1Cellular and Systems Neurobiology Section, Laboratory of Neural Control, National Institute for Neurological Disorders and Stroke, National Institutes of Health, Bethesda, Maryland 20892-4455; and 2School of Electrical and Computer Engineering, Institute for Bioengineering and Biosciences, Georgia Institute of Technology, Atlanta, Georgia 30332-0363
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ABSTRACT |
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Del Negro, Christopher A., Sheree M. Johnson, Robert J. Butera, and Jeffrey C. Smith. Models of Respiratory Rhythm Generation in the Pre-Bötzinger Complex. III. Experimental Tests of Model Predictions. J. Neurophysiol. 86: 59-74, 2001. We used the testable predictions of mathematical models proposed by Butera et al. to evaluate cellular, synaptic, and population-level components of the hypothesis that respiratory rhythm in mammals is generated in vitro in the pre-Bötzinger complex (pre-BötC) by a heterogeneous population of pacemaker neurons coupled by fast excitatory synapses. We prepared thin brain stem slices from neonatal rats that capture the pre-BötC and maintain inspiratory-related motor activity in vitro. We recorded pacemaker neurons extracellularly and found: intrinsic bursting behavior that did not depend on Ca2+ currents and persisted after blocking synaptic transmission; multistate behavior with transitions from quiescence to bursting and tonic spiking states as cellular excitability was increased via extracellular K+ concentration ([K+]o); a monotonic increase in burst frequency and decrease in burst duration with increasing [K+]o; heterogeneity among different cells sampled; and an increase in inspiratory burst duration and decrease in burst frequency by excitatory synaptic coupling in the respiratory network. These data affirm the basis for the network model, which is composed of heterogeneous pacemaker cells having a voltage-dependent burst-generating mechanism dominated by persistent Na+ current (INaP) and excitatory synaptic coupling that synchronizes cell activity. We investigated population-level activity in the pre-BötC using local "macropatch" recordings and confirmed these model predictions: pre-BötC activity preceded respiratory-related motor output by 100-400 ms, consistent with a heterogeneous pacemaker-cell population generating inspiratory rhythm in the pre-BötC; pre-BötC population burst amplitude decreased monotonically with increasing [K+]o (while frequency increased), which can be attributed to pacemaker cell properties; and burst amplitude fluctuated from cycle to cycle after decreasing bilateral synaptic coupling surgically as predicted from stability analyses of the model. We conclude that the pacemaker cell and network models explain features of inspiratory rhythm generation in vitro.
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INTRODUCTION |
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Rhythmic breathing
movements in mammals are hypothesized to originate from patterns of
neural activity generated in the pre-Bötzinger complex
(pre-BötC), a specialized region of the ventrolateral medulla
(Gray et al. 1999; Smith et al. 1991
).
Neurons in the pre-BötC are both necessary and sufficient to
generate inspiratory-related motor output in vitro (Rekling and
Feldman 1998
; Smith et al. 1991
), and
perturbations or lesions of this region disrupt inspiratory activity in
vivo (Hsieh et al. 1998
; Koshiya and Guyenet
1996
; Ramirez et al. 1998
; Solomon
et al. 1999
). Therefore the oscillatory network contained in
the pre-BötC putatively represents the most rudimentary substrate
or kernel for generation and regulation of respiratory rhythm (at least
in vitro) and can be retained in thin slice preparations from neonatal
rodents that generate inspiratory-related motor activity.
Respiratory rhythm generation does not require synaptic
inhibition (Feldman and Smith 1989; Gray et al.
1999
), and a subset of inspiratory interneurons in the
pre-BötC are bursting-pacemaker neurons synchronized by
non-N-methyl-D-aspartate (NMDA) fast excitatory synapses (Johnson et al. 1994
; Koshiya and Smith
1999a
; Smith et al. 1991
; Thoby-Brisson
and Ramirez 2000
; Thoby-Brisson et al. 2000
).
These data suggest that the rhythm-generating mechanism in vitro
incorporates an excitatory network of synaptically coupled pacemaker
neurons (for review, see Rekling and Feldman 1998
).
In the first two papers of this series, Butera et al. created
mathematical models of inspiratory pacemaker neurons (Butera et
al. 1999a), which were assembled to form a network model of the
rhythm-generating kernel (Butera et al. 1999b
). These
models posited burst-generating mechanisms for pacemaker neurons and examined how cellular heterogeneity, excitatory synaptic coupling, and
tonic excitation could influence network-level rhythm generation as
well as the behavior of individual cells in the context of network
activity. We have now evaluated the basis for the models and the
testable predictions that emerged from the modeling studies at cellular
and network levels. We found that the pacemaker neuron and network
models successfully predicted many behaviors observed in vitro. These
new data affirm many of Butera et al. (1999a
,b
)'s theoretical conclusions regarding pacemaker cell behaviors and the
roles of excitatory synapses and cellular heterogeneity in generation
and control of respiratory rhythm in vitro. Several deficiencies of the
models are also identified here and we suggest extensions of the models
to refine our understanding of rhythm generation.
