Machine learning used to understand and predict dynamics of worm behavior

The roundworm C. elegans is a well-established laboratory model system. While the worm is a fairly simple living system, it is complicated enough to serve as "a kind of sandbox" for testing out methods of automated inference, says Emory biophysicist Ilya Nemenman. (Getty Images)

By Carol Clark

Biophysicists have used an automated method to model a living system — the dynamics of a worm perceiving and escaping pain. The Proceedings of the National Academy of Sciences (PNAS) published the results, which worked with data from experiments on the C. elegans roundworm.

“Our method is one of the first to use machine-learning tools on experimental data to derive simple, interpretable equations of motion for a living system,” says Ilya Nemenman, senior author of the paper and a professor of physics and biology at Emory University. “We now have proof of principle that it can be done. The next step is to see if we can apply our method to a more complicated system.”

The model makes accurate predictions about the dynamics of the worm behavior, and these predictions are biologically interpretable and have been experimentally verified.

Collaborators on the paper include first author Bryan Daniels, a theorist from Arizona State University, and co-author William Ryu, an experimentalist from the University of Toronto.

The researchers used an algorithm, developed in 2015 by Daniels and Nemenman, that teaches a computer how to efficiently search for the laws that underlie natural dynamical systems, including complex biological ones. They dubbed the algorithm “Sir Isaac,” after one of the most famous scientists of all time — Sir Isaac Newton. Their long-term goal is to develop the algorithm into a “robot scientist,” to automate and speed up the scientific method of forming quantitative hypotheses, then testing them by looking at data and experiments.

While Newton’s Three Laws of Motion can be used to predict dynamics for mechanical systems, the biophysicists want to develop similar predictive dynamical approaches that can be applied to living systems.

For the PNAS paper, they focused on the decision-making involved when C. elegans responds to a sensory stimulus. The data on C. elegans had been previously gathered by the Ryu lab, which develops methods to measure and analyze behavioral responses of the roundworm at the holistic level, from basic motor gestures to long-term behavioral programs.

C. elegans is a well-established laboratory animal model system. Most C. elegans have only 302 neurons, few muscles and a limited repertoire of motion. A sequence of experiments involved interrupting the forward movement of individual C. elegans with a laser strike to the head. When the laser strikes a worm, it withdraws, briefly accelerating backwards and eventually returning to forward motion, usually in a different direction. Individual worms respond differently. Some, for instance, immediately reverse direction upon laser stimulus, while others pause briefly before responding. Another variable in the experiments is the intensity of the laser: Worms respond faster to hotter and more rapidly rising temperatures.

For the PNAS paper, the researchers fed the Sir Isaac platform the motion data from the first few seconds of the experiments — before and shortly after the laser strikes a worm and it initially reacts. From this limited data, the algorithm was able to capture the average responses that matched the experimental results and also to predict the motion of the worm well beyond these initial few seconds, generalizing from the limited knowledge. The prediction left only 10 percent of the variability in the worm motion that can be attributed to the laser stimulus unexplained. This was twice as good as the best prior models, which were not aided by automated inference.

“Predicting a worm’s decision about when and how to move in response to a stimulus is a lot more complicated than just calculating how a ball will move when you kick it,” Nemenman says. “Our algorithm had to account for the complexities of sensory processing in the worms, the neural activity in response to the stimuli, followed by the activation of muscles and the forces that the activated muscles generate. It summed all this up into a simple and elegant mathematical description.”

The model derived by Sir Isaac was well-matched to the biology of C. elegans, providing interpretable results for both the sensory processing and the motor response, hinting at the potential of artificial intelligence to aid in discovery of accurate and interpretable models of more complex systems.

“It’s a big step from making predictions about the behavior of a worm to that of a human,” Nemenman says, “but we hope that the worm can serve as a kind of sandbox for testing out methods of automated inference, such that Sir Isaac might one day directly benefit human health. Much of science is about guessing the laws that govern natural systems and then verifying those guesses through experiments. If we can figure out how to use modern machine learning tools to help with the guessing, that could greatly speed up research breakthroughs.”

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Biology may not be so complex after all

Songbird data yields new theory for learning sensorimotor skills

"Our findings suggest that an animal knows that even the perfect neural command is not going to result in the right outcome every time," says Emory biophysicist Ilya Nemenman. (Image courtesy Samuel Sober.)

By Carol Clark

Songbirds learn to sing in a way similar to how humans learn to speak — by listening to their fathers and trying to duplicate the sounds. The bird’s brain sends commands to the vocal muscles to sing what it hears, and then the brain keeps trying to adjust the command until the sound echoes the one made by the parent.

During such trial-and-error processes of sensorimotor learning, a bird remembers not just the best possible command, but a whole suite of possibilities, suggests a study by scientists at Emory University.

The Proceedings of the National Academy of the Sciences (PNAS) published the study results, which include a new mathematical model for the distribution of sensory errors in learning.

“Our findings suggest that an animal knows that even the perfect neural command is not going to result in the right outcome every time,” says Ilya Nemenman, an Emory professor of biophysics and senior author of the paper. “Animals, including humans, want to explore and keep track of a range of possibilities when learning something in order to compensate for variabilities.”

Nemenman uses the example of learning to swing a tennis racket. “You’re only rarely going to hit the ball in the racket’s exact sweet spot,” he says. “And every day when you pick up the racket to play your swing is going to be a little bit different, because your body is different, the racket and the ball are different, and the environmental conditions are different. So your body needs to remember a whole range of commands, in order to adapt to these different situations and get the ball to go where you want.”

First author of the study is Baohua Zhou, a graduate student of physics. Co-authors include David Hofmann and Itai Pinkoviezky (post-doctoral fellows in physics) and Samuel Sober, an associate professor of biology.

