Mathematical Neuroscience Is First-Year Focus at MBI

October 7, 2002

"The use of mathematics in studying the brain has had profound impact on the field of neuroscience," says John Rinzel of New York University, one of the organizers of the year-long program in neuroscience now under way at the Mathematical Biosciences Institute. Based at Ohio State University, MBI is one of the three new institutes in the mathematical sciences established this year with funding from the National Science Foundation (see accompanying article).

Neurons receive and transmit signals by means of electrical oscillations. Ever since the discovery of the fundamental Hodgkin-Huxley equations, which model electrical impulses and oscillations in neurons, mathematicians have been involved in developing models and computational schemes for systems of neurons. Two basic and intriguing difficulties arise. The first results from the large number of neurons-roughly 100 billion-in the human brain, the second from the large disparity of temporal and spatial scales in neuronal oscillations. An important set of issues in computational neuroscience is centered on bridging these scales.

"At present," Rinzel says, "this can only be achieved by making substantial simplification in the characterization of single neurons." Program co-organizers Bard Ermentrout of the University of Pittsburgh and David Terman of Ohio State University add: "One of our goals this year at the MBI is to connect the biophysically detailed models of single neurons and dendrites to the simplified units required in large-scale simulations."

Rinzel and Barry Horwitz of the National Institutes of Health plan to address systems-level modeling that correlates neurophysiology with lower-level (cellular/circuit) modeling, possibly utilizing data from brain-imaging studies. "For example," Rinzel explains, "we would like to consider relations between the motor-control system and Parkinsonian tremor; we would also like to explore the dynamics of interconnected brain areas during cognition."

The year's program will include a workshop devoted to the auditory system, where mathematics is already a serious player. "We will focus on areas where recent experimental advances pose challenging modeling problems," says organizer Catherine Carr of the University of Maryland. Such areas, she points out, "include complex sound processing, spatial processing, and interaural time differences."

Another workshop will deal with olfaction, which, according to Ermentrout, is an ideal model for distributed neural code. This is so because odors are processed more directly, passing from the receptors to the bulb, then to the cortex, and finally input to other sensory systems. "This processing," Ermentrout points out, "involves complex oscillations which appear to be crucial in order for the animal to discriminate between odors."

One of the year's goals is a better understanding of neurophysiological diseases. An area of current intense research is the dysfunction associated with such disorders as Parkinson's disease and Huntington's chorea. There is a rich array of data on basal ganglia physiology, and evidence of similarities between mammals and birds. "These connections," says David Terman, "will stimulate the development of models realistic enough to test hypotheses on the role of neuronal activity within the basal ganglia in both normal and pathological states."

Although a great deal is known about the relations between stimulus and response of nerve cells in a variety of systems, much less is known about neural coding-that is, the representation of information within the nervous system. "There are several different approaches that attempt to understand neural codes," says John Miller of Montana State University, "and the whole field is ripe for rigorous examination, comparison, and normalization of the different approaches." Miller and Emery Brown of Massachusetts General Hospital plan to address the state of the science of neural coding in an MBI workshop.

The MBI program will bring together theoretical and experimental bioscientists with mathematical scientists, including statisticians, mathematicians, and computational researchers. "This is going to be an exciting year," says MBI director Avner Friedman, expressing his belief that mathematics will play an ever increasing role in deciphering the brain's secrets.

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