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METHODS |
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Experimental methods
Thin transverse slices (350 µm-thick) with rostral and caudal
ends bordering the pre-BötC were cut from the medulla of neonatal rats (P0-P3) in artificial cerebrospinal fluid (ACSF) containing (in
mM) 128.0 NaCl, 3.0 KCl, 1.5 CaCl2, 1.0 MgSO4, 21.0 NaHCO3, 0.5 NaH2PO4, and 30.0 D-glucose, equilibrated with 95%
O2-5% CO2 (27°C, pH = 7.4), as originally described (Smith et al. 1991). Slices were pinned down in a 2-ml recording chamber and perfused with
ACSF at 5 ml/min. Rhythmic respiratory activity was maintained by
raising the ACSF K+ concentration
([K+]o) to 5-8 mM.
Inspiratory-related motor discharge (Smith et al. 1990
)
was recorded from the hypoglossal nerve (XIIn) rootlets (also captured
in the slice) using fire-polished glass suction electrodes (60-90 µm
ID) and a Cyberamp 360 (Axon Instruments, www.axon.com) with variable
gain and a 0.3- to 1-kHz band-pass filter (Fig.
1). In many experiments, inspiratory
neuron population activity was simultaneously recorded locally in the
pre-BötC using "macropatch" suction electrodes (~100 µm
ID; Fig. 1). The slices were typically cut so that the caudal end of
the pre-BötC was exposed, and the population recordings were made
from this caudal surface. Both the XIIn and pre-BötC recordings
were rectified and smoothed by analog integration and acquired
digitally with raw signals at 4 kHz in PowerLab (ADInstruments,
www.ADInstruments.com). Inspiratory neurons were recorded
extracellularly in the pre-BötC using 0.5-M sodium acetate-filled
microelectrodes (8-12 M
).
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To identify pacemaker neurons, the excitatory synaptic transmission
critical for respiratory network function in vitro (Funk et al.
1993; Ge and Feldman 1998
; Koshiya and
Smith 1999a
) was blocked using 20-µM
6-cyano-7-nitroquinoxaline-2,3-dione disodium (CNQX). All sources of
chemical synaptic transmission were blocked using
low-Ca2+ ACSF containing (in mM) 120 NaCl, 8-12
mM KCl, 0.2 CaCl2, 1 MgSO4, 4 MgCl2, 21 NaHCO3, 0.5 NaHPO4, and 30 mM D-glucose (27°C,
pH = 7.4).
In some experiments, the slice preparation was severed along the midline resulting in two bilaterally separated symmetrical "split slices" (Fig. 10A); inspiratory activity was monitored simultaneously bilaterally via local recordings in the pre-BötC.
Experimental data analysis
Measurements of cellular and network activity such as inspiratory burst period, frequency, and duration were determined off-line using automated algorithms, hand-checked for accuracy. Inspiratory bursts obtained from XIIn or local pre-BötC recordings were detected by threshold crossings. We constructed baseline noise histograms (105 points) from quiescent intervals between bursts (i.e., the network expiratory phase) and fit Gaussian functions to the baseline noise distribution to determine the standard deviation. The event threshold was set at 2 SD greater than mean baseline noise, which ensures that the probability of selecting spurious events was P < 0.05. At high levels of excitability where net inspiratory discharge declined (see Fig. 9), we used fast Fourier transforms to corroborate the mean frequency calculations from the time domain. The threshold-crossing criteria applied to rhythmic XIIn discharge were used to cycle-trigger running averages of XIIn and pre-BötC activity (Figs. 8 and 9).
The action potentials and bursts from pacemaker neurons greatly
exceeded baseline noise (e.g., Figs. 4 and 5) and were also selected by
threshold-crossing algorithms. The first spike of four that occurred
within a sliding 133-ms window (30 Hz) defined burst onset. The last
action potential in the burst was determined from interspike intervals
(ISIs) if two criteria were satisfied: the last spike preceded an ISI
500 ms and the next spike marked subsequent burst onset (defined by
the onset criteria). Action potentials that occurred in the sliding
window but failed to satisfy onset criteria were ignored. These
criteria were also applied to model data and allowed us to distinguish
inspiratory bursts from low-frequency spiking activity that sometimes
occurred between inspiratory cycles. Burst duration was defined as the
time spanning burst onset to offset.