Traditional theories of learning propose that animals use sensory error signals to zero in on the optimal motor command, based on a normal distribution of possible errors around it — what is known as a bell curve. Those theories, however, cannot explain the behavioral observations that small sensory errors are more readily corrected, while the larger ones may be ignored by the animal altogether.

For the PNAS paper, the researchers analyzed experimental data on Bengalese finches collected in previous work with the Sober lab. The lab uses finches as a model system for understanding how the brain controls complex vocal behavior and motor behavior in general.

Miniature headphones were custom-fitted to adult birds and used to provide auditory feedback in which the pitch that the bird perceives it vocalizes at could be manipulated, replacing what the bird hears — its natural auditory feedback — with the manipulated version. The birds would try to correct the pitch they were hearing to match the sound they were trying to make. Experiments allowed the researchers to record and measure the relationship between the size of a vocal error the bird perceives, and the probability of the brain making a correction of a specific size.

The researchers analyzed the data and found that the variability of errors in correction did not have the normal distribution of a bell curve, as previously proposed. Instead, the distribution had long tails of variability, indicating that the animal believed that even large fluctuations in the motor commands could sometimes produce a correct pitch. The researchers also found that the birds combined their hypotheses about the relationship between the motor command and the pitch with the new information that their brains received from their ears while singing. In fact, they did this surprisingly accurately.

“The birds are not just trying to sing in the best possible way, but appear to be exploring and trying wide variations,” Nemenman says. “In this way, they learn to correct small errors, but they don’t even try to correct large errors, unless the large error is broken down and built up gradually.”

The researchers created a mathematical model for this process, revealing the pattern of how small errors are corrected quickly and large errors take much longer to correct, and might be neglected altogether, when they contradict the animal’s “beliefs” about the errors that its sensorimotor system can produce.

“Our model provides a new theory for how an animal learns, one that allows us to make predictions for learning that we have tested experimentally,” Nemenman says.

The researchers are now exploring if this model can be used to predict learning in other animals, as well as predicting better rehabilitative protocols for people dealing with major disruptions to their learned behaviors, such as when recovering from a stroke.

The work was funded by the National Institutes of Health BRAIN Initiative, the James S. McDonnell Foundation, and the National Science Foundation. The NVIDIA corporation donated high-performance computing hardware that supported the work.

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How songbirds learn to sing

BRAIN grant to fund study of how the mind learns

Biophysicist Ilya Nemenman, left, is developing theories about the brain that can be tested in the lab of biologist Sam Sober, right. (Emory Photo/Video).

By Carol Clark

How does the brain correct mistakes and guide the process of learning a skill? Why do some individuals learn faster than others?

Two Emory researchers – biophysicist Ilya Nemenman and biologist Sam Sober – recently received a $1 million grant from the National Institutes of Health BRAIN Initiative to explore these questions through a theoretical-experimental framework. Their research into how the sensory-motor loop controls and optimizes learning could lead to better protocols to help those dealing with major disruptions to their learned behaviors, such as when recovering from a stroke.

The BRAIN Initiative (Brain Research through Advancing Innovative Neurotechnologies) was launched by President Obama in 2014 as part of a widespread effort to gain fundamental insights for treating a range of brain disorders.

Emory has received other grants from the BRAIN Initiative: In 2015, a $1.7 million award went to neuroscientists Dieter Jaeger (Department of Biology) and Garrett Stanley (Emory-Georgia Tech’s Wallace H. Coulter Department of Biomedical Engineering). They will use the award to explore neural circuits related to sensing and physical action. In 2016, neurosurgeon Robert Gross in the School of Medicine received a $5 million grant to focus on optimizing neurostimulation therapies for epilepsy.

The grant received by Nemenman and Sober is part of a new cohort, opening another phase of the BRAIN Initiative: The development of theoretical, computational and statistical tools.

“Big data by itself is not useful,” Nemenman says. “We also need to come up with methods for understanding such data.”

Nemenman is working on a theory to help explain how the brain learns. “If you are learning something similar to something that you already know, it’s easier than if you are learning something entirely new,” he says. “We see this effect across the animal kingdom, including in humans. And this ability to learn something new changes with age.”

He gives the example that he will always speak English with an accent, since he is a native of Belarus and did not move to an English-speaking country until shortly before he became a student at Princeton. His children, however, will speak English without an accent since they were born in the United States and immersed in English from birth.

Nemenman is collaborating with Sober, who conducts experiments with Bengalese finches. “These songbirds are one of the best model systems available for studying how the brain learns to communicate,” Sober says.

The male songbirds sing to attract a mate, but they are not born with this ability, Sober explains. Instead, the young males learn to sing by memorizing, and then imitating, the singing of their fathers. When a young bird sings the wrong note, it tries to correct its mistake to match the memorized “target” sound.

In experiments, the Sober lab places tiny earphones on a songbird. When the bird sings, the researchers distort some of the notes slightly and play back the sound through the earphones. The bird is tricked into thinking it has sung a note incorrectly and tries to correct it.

Through this method, the lab has found that the birds are able to correct small distortions of sound, but they cannot correct large distortions.

“Many errors are distributed as a bell-shaped curve, but the distribution of singing errors in the birds is not bell-shaped,” Nemenman says. He is developing theories to explain how the difficulty of learning and correcting for large disturbances is related to this peculiar shape of the distribution of errors produced by the brain during learning.

“We can test the theories through experiments and learn more about the process,” he says. “The ultimate goal is to develop predictive models of how individuals learn from their errors that can be extended to other organisms, including humans.”

Nemenman also recently received a grant from the Kavli Foundation, to support workshops, symposiums and journal clubs that foster interdisciplinary theoretical and computational approaches to neuroscience, and bridge researchers at Emory and Georgia Tech.

