Category: Mathematics Page 7 of 8

Spherical Cows Help Turn Proteins to Crystals

On November 13, 2013

In Biology, Chemistry, Engineering, Mathematics

By Ashley Yeager

"Physicists want to do what to me?" (Courtesy SXC.HU)

The spherical cow is a long-standing physics joke, funny to us, but maybe not to her. (Courtesy Marijn van Braak)

It may be impossible to tip a spherical cow. But by searing one on the computer, scientists may have found the best recipe yet for transforming proteins into crystals.

Crystallizing a protein is not as simple as throwing it in the freezer and letting it chill, the way liquid water turns to ice. “We would like to know what is going on at that fundamental level when we crystallize a protein. But we don’t,” said Patrick Charbonneau, an assistant professor of chemistry, physics and computational biology at Duke.

But by looking at each protein as if it were a spherical cow with sticky patches, Charbonneau said scientists could learn more about the standard set of interactions that transform proteins from a liquid solution into crystals.

The idea of a spherical cow is not new. It comes from an old physics joke where a farmer calls the local university for advice on getting his cows to produce more milk. The university sends a physicist who looks at the barn, the cows and their production and says, “First, assume the cows are spherical and in a vacuum . . . ”

“Physicists idealize everything to the extreme, which could be why their most recent attempts to explain protein crystallization don’t quite work,” Charbonneau said.

Scientists want to know the fundamentals of protein crystallization because proteins are essential for living creatures to survive. Proteins come in many different shapes and have a variety of functions, and their structures explain how they interact with other molecules in the human body — information that often leads to more targeted medications.

To study protein shape, scientists precipitate them from liquid solutions into crystals, which is how DNA’s double helix structure was revealed. Physicists have also tried to model protein shape through computer simulations. In Charbonneau’s new model, he combines physicists’ past simulations based on the spherical cow model with the best protein-crystal-making insights from structural biology.

The new hybrid is what Charbonneau calls the patchy cow model. To develop it, he and his students digitally recreated the structure of the protein rubredoxin as a spherical cow, making it resemble a basic blob-like molecule. The team then applied patchy areas, which acted like the atomic interactions shaping the structure of a protein.

“We found the model actually works, giving us a patchy picture that does predict some of the crystal structure of proteins,” Charbonneau said. It is the first time a simulated model of protein crystallization has matched well with the temperature, salinity and other crystal-forming conditions structural biologists observe in the lab. And “it’s the first time that we can draw clear physical insights from how the model compares with experiments,” he added.

A single protein crystal of lysozyme (Courtesy Wikimedia)

Charbonneau first began working on the protein crystallization problem as a post-doc at Amolf in the Netherlands. When he came to Duke in 2008, he met David and Jane Richardson — leaders in the field of protein crystallization and structural biology. From them, Charbonneau began to realize that physicists and structural biologists don’t know each other’s work. “We don’t cite each other, and we don’t trust each others’ descriptions of protein crystallization,” he said. The goal of his work, he explained, is to convince the disciplines to begin talking to each other.

The biggest problem for both camps is that they know the atomic and molecular interactions that should be involved in crystallizing a protein, but they “cannot make sense of what is going on. It’s figuring out the mechanism, the physical process, that is frustrating,” Charbonneau said. His new model tries to paint the physicists’ spherical cows from the perspective of the observations the Richardsons and others have already made in the crystallography community.

Charbonneau anticipates that the patchy spherical cow model might help structural biologists predict what conditions they need to crystallize any protein of their choice. But first, he said, the team needs to put their model to another test, simulating crystallization in more complex proteins, such as physicists’ favorite, lysozyme.

Citation: “Characterizing protein crystal contacts and their role in crystallization: rubredoxin as a case study,” Diana Fusco, Jeffrey Headd, Alfonso De Simone, Jun Wang, and Patrick Charbonneau. Soft Matter, November 8, 2013. 10.1039/C3SM52175C.

High School Project Lands Freshman in Top Journal

By Pranali Dalvi

On November 13, 2013

In Animals, Biology, Engineering, Mathematics, Students

By Pranali Dalvi

Hayes Griffin is no ordinary freshman at Duke. He hasn’t even been in college for one semester and he’s already published in the top-tier science journal Evolution. During his junior year in high school, Griffin worked alongside his classmate Dalton Chaffee and used mathematical models to forecast what happens when sexual imprinting is introduced. Sexual imprinting is when individuals prefer mates with traits similar to those of their mother, father, or another adult member of their population.

While most research in this area examines how imprinting changes the population, Griffin focused on how imprinting itself evolves.