All data presented as burst frequency in this study were first analyzed by computing burst period, defined as the interval from onset to onset in two consecutive bursts. Statistical tests were performed using periods before plotting as frequency (reciprocal of period) to avoid error that can arise from prior conversion to frequency. The changes in burst period and burst duration of single cells before and after CNQX application and/or low-Ca2+ solutions were assessed using paired t-tests.
Mathematical modeling and numerical methods
PACEMAKER NEURON MODEL.
Butera et al. (1999a) modeled inspiratory pacemaker
neurons of the pre-BötC using the fewest number of state
variables and parameters needed to reproduce intracellular data. In
this study, we used their model 1 (see Butera et al.
1999a
for discussion of why model 1 is favored), where a
fast-activating, slowly inactivating persistent
Na+ current
(INaP) primarily constitutes the
burst-generating mechanism. Other currents include Hodgkin-Huxley-like
Na+ current
(INa) and delayed-rectifier-like
K+ current (IK)
for action potential generation, K+- and
Na+-dominated leakage currents
(IL(K) and
IL(Na)), and tonic excitatory synaptic
current (Itonic(e)). In published
classification schemes for modeled bursting neurons, this model
conforms to type I (Bertram et al. 1995
) or
fold-homoclinic (Izhikevich 2000
).
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PACEMAKER-NETWORK MODEL.
The respiratory rhythm-generating kernel was modeled as N
heterogeneous pacemaker neurons, coupled by non-NMDA fast excitatory synapses (Butera et al. 1999b). Phasic synaptic current
(Isyn(e)) was incorporated into
Eq. 1 for cells of the network.
Isyn(e) in neuron j is the
sum of excitatory synaptic input from N
1 non-j cells in the population (all-to-all coupling)
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Numerical methods
Computer simulations of the isolated pacemaker model used the
CVODE numerical integrator (Scott D. Cohen and Alan C. Hindmarsh, www.netlib.org) and XPP software (Bard Ermentrout,
ftp.math.pitt.edu/pub/bardware). Network simulations were coded in
the C programming language and run on Pentium-Linux (Dell,
www.dell.com) and Ultrasparc-Solaris (Sun Microsystems, www.sun.com)
workstations, using a fifth-order Runge-Kutta-Fehlberg integration
method with Cash-Karp parameters and adaptive time step (initial
conditions randomly assigned) (Butera et al. 1999b;
Press et al. 1992
). Before collecting model data,
90 s of simulated time was allowed for initial transient decay.
Network activity was displayed as a running histogram (adjustable bin
size: 10-100 ms) of spike times computed across the network or as a
raster plot of spike times in the population (Figs. 7 and 8).
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RESULTS |
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Evaluation of pacemaker neuron model
SIMULATIONS.
Butera et al. (1999a) proffered model 1 as a minimal
mathematical model of voltage-dependent bursting pacemaker neurons in the pre-BötC. Bursting is influenced by the
excitability parameters that control baseline membrane potential
(VM) such as applied current
(Iapp) or
EK, which acts via the
K+-dominated leakage current. Here we selected
EK for the adjustable excitability
parameter to more accurately compare our simulations with in vitro
experiments where [K+]o
was used to control excitability (see METHODS). At
hyperpolarized VM, the model is
quiescent (e.g., VM =
56 mV at
EK =
80 mV, Fig.
2A). Bursting oscillations,
the periodic alternation between bursts of action potentials and
quiescent interburst intervals, emerge as
EK is used to depolarize baseline
VM. At the highest EK, the neuron exhibits tonic spiking
(e.g., EK =
72 mV, Fig. 2A). Therefore the neuron is a "conditional" pacemaker
since its oscillatory activity depends on voltage. As baseline
VM depolarizes, burst frequency
increases monotonically due to progressive shortening of the interburst
interval and burst duration decreases monotonically due to cumulative
voltage-dependent inactivation of the burst-generating current
INaP (Fig. 2, B and
C). During bursts, spike frequency is highest at burst onset
then declines monotonically until burst termination (Fig.
2B), reflecting the inactivation kinetics of INaP.
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EXPERIMENTAL RECORDINGS IN VITRO.