It is important for physicists to share their expertise and collaborate with other scientists focused on understanding the brain, Nemenman says. As chair of the American Physical Society’s division of biological physics, he strives to establish programs that attract young physicists to neuroscience.

“Physicists are well posed to have a dramatic impact in this area,” he says. “We are trained to do science by combining theory and experiments. We can apply the same techniques to study the brain that we use to study other mysteries of the universe. Many graduate students in physics who came in intending to work on string theory, like I did, are coming out with a PhD focused on theoretical neuroscience.”

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Biology may not be so complex after all

Cells talk to their neighbors before making a move

Cells trade information with adjoining cells and, like the telephone game, the original message becomes garbled the further it travels down the line.

By Carol Clark

To decide whether and where to move in the body, cells must read chemical signals in their environment. Individual cells do not act alone during this process, two new studies on mouse mammary tissue show. Instead, the cells make decisions collectively after exchanging information about the chemical messages they are receiving.

“Cells talk to nearby cells and compare notes before they make a move,” says Ilya Nemenman, a theoretical biophysicist at Emory University and a co-author of both studies, published by the Proceedings of the National Academy of Sciences (PNAS). The co-authors also include scientists from Johns Hopkins, Yale and Purdue.

The researchers discovered that the cell communication process works similarly to a message relay in the telephone game. “Each cell only talks to its neighbor,” Nemenman explains. “A cell in position one only talks to a cell in position two. So position one needs to communicate with position two in order to get information from the cell in position three.”

And like the telephone game – where a line of people whisper a message to the person next to them – the original message starts to become distorted as it travels down the line. The researchers found that, for the cells in their experiments, the message begins to get garbled after passing through about four cells, by a factor of about three.

“We built a mathematical model for this linear relay of cellular information and derived a formula for its best possible accuracy,” Nemenman says. “Directed cell migration is important in processes from cancer to the development of organs and tissues. Other researchers can apply our model beyond the mouse mammary gland and analyze similar phenomena in a wide variety of healthy and diseased systems.”

Since at least the 1970s, and pivotal work by Howard Berg and Ed Purcell, scientists have been trying to understand in detail how cells decide to take an action based on chemical cues. Every cell in a body has the same genome but they can do different things and go in different directions because they measure different chemical signals in their environment. Those chemical signals are made up of molecules that randomly move around.

“Cells can sense not just the precise concentration of a chemical signal, but concentration differences,” Nemenman says. “That’s very important because in order to know which direction to move, a cell has to know in which direction the concentration of the chemical signal is higher. Cells sense this gradient and it gives them a reference for the direction in which to move and grow.”

Berg and Purcell understood the best possible margin of error – the detection limit – for such gradient sensing. During the subsequent 30 years, researchers have established that many different cells, in many different organisms, work at this detection limit. Living cells can sense chemicals better than any man-made device.

It was not known, however, that cells can sense signals and make movement decisions collectively.

“Previous research has typically focused on cultured cells,” Nemenman says. “And when you culture cells, the first thing to go away is cell-to-cell interaction. The cells are no longer a functioning tissue, but a culture of individual cells, so it’s difficult to study many collective effects.”

The first PNAS paper drew from three-dimensional micro-fluidic techniques from the Yale University lab of Andre Levchenko, a biomedical engineer who studies how cells navigate; research on mouse mammary tissue at the Johns Hopkins lab of Andrew Ewald, a biologist focused on the cellular mechanisms of cancer; and the quantification methods of Nemenman, who studies the physics of biological systems, and Andrew Mugler, a former post-doctoral fellow in Nemenman’s lab at Emory who now has his own research group at Purdue.

The 3D micro fluidics allowed the researchers to experiment with functional organoids, or clumps of cells. The method does not disrupt the interaction of the cells. The results showed that epidermal growth factor, or EGF, is the signal that these cells track, and that the cells were not making decisions about which way to move as individuals, but collectively.

“The clumps of cells, working collectively, could detect insanely small differences in concentration gradients – such as 498 molecules of EGF versus 502 molecules – on different sides of one cell,” Nemenman says. “That accuracy is way better than the best possible margin of error determined by Berg and Purcell of about plus or minus 20. Even at these small concentration gradients, the organoids start reshaping and moving toward the higher concentration. These cells are not just optimal gradient detectors. They seem super optimal, defying the laws of nature.”

Collective cell communication boosts their detection accuracy, turning a line of about four cells into a single, super-accurate measurement unit.

In the second PNAS paper, Nemenman, Mugler and Levchenko looked at the limits to the cells’ precision of collective gradient sensing not just spatially, but over time. “We hypothesized that if the cells kept on communicating with one another over hours or days, and kept on accumulating information, that might expand the accuracy further than four cells across,” Nemenman says. “Surprisingly, however, this was not the case. We found that there is always a limit of how far information can travel without being garbled in these cellular systems.”

Together, the two papers offer a detailed model for collective cellular gradient sensing, verified by experiments in mouse mammary organoids. The collective model expands the classic Berg-Purcell results for the best accuracy of an individual cell, which stood for almost forty years. The new formula quantifies the additional advantages and limitations on the accuracy coming from the cells working collectively.

 “Our findings are not just intellectually important. They provide new ways to study many normal and abnormal developmental processes,” Nemenman says.

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Biophysicists take small step in quest for 'robot scientist'

Biophysicists take small step in quest for 'robot scientist'

The researchers dubbed their algorithm "Sir Isaac," in a nod to one of the greatest scientists of all time, Sir Isaac Newton. 

By Carol Clark

Biophysicists have taken another small step forward in the quest for an automated method to infer models describing a system’s dynamics – a so-called robot scientist. Nature Communications published the finding – a practical algorithm for inferring laws of nature from time-series data of dynamical systems.

