MATH NEWS

March 09, 2010 How the human genome folds in 3-D tech.mit.edu Erez Lieberman-Aiden G invented a way to find out how the genome folds. Lieberman-Aiden wins 2010 Lemelson-MIT Student Prize By Ana Lyons NEWS EDITOR March 9, 2010 Until recently, the process of how genomic DNA neatly folds itself into the nucleus of a cell — twisting and contorting into a work of astonishingly compact molecular origami — had perplexed biologists. When unstretched onto its two-dimensional, double-helix form, the human genome spans nearly two meters in length, yet it must fit inside the cell nucleus, which is only a hundredth of a millimeter in diameter. How exactly the genome can compress into an unknown three-dimensional structure and retain some sort of underlying order, all while persisting tangle-free, remained a fundamental mystery in structural biology. But last fall, Erez Lieberman-Aiden — a seventh year graduate student at the Harvard-MIT Division of Health Sciences and Technology — developed a new technique for creating 3-D genomic maps called “Hi-C.” His results led him to theorize that the structure of the human genome follows a fractal-like pattern, forming super-dense, knot-free “globules of globules of globules” in order to overcome their troublesome spatial and entanglement problems. For leading this groundbreaking research, Lieberman-Aiden was awarded this year’s $30,000 Lemelson-MIT 2010 Student Prize last Wednesday at a ceremony held in the Bartos Theater at the MIT Media Lab. In contrast to previous “equilibrium globule” model of the human genome — where related regions often occur far apart in three dimensions and various components are highly entangled — Lieberman-Aiden’s “fractal globule” model suggests that the genome separates into two clear compartments: one where stretches of DNA are known to be active, and another where DNA is inactive and stowed away for future use. Whether or not this organizational model will hold for other cell types, however, is currently unclear. Lieberman-Aiden was also recognized by the Prize committee for his linguistics research (which appeared on the cover of Nature in 2007), for founding a new field of mathematical biology known as “evolutionary graph theory” (published in Nature in 2005), and for developing an electronic insole for diagnosing poor balance in the elderly (called the “iShoe”). Other finalists were Barry M. Kudrowitz and Amos G. Winter, both current Ph.D. students in Mechanical Engineering. According to the Lemelson Foundation, the $30,000 Lemelson-MIT Student Prize is awarded annually to “an MIT senior or graduate student who has created or improved a product or process, applied a technology in a new way, redesigned a system, or demonstrated remarkable inventiveness in other ways.” Students apply to the competition in an intensive process that requires essays and letters of recommendation. A panel of ten MIT judges who are “alumni including scientists, technologists, engineers and entrepreneurs” then choose the winner. “I was very, very excited,” said Lieberman-Aiden. Applications are now being accepted for the 2011 Lemelson-MIT Student Prize. Full details on the application process can be found here: http://web.mit.edu/invent/a-student.html How Hi-C Works To develop the “Hi-C” method — which constructs three-dimensional maps of entire genomes — Lieberman-Aiden worked with postdoctoral student Nynke van Berkum of UMass Medical School, and their advisors Eric S. Lander and Job Dekker. The team also collaborated with Leonid Mirny’s group (in the MIT Department of Physics and Harvard-MIT Division of Health Sciences and Technology) as well as graduate student Maksim V. Imakaev to simulate of the dynamic behavior of the fractal globule. “I’ve thought about [the idea] for quite some time,” Lieberman-Aiden said. “Earlier in 2007, I saw a talk where I heard it took six months to figure out that two pieces in the genome were touching,” he said. “I remember thinking ‘gosh, that’s a really long time.’” After seeing this talk, “I thought we could do better and take advantage of modern sequencing technology,” he said. Based on these initial ideas, Lieberman-Aiden and his colleagues developed their “Hi-C” method, which uses formaldehyde to freeze linkages of DNA that are far apart in the linear genome, but adjacent to each other in 3-D. The linked pieces of DNA are then marked with biotin, extracted, and mapped onto the reference copy of the human genome to determine which loci neighbor each other. To complete the process, a computer cross-references neighboring gene pairs and assemble the genome’s 3-D portrait. In Lieberman-Aiden’s words, Hi-C is like “figuring out who is friends with who.” “Imagine one day there is a security breach on Facebook, and all the pictures were now leaked to the public,” he said. From the leaked data, you can see if there are patterns where people show up in the same pictures. “If people keep showing up in the same pictures over and over again, you can concluded that they’re probably friends,” he said. “It’s the same idea is behind the 3-D technique, but instead of determining friends, we’re determining who’s nearby in 3-D space,” he said. “We know the 1-D sequence of the human genome, so we can use this as a reference when we reconstruct what the 3-D architecture must be like.” Lieberman-Aiden also posted an interpretive dance of how the technique works, which can be found on YouTube at: http://www.youtube.com/watch?v=06UouUmuEbw Local biochemical vs. global spatial modifications “A very interesting idea at the core [of this research] is that all cells have the same genome, but perform very different functions,” Lieberman-Aiden said. “There’s an incredible variety of functions among cells, despite them all having the same information.” In the past, differing function “has all been associated with local biochemical modifications: biochemical changes at certain sites in the genome, making certain [information] get turned on and off,” he said. For example, “by adding or subtracting methyl groups, you can introduce instructions saying things like ‘you should express this more,’ but these biochemical changes are all occurring locally.” But “here we find that it’s actually spatial modifications that can influence expression,” on the “global scale,” he explained. “It’s a totally different type of modification.” Lieberman-Aiden used an analogy, likening the genome to a newspaper. When thinking of the genome, “imagine a paper with writing on it, maybe even a newspaper....maybe even The Tech,” he said. If everything on the page you were reading were the same dull font, you’d start reading somewhere at random, with no idea of what was most important that day, he said. Suppose you’d like to change how various things are emphasized. “One thing you can do [to emphasize what’s most important] is underline things, make boxes around words — make various local modifications.” “These modifications would tell you ‘Ahh...I should pay attention to this,” he said. In a newspaper, these modifications might be the style of a headline or a box of color, and in the case of the genome, these would all be biochemical modifications. But then say you realize there’s also another way to emphasize different things, which would affect the organization of the contents more globally: “Let me fold the paper in little ways and actually change what appears on the front page.” Just as the different types of cells fold their genomes differently depending on their function. “Depending who you are and what you want to read about, you might fold the newspaper in different ways,” he said. For example, “if you’re trying to sell the paper at a newstand, you might fold the paper in one way. But if you’re the president of the MIT origami club, you might decide to fold it into a crane instead.” Similarly, if you put different sections in the front, you’ll get different newspapers, explains