium spiny neurons in a portion of the brain known as the striatum. Such changes certainly occur. But the BU group has shown, both mathematically and experimentally, that the exaggerated dynamics can result more simply from neuromodulation in a normal network involving only medium spiny neurons.

Their work has implications for schizophrenia as well, for which the relevant oscillations are gamma rhythms (30–90 Hz). Structural changes are also evident in schizophrenics’ brains, but the mathematical biologists propose that, again, these may be secondary, the product of pathological dynamics in an otherwise normal network. Viewing things this way could suggest new treatments for brain disorders. A possible testbed, Kopell notes, can be found in studies of anesthesia, in particular of the paradoxical “beta buzz” observed when low (non-knock-out) doses of the anesthetic propofol are administered. Because the effects of anesthetics are clearly not structural in origin, anesthesia might be a good setting for modeling the pathological dynamics that can arise as perturbations of normal ones. “There is a huge amount of work left to be done,” Kopell says.

For his part, Brown, who is an anesthesiologist at Massachusetts General Hospital, would like to know how drugs like propofol work. The physiological effects of general anesthesia—chiefly unconsciousness and analgesia (inability to feel pain), but also amnesia and akinesia (inability to move—surgeons don’t want patients thrashing about on the operating table)—are well known, but nobody knows how they are achieved. Nor is it understood how the most important part occurs: getting patients to return to consciousness.

“It’s rather embarrassing,” Brown says, “when you walk into a room and you say you do something every day and you don’t know how it works.”

EEG-wise, general anesthesia has more in common with being in a coma than with being asleep, but patients prefer the latter, more reassuring term. Emery Brown is among the researchers who are studying mathematically what happens in the brain when drugs like propofol are administered. Reprinted with permission from “General Anesthesia, Sleep, and Coma,” December 10, 2010, New England Journal of Medicine, copyright 2013. |

Data-gathering opportunities abound: In the United States alone, general anesthesia is induced in nearly 60,000 patients every day. Brown and colleagues have worked with neurosurgeons who operate on epileptic patients who previously had high-density electrode grids implanted in their brains. “It gives us an opportunity to see a fair amount of natural brain,” Brown says. (Only a neuroscientist, accustomed to electrodes attached to isolated cells or brain slices, would describe tissue with implants as “natural.”) Their studies, which combine a wide array of signal processing techniques, have begun to offer specific hypotheses on how changes in activity level in neural circuits relate to unconsciousness. One of the promising possible applications is to the all-important step of helping patients regain consciousness: Instead of simply letting patients passively come to as the anesthetic wears off, with the common side effects of grogginess and disorientation, not to mention nausea, it might be possible to actively induce emergence in a way that returns the brain to a normal, alert state. Advances in understanding the neural pathways involved in anesthesia will likely further benefit the millions of people every year who go under the knife without having to watch.

### “A Place Where People Are Shaping a Field”

MBI is one of eight mathematical research institutes now funded by the National Science Foundation. (Its siblings, in alphabetical order, are the American Institute of Mathematics (AIM), in Palo Alto, California; the Institute for Advanced Study (IAS), in Princeton; the Institute for Computational and Experimental Research in Mathematics (ICERM), at Brown University; the Institute for Mathematics and its Applications (IMA), at the University of Minnesota; the Institute for Pure and Applied Mathematics (IPAM), at UCLA; the Mathematical Sciences Research Institute (MSRI), at UC Berkeley; and the Statistical and Applied Mathematical Sciences Institute (SAMSI), in Research Triangle Park, North Carolina.) MBI’s first program, in 2002–03, was in mathematical neuroscience, followed by programs on cell processes (2003–04), bioinformatics (2003–04), ecology and evolution (2004–05), and systems physiology (2005–06). The institute is revisiting neuroscience in its current program. It will dive into ecosystems this fall, look at imaging for the life sciences in the spring of 2014, and tackle cancer in 2014–15.

“The institute is about bringing people together,” says Marty Golubitsky, who took over as director of MBI in 2008. In remarks at the banquet honoring his predecessor, Golubitsky noted that more than 9000 visitors have attended over a hundred workshops and other events since MBI opened shop. A substantial portion of them are MBI’s postdocs, whom Golubitsky calls “the lifeblood of the institute.”

Two postdocs also spoke at the banquet. “We were here when MBI was new and exciting,” says Janet Best (to laughter at the implication that MBI is now old and exciting). Best, who is now in the mathematics department at Ohio State, was in the second cohort of postdocs, back when the institute was in an old space “centered around an espresso machine—a highly caffeinated but very, very warm experience.” She thanked Friedman for being “both a scientific and a professional mentor,” and described MBI as “a place you can come and take a chance.”

“I had a really fantastic time,” enthused Marisa Eisenberg, who was a postdoc from 2009 to 2012 and is now an assistant professor of epidemiology at the University of Michigan. “I feel like I really grew up as a researcher.” Eisenberg especially liked the blend of independence and mentoring she experienced. “The community at MBI is amazing,” she says. “You get to be in a place where people are shaping a field.”

And what shape is the field taking? Mike Reed, the senior scientific adviser of MBI, pointed out that mathematical bioscience has broadened in two important directions. On the one hand, the application of mathematics to medical and field biology is coming to the fore, he says, while on the other hand, “pure mathematics has discovered all the fantastic problems that arise in mathematical biology.” As for MBI’s role in the field’s future, Golubitsky summed it up this way: “We’ll just try to do better what we already do well.”

*Readers can find “Modeling the Origin of Eusociality,” William Kolata’s report on Martin Nowak’s keynote presentation at the MBI 10th-anniversary meeting, in the March 2013 issue of *SIAM News*.