“Our algorithm is a small step,” says Ilya Nemenman, lead author of the study and a professor of physics and biology at Emory University. “It could be described as a toy version of a robot scientist, but even so it may have practical applications. For the first time, we’ve taught a computer how to efficiently search for the laws that underlie arbitrary, natural dynamical systems, including complex, non-linear biological systems.”

Nemenman’s co-author on the paper is Bryan Daniels, a biophysicist at the University of Wisconsin.

Everything that is changing around us and within us – from the relatively simple motion of celestial bodies, to weather and complex biological processes – is a dynamical system. A large part of science is guessing the laws of nature that underlie such systems, summarizing them in mathematical equations that can be used to make predictions, and then testing those equations and predictions through experiments.

“The long-term dream is to harness large-scale computing to make the guesses for us and speed up the process of discovery,” Nemenman says.

Isaac Newton contemplates gravity beneath an apple tree. The intuition of a genius like Newton is one quality that distinguishes human intelligence from even the highest-powered computer and algorithmic program.

While the quest for a true robot scientist, or computerized general intelligence, remains elusive, this latest algorithm represents a new approach to the problem. “We think we have beaten any automated-inference algorithm that currently exists because we focus on getting an approximate solution to a problem, which we can get with much less data,” Nemenman says.

In previous research, John Wikswo, a biophysicist at Vanderbilt University, along with colleagues at Cornell University, applied a software system to automate the scientific process for biological systems.

“We came up with a way to derive a model of cell behavior, but the approach is complicated and slow, and it is limited in the number of variables that it can track – it can’t be scaled to more complicated systems,” Wikswo says. “This new algorithm increases the speed of the necessary calculation by a factor of 100 or more. It provides an elegant method to generate compact and effective models that should allow prediction and control of complex systems.”

Nemenman and Daniels dubbed their new algorithm “Sir Issac.”

The real Sir Isaac Newton serves as a classic example of how the scientific method involves forming hypotheses, then testing them by looking at data and experiments. Newton guessed that the same rules of gravity applied to a falling apple and to the moon in orbit. He used data to test and refine his guess and generated the law of universal gravitation.

To test their algorithm, Nemenman and Daniels created an artificial, model solar system by generating numerical trajectories of planets and comets that move around a sun. In this simplified solar system, only the sun attracted the planets and comets.

Images of the moon by NASA's Galileo spacecraft. Everything that is changing around us and within us – from the relatively simple motion of celestial bodies, to weather and complex biological processes – is a dynamical system.

“We trained our algorithm how to search through a group of laws which were limited enough to be practical, but also flexible enough to explain many different dynamics,” Nemenman explains. “We then gave the algorithm some simulated planetary trajectories, and asked it what makes these planets move. It gave us the universal gravitational force. Not perfectly, but with very good accuracy. The error was just a few percent.”

The algorithm also figured out that force changes velocity, not the position directly. “It gets Newton’s First Law,” Nemenman says, “the fact that in order to predict the possible trajectory of a planet, whether it stays near the sun or flies off into infinity, just knowing its initial position is not enough. The algorithm understands that you also need to know the velocity.”

While most modern-day high school student know Newton’s First Law, it took humanity 2,000 years beyond the time of Aristotle to discover it.

One limitation of the algorithm is inexactness. Getting an approximate model, however, is beneficial as long as the approximation is close enough to make good predictions, Nemenman says.

“Newton’s laws are also approximate, but they have been remarkably beneficial for 350 years,” he says. “We’re still using them to control everything from electron microscopes to rockets.”

Getting an exact description of any complex dynamical system requires large amounts of data, he adds. “In contrast, with our algorithm, we can get an approximate description by using just a few measurements of a system. That makes our method practical.”

The researchers demonstrated, for example, that the algorithm can infer the dynamics of a caricature of an immune receptor in a leukocyte. This type of model could lead to a better understanding of the time-course for the response to an infection or a drug.

In another experiment, the researchers fed the algorithm data on concentrations of just three different species of chemicals involved in glycolysis in yeast. The algorithm generated a model that makes accurate predictions for the full system of this basic metabolic process to consume glucose, which involves seven chemical species.

“If you applied other methods of automatic inference to this system it would typically take tens of thousands of examples to reliably generate the laws that drive these chemical transformations,” Nemenman says. “With our algorithm, we were able to do it with fewer than 100 examples.”

With their experimental collaborators, the researchers are now exploring whether the algorithm can model more complex biological processes, such as the dynamics of insulin secretion in the pancreas and its relationship to the onset of a disease like diabetes. “The biology of insulin secreting cells is extremely complex. Understanding their dynamics on multiple scales is going to be difficult, and may not be possible for years with traditional methods,” Nemenman says. “But we want to see if we can get a good enough approximation with our method to deliver a practical result.”

The intuition of a genius mind like that of Isaac Newton is one quality that distinguishes human intelligence from even the highest-powered computer and algorithmic program.

“You can’t give a machine intuition – at least for now,” Nemenman says. “What we’re hoping we can do is get our computer algorithm to spit out models of phenomena so that we, as scientists, can use them and our intuition to make useful generalizations. It’s easier to generalize from models of specific systems then it is to generalize from various data sets directly.”

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Biology may not be so complex after all

Birdsong study reveals how brain uses timing during motor activity

Songbirds are one of the best systems for understanding how the brain controls complex behavior.  Image credit: Sam Sober.

By Carol Clark

Timing is key for brain cells controlling a complex motor activity like the singing of a bird, finds a new study published by PLOS Biology.