Lieberman-Aiden. For example “If you put business in front, you’ll have the Wall Street Journal.” And in the case of the cell, “in doing these reconfigurations [of the genome], you can control what’s on and off and thereby change the function of the cell as a whole.” “It’s another type of way to modify a sort of universal substrate, and the genome is basically doing the same thing….different ways you configure the genome could give you different functions or identities,” he said. Human genome is organized like a library…made of ramen Lieberman-Aiden’s and his team also zoomed in further, examining how the genome folds at the scale of a megabase, or one million of the genome’s biochemical ‘letters’. The question was: “How does this megabase fold up?” To help think this question, Lieberman-Aiden recalled an analogy that had been suggested to him by Leonid Mirny, Professor of Physics and Health Science and Technology. “A genome contains information, a library of information.” In this case, “you can imagine that [the human genome] should therefore be organized like a library,” he said. “How should you organize a library? Well, you want it to be compact: everything is in one place. You want it to be organized: books on similar topics should be physically near each other. And you want it to be accessible: when you find the book you want, it shouldn’t be behind glass; you should be able to pull it off the shelf, read through it, and then put it back the same way you found it.” Knowing this, the next question he said one might ask is: “how might one design such a library?” “It turns out the standard way that a polymer might fold is totally incoherent with that [ideal library]; it’d be dense, but it would be totally disorganized and completely knotted,” he explained. And “because it’s highly knotted, the information isn’t at all accessible,” he said. But his Hi-C data, suggests that the genome forms an unknotted macroglobule or what the team calls a “fractal globule” — which interestingly, Lieberman-Aiden says in many ways is like a package of ramen noodles. “It turns out actually that the fractal globule pretty deeply resembles the model of uncooked ramen noodles,” he said. “You can contrast this with the classic polymer structure, which is the arrangement that the noodles take once you’ve cooked them.” If you “turn up the heat, and the noodles are going to oscillate and wiggle...and in the process they’ll get deeply, deeply entangled,” he said. According to Lieberman-Aiden, “this is similar to the classic polymer conformation,” called the “equilibrium globule model.” In the ramen analog of the equilibrium globule model of the genome, “the most salient property was that if you stick a fork in them, you can’t pull apart one or two noodles: you end up pulling out a whole clump because they are so entangled.” “The fractal globule module is more like the uncooked ramen, whereas the classic equilibrium model of condensed polymers is more like the cooked noodles,” he said. “Space-filling fractal curves pack space very, very densely, but can do this without knotting,” he said. If you want to access something from a fractal globule structure, “you can just pull out a little piece and stretch it out to examine it. When you’re finished, you can just crumple it back up, and put it back where it came from,” making their use especially advantageous in the genome. As one additional property of the “fractal globular” model — like in the case of ramen — is “if something is nearby in 1-D, it will be nearby in physical space,” he said. “This may be why genes that are related in function tend to cluster in 1-D; by doing so, they are actually forming a spatial cluster when they fold up in 3-D.” Peano curves appear in genome Lieberman-Aiden’s research showed that the human genome likely forms fractal-like structures, but that’s only the half of it. These fractals can then be reduced down even further to “Peano curves” in order to store less often-used genes and pack them more densely — a type of curve which Lieberman-Aiden says has a particularly interesting history. As the first person who discovered such a curve, back in 1890, Giuseppe Peano was motivated by mathematics of the time to construct what Lieberman-Aiden calls “an extremely, extremely peculiar curve.” Lieberman-Aiden said the Peano curve is what’s known is mathematics as a “space-filling curve.” “Even though it is one dimensional, it can fill space so densely that it resembles higher dimensional objects,” he said. The discovery of this type of curve “blew mathematicians minds, and it really messed with their ideas of dimension.” But after “Peano constructed this thing, and it led to a lot of rethinking of basic questions in math, eventually the mathematical agenda moved on.” “It never really occurred to anyone that any actual existing contour in the world would resemble this structure,” he said, “until a team of physicists, nearly 100 years later, suggested that the initial state of a condensing polymer might resemble a Peano curve. But the observational evidence was limited until now.” So for Lieberman-Aiden, a trained mathematician, to discover than the human genome may actually incorporate these curves is especially exciting. Influence of cross-training in math and physics Before coming to MIT as a graduate student, Lieberman-Aiden studied mathematics, physics, and philosophy at Princeton as an undergrad. When asked about the influence of this training on his interdisplinary work in biology, he said that it doubtlessly contributed to his current views on research. “I think that the analytic techniques you learn by doing math and physics are very powerful and really can help you,” he said. “It really helps me usually when I’m analyzing data; sometimes I’m not really straining myself because I got really comfortable with thinking quantitatively as an undergrad.” “Because of background, that actually means that I have an extra gear or two,” he said. “If I find a problem where I think that there might be a good opportunity, I’ll use that extra gear. It also means that the extra exposure to mathematical and physical techniques and literature exposes me to ideas like the fractal globule,” he said. After completing graduate school, likely within the next year, Lieberman-Aiden said that he will continue his research on Hi-C on a Harvard Junior Fellowship at the Harvard Society of Fellows. How the human genome folds in 3-D

March 09, 2010 Charles P. Thacker Named Recipient of 2009 ACM A.M. Turing Award www.acm.org Photo Courtesy of the NAE Pioneer Honored for Design of First Modern Personal Computer and Other Major Innovations ACM has named Charles P. Thacker the recipient of the 2009 ACM A.M. Turing Award for his pioneering design and realization of the Alto, the first modern personal computer, and the prototype for networked personal computers. Alto incorporated bitmap (TV-like) displays, which enable modern graphical user interfaces (GUIs), including What You See Is What You Get (WYSIWYG) editors. Thacker's design, which he built while at Xerox PARC (Palo Alto Research Center), reflected a new vision of a self-sufficient, networked computer on every desk, equipped with innovations that are standard in today's models. Dr. Thacker is also recognized for his contributions to the Ethernet local area network, the "interconnection fabric" that allows multiple digital devices such as workstations, printers, scanners, file servers, and modems to communicate with each other. Today's Ethernets, which are thousands of times faster than the original version, have become the dominant local area networking technology. He also designed the first multiprocessor workstation, and the prototype for today's most used tablet PC, with its capabilities for direct user interaction. The ACM A.M. Turing Award is ACM's most prestigious technical award. It recognizes contributions of lasting and major technical importance, and honors individuals whose work has advanced the field of computing. First presented in 1966, and named for British mathematician Alan M. Turing, the Turing Award is widely considered to be the "Nobel Prize in Computing." It carries a $250,000 prize, with financial support provided by Intel Corporation and Google Inc. Learn more, read the ACM Press Release or visit the ACM A.M. Turing Award site. Charles P. Thacker Named Recipient of 2009 ACM A.M. Turing Award

