New method calculates equilibrium constant at the small scale

Mixing computational chemistry and theoretical math proved a winning formula for Emory chemist James Kindt (center), his graduate students (from left) Xiaokun Zhang and Lara Patel, and mathematics graduate students Olivia Beckwith and Robert Schneider. Photo by Stephen Nowland, Emory Photo/Video.

By Carol Clark

Computational chemists and mathematicians have developed a new, fast method to calculate equilibrium constants using small-scale simulations — even when the Law of Mass Action does not apply.

The Journal of Chemical Theory and Computation published the resulting algorithm and software, which the researchers have named PEACH — an acronym for “partition-enabled analysis of cluster histograms” and a nod to the method’s development in Georgia at Emory University.

“Our method will allow computational chemists to make better predictions in simulations for a wide range of complex reactions — from how aerosols form in the atmosphere to how proteins come together to form amyloid filaments implicated in Alzheimer’s disease,” says James Kindt, an Emory professor of computational chemistry, whose lab led the work.

Previously it would require at least a week of computing time to do the calculations needed for such predictions. The PEACH system reduces that time to seconds by using tricks derived from number theory.

“Our tool can use a small set of data and then extrapolate the results to a large-system case to predict the big picture,” Kindt says.

“What made this project so fun and interesting is the cross-cultural aspects of it,” he adds. “Computational chemists and theoretical mathematicians use different languages and don’t often speak to one another. By working together we’ve happened onto something that appears to be on the frontiers of both fields.”

The research team includes Lara Patel and Xiaokun Zhang, who are both PhD students of chemistry in the Kindt lab, and number theorists Olivia Beckwith and Robert Schneider, Emory PhD candidates in the Department of Mathematics and Computer Science. Chris Weeden, as an Emory undergraduate, contributed to early stages of the work.

The equilibrium constant is a basic concept taught in first-year college chemistry. According to the Law of Mass Action, at a given temperature, no matter how much of a product and a reactant are mixed together — as long as they are at equilibrium — a certain ratio of product to reactant will equal the equilibrium constant.

“That equation always holds true at equilibrium for huge numbers of molecules,” Kindt says. “It doesn’t matter if it’s applied to a bucket of water or to a single drop of water — which consists of about a billion trillion molecules.”

At much smaller scales of around dozens of molecules, however, the Law of Mass Action breaks down and does not apply.

The Kindt lab uses computers to simulate the behavior of molecules, in particular how they self-assemble into clusters. Sodium octyl sulfate, or SOS, is one of the compounds the lab uses as an experimental model. SOS is a surfactant that can act as a detergent. It forms little clusters in water that can encapsulate oil and grease. Simulations of how SOS molecules come together can predict the distribution of sizes of clusters formed under different conditions, in order to improve the design of soaps and detergents, and to better understand biological processes such as how bile salts break down globules of fat during the digestive process.

In a key test of their model, the lab needed to make sure that the equilibrium for the assembly reaction of SOS molecules into clusters matched up with experiments.

“If we were to run simulations with huge numbers of molecules, we could count the clusters that were formed of each size, count the molecules that remained free of the clusters, and use this information to calculate the equilibrium constant for forming each size cluster,” Kindt says. “The challenge we faced was that it would take too long for the computers to perform simulations of sufficiently huge numbers of molecules to get this to work, and for the numbers of clustering molecules we could practically handle — around 50 — the Law of Mass Action wouldn’t work.”

Kindt decided to approach the problem by considering all the different ways the molecules in a reaction could group into clusters of different sizes in order to arrive at an average. After doing some reading, he realized that these different ways of molecules grouping were what number theorists call integer partitions.

A partition of a number is a sequence of positive integers that add up to that number. For instance, there are five partitions of the number 4 (4 = 3+1 = 2+2 = 2+1+1 = 1+1+1+1). The partition numbers grow at an incredible rate. The amount of partitions for the number 10 is 42. For the number 100, the partitions explode to more than 190,000,000.

That same explosion of possibilities occurs for the ways that molecules can cluster.