“You can learn much more about what a bird is singing by looking at the timing of neurons firing in its brain than by looking at the rate that they fire,” says Sam Sober, a biologist at Emory University whose lab led the study. “Just a millisecond difference in the timing of a neuron’s activity makes a difference in the sound that comes out of the bird’s beak.”

The findings are the first to suggest that fine-scale timing of neurons is at least as important in motor systems as in sensory systems, and perhaps more critical.

“The brain takes in information and figures out how to interact with the world through electrical events called action potentials, or spikes in the activity of neurons,” Sober says. “A big goal in neuroscience is to decode the brain by better understanding this process. We’ve taken another step towards that goal.”

Sober’s lab uses Bengalese finches, also known as society finches, as a model system. The way birds control their song has a lot in common with human speech, both in how it’s learned early in life and how it’s vocalized in adults. The neural pathways for birdsong are also well known, and restricted to that one activity.

“Songbirds are the best system for understanding how the brain controls complex vocal behavior, and one of the best systems for understanding control of motor behavior in general,” Sober says.



Researchers have long known that for an organism to interpret sensory information – such as sight, sound and taste – the timing of spikes in brain cells can matter more than the rate, or the total number of times they fire. Studies on flies, for instance, have shown that their visual systems are highly sensitive to the movement of shadows. By looking at the timing of spikes in the fly’s neurons you can tell the velocity of a shadow that the fly is seeing.

An animal’s physical response to a stimulus, however, is much slower than the millisecond timescale on which spikes are produced. “There was an assumption that because muscles have a relatively slow response time, a timing code in neurons could not make a difference in controlling movement of the body,” Sober says.

An Emory undergraduate in the Sober lab, Claire Tang, got the idea of testing that assumption. She proposed an experiment involving mathematical methods that she was learning in a Physical Biology class. The class was taught by Emory biophysicist Ilya Nemenman, an expert in the use of computational techniques to study biological systems.

“Claire is a gifted mathematician and programmer and biologist,” Sober says of Tang, now a graduate student at the University of California, San Francisco. “She made a major contribution to the design of the study and in the analysis of the results.”

Co-authors also include Nemenman; laboratory technician Diala Chehayeb; and Kyle Srivastava, a graduate student in the Emory/Georgia Tech graduate program in biomedical engineering.

The researchers used an array of electrodes, each thinner than a human hair, to record the activity of single neurons of adult finches as they were singing.

“The birds repeat themselves, singing the same sequence of ‘syllables’ multiple times,” Sober says. “A particular sequence of syllables matches a particular firing of neurons. And each time a bird sings a sequence, it sings it a little bit differently, with a slightly higher or lower pitch. The firing of the neurons is also slightly different.”

The acoustic signals of the birdsong were recorded alongside the timing and the rate that single neurons fired. The researchers applied information theory, a discipline originally designed to analyze communications systems such as the Internet or cellular phones, to analyze how much one could learn about the behavior of the bird singing by looking at the precise timing of the spikes versus their number.

The result showed that for the duration of one song signal, or 40 milliseconds, the timing of the spikes contained 10 times more information than the rate of the spikes.

“Our findings make it pretty clear that you may be missing a lot of the information in the neural code unless you consider the timing,” Sober says.

Such improvements in our understanding of how the brain controls physical movement hold many potential health applications, he adds.

“For example,” he says, “one area of research is focused on how to record neural signals from the brains of paralyzed people and then using the signals to control prosthetic limbs. Currently, this area of research tends to focus on the firing rate of the neurons rather than taking the precise timing of the spikes into account. Our work shows that, in songbirds at least, you can learn much more about behavior by looking at spike timing than spike rate. If this turns out to be true in humans as well, timing information could be analyzed to improve a patient’s ability to control a prosthesis.”

The research was supported by grants from the National Institutes of Health, the National Science Foundation, the James S. McDonnell Foundation and Emory’s Computational Neuroscience Training Program.

Bird graphic courtesy of Sam Sober.

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Physicists eye neural fly data, find formula for Zipf's law

The Zipf's law mechanism was verified with neural data of blowflies reacting to changes in visual signals.

By Carol Clark

Physicists have identified a mechanism that may help explain Zipf’s law – a unique pattern of behavior found in disparate systems, including complex biological ones. The journal Physical Review Letters is publishing their mathematical models, which demonstrate how Zipf’s law naturally arises when a sufficient number of units react to a hidden variable in a system.

“We’ve discovered a method that produces Zipf’s law without fine-tuning and with very few assumptions,” says Ilya Nemenman, a biophysicist at Emory University and one of the authors of the research.

The paper’s co-authors include biophysicists David Schwab of Princeton and Pankaj Mehta of Boston University. “I don’t think any one of us would have made this insight alone,” Nemenman says. “We were trying to solve an unrelated problem when we hit upon it. It was serendipity and the combination of all our varied experience and knowledge.”

Their findings, verified with neural data of blowflies reacting to changes in visual signals, may have universal applications. “It’s a simple mechanism,” Nemenman says. “If a system has some hidden variable, and many units, such as 40 or 50 neurons, are adapted and responding to the variable, then Zipf’s law will kick in.”

That insight could aid in the understanding of how biological systems process stimuli. For instance, in order to pinpoint a malfunction in neural activity, it would be useful to know what data recorded from a normally functioning brain would be expected to look like. “If you observed a deviation from the Zipf’s law mechanism that we’ve identified, that would likely be a good place to investigate,” Nemenman says.

“Letters and words in language are sequences that encode a description of something that is changing over time, like the plot line in a story,” Nemenman says.

Zipf’s law is a mysterious mathematical principle that was noticed as far back as the 19th century, but was named for 20th-century linguist George Zipf. He found that if you rank words in a language in order of their popularity, a strange pattern emerges: The most popular word is used twice as often as the second most popular, and three times as much as the third-ranked word, and so on. This same rank vs. frequency rule was also found to apply to many other social systems, including income distribution among individuals and the size of cities, with a few exceptions.