March 09, 2010 Leaf veins inspire a new model for distribution networks newswire.rockefeller.edu Veins’ looped network allows water and nutrients to flow around an injury (green dot) on the main vein of a lemon leaf. Credit: E. Katifori et al/PRL 2010 Posted: February 9, 2010 A straight line may be the shortest path from A to B, but it’s not always the most reliable or efficient way to go. In fact, depending on what’s traveling where, the best route may run in circles, according to a new model that bucks decades of theorizing on the subject. A team of biophysicists at Rockefeller University developed a mathematical model showing that complex sets of interconnecting loops — like the netted veins that transport water in a leaf — provide the best distribution network for supplying fluctuating loads to varying parts of the system. It also shows that such a network can best handle damage. The findings could change the way engineers think about designing networks to handle a variety of challenges like the distribution of water or electricity in a city. Operations researchers have long believed that the best distribution networks for many scenarios look like trees, with a succession of branches stemming from a central stalk and then branches from those branches and so on, to the desired destinations. But this kind of network is vulnerable: If it is severed at any place, the network is cut in two and cargo will fail to reach any point “downstream” of the break. By contrast, in the leaves of most complex plants, evolution has devised a system to distribute water that is more supple in at least two key ways. Plants are under constant attack from bugs, diseases, animals and the weather. If a leaf’s distribution network were tree-like and damaged, the part of the leaf downstream of the damage would starve for water and die. In some of the Earth’s more ancient plants, such as the gingko, this is the case. But many younger, more sophisticated plants have evolved a vein system of interconnected loops that can reroute water around any damage, providing many paths to any given point, as in the lemon leaf . Operations researchers have appreciated that these redundancies are an effective hedge against damage. What’s most surprising in the new research, according to Marcelo O. Magnasco, head of the Laboratory of Mathematical Physics at Rockefeller University, is that the complex network also does a better job of handling fluctuating loads according to shifts in demand from different parts of the system — a common real-world need within dynamic distribution networks. “For decades, people have believed that the tree-like network was optimal for fluctuating demand,” Magnasco says. “These findings could seriously shake things up. People will have to take another look at how they design these kinds of systems.” In a paper published as the cover story of the January 29 Physical Review Letters, Magnasco, lead researcher Eleni Katifori, a fellow at Rockefeller’s Center for Studies in Physics and Biology, and colleagues lay out a model that assigns a cost to each section of leaf vein proportional to how much water it can carry. They looked for networks that suffered the least strain in the face of two challenges common in both leaves and human-built networks: damage to a randomly chosen segment of the network and changes in the load demanded by different parts of the network. In both scenarios, they found the most robust system was a complex, hierarchical network of nested loops, similar to the fractal-like web of veins that transport water in leaves. This loopy network design is also found in the blood vessels of the retina, the architecture of some corals and the structural veins of insect wings. Katifori is now extending the research to delve more deeply into how distribution networks handle fluctuating loads, guided by nature’s own solution in the leaf. “It is tempting to ignore the loops, because the central veins stand out and have a tree-like form,” Katifori says. “But they are all connected, and the loops are right there to see, if you just look at the leaf.” Leaf veins inspire a new model for distribution networks

March 09, 2010 Mathematician, longtime Vanderbilt professor Charles K. Megibben dies sitemason.vanderbilt.edu Charles K. Megibben 3/5/2010 10:12 am Charles K. Megibben, who played a major role in developing the mathematics department of Vanderbilt University into a major research center, has died. He was 73. Megibben, an internationally acknowledged leader in the theory of abelian groups, a major field of algebra, died March 2 in Nashville while undergoing heart surgery. He was a professor of mathematics, emeritus. “Charles Megibben is one of the people who steered us in the right direction,” said Matthew Gould, professor of mathematics, emeritus. “He pushed very hard for more research in the department.” Megibben, a native of Lexington, Ky., came to Vanderbilt in 1967 after earning a Ph.D in math from Auburn University and short teaching stints at Texas Tech College and the University of Washington. He was known to eschew the published textbooks, instead preparing and distributing lecture notes to present mathematical theories. Some of his colleagues taught using Megibben’s lecture notes, Gould said. “My office was rather near his,” Gould said. I’d very often hear him speaking with undergrads with math questions, and his blackboard was always filled with notations from those sessions. He was very popular among students.” Megibben became a professor of mathematics, emeritus, in 2005. Survivors include wife Dottie Megibben, four sons, one daughter, one brother, nieces, nephews, grandchildren and great-grandchildren. Funeral services were scheduled for 4 p.m. March 5 at Phillips-Robinson Funeral Home, 2707 Gallatin Road. Media contact: Jim Patterson, (615) 322-NEWS jim.patterson@vanderbilt.edu Mathematician, longtime Vanderbilt professor Charles K. Megibben dies

March 02, 2010 The Mathematics Of Cancer www.forbes.com Larry Norton Larry Norton is pushing a radical new theory of how cancer spreads--and how to cure it. Robert Langreth, 02.25.10, 08:40 AM EST Forbes Magazine dated March 15, 2010 Larry Norton sees some of the toughest cases as deputy physician-in-chief for breast cancer at Memorial Sloan-Kettering Cancer Center. He has access to the most advanced imaging machines, the best surgeons and numerous new tumor-fighting drugs. But often the fancy technology helps only temporarily. Sometimes a big tumor will shrink dramatically during chemotherapy. Then all of a sudden it comes back in seven or eight locations simultaneously. Norton thinks adding more mathematics to the crude science of cancer therapy will help. He says that oncologists need to spend much more time devising and analyzing equations that describe how fast tumors grow, how quickly cancer cells develop resistance to therapy and how often they spread to other organs. By taking such a quantitative approach, researchers may be able to create drug combinations that are far more effective than the ones now in use. "I have a suspicion that we are using almost all the cancer drugs in the wrong way," he says. "For all I know, we may be able to cure cancer with existing agents." His strategy is unusual among cancer researchers, who have tended to focus on identifying cancer-causing genes rather than writing differential equations to describe the rate of tumor spread. Yet adding a dose of numbers