Lara Patel and Xiaokun Zhang worked on a “brute force” method to get a computer to run through every single way to combine 10 molecules of one type with 10 molecules of another type. The problem was it took one computer working a couple of days to do a single analysis. And the computational time needed if just a few more molecules were added to the analysis went up exponentially.

The computational chemists had hit a wall.

Kindt reached out to Ken Ono, a world-renowned number theorist in Emory's Mathematics and Computer Science Department, to see if any of his graduate students would be interested in taking a crack at the problem.

Olivia Beckwith and Robert Schneider jumped at the chance.

“The Kindt lab’s computer simulations show that classical theorems from partition theory actually occur in nature, even for small numbers of molecules,” Schneider says. “It was surprising and felt very cosmic to me to learn that number theory determines real-world events.”

“It was definitely unexpected,” adds Beckwith. “In theoretical math we tend to work in isolation from physical phenomena like the interaction of molecules.”

The chemists and mathematicians began meeting regularly to discuss the problem and to learn one another’s terminology. “I had to pull out my son’s high school chemistry book and spend a weekend reading through it,” Schneider says.

“It happened so organically,” Patel says of the process of blending their two specialties. “Olivia and Robert would write equations on the board and as soon as a formula made sense to me I’d start thinking in my head, ‘How can we code this so that we can apply it?’”

The two mathematicians suggested a strategy that could make the problem much easier to calculate, based on a theorem known as Faà di Bruno’s Formula.

“It was surprising,” Zhang says, “because it was an idea that never would have occurred to me. They helped us get unstuck and to find a way to push our research forward.”

“They helped us find a shortcut so that we didn’t have to generate all the partitions for ways that the molecules could clump together,” Kindt adds. “Their algorithm is a much more elegant and simple way to find the entire average overall.”

Patel and Zhang used this new algorithm to put together a piece of software to analyze data from the computer simulations. The resulting system, PEACH, speeds up calculations that previously took two hours to just one second. After demonstrating how PEACH simplifies simulations of SOS assemblages, the research team is moving on to simulate this process for a range of other molecules.

“We’re interested in describing how molecular structures dictate assembly in any type of scenario, such as the early stages of crystal formation,” Kindt says. “We’re also working on quantifying just where the Law of Mass Action breaks down. We could then refine the PEACH strategy to make it even more efficient.”

Related:
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Chimpanzee studies highlight disease risk to all endangered wildlife

Famed primatologist Jane Goodall with Emory disease ecologist Thomas Gillespie, who is working with the Jane Goodall Institute to study the health of chimpanzees in Tanzania's Gombe National Park.

The American Journal of Primatology just published a special edition bringing together experts who have contributed to the understanding of chimpanzee health at Gombe National Park in Tanzania and beyond. Gombe is the site where Jane Goodall pioneered her behavioral research of chimpanzees. Goodall’s work at Gombe began in 1960, and continues today through the Jane Goodall Institute, making it the longest field study of any animal.

Thomas Gillespie, associate professor in Emory’s Department of Environmental Sciences, was a guest editor of the special journal edition, along with fellow scientists Dominic Travis and Elizabeth Lonsdorf. Gillespie works at the interface of biodiversity conservation and global health. Much of his research examines how and why anthropogenic influences within tropical forests alter disease dynamics and place wild primates, people and other animals in such ecosystems at increased risk of pathogen exchange.

Following is an interview with Gillespie about the special journal issue and why research on chimpanzee health is important.

What is the current status of chimpanzees?

Both the common chimpanzee and the bonobo, the two chimpanzee subspecies, are endangered. Chimpanzees are the most closely related species to humans and we see them declining precipitously due to habitat loss and poaching. Typical estimates for the chimpanzee population are in the hundreds of thousands. That’s far less than the number of people in Atlanta for the entire chimpanzee species spread across all of Africa. There is a real risk of chimpanzees going locally extinct in core parts of their habitat. Chimpanzee communities in West Africa, for instance, have very little habitat left. They’re often found living in scraps of habitat between villages.

How important is health to conservation? 

Wildlife health is a critical conservation issue, but that’s something that’s only recently been recognized. Wildlife populations already dealing with poaching and habitat loss are more vulnerable to being knocked out by disease. It becomes even more difficult when they are exposed to new pathogens, from humans or domesticated animals.