More recently, laboratory experiments suggest that Zipf’s power-law structure also applies to a range of natural systems, from the protein sequences of immune receptors in cells to the intensity of solar flares from the sun.

“It’s interesting when you see the same phenomenon in systems that are so diverse. It makes you wonder,” Nemenman says.

Scientists have pondered the mystery of Zipf’s law for decades. Some studies have managed to reveal how a feature of a particular system makes it Zipfian, while others have come up with broad mechanisms that generate similar power laws but need some fine-tuning to generate the exact Zipf’s law.

“Our method is the only one that I know of that covers both of these areas,” Nemenman says. “It’s broad enough to cover many different systems and you don’t have to fine tune it: It doesn’t require you to set some parameters at exactly the right value.”

Neurons turn visual stimuli into units of information.

The blowfly data came from experiments led by biophysicist Rob de Ruyter that Nemenman worked on as a graduate student. Flies were turned on a rotor as they watched the world go by, hundreds of times. The moving scenes that the flies repeatedly experienced simulated their natural flight patterns. The researchers recorded when neurons associated with vision spiked, or fired. All sets of the data largely matched within a few hundred microseconds, showing that the flies’ neurons were not randomly spiking, but instead operating like precise coding machines.

If you think of a neuron firing as a “1” and a neuron not firing as a “0,” then the neural activity can be thought of as words, made up of 1s and 0s. When these “words,” or units, are strung together over time, they become “sentences.”

The neurons are turning visual stimuli into units of information, Nemenman explains. “The data is a way for us to read the sentences the fly’s vision neurons are conveying to the rest of the brain.”

Nemenman and his co-authors took a fresh look at this fly data for the new paper in Physical Review Letters. “We were trying to understand if there is a relationship between ideas of universality, or criticality, in physical systems and neural examples of how animals learn,” he says.

The physicists are now researching whether they can bring their work full circle, by showing that the mechanism they identified applies to Zipf’s law in language.

In order to navigate in flight, the flies’ visual neurons adapt to changes in the visual signal, such as velocity. When the world moves faster in front of a fly, these sensitive neurons adapt and rescale. These adaptions enable the flies to adjust to new environments, just as our own eyes adapt and rescale when we move from a darkened theater to a brightly lit room.

“We showed mathematically that the system becomes Zipfian when you’re recording the activity of many units, such as neurons, and all of the units are responding to the same variable,” Nemenman says. “The fact that Zipf’s law will occur in a system with just 40 or 50 such units shows that biological units are in some sense special – they must be adapted to the outside world.”

The researchers provide mathematical simulations to back up their theory. “Not only can we predict that Zipf’s law is going to emerge in any system which consists of many units responding to variable outside signals,” Nemenman says, “we can also tell you how many units you need to develop Zipf’s law, given how variable the response is of a single unit.”

They are now researching whether they can bring their work full circle, by showing that the mechanism they identified applies to Zipf’s law in language.

“Letters and words in language are sequences that encode a description of something that is changing over time, like the plot line in a story,” Nemenman says. “I expect to find a pattern similar to how vision neurons fire as a fly moves through the world and the scenery changes.”

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Biology may not be so complex after all 

Photos: iStockphoto.com

Helping everyone see the light of evolution

"If we don’t help everyone understand what constitutes science and what constitutes faith, we’re bound to run into more problems," says evolutionary biologist Jaap de Roode.

By Carol Clark

Jaap de Roode likes to tell his Evolutionary Biology students: “I don’t believe in evolution.”

It gets their attention. Then he explains: “Evolution isn’t a belief, it’s a theory. You may believe in God and have faith in a religion, but when it comes to science, you look at the evidence for a theory and then decide whether to accept it.”

Any perceived conflict between science and religious beliefs often comes down to semantics, says de Roode, assistant professor of biology at Emory. “I want all of my students to understand the meaning of ‘scientific theory’ and why science is different from faith, but doesn’t have to be in conflict with it,” he says.

Adding to the confusion is the popular use of the word “theory” to describe a hunch or a guess. In science, a hypothesis is more akin to a hunch or a guess, while a theory refers to a body of knowledge supported by considerable evidence, such as gravitational theory or cell theory.

Despite his efforts, at the end of 16 weeks of teaching evolution theory, de Roode sometimes has one or two students complain on their class evaluation forms that he should include opposing views.

“It’s shocking to me that even some seniors, after taking many science courses, still don’t understand that scientifically, there is no alternative to evolution theory,” de Roode says. “They don’t want to fail the class, so they give me the answers they know that I want to see, but they remain skeptical. That bugs me as a scientist, and as a teacher.”

Forty-six percent of Americans responding to a Gallup poll in 2012 said that they believe God created humans in their present form within the past 10,000 years or so, a belief sometimes referred to as “creationism.”

While only a tiny fraction of Emory students report feeling that way to de Roode, even one is too many for him.

“Part of the reason that some of these students don’t want to accept evolution is fear,” he says. “They see and understand the evidence, but they are afraid that it means they will have to give up their faith. I feel strongly that it is my role to help students resolve this conflict.”

The issue came to a head last year, when Emory tapped Ben Carson for its 2012 commencement speaker. In addition to being a renowned neurosurgeon, Carson is a 7th Day Adventist and an advocate of creationism.

A student in de Roode’s class brought Carson’s views on evolution to his attention. De Roode joined with several other faculty to write a letter, published by the Emory Wheel, aimed not at disinviting Carson, but to call attention to Carson’s denial of evolution, and a statement he made implying that accepting evolution was akin to dismissing ethics.

