INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

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.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

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).

View larger version (20K): [in this window] [in a new window]   Fig. 1. A schematic showing the 350-µm-thick neonatal rat medullary slice preparation and typical recording configuration. Population-level recordings obtained using "macropatch" suction electrodes applied locally in the pre-Bötzinger complex (pre-BötC) and from roots of the XIIn were acquired and displayed as raw signals and after rectification/smoothing with a leaky analog integrator (pre-BötC and XII). Sample traces show consecutive inspiratory bursts recorded from the pre-BötC and XIIn at 8-mM [K+]o and cycle-triggered averages of burst activity (average of 60 consecutive respiratory cycles) on an expanded time scale.

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 (I_NaP) primarily constitutes the burst-generating mechanism. Other currents include Hodgkin-Huxley-like Na⁺ current (I_Na) and delayed-rectifier-like K⁺ current (I_K) for action potential generation, K⁺- and Na⁺-dominated leakage currents (I_L(K) and I_L(Na)), and tonic excitatory synaptic current (I_tonic(e)). In published classification schemes for modeled bursting neurons, this model conforms to type I (Bertram et al. 1995) or fold-homoclinic (Izhikevich 2000).

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

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 (I_syn(e)) was incorporated into Eq. 1 for cells of the network. I_syn(e) in neuron j is the sum of excitatory synaptic input from N  1 non-j cells in the population (all-to-all coupling)

(12)

(13)

where _syn(e),i,j is synaptic conductance between neurons i and j, and s_i is the synaptic gating variable. Presynaptic action potentials activate s_i, whose kinetics approximate fast excitatory synapses (_s = 5 ms and k_r = 1) in respiratory neurons (Funk et al. 1993; Ge and Feldman 1998). The function s(V_M) determines the steady-state postsynaptic receptor activation based on presynaptic membrane potential in neuron i. All simulations use N = 50 (see Butera et al. 1999b for choice of N).

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).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

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 (V_M) such as applied current (I_app) or E_K, which acts via the K⁺-dominated leakage current. Here we selected E_K 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 V_M, the model is quiescent (e.g., V_M = 56 mV at E_K = 80 mV, Fig. 2A). Bursting oscillations, the periodic alternation between bursts of action potentials and quiescent interburst intervals, emerge as E_K is used to depolarize baseline V_M. At the highest E_K, the neuron exhibits tonic spiking (e.g., E_K = 72 mV, Fig. 2A). Therefore the neuron is a "conditional" pacemaker since its oscillatory activity depends on voltage. As baseline V_M 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 I_NaP (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 I_NaP.

View larger version (40K): [in this window] [in a new window]   Fig. 2. Behaviors of the pacemaker neuron model. A: 40 s of simulated activity in the model (synaptically isolated) at several EK, using NaP = 2.8 nS and L(K) = 2.4 nS. B: sample traces from A on an expanded time scale at EK = 78.9, 78, and 76.5 mV (left), and single bursts expanded and plotted side-by-side with their corresponding instantaneous spike frequency on the same time scale (middle and right). C: the frequency and duration of oscillatory bursts plotted versus EK in the cell from A and B. EK(Min) and EK(Max) were 79 and 73.5 mV, respectively. D: burst frequency vs. EK plotted for several L(K) between 1.75 and 2.75 nS (NaP = 2.4 nS). E and F: burst frequency (E) and burst duration (F) vs. EK plotted for several NaP between 2.1 and 2.9 nS (L(K) = 2.4 nS).

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.

View larger version (32K): [in this window] [in a new window]   Fig. 3. Extracellular recordings of pacemaker neurons in vitro. A: inspiratory pacemaker neuron before (top and middle) and after (bottom) 20-µM CNQX application, which blocks rhythmic activity in the slice. B: preinspiratory pacemaker neuron before (top) and after (bottom) application of low-Ca2+ solution to block network activity. Middle: an expanded burst from above to accentuate the preinspiratory spike discharge. In both A and B, [K+]o = 9 mM, and inspiratory motor output is displayed via the integrated XIIn activity (XIIn). Ectopic bursts that occurred between XIIn bursts are indicated (). C and D: inspiratory cycle-triggered spike histograms (bin size =20 ms) for the inspiratory (A) and preinspiratory (B) neurons above, displayed with the synchronized cycle-triggered averages of XIIn discharge. Spike frequency histograms and XIIn averages were computed from 10 min of continuous network activity.

