Volume 17, Number 15,
Issue of August 1, 1997
pp. 5666-5677
Copyright ©1997 Society for Neuroscience
Quantal Neurotransmitter Secretion Rate Exhibits Fractal
Behavior
Received June 20, 1996; revised April 8, 1997; accepted May 13, 1997.
Steven B. Lowen1,
Sydney S. Cash2,
Mu-ming Poo3, and
Malvin C. Teich4
1 Department of Electrical and Computer Engineering,
Boston University, Boston, Massachusetts 02215, 2 Department of Biological Sciences, Columbia University,
New York, New York 10027, 3 Department of Biology,
University of California at San Diego, La Jolla, California 92093, and
4 Departments of Electrical and Computer Engineering,
Physics, Biomedical Engineering, and Cognitive and Neural Systems,
Boston University, Boston, Massachusetts 02215
The rate of exocytic events from both neurons and non-neuronal
cells exhibits fluctuations consistent with fractal (self-similar) behavior in time, as evidenced by a number of statistical measures. We
explicitly demonstrate this for neurotransmitter secretion at
Xenopus neuromuscular junctions and for rat hippocampal
synapses in culture; the exocytosis of exogenously supplied
neurotransmitter from cultured Xenopus myocytes and from
rat fibroblasts behaves similarly. The magnitude of the fluctuations of
the rate of exocytic events about the mean decreases slowly as the rate
is computed over longer and longer time periods, the periodogram
decreases in power-law manner with frequency, and the Allan factor
(relative variance of the number of exocytic events) increases as a
power-law function of the counting time. These features are hallmarks
of self-similar behavior. Their description requires models that exhibit long-range correlation (memory) in event occurrences. We have
developed a physiologically plausible model that accords with all of
the statistical measures that we have examined. The appearance of
fractal behavior at synapses, as well as in systems comprising
collections of synapses, indicates that such behavior is ubiquitous in
neural signaling.
Key words:
quantal secretion;
vesicular exocytosis;
miniature
endplate currents;
fractal;
long-term correlation;
lognormal process;
Xenopus neuromuscular junction;
myocyte autoreception;
fibroblast;
hippocampal synapse
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