has already led to important changes in breast cancer treatment. The math of tumor growth led to the discovery that just changing the frequency of chemo treatments can boost their effect significantly. In the future Norton's theorizing may lead to new classes of drugs. Researchers have always assumed tumors grow from the inside out. His latest theory, developed in collaboration with Sloan-Kettering biologist Joan Massagué, asserts that tumors grow more like big clusters of weeds. They are constantly shedding cells into the circulatory system. Some of the cells form new tumors in distant places. But other wayward cells come back to reseed the original tumor, making it grow faster. It's like hardened terrorists returning to their home villages after being radicalized abroad and recruiting even more terrorists, says Massagué, who in December showed that the self-seeding process happens in laboratory mice. If this model works in humans, it will open up new avenues for treatment. It suggests that to cure cancer, doctors need to come up with drugs that stop the seeding process. These drugs may be different from the current crop of drugs, which are designed to kill fast-dividing cells. Among other mysteries, self-seeding may explain why tumors sometimes regrow in the same location after being surgically removed: not necessarily because surgeons failed to remove part of the original tumor but because some itinerant cancer cells returned later to their original home to start a new tumor in the same place. Norton, 62, got a degree in psychology from the University of Rochester, then an M.D. from Columbia University. For a while during college he thought he would make a career as a saxophonist and percussionist. The remnant of that dream is a vibraphone in his office in Memorial's new 16-story breast cancer center. Ever since he was a fellow at the National Cancer Institute in the 1970s he has been trying to come up with mathematical laws that describe tumor growth. He treated a lymphoma patient whose tumor shrank rapidly during chemotherapy. A year later the cancer returned worse than ever. The speed with which the tumor grew back didn't jibe with the prevailing notion that most tumors grew in a simple exponential fashion. Working with NCI statistician Richard Simon, Norton came up with a new model of tumor growth based on the work of the 19th-century mathematician Benjamin Gompertz. The concept (which other researchers proposed in the 1960s) holds that tumor growth generally follows an S-shape curve. Microscopic tumors below a certain threshold barely grow at all. Small tumors grow exponentially, but the rate of growth slows dramatically as tumors get bigger, until it reaches a plateau. A corollary of this: The faster you shrink a tumor with chemo, the quicker it will grow back if you haven't killed it all. Based on these rates of growth, Norton argued that giving the same total dose of chemotherapy over a shorter period of time would boost the cure rate by limiting the time tumors could regrow between treatments. The concept got a skeptical reaction initially. "People said it was a total waste of time," he recalls. It took decades before Norton was able to prove his theory. But in 2002 a giant government trial showed that giving chemotherapy every two weeks instead of every three lowered the risk of breast cancer recurrence by 26% over three years, even though the two groups got the same cumulative dose. Today Norton's "dose-dense" regimen is common practice for certain breast cancer patients at high risk of relapse after surgery. Timing adjustments are also showing promise in other tumor types. Last October a Japanese trial found that ovarian cancer patients lived longer if they received smaller doses of chemotherapy weekly rather than getting larger doses every three weeks, according to results published in The Lancet. "Larry has been one of the real thinkers in this area," says Yale University professor and former NCI head Vincent DeVita. But designing better treatment schedules doesn't get as much credit as the glamorous business of inventing drugs. Norton's latest theory about how tumors grow is derived from Massagué's pioneering research. It is consistent with Gompertz's growth curves and ties together two essential features of cancer that researchers had long considered separate--cell growth and metastasis. Their collaboration started five years ago, when Massagué called Norton and shared a startling finding that was emerging from his laboratory. Massagué was studying how tumors spread from an organ such as the breast to the lungs, brain and other faraway places. He took human breast tumor cells, implanted them in mice and waited for metastases to occur. He analyzed cells that had metastasized to see what genes were overactive. None of the genes implicated in the spread of cancer to distant organs had to do with excessive cell division, it turned out. Instead, they all related to the ability to infiltrate and adapt to new environments. The finding seemed to contradict doctors' impression that the fastest-growing tumors are also the most likely to spread. Pondering how to reconcile the two ideas, Norton and Massagué theorized that tumor cells released into the bloodstream sometimes are attracted back to the original tumor and help it expand. Self-seeding may explain why large tumors tend to grow (in percentage terms) more slowly than small tumors: It could be that growth is a function of surface area rather than volume. Tumors that are efficient seeders may kill people by promoting the seeding process, not because they have a higher exponential growth rate. It took Massagué four years of work to prove that self-seeding occurs in laboratory mice. Now comes the tricky part: coming up with drugs that block tumor seeding. Massagué and Norton have identified four genes involved in seeding and are testing for drugs to block them. Convincing drug companies to go along could be difficult; it's easier to see whether a drug shrinks tumors than to see whether it stops evil cells from spreading. But Norton believes that doing this hard work may be the key to a cure. The Mathematics Of Cancer

March 02, 2010 Fill in the Blanks: Using Math to Turn Lo-Res Datasets Into Hi-Res Samples www.wired.com Using a mathematical concept called sparsity, the compressed-sensing algorithm takes lo-res files and transforms them into sharp images. Illustration: Gabriel Peyre By Jordan Ellenberg February 22, 2010 | 12:00 pm | Wired March 2010 In the early spring of 2009, a team of doctors at the Lucile Packard Children’s Hospital at Stanford University lifted a 2-year-old into an MRI scanner. The boy, whom I’ll call Bryce, looked tiny and forlorn inside the cavernous metal device. The stuffed monkey dangling from the entrance to the scanner did little to cheer up the scene. Bryce couldn’t see it, in any case; he was under general anesthesia, with a tube snaking from his throat to a ventilator beside the scanner. Ten months earlier, Bryce had received a portion of a donor’s liver to replace his own failing organ. For a while, he did well. But his latest lab tests were alarming. Something was going wrong — there was a chance that one or both of the liver’s bile ducts were blocked. Shreyas Vasanawala, a pediatric radiologist at Packard, didn’t know for sure what was wrong, and hoped the MRI would reveal the answer. Vasanawala needed a phenomenally hi-res scan, but if he was going to get it, his young patient would have to remain perfectly still. If Bryce took a single breath, the image would be blurred. That meant deepening the anesthesia enough to stop respiration. It would take a full two minutes for a standard MRI to capture the image, but if the anesthesiologists shut down Bryce’s breathing for that long, his glitchy liver would be the least of his problems. However, Vasanawala and one of his colleagues, an electrical engineer named Michael