On top of that, primates are dealing with shifts in the dynamics of pathogens like Ebola. Ebola’s been around for a long time in natural systems but now we’re seeing big mortality events in wild chimpanzees and other apes. The Lowland Gorillas are actually listed as critically endangered due to Ebola.

How did you become involved with Gombe and the Jane Goodall Institute?

Fifteen years ago, as evidence mounted that disease was playing an important role in the population declines observed in Gombe chimpanzees in Tanzania, Dominic Travis and Elizabeth Lonsdorf developed a prospective health monitoring system. They began to collect specific behavioral data on signs of respiratory and gastrointestinal illnesses, combined with body condition scoring on a monthly basis for the chimpanzee communities at Gombe, that paralleled efforts by the Mountain Gorilla Veterinary Project in Rwanda and Uganda.

When I met Dom and Elizabeth at a workshop in Germany in 2004, I was six years into efforts to understand how logging and forest fragmentation in and around Kibale National Park, Uganda, affected disease dynamics in resident primates. My findings in Uganda highlighted that some forms of anthropogenic disturbance can alter the dynamics of natural pathogens in wildlife, such as a legacy of selective logging. It also revealed that other forms of disturbance, such as active forest fragmentation, can lead to opportunities for pathogens to jump between species, including the introduction of pathogens from people and domesticated animals to wild primates.

Dom and Elizabeth asked me to join their effort and expand the scope of their project to a One Health approach. I initiated diagnostic surveillance linked to geographical indicators of species overlap for Gombe’s chimpanzees and baboons, as well as the people and domesticated animals within the Greater Gombe Ecosystems. It serves as a map of all the places these species are interacting, for a greater sense of how transmission may be occurring. Integration of these new data streams, along with the ongoing observational health data and in-depth post-mortem necropsies, have allowed us to establish baselines of health indicators to inform outbreak contingency plans.

Dom, Elizabeth and I now co-direct this effort, which is known as the Gombe Ecosystem Health Project.

How does Gombe fit into the bigger picture of wildlife conservation? 

As a result of Jane Goodall’s initial observations of disease outbreaks impacting Gombe’s chimpanzees, it became apparent that infectious diseases have the capacity to threaten the conservation of endangered species.

Some people call Gombe “a living laboratory.” It’s unique in the sense that it’s a place where there has been long-term data collection on the behavior patterns of chimpanzees, and for the past 15 years we’ve been collecting all this data on their health.

Methods have been developed at Gombe that allow us to monitor chimpanzee health non-invasively, through fecal sampling, so that we don’t have to dart the animals and tranquilize them to take blood samples. Many of the tools and approaches developed at Gombe have the capacity to manage disease-related threats to other wildlife populations globally.

Ashley Sullivan from the Jane Goodall Institute contributed to this report.

Related:
Disease poses risk to chimpanzee conservation, Gombe study finds
Sanctuary chimps show high rates of drug-resistant staph

Studying how genetic differences contribute to addiction

Psychology professor Rohan Palmer has earned a $2.4 million grant to examine why some people become addicted to alcohol or drugs, while others don't. Emory Photo/Video

By April Hunt
Emory Report

Rohan Palmer, an assistant professor of psychology in Emory College, started on the path to becoming a researcher as an undergraduate, when he worked in a lab studying whether female mice could overcome their anxiety to leave the safety of the nest to retrieve babies that he and other researchers had moved away.

Intriguingly, the work showed that some strains of mice performed very differently than others in overcoming their emotions to perform their motherly duties. Moreover, females exposed to more testosterone in the uterus performed worst at this and other maternal tasks.

“It was understanding behavior at its core,” says Palmer, now an expert in the field of behavioral genetics. “What helps us understand what makes us individuals better than looking at the environment and the biology?”

Palmer now runs his own behavioral genetics lab at Emory that turns that question to one of today’s most pressing issues: What makes some people addicted to drugs or alcohol, and not others?