We compared pacemaker neurons in vitro with the model. Extracellular
recordings were performed to avoid altering cytosolic contents and thus
intrinsic properties and to facilitate random sampling throughout the
pre-BötC. Respiratory pacemakers discharged bursts of
spikes coincident with XIIn motor discharge at 9 mM [K+]o (n = 28). Sixty-four percent of these neurons also discharged ectopic
bursts between XIIn cycles (Fig. 3,
A and B, ), as
previously shown (Koshiya and Smith 1999a
). Figure 3
shows an inspiratory pacemaker neuron with spiking coincident with the
onset of XIIn discharge (A) and a pacemaker neuron in
B with preinspiratory spiking that precedes XIIn discharge
(spiking precedes XIIn discharge) (Johnson et al. 1994
).
Spike discharge patterns were determined by inspiratory cycle-triggered
spike histograms (C and D). To confirm that these
cells had pacemaker properties (i.e., could burst intrinsically in the
absence of rhythmic synaptic drive), we applied CNQX or low
Ca2+ solution, which eliminate network activity
by blocking excitatory synaptic transmission to respiratory neurons
(Funk et al. 1993
; Ge and Feldman 1998
;
Johnson et al. 1994
; Koshiya and Smith
1999a
). The concentration of CNQX used (20 µM) has previously
been shown from whole cell recording to completely block rhythmic
excitatory synaptic drive currents in pacemaker neurons (Koshiya
and Smith 1999a
; Del Negro, unpublished observations). CNQX or
low Ca2+ conditions were maintained afterward to
examine intrinsic cellular properties in the absence of respiratory
rhythm.
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Effects of excitatory synaptic coupling on pacemaker neuron activity
In network simulations the synaptic drive current
Isyn(e) generally prolongs pacemaker
burst duration and decreases burst frequency compared with intrinsic
cell activity in the absence of
Isyn(e) (Butera et al.
1999b). To examine the role of excitatory synaptic input in
vitro and evaluate these model predictions, we measured burst frequency
and duration in 19 pacemaker cells before and after blocking network
activity with CNQX and in 14 pacemaker neurons after blocking all
chemical synaptic transmission with low-Ca2+ solution.
To directly compare these experiments with model predictions, we performed new simulations using the 50-cell pacemaker network with the parameter distributions specified in Table 1. Figure 6A shows synchronized rhythmic activity in the synaptically coupled network and after removal of coupling. Isyn(e) synchronizes neuronal activity to produce population-level bursts. After uncoupling, cells desynchronize their bursting or show tonic spiking or quiescence (due to heterogeneity). One pacemaker neuron exhibiting bursting in both coupled and uncoupled conditions was randomly selected in each of 19 network simulations to mimic sampling one pacemaker neuron per slice preparation in vitro. Burst frequency and duration in the sample cell were computed for coupled and uncoupled states.
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EFFECTS ON BURST FREQUENCY.
Figure 6B (middle) shows the burst frequency of
pacemaker neurons in vitro before and after CNQX application on the
abscissa and ordinate, respectively. From control to CNQX conditions,
burst frequency decreased in the majority of cells, resulting in a
significant mean decrease from 0.22 to 0.18 Hz (P < 0.05, n = 19). Contrary to these in vitro results,
Butera et al. (1999b) reported that removal of
Isyn(e) generally increased burst
frequency in simulations. What could cause this difference between
model predictions and experimental measurements? The original synaptic
uncoupling simulations by Butera et al. eliminated
Isyn(e) but not
Itonic(e), which regulates VM and thus voltage-dependent bursting
behavior. However, pre-BötC neurons putatively receive
both CNQX-sensitive tonic and phasic excitatory synaptic input
(Funk et al. 1993
; Ge and Feldman 1998
), modeled by Itonic(e) and
Isyn(e), respectively. Pharmacological removal of both types of excitatory input by CNQX in vitro could explain the disparity between experiment and theory. To explore this
possibility, we performed new synaptic uncoupling simulations and
simultaneously blocked Isyn(e) and
Itonic(e) in the model to mimic the
effects of CNQX (e.g., Fig. 6A). Mean burst frequency in the
19 randomly selected pacemaker neurons decreased after blockade of
Isyn(e) and
Itonic(e), from 0.34 to 0.26 Hz (Fig. 6B, left, P < 0.05), which
matched experimental results.
EFFECTS ON BURST DURATION.
Isyn(e) generally increased burst
duration in model cells by contributing additional inward current
during the inspiratory phase (Butera et al. 1999b).
Figure 6C (left) shows burst duration for new
simulations before and after removing
Itonic(e) and
Isyn(e) (same cells as Fig.