View larger version (39K): [in this window] [in a new window]   Fig. 4. Properties of pacemaker neurons in vitro. A: 40 s of recorded activity in a representative pacemaker neuron at several [K+]o in the presence of 20-µM CNQX. B: traces from A at [K+]o = 8, 10, and 12 mM and single bursts on an expanded 600-ms time scale. Expanded bursts are displayed side-by-side with corresponding instantaneous spike frequency (, plotted left ordinate: 0-75 Hz) and spike-frequency-time histograms (, right ordinate, bin size = 20 ms) for all the bursts recorded during 10 min of continuous acquisition. C: burst frequency vs. [K+]o for 5 pacemaker neurons in 20 µM CNQX conditions demonstrating heterogeneity. D: mean burst duration (±SD) in sample pacemaker neurons from C.  in C and D illustrate burst frequency and duration for the cell in A and B.

View larger version (17K): [in this window] [in a new window]   Fig. 5. Effects of low-Ca2+ solution on bursting-pacemaker properties. A: an 8-s sample of pacemaker activity in 20 µM CNQX and 9 mM [K+]o before and after application of low-Ca2+ solution. Spike frequency-time histograms (bin size = 20 ms) are shown for both CNQX (top) and CNQX + low-Ca2+ conditions (bottom). B: category plot of mean burst duration (±SE) in control, CNQX, and CNQX + low-Ca2+ conditions (n = 5); the statistically significant change in burst duration is shown (*, P < 0.05).

Effects of excitatory synaptic coupling on pacemaker neuron activity

In network simulations the synaptic drive current I_syn(e) generally prolongs pacemaker burst duration and decreases burst frequency compared with intrinsic cell activity in the absence of I_syn(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. I_syn(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.

View larger version (38K): [in this window] [in a new window]   Fig. 6. Effects of removing excitatory synaptic input in model pacemaker neurons and in pacemaker neurons in vitro. A: 20 s of pacemaker-network activity during synaptically coupled and uncoupled states in the model. Top traces are running spike frequency-time histograms, computed from spike times in the 50-cell population (bin size = 10 ms). Below are raster plots for spike times in all 50 cells, sorted on the ordinate axis by cell index number. B: scatter plots of burst frequency (in Hz) before and after synaptic uncoupling, plotted on the abscissa and ordinate respectively. From left to right, the synaptic uncoupling experiments were performed in the model (n = 19), in the slice preparation using 20 µM CNQX (n = 19), and in the slice using low-Ca2+ solution (n = 14). C: scatter plots of burst duration (in s) before and after synaptic uncoupling, plotted on the abscissa and ordinate respectively. Left and middle: the synaptic uncoupling experiments were performed in the model (n = 19) and in the slice using 20 µM CNQX (n = 19). Right: the duration of inspiratory bursts are plotted vs. ectopic bursts in the same cell (n = 11).

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 I_syn(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 I_syn(e) but not I_tonic(e), which regulates V_M 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 I_tonic(e) and I_syn(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 I_syn(e) and I_tonic(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 I_syn(e) and I_tonic(e), from 0.34 to 0.26 Hz (Fig. 6B, left, P < 0.05), which matched experimental results.

EFFECTS ON BURST DURATION. I_syn(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 I_tonic(e) and I_syn(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 I_tonic(e) and I_syn(e). This subset of neurons expressed relatively large _NaP (due to random assignment) and was entrained by network rhythms at burst periods too short to allow for complete time-dependent deinactivation of I_NaP during the interburst interval. We did not observe a similar subset of neurons experimentally. In vitro, burst duration consistently decreased after CNQX application; the mean decreased from 0.37 to 0.27 s (P < 0.001, n = 19; Figs. 5B and 6C, middle). To further examine the relationship between I_syn(e) and burst duration in vitro, we compared inspiratory bursts to ectopic bursts that occur when the XIIn is silent. Inspiratory burst duration always exceeded ectopic burst duration, 0.37 versus 0.2 s (P < 0.001, n = 11; Fig. 6C, right). In network simulations, highly depolarized neurons also exhibited ectopic bursts that were shorter in duration and contained fewer spikes than inspiratory bursts (Figs. 6A, raster plots, and 7, cell 28).

View larger version (34K): [in this window] [in a new window]   Fig. 7. Simulations of the pacemaker-network coupled to a follower population. A: 12 s of simulated activity in the pacemaker-network displayed as a running spike frequency-time histogram (bin size = 10 ms) computed from spike times in the 50-cell network (top), to show population activity (similar to pre-BötC in vitro). Membrane potential trajectories are shown below population activity for cells 1, 6, 28, and 45 in the pacemaker network; the voltage calibration for cell 6 applies to all pacemaker and follower cells illustrated. Below the sample voltage traces is raster plot of spike activity in all 50 cells of the pacemaker network. B: activity in the follower population (bottom) displayed as a running spike frequency-time histogram (bin size = 10 ms), which approximately mimics the XIIn in vitro. Sample voltage traces for cells 1, 3, and 19 are shown and a raster plot of spike activity for all 50 neurons of the follower population. Note that intrinsic heterogeneity causes dispersion of cellular spiking activity in both the pacemaker and follower populations, but the dispersion is more pronounced in pacemaker cells.