Lustig, were going to use a new and much faster scanning method. Their MRI machine used an experimental algorithm called compressed sensing — a technique that may be the hottest topic in applied math today. In the future, it could transform the way that we look for distant galaxies. For now, it means that Vasanawala and Lustig needed only 40 seconds to gather enough data to produce a crystal-clear image of Bryce’s liver. Compressed sensing was discovered by chance. In February 2004, Emmanuel Candès was messing around on his computer, looking at an image called the Shepp-Logan Phantom. The image — a standard picture used by computer scientists and engineers to test imaging algorithms — resembles a Close Encounters alien doing a quizzical eyebrow lift. Candès, then a professor at Caltech, now at Stanford, was experimenting with a badly corrupted version of the phantom meant to simulate the noisy, fuzzy images you get when an MRI isn’t given enough time to complete a scan. Candès thought a mathematical technique called l1 minimization might help clean up the streaks a bit. He pressed a key and the algorithm went to work. Candès expected the phantom on his screen to get slightly cleaner. But then suddenly he saw it sharply defined and perfect in every detail — rendered, as though by magic, from the incomplete data. Weird, he thought. Impossible, in fact. “It was as if you gave me the first three digits of a 10-digit bank account number — and then I was able to guess the next seven,” he says. He tried rerunning the experiment on different kinds of phantom images; they resolved perfectly every time. Candès, with the assistance of postdoc Justin Romberg, came up with what he considered to be a sketchy and incomplete theory for what he saw on his computer. He then presented it on a blackboard to a colleague at UCLA named Terry Tao. Candès came away from the conversation thinking that Tao was skeptical — the improvement in image clarity was close to impossible, after all. But the next evening, Tao sent a set of notes to Candès about the blackboard session. It was the basis of their first paper together. And over the next two years, they would write several more. That was the beginning of compressed sensing, or CS, the paradigm-busting field in mathematics that’s reshaping the way people work with large data sets. Only six years old, CS has already inspired more than a thousand papers and pulled in millions of dollars in federal grants. In 2006, Candès’ work on the topic was rewarded with the $500,000 Waterman Prize, the highest honor bestowed by the National Science Foundation. It’s not hard to see why. Imagine MRI machines that take seconds to produce images that used to take up to an hour, military software that is vastly better at intercepting an adversary’s communications, and sensors that can analyze distant interstellar radio waves. Suddenly, data becomes easier to gather, manipulate, and interpret. Compressed sensing works something like this: You’ve got a picture — of a kidney, of the president, doesn’t matter. The picture is made of 1 million pixels. In traditional imaging, that’s a million measurements you have to make. In compressed sensing, you measure only a small fraction — say, 100,000 pixels randomly selected from various parts of the image. From that starting point there is a gigantic, effectively infinite number of ways the remaining 900,000 pixels could be filled in. The key to finding the single correct representation is a notion called sparsity, a mathematical way of describing an image’s complexity, or lack thereof. A picture made up of a few simple, understandable elements — like solid blocks of color or wiggly lines — is sparse; a screenful of random, chaotic dots is not. It turns out that out of all the bazillion possible reconstructions, the simplest, or sparsest, image is almost always the right one or very close to it. But how can you do all the number crunching that is required to find the sparsest image quickly? It would take way too long to analyze all the possible versions of the image. Candès and Tao, however, knew that the sparsest image is the one created with the fewest number of building blocks. And they knew they could use l1 minimization to find it and find it quickly. To do that, the algorithm takes the incomplete image and starts trying to fill in the blank spaces with large blocks of color. If it sees a cluster of green pixels near one another, for instance, it might plunk down a big green rectangle that fills the space between them. If it sees a cluster of yellow pixels, it puts down a large yellow rectangle. In areas where different colors are interspersed, it puts down smaller and smaller rectangles or other shapes that fill the space between each color. It keeps doing that over and over. Eventually it ends up with an image made of the smallest possible combination of building blocks and whose 1 million pixels have all been filled in with colors. That image isn’t absolutely guaranteed to be the sparsest one or the exact image you were trying to reconstruct, but Candès and Tao have shown mathematically that the chance of its being wrong is infinitesimally small. It might still take a few hours of laptop time, but waiting an extra hour for the computer is preferable to shutting down a toddler’s lungs for an extra minute. Compressed sensing has already had a spectacular scientific impact. That’s because every interesting signal is sparse — if you can just figure out the right way to define it. For example, the sound of a piano chord is the combination of a small set of pure notes, maybe five at the most. Of all the possible frequencies that might be playing, only a handful are active; the rest of the landscape is silent. So you can use CS to reconstruct music from an old undersampled recording that is missing information about the sound waves formed at certain frequencies. Just take the material you have and use l1 minimization to fill in the empty spaces in the sparsest way. The result is almost certain to sound just like the original music. With his architect glasses and slightly poufy haircut, Candès has the air of a hip geek. The 39-year-old Frenchman is soft-spoken but uncompromising when he believes that something isn’t up to his standards. “No, no, it is nonsense,” he says when I bring up the work of a CS specialist whose view on a technical point differs — very slightly, it seems to me — from his own. “No, no, no, no. It is nonsense and it is nonsense and it is wrong.” Candès can envision a long list of applications based on what he and his colleagues have accomplished. He sees, for example, a future in which the technique is used in more than MRI machines. Digital cameras, he explains, gather huge amounts of information and then compress the images. But compression, at least if CS is available, is a gigantic waste. If your camera is going to record a vast amount of data only to throw away 90 percent of it when you compress, why not just save battery power and memory and record 90 percent less data in the first place? For digital snapshots of your kids, battery waste may not matter much; you just plug in and recharge. “But when the battery is orbiting Jupiter,” Candès says, “it’s a different story.” Ditto if you want your camera to snap a photo with a trillion pixels instead of a few million. The ability to gather meaningful data from tiny samples of information is also enticing to the military: Enemy communications, for instance, can hop from frequency to frequency. No existing hardware is fast enough to scan the full range. But the adversary’s signal, wherever it is, is sparse — built up from simple signals in some relatively tiny but unknown portion of the frequency band. That means CS could be used to distinguish enemy chatter on a random band from crackle. Not surprisingly, Darpa, the Defense Department’s research arm, is funding CS research. Compressed sensing isn’t