The Emory faculty countered that evolution and the scientific method are not at odds with being moral or religious. “Dr. Carson insists on not seeing a difference between science, which is predictable and falsifiable, and religious belief systems, which by their very nature cannot be falsified,” they wrote. “This is especially troubling since his great achievements in medicine allow him to be viewed as someone who ‘understands science.’”

"Science doesn't invent nature. Science reveals nature," says Joel Martin, author of "The Prism and the Rainbow: A Christian Explains Why Evolution is Not a Threat."

Four hundred others from across the Emory community signed in support of the letter. De Roode points out that he is a great admirer of Carson as a physician. “But it’s important to pay attention to this issue of anti-scientific views,” de Roode says, “because it is standing in the way of scientific progress and the future of this nation. As a university, we are training the country’s future leaders.”

De Roode and other Emory faculty, including biologist Arri Eisen, biophysicist Ilya Nemenman and chemist David Lynn got together with Emory President James Wagner to discuss how to help students struggling to resolve any perceived conflict between scientific evidence and their religious beliefs. They launched a series of small, informal dinners and speaker seminars called “The Nature of Knowledge.”

Five students turned up to discuss evolution and faith at the first dinner, hosted by de Roode and Lynn, and including representatives from Campus Life and the Dean of the Chapel and Religious Life.

“I grew up in a fundamentalist Christian family,” said a freshman majoring in neuroscience and behavioral biology, explaining why he attended the dinner. “I asked my youth counselor in church about the science of evolution that I was learning in high school and he just said, ‘Don’t pay any attention to that.’ But as you grow older, you have to make your own decisions.”

The student added that he has long been a fan of Bill Nye “the science guy,” and a recent video by Nye called “Creationism is Not Appropriate for Children,” prompted him to think more deeply about the topic.

While he accepts evolutionary theory, he finds it odd that, “when high school teachers talk about it, they feel like they have to say, ‘I don’t want to offend anyone’s religious beliefs.’”


In the above video, Bill Nye "the science guy" gives his views on teaching evolution.

The first “Nature of Knowledge” seminar speaker, Joel Martin, drew a standing-room-only audience to Emory’s Harland Cinema last fall. Martin is both an evolutionary biologist at the Natural History Museum of Los Angeles County and an ordained elder in the Presbyterian Church USA, where he works with high school youth ministry. He published a book in 2010 called “The Prism and the Rainbow: A Christian Explains Why Evolution is Not a Threat.”

“When light hits a drop of water, it refracts. It’s a stunning natural spectacle,” Martin told the Emory audience, adding that knowing how a rainbow works does not have to remove God from the picture. “Science does not invent nature. Science reveals nature,” he said. “If this is God’s world, science can only reveal God’s world.”

Martin described a growing disconnect between youth, science and faith. He noted that most major Christian denominations in the United States officially accept the science of evolution, even though some of the members may not.

“The most respected theologians that we have need to come forward and be much more vocal on this issue,” Martin said.

Kyle Niezgoda, a junior majoring in environmental studies, found Martin’s talk beneficial, although he has never doubted evolution.

“I think it’s important to understand how others think and feel, so you can work towards a common goal instead of just arguing,” said Niezgoda, who plans to go to graduate school to study atmospheric science. “The more I get involved in science, the more I realize the importance of being able to translate what I learn to the public, especially when it comes to things like climate change.”

In the spring, a second “Nature of Knowledge” seminar featured Emory primatologist Frans de Waal, who talked about his new book, “The Bonobo and the Atheist: In Search of Humanism Among the Primates.” He described the growing scientific evidence that morality predates religion.

“The Nature of Knowledge” program will continue the series in the fall, with plans to expand some of its events to involve resident life in the dorms.

“We don’t want to stage useless debates between evolution proponents and opponents,” de Roode said. “We’re trying to educate students about the wonderful world around us, rather than have fireworks. If we don’t help everyone understand what constitutes science and what constitutes faith, we’re bound to run into more problems and our children will suffer for it.”

Photos by iStockphoto.com

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Biochemical cell signals quantified for first time

Can you hear me now? When you feel symptoms of a nasty bug, you phone the doctor. Cells in your body are also receiving “calls,” through a biochemical signaling pathway that turns out to have surprisingly low data capacity. 

By Carol Clark

Just as cell phones and computers transmit data through electronic networks, the cells of your body send and receive chemical messages through molecular pathways. The term “cell signaling” was coined more than 30 years ago to describe this process.

Now, for the first time, scientists have quantified the data capacity of a biochemical signaling pathway and found a surprise – it’s way lower than even an old-fashioned, dial-up modem.

“This key biochemical pathway is involved in complex functions but can transmit less than one bit – the smallest unit of information in computing,” says Ilya Nemenman, an associate professor of physics and biology at Emory University. “It’s a simple result, but it changes our view of how cells access chemical data.”

The journal Science is publishing the discovery by Nemenman and colleagues from Johns Hopkins University, including Andre Levchenko, Raymond Cheong, Alex Rhee and Chiaochun Joanne Wang.

During the 1980s, cell biologists began identifying key signaling pathways such as nuclear factor kappa B (NF-kB), known to control the expression of genes in response to everything from invading pathogens to cancer. But the amount of information carried by chemical messengers along these pathways has remained a mystery.

“Without quantifying the signal, using math and computer analysis to attach a number to how much information is getting transmitted, you have a drastically incomplete picture of what’s going on,” says Nemenman, a theoretical biophysicist.

He and Levchenko, a biomedical engineer, began discussing the problem back in 2007 after they met at a conference.

Click on NF-kB graphic, below, to enlarge it:


NF-kB is a protein complex that is a key element of a biochemical signaling pathway involved in cellular responses to a range of stimuli. Graphic: Wikipedia Commons.