6B). Burst duration was generally lower after excitatory
synaptic blockade: the mean decreased from 0.75 to 0.58 s
(P = 0.06). This result was not statistically
significant at P < 0.05 because a subset of cells
showed the opposite effect, an increase in burst duration after
blocking Itonic(e) and
Isyn(e). This subset of neurons
expressed relatively large
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Evaluation of population-level activity in the pre-BötC and follower neurons
We tested model predictions regarding population-level activity in
the rhythm-generating kernel and in a hypothetical population of
follower neurons. The pacemaker network provided excitatory synaptic
drive to follower cells that attempt to model cells that transmit
inspiratory drive to hypoglossal motoneurons (see METHODS) (see also Wilson et al. 1999). Network activity in the
pacemaker and follower cells is displayed as a running histogram of
action potentials in the population and as a raster plot of spike times for the two groups of 50 cells (Fig. 7). Intrinsic heterogeneity in the
pacemaker population causes variability in spiking behavior: cells with
low
To test model predictions regarding population-level activity, we
recorded inspiratory discharge in vitro from the XIIn and locally in
the pre-BötC using suction electrodes applied to the caudal
surface of the slice; this exposes pacemaker neurons through the caudal
boundary of the pre-BötC (Fig. 1A). The temporal
relationship of these signals was obtained from cycle-triggered
averaging. Pre-BötC activity preceded XIIn activity by 100-400
ms (Fig. 8A), consistent with
the proposal that the rhythm originates in the pre-BötC
(Rekling and Feldman 1998; Smith et al.
1991
). Neural activity in the pre-BötC outlasted the XIIn
activity for 100-200 ms (Fig. 8A). Bilateral pre-BötC
recordings were synchronous and nearly identical (Fig. 8C).
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Analogous temporal relationships were observed in the model where we
compared activity in the pacemaker population to follower cells at
various EK. Rhythmic bursts in the
follower population display rapid onset followed by a ramp-like
activity decline similar to XIIn discharge, whereas the pacemaker
population discharge both preceded and then outlasted follower activity
by 100-200 ms (Fig. 8B). The temporal dispersion of spiking
activity in the pacemaker population results from heterogeneity
(Butera et al. 1999b). There was less dispersion in the
follower cells because they lack INaP
and thus are more homogenous (Fig. 7).
COMPARISON OF THE MODEL PACEMAKER POPULATION AND
PRE-BÖTC ACTIVITY WITH ELEVATED EXCITABILITY.
Butera et al. (1999b) found that elevating excitability
in the network depresses inspiratory burst amplitude even though burst frequency concomitantly increases. This is a unique feature of the
network composed of model 1 pacemaker cells and does not apply to
identical networks of Butera et al. (1999a)
's model 2 neurons (data not shown). The depression of burst amplitude occurs
because depolarization of model 1 pacemakers cumulatively inactivates INaP, causing fewer spikes per burst
in constituent cells (Fig. 2) and consequently smaller bursts in the
population (Butera et al. 1999b
: Fig. 7 and pp. 405, 413, 414). Originally, Butera et al. used a parameter other than
EK to control excitability. Here we
employed EK to mimic experimental
manipulation of [K+]o.
Pacemaker population activity is displayed in spike-time histograms and
in plots of mean burst area versus EK
in Fig. 9, A and B. The burst-area EK data were pooled
from 10 sets of simulations and normalized at
EK =
88 mV. The results of
these new simulations using EK matched
the original study (Butera et al. 1999b
, Fig. 7): net
activity in the model-1-pacemaker population decreased as a function of
EK (Fig. 9B, open circles).
Figure 9B also shows that generally 5-20% of the model
pacemaker neurons were in their intrinsic bursting state at each level
of EK (i.e., if synaptic coupling were
eliminated these cells would continue bursting and the others would
become silent or tonically active).
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RHYTHMIC-DRIVE TRANSMISSION TO MOTONEURONS AND FOLLOWER
NEURONS WITH ELEVATED EXCITABILITY.
To examine transmission properties of premotor circuits in vitro, we
compared XIIn discharge to pre-BötC population activity at several [K+]o. Average
traces are shown in Fig. 9C with plots of burst area (Fig.
9D, n = 14 slices normalized at 10 mM
[K+]o). Inspiratory XIIn
activity (Fig. 9D, ) declined as a function of
[K+]o, resembling the
pre-BötC-[K+]o
plot (
). This suggests that inspiratory activity is conveyed to
hypoglossal motoneurons by a nearly linear transmission pathway at many
levels of excitability. The model follower population failed to
reproduce these results (see DISCUSSION). Instead, follower activity increased as a function of EK
(Fig. 9B,
).