useful just for solving today’s technological problems; the technique will help us in the future as we struggle with how to treat the vast amounts of information we have in storage. The world produces untold petabytes of data every day — data that we’d like to see packed away securely, efficiently, and retrievably. At present, most of our audiovisual info is stored in sophisticated compression formats. If, or when, the format becomes obsolete, you’ve got a painful conversion project on your hands. But in the CS future, Candès believes, we’ll record just 20 percent of the pixels in certain images, like expensive-to-capture infrared shots of astronomical phenomena. Because we’re recording so much less data to begin with, there will be no need to compress. And instead of steadily improving compression algorithms, we’ll have steadily improving decompression algorithms that reconstruct the original image more and more faithfully from the stored data. That’s the future. Today, CS is already rewriting the way we capture medical information. A team at the University of Wisconsin, with participation from GE Healthcare, is combining CS with technologies called HYPR and VIPR to speed up certain kinds of magnetic resonance scans, in some cases by a factor of several thousand. (I’m on the university’s faculty but have no connection to this particular research.) GE Healthcare is also experimenting with a novel protocol that promises to use CS to vastly improve observations of the metabolic dynamics of cancer patients. Meanwhile, the CS-enabled MRI machines at Packard can record images up to three times as quickly as conventional scanners. And that was just enough for 2-year-old Bryce. Vasanawala, in the control room, gave the signal; the anesthesiologist delivered a slug of sedative to the boy and turned off his ventilator. His breathing immediately stopped. Vasanawala started the scan while the anesthesiologist monitored Bryce’s heart rate and blood oxygenation level. Forty seconds later, the scan was done and Bryce had suffered no appreciable oxygen loss. Later that day, the CS algorithm was able to produce a sharp image from the brief scan, good enough for Vasanawala to see the blockages in both bile ducts. An interventional radiologist snaked a wire into each duct, gently clearing the blockages and installing tiny tubes that allowed the bile to drain properly. And with that — a bit of math and a bit of medicine — Bryce’s lab test results headed back to normal. Jordan Ellenberg (ellenber@math.wisc.edu), an associate professor of mathematics at the University of Wisconsin, wrote about the Netflix Prize in issue 16.03. Fill in the Blanks: Using Math to Turn Lo-Res Datasets Into Hi-Res Samples

March 02, 2010 OKIE IN EXILE: My life as a scientist www.morningsun.net By BOBBY WINTERS The Morning Sun Posted Mar 01, 2010 @ 11:26 PM PITTSBURG — When I was a little boy, I wanted to be a scientist. More specifically, I wanted to be the Professor on Gilligan’s Island. (There was just something about Ginger...) I took all of the science that we had at dear old McLish High School, which wasn’t all that much. There was biology and chemistry, and that was it. The chemistry I had as a senior was the last chemistry course I ever had. The only experiment I remember from that was one in which we put a piece of aluminum in a test tube that had nitric acid in it. Or we might’ve put nitric acid in a test tube that had aluminum in it. I don’t remember. What I do remember is that nitric acid and aluminum don’t get along. There was a lot of bubbling and heat produced. And I got some nitric acid on my fingers and it turned my skin yellow, but I eventually got over that. I took some physics in college and a little biology, but that was it. The rest was math. Little did I know I would in the 47th year of my life I would be called upon to live among the chemists as their acting chairman. It’s been fun. I know that you are to call no man lucky until you know the manner of his death, such as total body submersion in a bathtub full of acid, but I’ve been enjoying myself. Mathematicians have a rather peculiar idea of fun, you understand, but I’ve got to say that it has been fun. The first half of the year was dominated by my learning about lab safety. Being a mathematician, the most dangerous thing that can happen to me is a paper cut, or, if things get really wild, getting poked with a pencil. Chemists, by way of contrast, deal with danger on a daily basis. I was briefed on this by Pittsburg State’s environmental officer, aka Jeff, the Safety Guy. He had me read an article about a young lady who’d been involved in a laboratory accident at a university on the West Coast. A substance she spilled on herself caused flesh to pull away from bone. It took her weeks to die. It had the same effect on me that the driver’s education film “Blood on the Road” did. It made an impression. If you hear a student complain because they were thrown out of a chemistry lab for being inappropriately dressed, you can blame me. Another difference between math and chemistry is that chemists use up more stuff. In math, it is mainly — and I know I am being repetitive — pencils and paper. They use up rubber gloves, bottles of gas and chemicals by the jug full. In addition, once they use the chemicals, many times we have to pay to have them disposed of in a green, sustainable fashion. In math, wad up the paper, put it in the basket, and that’s it. The other day in a Chemistry Department meeting, we began the discussion of buying periodic tables of the elements for a couple of classrooms. For those of you who don’t know, the periodic table of elements is a list of all of the chemical elements. Chemistry, of course, consists of putting together these elements in various ways to get all sorts of neat stuff. It makes sense that you would want one of these tables in a chemistry classroom. In the course of the discussion, it was mentioned that perhaps we should hold off on buying any such charts right now because element 118 was recently created by some physicists who slammed some atoms together. There is, as it turns out, a process for naming these new elements and the name hasn’t been decided on yet, so any chart we bought now would be out of date almost immediately. This is something else we don’t run into in math. We don’t have to worry about anybody coming up with a new number and not knowing the name of it. This scientist stuff is complicated, but I am just a visitor in the department. Gilligan and the Captain took the professor and the rest on a three-hour tour, and my time with the chemists is temporary too. While it’s not been a shipwreck, living my dream as a scientist has been an adventure. Bobby Winters is Assistant Dean of the College of Arts and Sciences, Professor of Mathematics, and Acting Chair of the Department of Chemistry at Pittsburg State University. Copyright 2010 Morning Sun. Some rights reserved. OKIE IN EXILE: My life as a scientist

