A conversation with Reka Albert swings rapidly from the most abstract concepts to the most tangible details and back again.
That's because Albert, associate professor in both physics and biology, has forged a hybrid career that investigates problems in biological systems—drought stress in plants or disease in animals—by creating computational representations called network models.
Models, explains Albert, are sets of assumptions about how something in nature works, paired with algorithms that calculate the consequences of interactions within the system. "For each of the systems I study," she says, "I'm trying to find the mathematical model that will most accurately describe how the system changes over time. The goal is for it to be predictive."
Albert's approach to network modeling was honed by her graduate studies at the University of Notre Dame with noted network researcher Albert-Laszlo Barabasi. With their co-authorship of the influential 1999 Science article, "Emergence of scaling in random networks," Albert garnered notice as a rising star in her field. "I was very fortunate to be involved with this project," she reflects. "The work we did was just a beginning, but from it a new discipline—network theory—was born."
The groundbreaking idea that Albert and Barabasi put forward was that certain universal rules govern the workings of all networks, whether they be social, technological or biological. Says Albert, "To arrive at these principles, we re-constructed many networks, including one based on collaborations among scientists who co-authored papers and another that examines connections among movie co-stars, based on the Internet Movie Data Base."
When creating a network model, notes Albert, the object—a cell, an author, an actor—is called a node. The connection or relationship between two nodes—such as when two actors appear in the same movie together—is called an edge. "You represent the network with nodes and edges," she explains, "and you can count how many edges each node has, called the node's degree. Then you can construct a histogram—a statistical graph—that depicts the fraction of nodes with a given degree. That's called the degree distribution and you can compare networks based on the functional form of their degree distributions."
In network theory jargon, a scientist who has co-authored many papers is described as a hub or high degree node, meaning a node with a large number of edges. In all the networks Albert and Barabasi examined, they saw "a small number of hub nodes with lots of connections, a large number of low degree nodes, and everything in between."
When they looked at the exact degree distribution for diverse networks, they were intrigued. Says Albert, all the networks followed the well-known Pareto principle of wealth distribution, also called the 80-20 rule for its assertion that 80 percent of the wealth in a given society is owned by 20 percent of the population. "That's very similar to the function we found," she comments. "Many different networks have the same kind of unequal distribution as the distribution of wealth. We were quite surprised!"
Further experimentation led them to put forward the concept—now referred to as the Barabasi-Albert (BA) model—that all networks grow over time and follow the law of preferential attachment. "It's basically the 'rich get richer' idea," laughs Albert. "We found that nodes with a high number of edges—connections—have a higher chance of acquiring new connections."
Courtesy Reka Albert
A network-based model of guard cell signaling in plants, created by physicist Reka Albert in collaboration with plant physiologist Sarah Assmann. Drought conditions cause plants to produce the hormone abscisic acid (ABA, top), which triggers guard cells to close leaf pores (bottom), conserving water. The color of the nodes represents their function: enzymes are shown in red, signal transducstion proteins are green, membrane transport-related nodes are blue, and secondary messengers and small molecules are orange.
Putting theory to use
Despite her successful debut as a pure network theorist, Albert was pulled in another direction. "As I learned more about the dynamics of networks, I realized that I wanted to specialize," she explains. "I was always the most intrigued by biological networks, particularly those on the molecular level." While the diversity of biological systems makes them difficult to model, Albert was eager to use her knowledge in an interdisciplinary academic setting. "Penn State's goal was to find someone to collaborate closely with biologists, and that's exactly what I wanted to do."
During the past four years, Albert has worked with a number of researchers, among them microbiologist Eric Harvill and population ecologists Peter Hudson and Isabella Cattadori, all affiliated, as she is, with the fledgling Center for Infectious Disease Dynamics. However, Albert's most extensive collaboration thus far has been with plant physiologist Sarah (Sally) Assmann, whose research focuses on how and why plants—specifically the guard cells that control the pore size of leaves—respond to environmental changes. Recalls Albert, "Sally told me that the information about guard cells is starting to get so complicated that only network-based modeling can take her field forward."
Assmann's guard cell work addresses a very tangible global problem: drought. Plants respond to dry conditions by producing the hormone abscisic acid (ABA), which causes the stomata—the leaf's pores—to close, conserving water. Explains Albert, "The guard cells surround the pores and mechanically determine their size. When these cells are full of water, they bow out and the pore is large, but when the cells lose water and become flaccid, the pore is smaller."
"Sally's aim," notes Albert, "was to see what the most important determinant is in the opening and closing of guard cells." With this knowledge in hand, she adds, "we could better understand what we could change about this process to make plants more responsive to the ABA hormone and thus more drought-resistant."
With the assistance of graduate student Song Li (and the support of a USDA grant), Assmann and Albert constructed a network model depicting how a population of stomata react over a specific time period. "Our model points to the least and most critical components of the guard cell regulation process," Albert explains. One intriguing prediction was that inhibiting calcium has a less detrimental effect than expected, whereas decreasing a plant component's pH level leads to a higher than expected defect.
Are the conclusions of a mathematical model foolproof? No such luck, says Albert. "There is a quote that says every model is wrong. Models are based on abstractions and assumptions, so there is always a level at which they're incorrect. But even a model that is not exactly right can be tremendously useful," she says. The way many envision progress in her field, Albert notes, is "by continuous iteration between experiments and modeling." Ideally, she says, network models can save researchers time by generating "a short list of what's most important in the system they're studying."
"My goal," concludes Albert, "is to lead to new biological knowledge. I'm not satisfied to just give predictions. I also want those predictions tested and validated. And I'm happiest when my model leads to new biological discoveries."
Reka Albert, Ph.D. is associate professor of physics and biology in the Eberly College of Science, ralbert@phys.psu.edu. The results of Albert's collaboration with Sarah Assmann were published in their co-authored paper, ""Predicting Essential Components of Signal Transduction Networks: A Dynamic Model of Guard Cell Abscisic Acid Signaling," published in PLoS Biology in 2006.