Contributions of synaptic coupling to network rhythm: experimental tests with split-slice preparations and modeling results with split-pacemaker networks
Excitatory coupling synchronizes pacemaker cell activity
(Koshiya and Smith 1999a). Butera et al.
(1999b)
examined the role of
Isyn(e) by varying the coupling
conductance
, Figs. 1, 2, and 8). Second, coupling strength influences the cycle-to-cycle stability of network activity: weak coupling caused irregular activity patterns where net population activity fluctuated periodically (Butera et
al. 1999b
, their Fig. 4).
To evaluate these theoretical roles for
Isyn(e), we performed in vitro
experiments and new simulations that reduce (but do not eliminate)
Isyn(e). Midline-crossing projections
in the slice connect pacemaker cells in the pre-BötC bilaterally
(Koshiya and Smith 1999a). We surgically ablated these
connections by splitting the slice through the midline, which created
two split slices that continued to oscillate independently
(Fig. 10). Pre-BötC activity was
bilaterally synchronous in intact slices (Figs. 8C and
10A) but became independent and temporally uncorrelated in split slices (cross correlograms not shown).
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To simulate the split-slice experiment, we synaptically uncoupled model pacemaker neurons 1-25 from 26-50, leaving all other parameters intact (including gtonic(e), see METHODS). The separated subpopulations (each with n = 25) were monitored separately before and after applying the split-slice condition (Fig. 10B) to mimic recording separately from left and right halves of the pre-BötC in vitro. Rhythmic activity in the network was synchronous when intact but became completely independent and uncorrelated in the split-network conditions, which resembled activity in the left and right split slices in vitro. In both modeling and experiments, splitting the slice/network resulted in lower population activity signal-to-noise ratios.
SPLIT SLICES.
Effects on oscillation frequency.
To test the prediction that weaker coupling, induced by severing
midline-crossing connections, increases the inspiratory frequency, we
measured frequency in intact whole slices over a range of
[K+]o and then repeated the experiment in
split slices for comparison. Intact slices became rhythmically active
at 5 mM [K+]o and the mean frequency
increased monotonically until 16 mM, with
fMin 0.05 Hz and
fMax
0.5 Hz. At
[K+]o
16 mM, mean frequency declined
slightly (Fig. 11A2,
, n = 14). Split slices became rhythmically
active at 4 mM [K+]o, and the mean frequency
increased monotonically as a function of
[K+]o until 12 mM, with
fMin
0.1 Hz and
fMax
0.45 Hz. At
[K+]o
12 mM, the split slice mean
frequency declined slightly (Fig. 11A, 1 and
2,
, n = 17). Splitting the slice
resulted in a higher mean frequency at all
[K+]o
12 mM due to a leftward shift
of the frequency-[K+]o relationship (Fig.
11A2).
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DISCUSSION |
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We performed experiments in vitro and new simulations to evaluate
mathematical models of neonatal rat inspiratory pacemaker neurons and
the excitatory pacemaker-network that is hypothesized to generate
respiratory rhythm in the pre-BötC in vitro. Butera et al.
(1999a,b
) developed these models in the first two articles of
this series; here we tested fundamental bases of the models and novel
model predictions regarding cellular and population-level contributions
to generation and control of respiratory rhythm. Can bursting
properties of pre-BötC pacemaker neurons be replicated by the
minimal mathematical model (model 1) incorporating a sole burst-generating current INaP? How
does excitatory coupling strength affect the network rhythm? Do
excitatory synapses (tonic and phasic) influence pacemaker cell
behaviors in the context of network activity? And how heterogeneous are
pacemaker neurons and does heterogeneity affect the temporal evolution
of the population-level inspiratory burst?
We found pre-BötC neurons that express silent, bursting, and tonic spiking states. Burst frequency increased and burst duration decreased as cellular excitability increased, consistent with model-1-like behavior. Intrinsic properties were heterogeneous, as reflected in cell-to-cell differences in the range of oscillation frequencies, and the levels of excitability at which cells undergo transition from silence to bursting and from bursting to tonic spiking. The burst-generating mechanism did not require intrinsic Ca2+ currents, consistent with an INaP-like ionic mechanism. Fast excitatory synapses synchronized inspiratory bursting in the pre-BötC and generally prolonged burst duration. Inspiratory synaptic drive reduced population burst frequency, although this effect was difficult to distinguish due to multiple ongoing synaptic influences (not all of which were included in the model). Elevating neuronal excitability via [K+]o increased single cell and population burst frequency and reduced pacemaker cell and population burst duration and amplitude, respectively. Cellular heterogeneity caused temporal dispersion of activity in the rhythm-generating model network, which was mirrored in vitro by inspiratory population bursts in the pre-BötC that arise prior to (and outlast) inspiratory XIIn motor discharge. Finally, weak excitatory coupling caused irregular network rhythms.