Levchenko provided the experimental framework to measure the transmissions occurring on the pathway in many thousands of cells at one time. Nemenman formulated the theoretical framework to analyze and quantify the results of the experiments. Graduate student Raymond Cheong developed and conducted the experiments and performed much of the analysis.

“It was a shock to learn that the amount of information getting sent through this pathway is less than one bit, or binary digit,” Nemenman says. “That’s only enough information to make one binary decision, a simple yes or no.”

And yet NF-kB is regulating all kinds of complex decisions made by cells, in response to stimuli ranging from stress, free radicals, bacterial and viral pathogens and more. “Our result showed that it would be impossible for cells to make these decisions based just on that pathway because they are not getting enough information,” Nemenman says. “It would be like trying to send a movie that requires one megabit per second through an old-style modem that only transmits 28 kilobits per second.”

They analyzed the signals of several other biochemical pathways besides NF-kB and got a similar result, suggesting that a data capacity of less than one bit could be common. So if cells are not getting all the information through signaling pathways, where is it coming from?

“We’re proposing that cells somehow talk with each other outside of these known pathways,” Nemenman says. “A single cell doesn’t have enough information to consider all the variables and decide whether to repair some tissue. But when groups of cells talk to each other, and each one adds just a bit of knowledge, they can make a collective decision about what actions to take.”


He compares it to a bunch of people at a cocktail party, with cell phones that have weak signals pressed to their ears. Each person is receiving simple messages via their phones that provide a tiny piece to a puzzle that needs to be solved. When the people chatter together and share their individual messages, they are able to collectively arrive at a reliable solution to the puzzle.

A similar phenomenon, called population coding, had been identified for the electrical activity of neural networks, but Nemenman and his colleagues are now applying the idea to bio-chemical pathways.

They hope to build on this research by zeroing in on the role of cell signaling in specific diseases.

In particular, Nemenman wants to analyze and compare the signaling capacities of a cancerous cell versus a normal cell.

“Cancerous cells divide when they shouldn’t, which means they are making bad decisions,” he says. “I would like to quantify that decision-making process and determine if cancer cells have reduced information transduction capacities, or if they have the same capacities as healthy cells and are simply making wrong decisions.”

Nemenman uses a malfunctioning computer as an example. “If you push the ‘a’ key on your computer and a ‘d’ always shows up, that means the computer is misprogrammed but the information from your keystroke gets through just fine,” he says. “But if you keep pressing the letter ‘a’ and different, random letters show up, that indicates a problem with the way the information is being transmitted.”

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Biology may not be so complex after all

Biology may not be so complex after all

By Carol Clark

Centuries ago, scientists began reducing the physics of the universe into a few, key laws described by a handful of parameters. Such simple descriptions have remained elusive for complex biological systems – until now.

Emory biophysicist Ilya Nemenman has identified parameters for several biochemical networks that distill the entire behavior of these systems into simple equivalent dynamics. The discovery may hold the potential to streamline the development of drugs and diagnostic tools, by simplifying the research models.

The resulting paper, now available online, will be published in the March issue of Physical Biology.

"It appears that the details of the complexity of these biological systems don't matter, as long as some aggregate property, which we've calculated, remains the same," says Nemenman, associate professor of physics and biology. He conducted the analysis with Golan Bel and Brian Munsky of the Los Alamos National Laboratory.

The simplicity of the discovery makes it “a beautiful result,” Nemenman says. “We hope that this theoretical finding will also have practical applications.”

He cites the air molecules moving about his office: “All of the crazy interactions of these molecules hitting each other boils down to a simple behavior: An ideal gas law. You could take the painstaking route of studying the dynamics of every molecule, or you could simply measure the temperature, volume and pressure of the air in the room. The second method is clearly easier, and it gives you just as much information.”


Nemenman wanted to find similar parameters for the incredibly complex dynamics of cellular networks, involving hundreds, or even thousands, of variables among different interacting molecules. Among the key questions: What determines which features in these networks are relevant? And if they have simple equivalent dynamics, did nature choose to make them so complex in order to fulfill a specific biological function? Or is the unnecessary complexity a “fossil record” of the evolutionary heritage?

For the Physical Biology paper, Nemenman and co-authors investigated these questions in the context of a kinetic proofreading (KPR) scheme.

KPR is the mechanism a cell uses for optimal quality control as it makes protein. KPR was predicted during the 1970s and it applies to most cellular assembly processes. It involves hundreds of steps, and each step may have different parameters.

Nemenman and his colleagues wondered if the KPR scheme could be described more simply. "Our calculations confirmed that there is, in fact, a key aggregate rate," he says. "The whole behavior of the system boils down to just one parameter."

That means that, instead of painstakingly testing or measuring every rate in the process, you can predict the error and completion rate of a system by looking at a single aggregate parameter.


Charted on a graph, the aggregate behavior appears as a straight line amid a tangle of curving ones. “The larger and more complex the system gets, the more the aggregate behavior is visible,” Nemenman says. “The completion time gets simpler and simpler as the system size goes up.”

Nemenman is now collaborating with Emory theoretical biologist Rustom Antia, to see if the discovery can shed light on the processes of immune cells. In particular, they are interested in the malfunction of certain immune receptors involved in most allergic reactions.

"We may be able to simplify the model for these immune receptors from about 3,000 steps to three steps," Nemenman says. "You wouldn't need a supercomputer to test different chemical compounds on the receptors, because you don't need to simulate every single step, just the aggregate."

Just as the discovery of an ideal gas law led to the creation of engines and automobiles, Nemenman believes that such simple biochemical aggregates could drive advancements in health.

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Biochemical cell signals quantified for first time