March 02, 2010 Descartes Letter Found, Therefore It Is www.nytimes.com By PATRICIA COHEN Published: February 24, 2010 It was the Great Train Robbery of French intellectual life: thousands of treasured documents that vanished from the Institut de France in the mid-1800s, stolen by an Italian mathematician. Among them were 72 letters by René Descartes, the founding genius of modern philosophy and analytic geometry. Now one of those purloined letters has turned up at a small private college in eastern Pennsylvania, providing scholars with another keyhole into one of the Western world’s greatest minds. The letter, dated May 27, 1641, concerns the publication of “Meditations on First Philosophy,” a celebrated work whose use of reason and scientific methods helped to ignite a revolution in thought. The document, experts say, reveals just how much Descartes tailored his writings to answer his contemporary critics. Frequently suspected of heresy, Descartes sent copies of his arguments to well-known theologians to gauge their opinions and answer their objections within his text. If old-fashioned larceny was responsible for the document’s loss, advanced digital technology can be credited for its rediscovery. Erik-Jan Bos, a philosophy scholar at Utrecht University in the Netherlands who is helping to edit a new edition of Descartes’s correspondence, said that during a late-night session browsing the Internet he noticed a reference to Descartes in a description of the manuscript collection at Haverford College in Pennsylvania. He contacted John Anderies, the head of special collections at Haverford, who sent him a scan of the letter. “This was exhilarating,” Mr. Bos wrote in an e-mail message. “Seeing Descartes’ handwriting appear on my screen took my breath away.” Descartes, the author of “Cogito, ergo sum” — “I think, therefore I am” — spent two decades living in Holland. Mr. Bos’s research is part of a large project sponsored by the Netherlands Organization for Scientific Research. It turns out the letter had been donated in 1902 to Haverford’s library by Lucy Branson Roberts, whose husband, Charles Roberts, was an avid autograph collector. He had bought the letter without knowing that it was stolen. As soon as Haverford’s president, Stephen G. Emerson, understood the letter’s history, he contacted the Institut de France (coincidentally on Feb. 11, the anniversary of Descartes’ death in 1650) and offered to return the item. “I was frankly shocked because I didn’t know we had the letter at all,” said Mr. Emerson, who was a philosophy major in college. “But it’s really not ours.” Scholars have known of the letter’s existence for more than 300 years, but not its contents. Apparently the only person who had really studied it was a Haverford undergraduate who spent a semester writing a paper about the letter in 1979. (Mr. Bos called the paper “a truly fine piece of work.”) Gabriel de Broglie, chancellor of the Institut de France, an organization that manages thousands of donations and foundations, described the letter as “a wonderful discovery for science.” Delighted by the college’s offer, Mr. de Broglie awarded Haverford a prize of 15,000 euros (slightly more than $20,000), writing to Mr. Emerson that the offer “honors you and exemplifies the depth of moral values that you instill in your students.” France has recovered only 45 of the 72 stolen Descartes letters, Mr. de Broglie explained. One was offered at an auction in Switzerland in 2006 and 2009. “After I protested vociferously and publicly on both occasions in the name of the Institut, the letter didn’t find a buyer,” Mr. de Broglie wrote, “but it proved impossible for us to raise the very large sum that the seller demanded, and even though it can’t be sold, this 1638 letter remains in private hands.” The letters were among thousands of documents stolen by Guglielmo Libri, an Italian count and mathematician who served as secretary of the Committee for the General Catalog of Manuscripts in French Public Libraries in the 1840s. After learning that he might be arrested, Libri fled to London in 1848 with a collection of 30,000 books and manuscripts, including those by Descartes, Galileo, Fermat, Leibniz, Copernicus and Kepler and other scientific and mathematical giants. Claiming to be a political refugee, Libri was welcomed in Britain even though French courts eventually convicted him in absentia in 1850 and sentenced him to 10 years in prison. Libri raised money by selling his collection, and put a total of 7,628 lots up for sale at two auctions in 1861. To Mr. Bos, the most important information in the four-page letter written in French is in the last paragraph, which “shows that at a very late stage in the printing process, Descartes changed the outlook of the Meditations dramatically.” In that passage Descartes instructs Father Marin Mersenne, a close friend who was overseeing the book’s publication, “Neither the fourth part of the Discours de la méthode, nor the little preface I put in next, nor the one preceding the theologian’s objections, must be printed, but only the Synopsis.” In his e-mail note, Mr. Bos explained that “the reason for those changes is that a French visitor has convinced Descartes of the good intentions of Pierre Petit (1598-1677), who had been very critical on part 4 of the Discourse — criticism about which Descartes was extremely upset. Now that he knows that Petit changed his mind, Descartes has no reason to react to him personally — in the new preface he limits himself to a few general remarks about the criticisms that reached him concerning the Discourse, without naming anybody.” Mr. Bos added that the letter would be published in a collection later this year. Mr. Emerson of Haverford said he planned to deliver the document personally during an award ceremony at the Institut in June. And no, he isn’t planning to check the letter in his luggage. Descartes Letter Found, Therefore It Is

March 02, 2010 Mathematician Wins NSF CAREER to Study Geometric Group Theory tigger.uic.edu A relatively new branch of mathematics called geometric group theory that considers a broad range of spatial relationships is the research focus of Daniel Groves, University of Illinois at Chicago assistant professor of mathematics, statistics and computer science. Groves just won a five-year, $400,000 National Science Foundation Faculty Early Career Development award for the application of geometric group theory to surface bundles and logic. "Generally speaking, a group is the set of symmetries of some mathematical space, and geometric group theory studies groups and spaces via the interaction of these groups and spaces," said Groves. His NSF-funded project has three main components. First, Groves hopes to develop a general structure theory to understand spaces called surface bundles. "Surface bundles arise in many parts of pure mathematics, so I hope my structure theory for them has broad applications throughout topology, geometry, group theory and other fields," he said. Second, he will work with Henry Wilton, senior research fellow at the California Institute of Technology, to analyze the geometry of negative curvature from an algorithmic viewpoint. They will try to develop algorithms for general decision processes as applied to first-order logic and groups. First-order logic is used in mathematics, but also in such fields as linguistics and philosophy. This, they hope, will yield a method to determine the truth of a logical sentence, as applied to negatively curved groups. a Finally, Groves will run four annual summer workshops and conferences for graduate students. The workshops, Groves said, "will each be in a different subject at the interface of geometric group theory and another field, or fields, within pure mathematics." NSF's Faculty Early Career Development award is its most prestigious honor given to junior faculty members in the sciences and engineering who have shown a demonstrated commitment to research and education. a For more information about UIC, visit www.uic.edu Mathematician Wins NSF CAREER to Study Geometric Group Theory