Model and data limitations
MODEL LIMITATIONS.
Limitations of the mathematical models are covered in the first two
articles (Butera et al. 1999a,b
). Model 1 incorporates the minimum set of conductances to generate bursting similar to pacemaker cells in the pre-BötC. Real pacemaker neurons
most likely express a greater number of intrinsic membrane conductances than are represented in model 1, which was developed from limited data.
However, the goal was to represent essential burst-generating mechanisms and keep model 1 as simple as possible for computational tractability during network simulations. Alternative models for pacemaker cells were evaluated in the first article of the series, which favored model 1 (see Butera et al. 1999a
). In this
study, we more thoroughly evaluated model 1 by varying the main
parameter values (
LIMITATIONS OF EXPERIMENTAL DATA.
We propose that inspiratory bursting neurons coupled by fast excitatory
synapses generate respiratory rhythm in vitro based on these
observations: the rhythm persists after attenuation of synaptic
inhibition in vitro (Feldman and Smith 1989; Gray
et al. 1999
; Onimaru et al. 1990
);
pre-BötC pacemaker neurons have been identified in
neonatal rats (Johnson et al. 1994
; Koshiya and
Smith 1999a
) and mice (Lieske et al. 2000
;
Thoby-Brisson and Ramirez 2000
; Thoby-Brisson et
al. 2000
); and ionotropic excitatory synapses are required for
rhythm generation (Funk et al. 1993
; Ge and
Feldman 1998
; Smith et al. 1991
) and
synchronization of pacemaker cell bursting (Koshiya and Smith
1999a
).
Data-model comparisons: single pacemaker cell activity
INTRINSIC BURSTING PROPERTIES.
Model 1 proposes a voltage-dependent bursting mechanism: transitions
occur from quiescence to bursting and from bursting to tonic spiking as
cells depolarize as shown from intracellular recordings (Koshiya
and Smith 1999a; Smith et al. 1991
;
Thoby-Brisson and Ramirez 2000
). Here we manipulated
[K+]o in vitro to
depolarize EK and thus baseline
VM and test for voltage dependence.
Although changes in [K+]o
cannot be directly equated to EK in
the model (due to non-Nernstian behavior) (Forsythe and Redman
1988
), raising
[K+]o in vitro and
EK in the model caused similar
effects: in real and model neurons bursting commenced with a frequency
of ~0.05 Hz at low
[K+]o/EK
and exhibited maximum burst frequency of ~0.9 Hz at high [K+]o/EK.
EFFECTS OF INSPIRATORY PHASE EXCITATORY SYNAPTIC INPUT ON
PACEMAKER-CELL ACTIVITY.
Ionotropic excitatory synaptic transmission is required for rhythm
generation in vitro (Funk et al. 1993; Ge and
Feldman 1998
). To distinguish discrete roles for excitatory
synapses, Butera et al. (1999b)
separately manipulated
excitatory coupling strength between rhythm-generating neurons (which
increased burst duration and decreased burst frequency) and tonic
excitatory drive, which predominantly regulated frequency via baseline
VM. These findings predicted that
excitatory synaptic blockade would decrease burst duration and increase
burst frequency in pacemaker neurons. This prediction required that
tonic excitation, which could partially derive from pharmacologically
separate receptors, remain intact.
Population-level activity in the pre-BötC
INSPIRATORY DISCHARGE PATTERN.
We showed that pre-BötC activity develops prior to the
onset of respiratory-related motor activity recorded from the XIIn, which is required if the respiratory rhythm originates in the pre-BötC (Rekling and Feldman 1998;
Smith et al. 1991
). The envelope of
pre-BötC activity was bell-shaped in contrast to the
XIIn pattern, which displays a more rapid onset followed by a ramp-like decline to baseline (originally analyzed by Smith et al.
1990
). Activity in the pre-BötC also outlasted
XIIn discharge for 100-200 ms. These temporal relationships were
observed at all [K+]o
tested in vitro and were predicted by the pacemaker network coupled to
a follower population.
POPULATION BURST AMPLITUDE.