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 _NaP and/or high _L(K) show weak inspiratory activity (e.g., Fig. 7, cell 6); cells with high _NaP and/or low _L(K) exhibit strong inspiratory activity (cell 1) or strong inspiratory activity and ectopic bursts (cell 28). Cells with very low _L(K) are highly depolarized and show inspiratory-modulated tonic spiking (cell 45).

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).

View larger version (34K): [in this window] [in a new window]   Fig. 8. A: comparisons of local activity patterns recorded from the pre-BötC (gray traces) and XIIn (black traces) in a typical slice preparation at [K+]o = 8, 10, and 12 mM. B: comparison of local activity patterns (running spike frequency-time histograms with bin size = 10 ms) in the model pacemaker (gray trace) and follower populations (black traces) at EK = 82 mV, analogous to superimposed plots of local pre-BötC and XIIn recordings in slices. C: local pre-BötC recordings obtained bilaterally at 10-mM [K+]o from the slice preparation in A. Right (gray) and left (black) recordings are superimposed using normalized ordinate axes. Cycle-triggered averaging was applied to 30 consecutive bursts in the pre-BötC and XIIn in vitro to generate average traces in A and C. Inspiratory-like bursts displayed in B for the model populations were cycle-trigger averaged for 90 s of simulated time.

Analogous temporal relationships were observed in the model where we compared activity in the pacemaker population to follower cells at various E_K. 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 I_NaP 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 I_NaP, 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 E_K to control excitability. Here we employed E_K to mimic experimental manipulation of [K⁺]_o. Pacemaker population activity is displayed in spike-time histograms and in plots of mean burst area versus E_K in Fig. 9, A and B. The burst-area E_K data were pooled from 10 sets of simulations and normalized at E_K = 88 mV. The results of these new simulations using E_K matched the original study (Butera et al. 1999b, Fig. 7): net activity in the model-1-pacemaker population decreased as a function of E_K (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 E_K (i.e., if synaptic coupling were eliminated these cells would continue bursting and the others would become silent or tonically active).

View larger version (30K): [in this window] [in a new window]   Fig. 9. A: cycle-triggered averages of pacemaker-network activity and follower population activity at several EK in a typical simulation. Traces are displayed using spike frequency-time histograms (bin size =10 ms) and a 2-s time scale. The spikes/bin calibration applies to all traces, referenced to baseline. B: normalized mean burst area (±SE) in the pacemaker population plotted vs. EK (left ordinate, ). Follower population activity (not normalized) is also plotted vs. EK using arbitrary units (right ordinate, ). Mean pacemaker and follower population activities were computed from 10 sets of simulations at all EK. The bottom bar graph shows the percentage of conditional pacemakers in the 50-cell network in their voltage-dependent bursting state at each level of EK. C: cycle-triggered averages of pre-BötC and XIIn activity from 8 to 18 mM [K+]o in a typical slice preparation, plotted on a 2-s time scale. One-microvolt calibration applies to all traces referenced to baseline. D: normalized mean burst area (±SE) for pre-BötC and XIIn activity ( and , respectively) in 14 slice preparations plotted vs. [K+]o.

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 E_K (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 I_syn(e) by varying the coupling conductance _syn(e) and found two main effects. First, coupling strength and the network burst frequency were inversely related: weaker coupling results in higher frequency (and vice versa) (Butera et al. 1999b, 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 I_syn(e), we performed in vitro experiments and new simulations that reduce (but do not eliminate) I_syn(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).

View larger version (42K): [in this window] [in a new window]   Fig. 10. Split-slice preparations in vitro and in the model. A: schematic drawings of the intact and split-slice preparations with pre-BötC recordings obtained bilaterally. B: analogous states in the 50-cell pacemaker network before and after applying split-network conditions (see METHODS). Population activity is displayed separately for cells 1-25 and cells 26-50 using running spike frequency-time histograms (bin size = 100 ms).

To simulate the split-slice experiment, we synaptically uncoupled model pacemaker neurons 1-25 from 26-50, leaving all other parameters intact (including g_tonic(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 f_Min  0.05 Hz and f_Max  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 f_Min  0.1 Hz and f_Max  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).