As many of the articles in this feature have indicated, biology is at a crossroads. Biologists have more data than they know what to do with, and mathematicians have the tools and expertise to begin to make sense of it. But mathematicians lack the fundamental knowledge of biology necessary to understand the results. Meanwhile, biologists grasp the systems they're studying, but they lack the tools needed to properly analyze the reams of data they produce.
These days more than ever before, mathematics undergrads are matriculating with at least some exposure to biology. Yet a big gap remains between the words of traditional biology and mathematics. That divide is certain to narrow and, perhaps, eventually disappear, but in the meantime, representatives of both fields must wax interdisciplinary if the promise of the genetic revolution is to be fulfilled. And this--genetics--is just one of many fields of biology where mathematics has started to make its mark.
For mathematicians who grasp biology, opportunities are plentiful. But which mathematicians? And which math? "People outside of the field see it as one uniform thing, but there are definitely different disciplines," says Steve Lincoln, who is vice president of Bioinformatics at Affymetrix Inc. in Santa Clara, California. "Pure math is the study of systems and equations, and the logical structure of things that are generally pretty abstract in nature. [On the other hand] if you are trained as a biostatistician, you're trained to do applied [work]. Some people wind up doing basic research for a living, but most apply [statistics] to a problem, be it [in the] life sciences, or health care, or modeling the stock market."
Biostatistics is big, but such basic mathematics tools such as differential equations--especially partial differential equations--are also useful. These equations are handy for tracking quantities in time and space--a quality just right for investigating systems and mechanisms, biological or otherwise. Variables might include metabolites of a cell, the strength of a neuron's signal over time, or the number of patients infected by a virus as it spreads over a geographical area.
Ordinary differential equations typically apply when several variables are a function of time, while partial differential equations get used when a variable is dependent on both time and space, says Michael Reed, a professor of mathematics at Duke University who applies mathematics to physiology and medicine. For example, a protein in a cell might start life in the nucleus and then move into the cytoplasm to take part in cell signaling. Hence the amount of protein in one area of the cell depends both on time and on the amount of protein somewhere else.
Academia and the National Institutes of Health (NIH) figure to be important employers of mathematicians that cross over into biology. "The experience in the human genome project was that 25% to 30% of every project's budget went into informatics. If you need to coordinate a lot of data, you need to devote significant resources to doing that. If some significant fraction of the NIH budget is going to large-scale projects, and a substantial fraction of each project's budget goes into informatics, that translates into a lot of jobs," says David States, who is a professor of bioinformatics at the University of Washington, Seattle.
Mathematics departments are on the look out for mathematicians well versed in biology. "You get mathematicians who don't really know much biology, or biologists who don't know much math. It's not so easy to find a mathematician who is trained well enough in biology to talk to biologists and be taken seriously. I see a big opportunity there in the foreseeable future," says Reinhardt Laubenbacher, a research professor at the Virginia Bioinformatics Institute  (VBI) and a mathematics professor at Virginia Polytechnic Institute and State University in Blacksburg. Laubenbacher should know; VBI just added one new research professor, bringing the number of permanent faculty to 15, as well as two visiting research scientists.
If the outlook is bright in academia, will there be similar heady times in industrial sectors like pharmaceuticals and biotechnology? Newspaper and magazine articles often quote corporate managers describing grand visions of computer simulations of disease states, as well as "in silico" drug design that could, it is argued, replace the battery of compounds churned out today by synthetic chemists, as well as the expensive animal tests used to weed out poor performers.
"It's a nice long-term goal, but we have a lot of work to do [to get there]," says States. "I'm not sure the pharmaceutical companies are investing in it right now. I think there's more of an empirical [frame of mind]: Don't show me a model, show me experimental data that I can show the Food and Drug Administration. And some of that may be appropriate. A lot of the modeling opportunities are probably more academic than commercial."
Still, it isn't all bad news for employment at big pharma and big biotech. Biostatisticians are in demand to assist with analysis of clinical trial data. Genetic data and analysis is playing an increasing role in clinical trials, with companies beginning to track side effects and sometimes responses of patients based on genetic markers (pharmacogenomics). "Biostatistics is one of the biggest employment opportunities in the pharmaceutical industry," says Robert Jernigan, director of the Laurence H. Baker Center for Bioinformatics and Biological Statistics at Iowa State University.
"Biologists have to pick up the mathematics"
But the onus isn't all on mathematicians. Biologists could use an infusion of mathematics as well, says Iya Khalil, vice president of R&D at Gene Network Sciences Inc. in Ithaca, New York. Biologists frequently run experiments that generate large amounts of data, but the usefulness of the data will likely depend on the design of the experiment. "In the realm of high-throughput experiments, often times [mathematicians] figure out that if the biologist had done the experiment in a particular way, it would have improved the statistics of the analysis by an order of magnitude," she says. By then it's too late.
"Biologists have to pick up the mathematics," agrees Laubenbacher. "If you want to use your data to make a mathematical model, then you need to take the modeling method into account when you design new experiments. Different modeling methods will require different kinds of data."
Mathematicians are following in the footsteps of physicists, who have crossed into biology in droves, in part because the work looks familiar to them, says Lincoln. "[Automated experiments] produce very large data sets, which tend to be multivariate in nature. In any biological experiment you can do on a large sale, you're bound to capture a variety of phenomena. One is the one you are interested in, and the other six or 600 are either noise or confounding factors. It's fairly analogous to the kind of work that physicists have been doing for years."
There are no limits on opportunities for mathematicians. "The work may not look fancy to pure mathematicians ... you may be using 19th century math. The intellectual difficulty is in the biology, and how to use the mathematics to study it," says Reed. And much depends on mathematics departments embracing biology so that students can get proper training. "I think they will, but it's a slow transition."
Read the companion article Profile: The Scrutable and the Inscrutable , also part of this Next Wave feature.