“Our model suggests that paternal imprinting is superior to other types. In other words, it is more advantageous for animals to mate with individuals similar to their fathers,” Griffin explained. On the same note, other types of imprinting, including maternal and oblique – the latter one meaning imprinting on a non-parental adult – are more favorable than random mating.

Even though sexual imprinting is common in nature, it is not well understood and there is much variation from one species to the next. What is known is that females are choosier mating partners than males are. If females require a complex mechanism to select mates, then sexual imprinting will not evolve. However, if imprinting does evolve, a female is more likely to choose a mate similar to her father.

Griffin admits that doing research was very strenuous and time consuming. He spent about 25 hours a week on the project under the guidance of R. Tucker Gilman, a post-doc working with the National Institute for Mathematical and Biological Synthesis (NIMBioS) at the University of Tennessee.

“Reading the background information was also extremely difficult, because neither of us had any experience with scientific papers or evolutionary theory,” Griffin said.

Hayes Griffin (left) with Dalton Chaffee (right) at the Siemens Competition for Math, Science, and Technology.

His hard work did not go unnoticed though. Griffin and Chaffee were declared Regional Finalists in the Siemens Competition for Math, Science, and Technology. They also were invited to present their findings at the annual conference of the Society for Mathematical Biology.

“Overall, it was a good experience that pushed my limits, and I would definitely do it again,” said Griffin.

Griffin hopes his model will further the scientific community’s understanding of imprinting and selection in general.

For now, though, Griffin is excited about his time at Duke and is considering a major in mechanical engineering.

Duke Math Makes Final Four

By Ashley Yeager

On March 25, 2013

In Faculty, Mathematics, Visualization

By Ashley Yeager

This NCAA bracket is based on the quality of the school's math department. Courtesy of: Jordan Ellenberg, UW-Madison.

A few mathematicians made their NCAA bracket based on the quality of universities’ math departments. Courtesy of: Jordan Ellenberg, UW-Madison.

If NCAA basketball championships were won with math, Duke would move on to the Final Four.

At least, that’s what Jordan Ellenberg, a University of Wisconsin mathematician, and his friends think.

They didn’t use complex algorithms to make their bracket, but picked their winners based on the quality of each school’s math department.

With that ranking scheme, Harvard would win it all, with Cal second and UCLA and Duke rounding out the Final Four.

“Of course, these judgments are for entertainment only, and were produced by a group, so if you find any of the picks absurdly wrong, those were the ones I didn’t make,” Ellenberg wrote on his blog, where he posted the picks.

Sadly, the bracket isn’t doing so well as March Madness moves forward.

But it is a fun way to learn more about the math departments around the country and how well their quality does, or does not, correlate with the quality of the schools’ basketball teams.

Special thanks to Duke mathematician Jonathan Mattingly for pointing the bracket out to us.

Go Duke!

Higgs Hunters Seeing Double

By Ashley Yeager

On December 13, 2012

In Field Research, Mathematics, Physics

By Ashley Yeager

An stuffed animal artist’s conception of the Higgs boson. Credit: The Particle Zoo.

Scientists searching for the Higgs boson on the ATLAS experiment at the Large Hadron Collider near Geneva are reporting small discrepancies from the two main channels they use to look for the particle.

With these channels – the decay of a Higgs to two light particles (photons) or to two Z bosons – the scientists determined the mass of the Higgs-like particle to be roughly 125 GeV, about 125 times the mass of the proton.

They announced complimentary results from both channels in July 2012, and since then have been crunching more data to support the findings. The scientists gave updates on their work Dec. 13 at CERN.

“It’s turned out that for ATLAS the Zed-Zed channel and gamma-gamma channel differ quite a bit, by about 3 GeV, for the respective masses of the Higgs particle from which they decay,” says Duke physicist Mark Kruse, who is analyzing data from the ATLAS experiment. “It doesn’t sound like much, but the probability they could differ by this much or more is only about 0.5 percent.”

“This is probably not a big deal,” he says, noting that the new results explain why the ATLAS team was not ready to report the separate mass measurements at the November 2012 Hadron Collider Physics Symposium in Kyoto, Japan.

Kruse says there could be several reasons for the discrepancy. It could just be a statistical fluke. Or, there could be a subtle problem with one or both of the measurements. “There is a lot that goes into these analyses and it is not always possible at this stage to be absolutely certain every detail has been done perfectly,” Kruse says.

The more dramatic scenario is that these results could be due to two different Higgs-like particles.

