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The Journal of Neurophysiology Vol. 82 No. 1 July 1999, pp. 398-415
Copyright ©1999 by the American Physiological Society
1Cellular and Systems Neurobiology Section,
Butera Jr., Robert J.,
John Rinzel, and
Jeffrey C. Smith.
Models of Respiratory Rhythm Generation in the
Pre-Bötzinger Complex. II. Populations of Coupled Pacemaker
Neurons. J. Neurophysiol. 82: 398-415, 1999.
We have
proposed models for the ionic basis of oscillatory bursting of
respiratory pacemaker neurons in the pre-Bötzinger complex. In
this paper, we investigate the frequency control and synchronization of
these model neurons when coupled by excitatory amino-acid-mediated
synapses and controlled by convergent synaptic inputs modeled as tonic
excitation. Simulations of pairs of identical cells reveal that
increasing tonic excitation increases the frequency of synchronous
bursting, while increasing the strength of excitatory coupling between
the neurons decreases the frequency of synchronous bursting. Low levels
of coupling extend the range of values of tonic excitation where
synchronous bursting is found. Simulations of a heterogeneous
population of 50-500 bursting neurons reveal coupling effects similar
to those found experimentally in vitro: coupling increases the mean
burst duration and decreases the mean burst frequency. Burst
synchronization occurred over a wide range of intrinsic frequencies
(0.1-1 Hz) and even in populations where as few as 10% of the cells
were intrinsically bursting. Weak coupling, extreme parameter
heterogeneity, and low levels of depolarizing input could contribute to
the desynchronization of the population and give rise to quasiperiodic
states. The introduction of sparse coupling did not affect the burst
synchrony, although it did make the interburst intervals more irregular
from cycle to cycle. At a population level, both parameter
heterogeneity and excitatory coupling synergistically combine to
increase the dynamic input range: robust synchronous bursting persisted
across a much greater range of parameter space (in terms of mean
depolarizing input) than that of a single model cell. This extended
dynamic range for the bursting cell population indicates that cellular
heterogeneity is functionally advantageous. Our modeled system accounts
for the range of intrinsic frequencies and spiking patterns of
inspiratory (I) bursting cells found in the pre-Bötzinger complex
in neonatal rat brain stem slices in vitro. There is a temporal
dispersion in the spiking onset times of neurons in the population,
predicted to be due to heterogeneity in intrinsic neuronal properties,
with neurons starting to spike before (pre-I), with (I), or after
(late-I) the onset of the population burst. Experimental tests for a
number of the model's predictions are proposed.
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