We measured persistent Na+current and membrane properties of bursting-pacemaker and nonbursting inspiratory neurons of the neonatal rat pre-Bötzinger complex (pre-BötC) in brain stem slice preparations with a rhythmically active respiratory network in vitro. In whole-cell recordings, slow voltage ramps (≤100 mV/s) inactivated the fast, spike-generating Na+ current and yielded N-shaped current-voltage relationships with nonmonotonic, negative-slope regions between −60 and −35 mV when the voltage-sensitive component was isolated. The underlying current was a TTX-sensitive persistent Na+ current (I NaP) since the inward current was present at slow voltage ramp speeds (3.3–100 mV/s) and the current was blocked by 1 μM TTX. We measured the biophysical properties ofI NaP after subtracting the voltage-insensitive “leak” current (I Leak) in the presence of Cd2+ and in some cases tetraethylammonium (TEA). Peak I NaP ranged from −50 to −200 pA at a membrane potential of −30 mV. Decreasing the speed of the voltage ramp caused time-dependent I NaPinactivation, but this current was present at ramp speeds as low as 3.3 mV/s. I NaP activated at −60 mV and obtained half-maximal activation near −40 mV. The subthreshold voltage dependence and slow inactivation kinetics ofI NaP, which closely resemble those ofI NaP mathematically modeled as a burst-generation mechanism in pacemaker neurons of the pre-BötC, suggest thatI NaP predominantly influences bursting dynamics of pre-BötC inspiratory pacemaker neurons in vitro. We also found that the ratio of persistent Na+conductance to leak conductance (g NaP/g Leak) can distinguish the phenotypic subpopulations of bursting pacemaker and nonbursting inspiratory neurons: pacemaker neurons showedg NaP/g Leak>g NaP/g Leakin nonpacemaker cells (P < 0.0002). We conclude thatI NaP is ubiquitously expressed by pre-BötC inspiratory neurons and that bursting pacemaker behavior within the heterogeneous population of inspiratory neurons is achieved with specific ratios of these two conductances,g NaP andg Leak.
The neural rhythm for breathing in mammals is generated by a network in the brain stem. The intrinsic membrane and synaptic properties of constituent neurons in this network determine the mechanism of rhythm generation. Here we quantify biophysical properties of inspiratory neurons in the pre-Bötzinger complex (pre-BötC)—the critical locus for rhythm generation in the ventrolateral medulla that contains the neurons that are necessary and sufficient to generate inspiratory motor rhythms in vitro (Rekling and Feldman 1998; Smith et al. 1991, 2000) and in vivo (Koshiya and Guyenet 1996; Ramirez et al. 1998) and are required for normal breathing in intact awake adult rats in vivo (Gray et al. 2001). The pre-BötC contains a subset of inspiratory neurons that express autonomous oscillatory bursting behavior, i.e., “pacemaker” neurons (Johnson et al. 1994;Koshiya and Smith 1999a; Smith et al. 1991; Thoby-Brisson and Ramirez 2001) as well as nonbursting neurons. Rhythm generation does not require chloride-mediated postsynaptic inhibition (Feldman and Smith 1989; Gray et al. 1999) and inspiratory neuron activity is synchronized via excitatory synapses (Koshiya and Smith 1999a). Therefore we proposed that an excitatory network of pre-BötC neurons putatively constitutes the rhythm-generating kernel and that rhythm emerges at the population level from a dynamic interaction of intrinsic cellular properties and excitatory network synaptic interactions (Butera et al. 1999b; Smith et al. 2000).
Previously we modeled pre-BötC inspiratory neurons and hypothesized that a persistent Na+ current (I NaP) interacting with a K+-dominated, voltage-insensitive leak-type current (I Leak) can give rise to bursting pacemaker behavior in a subset of cells with appropriate levels of the key conductances–the persistent Na+ conductance (g NaP) and the leak conductance (g Leak) (Butera et al. 1999a). We then assembled a heterogeneous network model of the pre-BötC kernel containing bursting-pacemaker and nonbursting phenotypes (Butera et al. 1999b). The relative magnitudes of g NaP andg Leak determines whether model neurons exhibit bursting-pacemaker or nonbursting behavior when other biophysical properties are kept constant. Heterogeneity ofg NaP andg Leak was shown in the models to importantly affect network dynamic behavior, and parameter distributions were originally chosen to optimize network performance. Recently, in vitro experiments verified that the models can closely resemble neuronal and network behaviors recorded in vitro (Del Negro et al. 2001). However, several issues remain unresolved. If neonatal rat pre-BötC pacemaker neurons expressI NaP, then 1) what are its biophysical properties? and 2) how much heterogeneity is there in the magnitude of g NaP? Also, what intrinsic membrane parameters engender bursting pacemaker behavior in the subset of inspiratory neurons expressing these properties? In particular, 3) are the relative magnitudes ofg NaP andg Leak related to bursting pacemaker and nonbursting behaviors, as demonstrated in the models?
