Computational Biology, Neuroscience
University of California, Davis
Quantitative Biology: The Interdisciplinary Foundation for 21st Century Biology
Neuroscientist Mark Goldman says the same problems keep popping up in biology again and again. Take the question of how harvester ants in Arizona decide when it's worth venturing out into the blistering sun to collect food. That's not so different from the problem of how synapses in the brain decide whether to transmit signals to their targets or how the brain directs eye movements – problems Goldman has been studying for years.
“The colony looks like a synapse, where the little vesicles of neurotransmitters that get released from the synapse are analogous to ants that get sent out of the colony to forage,” he says. “How do I see that? It's because I look at the world through mathematical equations.”
Math's power to make sense of the world has long appealed to Goldman, who earned a PhD in physics from Harvard with theoretical work explaining how robust patterns can emerge from a system with variable components. His theory made sense of data that neuroscientists had collected from crustaceans, which generate rhythmic food-grinding movements despite variability in the properties of the neurons that control their guts. Goldman showed that the absence of specific ion channels in a neuron might not skew that cell's output, because combinations of channels work together in functional units and there is redundancy in the system.
During postdoctoral work in Sebastian Seung's lab at the Massachusetts Institute of Technology, Goldman moved from the study of single neurons to investigating how networks of neurons produce computations in the nervous systems. In 2003, he set up his own research program at Wellesley College, and in 2008, he moved his lab to the University of California, Davis. He has used mathematical modeling to propose several of the nervous system's computational strategies and works closely with experimental neuroscientists to test his theories.
His studies of how an animal maintains its gaze after the brain stops commanding the eyes to move address the fundamentals of short-term memory. A brain area known as the oculomotor integrator functions as a critical part of the gaze-control circuitry, transforming signals that direct the eyes to move. “This area of the brain literally does calculus,” Goldman says. “It keeps a running total of commands to move the eyes left or right by certain amounts. At every moment in time, it adds the commands to its previous total, just like a student of Calculus is taught.”
According to Goldman, circuits that integrate information in this way are crucial for a variety of decision-making tasks in which evidence about different alternatives are accumulated before a choice is made. In the eye-movement system, his models indicate that individual neurons can account for just one of the 20 seconds that an animal can hold its gaze; it takes a network to keep the eyes steady for the rest of the time. In more cognitive memory circuits, it remains unknown whether the same principles apply. Goldman hypothesizes that they do, but his recent research also suggests the presence of additional, complementary mechanisms that are specific to cognitive memory networks.
His team is also using the eye-movement system to tease apart mechanisms of motor learning. Animals use subtle eye movements to correct for movements of the head and prevent blurry vision. Goldman is investigating how neurons in an area broadly implicated in motor learning, the cerebellum, adjust these corrections as visual feedback changes.
With Stanford ecologist Deborah Gordon, Goldman is examining the foraging behavior of harvester ants. The insects appear to base their foraging decision on contacts with ants that return to the colony: each successful forager offers one piece of evidence that food is available. Like the integrator in the brain that adds up synaptic inputs, the ants appear to add up the evidence from these contacts to decide whether to forage or to retreat back into their nest.
Goldman's educational initiatives are aimed at training a new generation of biologists to think critically and glean more insight from their data through quantitative analyses. “In my ideal world,” Goldman says, “every biologist would be more quantitative.”
Integrating facts and data into critical reasoning takes practice, so when Goldman taught introductory neuroscience, students in his course spent a lot of time applying what they had learned to problem sets, making sense of data, and learning how to develop and adjust mathematical models. His “Math Tools for Neuroscience” course teaches undergraduates to apply differential equations, linear algebra, probability theory, and other mathematical techniques to neuroscience problems. “Students need to be able to connect math to something in the world,” he says.
At Wellesley, Goldman worked with colleagues to make the neurobiology major more flexible and accessible to students with diverse backgrounds, so that it could attract students with interests in math, physics, and computer science. At the same time, they introduced more quantitative components into the curriculum. He is now involved in a similar effort to revise the Neurobiology, Physiology, and Behavior program at UC Davis.
As an HHMI professor, Goldman is expanding these efforts, launching two new programs that will prepare students for the demands of modern biology. A large-enrollment neurobiology course will equip students with a hands-on understanding of the full range of research biology skills, from experimental design through quantitative data analysis, and demonstrate how computational modeling can complement experimentation to provide deep insights about biological systems. “We will capture the full scientific process so students understand how scientists create new knowledge,” Goldman says.
In addition, Goldman is leading the development of a new quantitative biology major. The core curriculum will give students a rigorous foundation in biology and the mathematics, statistics, physics, computer science, and mathematical modeling skills that they need to do modern biological research, before they specialize in a specific track later in the program. According to Goldman, the training will give students “the quantitative mindset to look at their data in a completely different framework than a traditional biology student would.”