March 02, 2010 15 Questions with John Banville www.thecrimson.com Courtesy Douglas Banville The award-winning novelist discusses good works, strong drink, and the life of a writer By Michelle B. Timmerman, CRIMSON STAFF WRITER Published: Friday, February 26, 2010 With his new book "The Infinities," John Banville, explores the life of a dying mathematician across two parallel universes, as seen from the perspective of the Greek gods. FM sat down with the author to talk about simpler things: "the gray north," brandy, and a love for words which has translated into an award-winning career. 1. Fifteen Minutes: You've stated that you desire to give your prose the "kind of denseness and thickness that poetry has," and you've published novels and plays, but no poetry. Why? John Banville: Well, my old friend, the wonderful Irish novelist John McGahern, used to say that "there's verse and there's prose and then there's poetry, and poetry can happen in either." Since he was a novelist, he used to say that it happened more often in prose. 2. FM: Your brother and sister are also published writers. Is there ever a feeling of sibling rivalry or competition? JB: I don't think so, but then there's always a feeling of competition or rivalry within families, isn't there? No, I'm happy for them and they're happy for me, I think. But of course, they may be working behind the scenes, destroying my reputation. 3. FM: After you finished school you worked as a clerk for Aer Lingus. How did this travel affect you and your writing? JB: Well, I went to work for the airline because I could get cheap travel or travel for nothing. I did lots of traveling. My first trip was to Rome and to Paris. I was about 18, 19. For an Irish boy to get to Paris or Rome was no great thing. I don't know if it had any effect on my writing, but it certainly had an effect on me as a person. 4. FM: Where did you most enjoy visiting? JB: My favorite country, I suppose, is Italy. I think it's everyone's favorite country, really. They've sorted out the basics of food and drink and sensuality. If I were given the choice of dying and going to heaven, it would be Italy I would go to. I couldn't live there. Life there would be too sweet and too soft. I need to live in the gray north in order to work. 5. FM: In what ways do you believe growing up in Ireland and being Irish have influenced the content and style of your writing? JB: All I can say is the most important thing for me is that I write in a peculiar version of English which we speak and write in here. English is not my first language. It's my mother-tongue, but I don't feel at home in it, which is a very good thing for a writer. It's a good thing not to feel at home in your language because you're constantly examining it from the outside. 6. FM: You've lived in both the United States and Ireland. What would you say are some of the biggest differences between the two? JB: Ireland is the past; America is the future. I mean, I still think of America as the last great hope. I'm a great admirer of America, you know, for all its faults. I get furious at Europe and the easy criticisms of America that Europeans constantly make. Mostly I think because I've been there. And of course the people who haven't been to America know the most about it, as you know, I'm sure. 7. FM: Describe a typical day in your writing process. JB: A typical day? I work nine to five. I stop in the middle of the day to have bread and cheese and a glass of water. 8. FM: Did you always want to be a writer? JB: Well, for as far back as I can remember. I started writing when I was about 12. And if I keep at it for another 20 years, I might actually learn how to do it. 9. FM: You won the Booker Prize for "The Sea" (2005) so I think some people would say that you've learned how to do it. How did it feel to win the prize and how has it affected you? JB: Well, it was great fun to win it, and my bank manager was deeply relieved. It hasn't affected my work. One would be a very poor writer indeed if winning a prize influenced one's writing. 10. FM: When asked how you would spend the $87,600 check that accompanies receipt of the Booker Prize, you replied, "Good works and strong drink." We'd love to know your preferences in both those categories. JB: I thought that was pretty clever, actually. Good works is taking care of the people one loves and people in the periphery of one's life. Strong drink of course is good wine and good brandy. Wine would be...a Tuscan wine and brandy would be Hennessy. 11. FM: Your new novel centers around a dying mathematician and his family, as the Greek gods hover above. What sort of statement, if any, does this make about religion and science? JB: There's absolutely no statement at all. My model is taken from Franz Kafka who said, "The artist is a man who has nothing to say." I have nothing to say. I have no statements to make, I have no messages to deliver. I simply want to recreate the world as I see it and to provide delight to readers. No messages. 12. FM: One of the main characters in "The Infinities" has proved the existence of parallel universes. If you could live in a parallel universe, what would it be like? JB: Oh it would be like this one. This is an amazing place to live. We have four seasons in a year, which is an astonishing thing. Everything changes. Come the end of February here in Ireland, it's dark and cold, but things are beginning to move, which is an astonishing thing and it's the greatest gift we could've been given. That the year changes, the sky changes from moment to moment. Who would want to be anywhere else? 13. FM: You have said that "Facility in art, or the appearance of facility, is nearly always suspect," and that you only write about a hundred words a day when working on literary novels. How does this difficulty contribute to the formation of your novels? JB: I don't think it's a difficulty...it's to do with concentration. When you concentrate that deeply at that level, it's impossible to write more than a few hundred words a day because every word is chosen. The cadences of every sentence have to be different. 14. FM: What advice would you offer to aspiring writers? JB: Learn your craft—as simple as that. Don't imagine that you can begin to express yourself or say things or deliver messages or any of that stuff, but just learn to write. Work away at it. Work away at getting the sentences right. And learn to love words. 15. FM: You've described the fact that you didn't attend university as "a great mistake...I regret not taking that four years of getting drunk and falling in love." Any retrospective advice for students at Harvard? JB: Oh, yes. Stay in school. Fall in love. Take the odd can of beer. Live as much as you can. 15 Questions with John Banville

March 02, 2010 Mathematical model for empirically optimizing large scale production of soluble protein domains 7thspace.com Efficient dissection of large proteins into their structural domains is critical for high throughput proteome analysis. So far, no study has focused on mathematically modeling a protein dissection protocol in terms of a production system. Here, we report a mathematical model for empirically optimizing the cost of large-scale domain production in proteomics research. Results: The model computes the expected number of successfully producing soluble domains, using a conditional probability between domain and boundary identification. Typical values for the model's parameters were estimated using the experimental results for identifying soluble domains from the 2,032 Kazusa HUGE protein sequences. Among the 215 fragments corresponding to the 24 domains that were expressed correctly, 111, corresponding to 18 domains, were soluble. Our model indicates that, under the conditions used in our pilot experiment, the probability of correctly predicting the existence of a domain was 81% (175/215) and that of predicting its boundary was 63% (111/175). Under these conditions, the most cost/effort-effective production of soluble domains was to prepare one to seven fragments per predicted domain. Conclusions: Our mathematical modeling of protein dissection protocols indicates that the optimum number of fragments tested per domain is actually much smaller than expected a priori. The application range of our model is not limited to protein dissection, and it can be utilized for designing various large-scale mutational analyses or screening libraries. Author: Eisuke ChikayamaAtsushi KurotaniTakanori TanakaTakashi YabukiSatoshi MiyazakiShigeyuki YokoyamaYutaka Kuroda Credits/Source: BMC Bioinformatics 2010, 11:113 Mathematical model for empirically optimizing large scale production of soluble protein domains