Kruse, however, thinks the two Higgs-like particle answer is highly unlikely, especially if scientists using the CMS experiment at LHC do not report the same discrepancy. CMS scientists have not yet released their new “two photon” result.

The ATLAS result is most likely due to a statistical fluctuation. Right now, though, the team has only crunched about half the data from the collisions. Of course, scientists will only know more once they have analyzed the full ATLAS dataset a couple of months from now, Kruse adds, suggesting that there is still the possibly for more Higgs mania to come.

From the basement, female physicists shaped Duke and German science

By Ashley Yeager

On December 5, 2012

In Lecture, Mathematics, Physics, Science Communication & Education

By Ashley Yeager

Google Doodle honors physicist Hedwig Kohn who fled Nazi Germany

Physicist Hedwig Kohn‘s brother was murdered in a Nazi concentration camp in 1941.

Yet, when she trained young German physicists at Duke University a little more than 10 years later, she bore no resentment against them. Those students later returned to Germany and helped educate the country’s students in quantum mechanics.

Kohn fled Nazi Germany with the help of several prominent scientists in 1940, teaching first at the Women’s College in Greensboro, now UNC–Greensboro, and then at Wellesley College in Massachusetts. In 1952, she retired from teaching and accepted a research associate position working with physicist Hertha Sponer at Duke.

“It’s important that Kohn’s and Sponer’s tenure at Duke not be forgotten,” said physicist Brenda Winnewisser, an adjunct professor at The Ohio State University. The women’s lives and their research helped shape the physics department’s early encouragement of women interested in science.

Winnewisser, who earned her Ph.D. in physics at Duke in 1965, spoke briefly about Sponer and mostly about Kohn during a Nov. 28 physics colloquium. During her talk, Winnewisser recounted Kohn’s history, explained how she saved Kohn’s letters and photographs from destruction and described how she is using the archived information to write Kohn’s biography, a book called Hedwig Kohn: A Passion for Physics.

In her lab, which was in the subbasement of the Duke physics building, Kohn measured the absorption features and concentrations of atomic species in flames. The research was a continuation of what she had worked on from 1912 until 1933, when the Nazis stripped her of her privilege to do research and teach because of her being Jewish and female.

Still, the Nazis couldn’t take away the quality or importance of her work, which had a resurgence in citations in the 1960s as researchers began to test rocket designs and study plasmas, Winnewisser said. She added that Kohn also had an “indirect impact on improving quantum mechanics education in Germany after World War II.”

Three of the four physicists Kohn mentored at Duke returned to Germany to teach at prominent universities, bringing with them what they had learned from Kohn about flames, absorption and also quantum mechanics. “Kohn gave them the technical basis for successful careers,” Winnewisser said.

Her biography of Kohn, who died in 1964, is slated for release by Biting Duck Press in the spring of 2014.

Film Presents Alan Turing In Full; Duke Preview Monday

By Karl Bates

On October 24, 2012

In Behavior/Psychology, Computers/Technology, Mathematics, Science Communication & Education

Guest post by Pender M. McCarter, Trinity College (1968), Senior Public Relations Counselor, IEEE-USA/Washington

A scene from the movie “Codebreaker” about the life of Alan Turing.

Alan Turing has been hailed as a digital Darwin, an Einstein and a Newton who helped to “catapult civilization in to the digital age.” The British mathematician laid the groundwork for everything we do with computers today, according to Apple co-founder Steve Wozniak. The Turing Machine incorporated all the basic aspects of computer input and output. His 1950 paper, “Computing Machinery and Intelligence,” posited that computers can be programmed to mimic human behavior. And at the end of his life, Turing wrote about pattern formation in biology, what he called morphogenesis, that could be observed in animal stripes and spirals and even exist in ecosystems and galaxies. Turing is best known for leading the British Bletchley Park code breakers team that cracked Germany’s Naval Enigma Code, helped end World War II, and saved perhaps millions of lives.

Yet until recently Turing’s contributions have been little known or appreciated outside of the sci-tech community. And his personal life as a gay man has generally been glossed over. In 2012, the centenary of Alan Turing’s birth, hundreds of events have been held worldwide. A new film, Codebreaker, presents Turing’s personal and professional life without flinching, including how his sexual nature contributed to his extraordinary achievements and tragic downfall.

The drama documentary emphasizes that the support and encouragement Turing enjoyed with other eccentric and brilliant technologists at Bletchley Park motivated and sustained him. When he lost this community after World War II, at a time when there was a craving for normalcy and scant tolerance for non-conformists, Turing learned how unforgiving the world could be.