Butera et al. (1999b) predicted that burst amplitude in
a network of model 1 neurons declines monotonically as neuronal
excitability increases; this does not apply to a network of model 2 pacemakers nor other generic pacemaker models (unpublished
simulations). Here we performed new simulations using
EK to compare network simulations with
experiments and obtained equivalent results. Our tests affirmed the
model predictions: at
[K+]o, >10 mM the
amplitude of pre-BötC population activity declined monotonically as a function of
[K+]o. In simulations,
this decline in population activity relates directly to cumulative
voltage-dependent inactivation of
INaP, the same voltage-dependent
mechanism that decreases burst duration in isolated model 1 pacemaker
neurons. Even though no more than 30% (usually 5-20%, Fig.
9B) of the model neurons are in their voltage-dependent
bursting state at a given level of EK,
the net population activity nevertheless reflects the voltage-dependent inactivation properties of INaP. This
suggests that the burst-generating mechanism may be qualitatively
and/or partially correct.
POPULATION-LEVEL FREQUENCY CONTROL.
A fundamental prediction of the model is that tonic excitation of the
pacemaker cells will increase the network oscillation frequency
monotonically, a principle we tested in vitro by manipulating [K+]o to depolarize
pacemaker neurons. In general, frequency increased with elevated
[K+]o except at high
levels of
[K+]o/EK.
At 17-18 mM in intact slices (and at 14-15 mM
[K+]o in split slices),
the inspiratory frequency declined slightly, resulting in nonmonotonic
frequency versus [K+]o
relationships. More recent experimental results show the predicted monotonic relationship when population activity is recorded in pre-BötC "islands" isolated from the thin slices
(Johnson et al. 2001). We therefore attribute the
depression of respiratory frequency at high
[K+]o to synaptic inputs
arising from cells extrinsic to the pre-BötC in the
slice that tend to depress excitability at high
[K+]o.
Bicuculline-sensitive GABAA receptors appear to
be activated in the pre-BötC and affect the level of
excitability at which the pacemaker cells burst (Johnson et al.
2001
). Thus it is clear that nonexcitatory synaptic inputs to
pacemaker cells, which have not yet been included in the model, are
endogenously active in vitro and cause the deviations from model predictions.
EFFECTS OF EXCITATORY SYNAPTIC COUPLING ON FREQUENCY AND STABILITY
OF POPULATION ACTIVITY.
The slice was bisected experimentally to test specific predictions that
a reduction, but not elimination, of
Isyn(e) would increase respiratory
frequency and decrease the regularity of rhythmic output (Butera
et al. 1999b). Rhythm was bilaterally synchronous in the
pre-BötC until splitting the slice, when it became
completely uncorrelated presumably via ablation of synchronizing connections. Therefore severing the midline likely reduced coupling strength as we intended and reduced the rhythm-generating population by
approximately half. Based on the additional effect of changing population size, we simulated the split-network model to examine whether the original predictions regarding reductions in coupling strength (Butera et al. 1999b
) applied if population
size and coupling strength decreased simultaneously. Split-slice
simulations confirmed both effects: an increase in frequency and a
decrease in the regularity of the rhythm.
FOLLOWER NEURONS AND RHYTHMIC DRIVE TRANSMISSION CIRCUITS IN VITRO.
Follower neurons were included in the model to begin constructing
rhythmic drive-transmission circuits, which convey inspiratory rhythm
from pre-BötC neurons to respiratory hypoglossal
motoneurons. The membrane properties of these cells are unknown,
although excitatory amino-acid receptors are involved in inspiratory
drive transmission (Funk et al. 1993; Ge and
Feldman 1998
). Therefore we parsimoniously constructed the
follower population using model 1 neurons with
Summary
Our tests of model predictions affirm that the burst-generating
mechanism in inspiratory pacemaker neurons is a
Ca2+-independent persistent
Na+ current, that pacemaker neurons are
heterogeneous, and that a heterogeneous network of pacemakers coupled
by excitatory synapses can account from many aspects of the inspiratory
rhythm and pattern generated in vitro. These results support many of
Butera et al. (1999a,b
)'s conclusions regarding
pacemaker cell behavior and the roles of excitatory synapses and of
cellular heterogeneity in rhythm generation in vitro.
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ACKNOWLEDGMENTS |
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C. A. Del Negro was supported by a National Institute of Neurological Disorders and Stroke Intramural Competitive Fellowship Award. S. M. Johnson was supported in part by Office of Naval Research Grant N00014-94-0523.
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FOOTNOTES |
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* S. M. Johnson contributed experimental data and R. J. Butera contributed simulations and data analyses.
Address for reprint requests: J. C. Smith, 49 Convent Dr., Rm. 3A50, Bethesda, MD 20892-4455 (E-mail: jsmith{at}helix.nih.gov).
Received 20 November 2000; accepted in final form 8 March 2001.
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REFERENCES |
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