Long-Time Interest in Biorhythems Settles Into Fascination with
Oscillations in Cognitions
By Michelle Sipics
SIAM News, March 2007
Nancy Kopell of Boston University, guest editor
(with Bard Ermentrout and Chris Johnson)
of this issue of SIAM News, will give
SIAM’s John von Neumann Lecture this
summer at ICIAM 2007.
It’s safe to say that Nancy Kopell, a professor of mathematics at Boston
University, often has math on her mind. But as a pioneer of computational neuroscience, the co-director
of BU’s Center
for Biodynamics is especially interested in the math of the mind, studying
networks of neurons
and brain rhythms—bands of electrical activity in the brain that are
associated with a variety of cognitive states.
“The major scientific question I’m after is how the dynamics of
the nervous system contributes
to all aspects of cognition—sensory processing through motor planning,” Kopell
says. “My corner
of this concerns the role of brain rhythms in cognition. The electrical activity
that can be measured
. . . in the nervous system can be parsed into frequency bands; different
combinations of frequency
bands are associated with different cognitive states.”
Kopell explains that experimental work in this area has been done in behaving
vivo), as well as in vitro, using brain slices from many parts of the nervous
“The central role of mathematics, modeling, and simulation is to tie
together these experimental
results, using clues from the physiology to help illuminate the way [brain]
rhythms are so
prominently correlated with neural function,” she says. “Methods
of dynamical systems can be
used to help understand the dynamical mechanisms underlying the behavior
of networks of neurons.”
Kopell, who will deliver SIAM’s 2007 John von Neumann lecture at ICIAM
2007, came to
applied mathematics by an indirect route—she is fond of describing her
career as a “biased random
walk.” As a doctoral student at Berkeley, she originally studied dynamical
her thesis on the actions of non-compact abelian groups on manifolds.
“My study of dynamical systems was sufficiently abstract that I didn’t
learn to actually solve
differential equations until I taught the subject,” she recalls with
Near the end of her graduate career, Kopell began to move in a different
that the kinds of questions that were being asked in my area felt too narrow
to me,” she says. “I
couldn’t imagine myself basing an entire intellectual career on those
Kopell says she was drawn to developmental biology, but did a lot of “thrashing
around” before she stumbled upon an oscillating and pattern-forming chemical reaction.
“[It] provided a wonderful situation in which to study the same issues
as in developmental biology, but with the underlying chemistry and
physics much better understood,” she says. From there, she became interested
in a series of questions involving different aspects of rhythms in
biology. One of the first was swimming in the eel-like lamprey; in this work,
the focus was mainly on the anatomical structure of the organism’s
spinal cord. She then moved on to crustacean nervous systems, studying how
the dynamics of individual neurons affect the dynamics of the network.
More recently, she has been studying oscillations associated with cognition,
which she says has been her obsession for the last decade.
One topic that has particularly caught Kopell’s attention involves
brain rhythm abnormalities associated with mental illness. She is currently
working with experimentalists and clinicians to study how rhythms differ
in patients with schizophrenia.
“The relevant brain rhythms, in the so-called ‘gamma frequency
band,’ at about 30–90 Hz, are thought by many to be involved in
of ‘neuronal ensembles’—sets of cells that briefly fire synchronously,” Kopell
explains. “Schizophrenics have pathologies in the formation of
gamma rhythms, and it has been argued that this could account for the disorganized
symptoms associated with [the] disease.”
The electrical activity within the gamma band is associated with early sensory
processing, attention, and awareness. Behavioral symptoms of
schizophrenia include hallucinations, problems with attention, and disordered
Kopell is working with colleagues Steve Stufflebeam and Peter Siekmeier,
and Dorea Vierling-Claassen, a student, to study pathological
changes in the responses of gamma rhythms to sensory input—tying abnormalities
on the cellular level to clinical symptoms of schizophrenia.
Earlier research suggests that most frequency bands display major changes in
patients with mental illnesses. Part of Kopell’s work is based on
a previous study related to the response of schizophrenic patients to certain
“If a normal human is given 40-Hz click sounds, the auditory cortex records
an output of 40 Hz—no surprise,” she explains. “But if
is given a 40-Hz input, the output is likely to have a very large component
of 20 Hz. We are trying to tie those results, and various
related observations, to known pathologies of cells and cell communication
Postmortem studies of the brains of schizophrenics have revealed damage to
some cells that function mainly as inhibitors of other cells—damage
that seems to make inhibitory pulses last longer. Analysis of the group’s
model, Kopell says, shows that the extended inhibition might
explain the different reactions of schizophrenics to auditory phenomena like
the click trains.
She is quick to point out, however, that the gamma band is not the only source
of abnormal rhythms in schizophrenic patients; many different
frequency bands are involved with the coordination of different parts of
the nervous system. Another band in which abnormalities are seen
is the “theta” frequency band, around 4–12 Hz, which is
thought to be involved in many aspects of learning and memory.
“How neural rhythms help coordinate interactions among parts of the nervous
system is still the Wild West,” she says. “There are hypotheses
floating around about which bands might be involved in which kinds of coordination,
[and they’re] still very preliminary.” She also stresses
that some of the same pathological rhythms are seen in multiple mental illnesses,
including bipolar disorder and schizophrenia.
Despite the many difficulties, Kopell is hopeful.
“I have the sense that the field is on the cusp of a breakthrough, and
that mathematics can both make sense of existing data and inspire more
experimental work in this area,” she says, adding that the greatest
challenge is formulating the specific questions that mathematics and simulations
need to address.
“What produces the various frequencies in the nervous system?” she
muses. “Why are these frequencies associated with specific cognitive
activities and states? . . . How does the brain make use of these dynamics?
How can changes at the level of gene expression translate into pathologies
of behavior, via changes in neural dynamics?”
The underlying issue in all of those unknowns, she admits, is very close
does the brain work, and how does it fail?”—a problem that
is obviously daunting. But Kopell thinks that modeling of neural dynamics—combined
with mathematical techniques including geometric
analysis, reduction of dimension, probability theory, and other areas—could
play a key role in unraveling the answers.
“Every result on the nature of the different rhythms, as understood from
in vitro, mathematical, and computational work, gives rise to new
questions about in vivo use of those rhythms, constrained by behavioral experiments,” Kopell
says. “The relation of neural rhythms to disease
is a natural follow up to the question of how the nervous system uses its
rhythms; what we had to say from modeling has led to a pair of experimental
collaborations on different aspects of schizophrenia.”
She doesn’t see the contributions stopping there.
“The more I read, the more I see places where an understanding of the
biophysical bases of neural rhythms can provide a new way of looking
at diseases as diverse as Parkinson’s disease, schizophrenia, bipolar
disorder, and epilepsy,” Kopell says. “I don’t expect to
run out of new
Michelle Sipics is a contributing editor at SIAM News.