The drama scenes in Codebreaker center on the psychotherapy sessions Turing participated in during the last 18 months of his life. In these final months, Turing faced persecution as a gay man under the same 19^th century British laws that were used to prosecute Oscar Wilde. In 1954, at the age of 41, Turing committed suicide leaving us to wonder about potential future accomplishments in a more accepting and tolerant time. In 2009, former British Prime Minister Gordon Brown apologized posthumously to Turing: “We’re sorry; you deserved so much better.”

Codebreaker will be screened at the Duke Center for LGBT Life (02 West Union Building) on Monday, Oct. 29, from 7-8:30 p.m., with underwriting from IEEE-USA, the Washington-based office of the IEEE, the world’s largest professional association for the advancement of technology. The drama documentary will be introduced by Executive Producer Patrick Sammon, who will also answer questions about the film.

Here’s a link to the trailer: http://www.turingfilm.com/

A second crack at the nature of glass

By Ashley Yeager

On August 13, 2012

In Computers/Technology, Faculty, Field Research, Mathematics, Physics, Visualization

By Ashley Yeager

Glassblowers shape molten silica before the glass transitions from liquid to a more solid structure. Credit: handblownglass.com.

Patrick Charbonneau and his collaborators have taken another crack at understanding the nature of glass. Their latest simulations show that a key assumption of theoretical chemists and physicists to explain the molecular structure of glass is wrong.

Glass forms when liquids are slowly compressed or super-cooled, but don’t crystallize the way cooled water turns to ice. The liquidy pre-cursors to glass, like molten silica, do become hard like a solid, but the atoms in the material don’t organize themselves into a perfect crystal pattern.

The result is a substance that is as hard as a solid but has the molecular arrangement of a liquid — a phenomenon that scientists can’t quite explain, yet.

Previous theories assumed that at the transition point between a liquid and glass, the material’s atoms become caged by each other in a “simple” Gaussian shape. This same shape describes the distribution of people’s height in the U.S. and is known as a bell-shaped curve.

But new simulations, described online Aug. 13 in PNAS, suggest this assumption is wrong. The simulations model the interactions of glass particles in multiple dimensions and show the shape of the particle cage is much more complex than a Gaussian distribution.

The discovery is a “paradigm shift in the sense that so many people have been having the same, wrong, conception for so long, and they should now revisit that basic assumption,” says Charbonneau, a theoretical chemist at Duke. “The assumption was actually constraining how they thought about the problem.”

Even with a new shine on the way scientists think about glass, it is not clear how close or far the theorists are from writing an accurate description of what happens at the liquid-glass transition. But “the path to get there seems clearer than it has been in a long time,” Charbonneau says.

The next step in the research is to understand the relationship between glassy states of matter and those that are jammed, like pieces of cereal wedged in a grain hopper. Charbonneau and collaborators are already at work about how to study the connections between the two forms of matter.

Citation:
“Dimensional study of the caging order parameter at the glass transition.” 2012. Charbonneau, P., et al. PNAS Early Edition. DOI: 10.1073/pnas.1211825109

'Chicken' Logic Secures Planes, Trains and Ports

By Ashley Yeager

On July 13, 2012

In Business/Economics, Computers/Technology, Lecture, Mathematics, Science Communication & Education, Students

By Ashley Yeager

U.S. goalkeeper Hope Solo deflects a penalty kick. Credit: AP

Soccer penalty kicks, ‘Chicken’ and other games may thwart terrorist attacks, drug smugglers and even freeloaders trying to board trains without tickets.

It’s not so much the intensity and adrenaline of the games that lead to better security, but the logic the players use, says Vincent Conitzer, a professor of computer science and economics at Duke.

This logic is called game theory and now scientists are using it to compute solutions for security issues, Conitzer explained at a July 11 talk with undergraduates completing summer research projects on campus.

During the talk, Conitzer gave a brief overview of game theory using real-world examples, such as penalty kicks in soccer and a set of drivers playing chicken. In the soccer example, he described a “zero-sum game” between the goalie and the kicker, where no matter the outcome, one player wins and the other loses.

But in the case of chicken, in which two cars drive straight at each other until one of the drivers “chickens out” and diverts course, the stakes of each choice are a bit higher. If both drivers stay straight, they crash. It’s no longer a zero-sum game.

When it comes to preventing security problems, there are more angles of attack, smuggler entry points and ways to board a train than the simple left, right or straight of these game examples.