His highly innovative approach, to find and characterize the layer of biology that combines with factors such as environment to find an answer, has earned him a 2017 Avenir Award for Genetics or Epigenetics of Substance Abuse Disorders (DP1) from the National Institutes of Health Director’s Pioneer Award program.

The five-year, $2.34 million award is among a handful of grants given to recognize “highly creative” scientists from the nation’s top universities and to encourage high-impact approaches to the broad area of biomedical and behavioral science.

“This is a special award, more so because very few beginning investigators receive this honor,” says Ronald Calabrese, the College’s senior associate dean for research.

Read more in Emory Report.

Aversion to holes driven by disgust, not fear, study finds

Clusters of holes, such as those of a lotus seed pod, may be evolutionarily indicative of contamination and disease — visual cues for rotten or moldy food or skin marred by an infection. (Photo by Peripitus/Wikipedia Commons.)

By Carol Clark

Trypophobia, commonly known as “fear of holes,” is linked to a physiological response more associated with disgust than fear, finds a new study published in PeerJ.

Trypophobia is not officially recognized in the American Psychiatric Association’s Diagnostic and Statistical Manuel of Mental Disorders (DSM). Many people, however, report feeling an aversion to clusters of holes — such as those of a honeycomb, a lotus seed pod or even aerated chocolate.

“Some people are so intensely bothered by the sight of these objects that they can’t stand to be around them,” says Stella Lourenco, a psychologist at Emory University whose lab conducted the study. “The phenomenon, which likely has an evolutionary basis, may be more common than we realize.”

Previous research linked trypophobic reactions to some of the same visual spectral properties shared by images of evolutionarily threatening animals, such as snakes and spiders. The repeating pattern of high contrast seen in clusters of holes, for example, is similar to the pattern on the skin of many snakes and the pattern made by a spider’s dark legs against a lighter background.

“We’re an incredibly visual species,” says Vladislav Ayzenberg, a graduate student in the Lourenco lab and lead author of the PeerJ study. “Low-level visual properties can convey a lot of meaningful information. These visual cues allow us to make immediate inferences — whether we see part of a snake in the grass or a whole snake — and react quickly to potential danger.”

It is well-established that viewing images of threatening animals generally elicits a fear reaction in viewers, associated with the sympathetic nervous system. The heart and breathing rate goes up and the pupils dilate. This hyperarousal to potential danger is known as the fight-or-flight response.

The researchers wanted to test whether this same physiological response was associated with seemingly innocuous images of holes.

They used eye-tracking technology that measured changes in pupil size to differentiate the responses of study subjects to images of clusters of holes, images of threatening animals and neutral images.

Unlike images of snakes and spiders, images of holes elicited greater constriction of the pupils — a response associated with the parasympathetic nervous system and feelings of disgust.

“On the surface, images of threatening animals and clusters of holes both elicit an aversive reaction,” Ayzenberg says. “Our findings, however, suggest that the physiological underpinnings for these reactions are different, even though the general aversion may be rooted in shared visual-spectral properties.”

In contrast to a fight-or-flight response, gearing the body up for action, a parasympathetic response slows heart rate and breathing and constricts the pupils. “These visual cues signal the body to be cautious, while also closing off the body, as if to limit its exposure to something that could be harmful,” Ayzenberg says.

The authors theorize that clusters of holes may be evolutionarily indicative of contamination and disease — visual cues for rotten or moldy food or skin marred by an infection.

The subjects involved in the experiments were college students who did not report having trypophobia. “The fact that we found effects in this population suggests a quite primitive and pervasive visual mechanism underlying an aversion to holes,” Lourenco says.

Since the time of Darwin, scientists have debated the relation between fear and disgust. The current paper adds to the growing evidence that — while the two emotions are on continuums and occasionally overlap — they have distinct neural and physiological underpinnings.

“Our findings not only enhance our understanding of the visual system but also how visual processing may contribute to a range of other phobic reactions,” Ayzenberg says.

A third co-author of the study is Meghan Hickey. She worked on the experiments as an undergraduate psychology major, through the Scholarly Inquiry and Research at Emory (SIRE) program, and is now a medical student at the University of Massachusetts.

Related:
How fear skews our spatial perception
Psychologists closing in on claustrophobia