Cars and buses wait to clear a security checkpoint at LAX. Credit: cardatabase.net

To make predictions about what the bad guys will do in the security scenarios, Conitzer is working with Milind Tambe and his group at USC. The team has designed game theory algorithms to set the schedule of security checkpoints and canine rounds at LAX airport, smuggler-scouting in Boston Harbor and even methods for preventing terrorist attacks in Mumbai.

Tambe “treats the problem of Mumbai personally” since that is his home city, Conitzer said, adding that he is only directly involved in this project with the USC group.

While the talk focused mainly on security applications, Conitzer also thinks that some “surprising new applications have yet to emerge” from the work. The new uses won’t necessarily help win a game of chicken or score a penalty kick.

But they could help scientists understand how to better use incentives to designgames with only good outcomes, such as encouraging smart energy use.

Citation: “Computing Game-Theoretic Solutions and Applications to Security.” Conitzer, V. In Proceedings of the 26th National Conference on Artificial Intelligence (AAAI-12), Toronto, ON, Canada, 2011.

Lab "cloud" goes global

By Ashley Yeager

On June 15, 2012

In Computers/Technology, Faculty, Genetics/Genomics, Mathematics, Physics

By Ashley Yeager

A network of individual computers are linked through a server. Credit: TAS Software

The National Science Foundation has awarded computer scientist Jeff Chase $300,000 to move a computer cloud he now has in his lab to the university’s campus network, and beyond.

Chase has been building the cloud to improve server networks. In his new model, servers, the computers that process requests and deliver data over a local network or the Internet, have become critical, public infrastructures with open, flexible, secure, robust and decentralized control.

The work, once reproduced outside of the lab, will let Duke scientists across campus and throughout the world to more easily connect to one another through existing networks and to share computational services and access data, according to Tracy Futhey, Duke’s vice president for information technology and chief information officer.

Based on software-defined networking and other technologies, the new, on-demand cloud services will be launched through a distinct network that connects science resources, such as the large datasets generated in physics and genomics experiments.

The project is part of the NSF-funded Global Environment for Networking Innovation, or GENI.

Chase’s work was also recognized on June 14 when the White House launched an initiative, US Ignite, to develop a publicly available system of advanced networks based on important contributions from GENI scientists. Duke is among more than 60 universities across the country that has participated in the project.

Betting on Bayesball

By Ashley Yeager

On June 13, 2012

In Behavior/Psychology, Faculty, Lecture, Mathematics, Physics, Science Communication & Education

By Ashley Yeager

Derek Jeter, upper left, and Alex Rodriguez, lower right, anticipate a grounder in a 2007 game . Credit: Wikimedia.

New York Yankees shortstop Derek Jeter has five golden gloves. Alex Rodriquez, a Yankees shortstop and third baseman, has three.

It wasn’t a surprise then when Sayan Mukherjee asked a crowd at Broad Street Café who was a better mid-fielder and Jeter got a few more cheers.

The question, and response, prompted Mukherjee, a statistician who studies machine learning, to launch into a discussion about intuition and statistics in sports, specifically in baseball. Mukherjee spoke on June 12 as part of Periodic Tables: Durham’s Science Café.

He admitted he was a Yankees fan, which elicited some booing. Laughing it off, he then showed a complex statistical equation his colleague, Shane Jensen at the University of Pennsylvania, and others use to calculate a player’s success at fielding ground and fly balls.

On the next slide, Mukherjee showed the results. Rodriquez was clearly on top, and Jeter closer to the bottom. “Jeter doesn’t have as big a range as other players, that’s all I’m suggesting,” Mukherjee said.

Of course, these statistics, called sabermetrics, aren’t new to Jeter and other players. The numbers, based on Bayesian statistics, are exactly what the Oakland A’s baseball team used in 2002 to build a winning team. And, when new numbers came out in 2008, the stats ranked Jeter fairly low as a defensive player. He responded by saying there was a “bug” in the model.

“He has a point. The exact conditions for each play are not the same, so it’s hard to truly compare them,” Mukherjee said. The equation, however, is a way to measure factors of the game, rather than rely on intuition, and statisticians are trying to add more factors to make the model more realistic. The next factor they want to add will account for the different designs of ballparks, Mukherjee said.

He added, though, that these stats don’t really put players’ jobs at jeopardy. Judging by the crowd’s first response, people obviously still rely on intuition when it comes to picking their favorite players. The cold, hard numbers therefore affect how players approach their game – ie Jeter’s post-2007 season focus on a training program to combat the effects of age, Mukherjee said.

The data also affect people betting on the games. “Betting is huge, in any sport,” Mukherjee said, and the numbers, it seems, can affect how people choose to risk their money, but not their team loyalty.