To address these questions we sampled inspiratory neurons using whole-cell patch-clamp recordings in the pre-BötC of neonatal rat thin brain stem slices in vitro. We determined thatI NaP is expressed in all inspiratory neurons that we sampled, both bursting pacemaker and nonbursting inspiratory cells, but that I NaPengenders bursting according to the relative magnitude ofg NaP andg Leak. We also examined the heterogeneity of membrane properties and thus obtained information on the distribution of inspiratory neuron properties within the pre-BötC. Preliminary reports of this work have appeared in abstract form (Koshiya and Smith 1999b; Koshiya et al. 2001).
In vitro brain stem slice preparation
Thin transverse slices (350-μm thick, Fig.1 A) containing 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 30.0d -glucose, equilibrated with 95% O2-5% CO2 (27°C, pH 7.4), as originally described (Smith et al. 1991). Slices were cut to expose the caudal surface of the pre-BötC (Koshiya and Smith 1999a). Low calcium solution used in some experiments contained 124.5 mM NaCl, 3.0 mM KCl, 0.5 mM CaCl2, 2.0 mM MgCl2, 25.0 mM NaHCO3, 30.0 mMd-glucose, and 100–200 μM CdCl2. Tetraethylammonium chloride (TEA, 20 mM) was substituted on an equimolar basis for NaCl for some experiments to attenuate K+ currents. TTX (Sigma) was bath applied at 1 μM and 6-cyano-7-nitroquinoxaline-2,3-dione disodium (CNQX, Sigma) was applied at 10–20 μM.
The slice was stabilized with the caudal surface up using a platinum ring anchor with nylon fibers (Edwards et al. 1989) in an approximately 0.5-ml recording chamber mounted on a fixed-stage videomicroscope (Zeiss Axioskop FS-1) with infrared-differential interference contrast (IR-DIC) optics and perfused with ACSF at 2–4 ml/min. These slices containing the pre-BötC, premotor circuits, and hypoglossal respiratory motoneurons spontaneously generate rhythmic inspiratory motor discharge that can be recorded from the hypoglossal (XII) nerve rootlets (also captured in the slice) (Smith et al. 1991) and maintained for ≥24 h by raising the ACSF K+ concentration ([K+]o) to 7–9 mM. XII inspiratory bursts were recorded using fire-polished glass suction electrodes (40–90 μm ID) and a differential amplifier (Cyberamp 360, Axon Instruments) with variable gain and a 0.3–1 kHz band-pass filter. XII activity was rectified and integrated (∫XII) with either an analog integrator or digitally with Chart software (ADInstruments).
Calcium imaging for functional identification of rhythmic pre-BötC neurons
In some experiments rhythmically active inspiratory neurons in the pre-BötC were first identified for whole-cell patch-clamp recording using Ca2+ imaging of neuron activity, as previously described in detail (Koshiya and Smith 1999a). Briefly, Calcium Green-1 AM (Molecular Probes) (CaG; 50 μg) dissolved in 5 μl of DMSO containing 25 μg of pluronic F-127 (BASF) and dispersed in 10 μl of ACSF was injected with a glass pipette (approximately 10-μm tip diam) into the slice near the midline to retrogradely label pre-BötC neurons. After 8–12 h, CaG fluorescence labeled inspiratory neurons were visualized in the pre-BötC with a 75-W xenon epiilluminator, optical filters (excitation 485 nm, emission 530 nm, 505 nm beam splitter, Omega Optical), and a CCD camera with image intensifier (ICCD-1000F, VideoScope International).
Whole-cell patch-clamp recordings were obtained with an EPC-9 amplifier (version C, HEKA). Electrodes were fabricated from capillary glass (1.5 mm OD, 0.87 mm ID, resistance 4–7 MΩ). Electrodes were filled with solution containing the following (in mM): 136.0 K-gluconate, 4.0 KCl, 10.0 HEPES, 4.0 Mg-ATP, 0.3 Na-GTP, and 2.0 sodium phosphocreatine, pH 7.3, or, for some experiments, 130.0 K-gluconate, 10 Na-gluconate, 4.0 NaCl, 10.0 HEPES, 4.0 Mg-ATP, 0.3 Na-GTP, and 4.0 sodium phosphocreatine, pH 7.3. A liquid junction potential of 8 mV was corrected off-line. Series resistance compensation was applied via the EPC-9. Intracellular data were acquired digitally at 10 kHz and combined with raw XII and integrated XII inspiratory activity acquired at 4 kHz using Pulse (HEKA) and Chart v4.0 (ADInstruments).
Cell capacitance (C M) was determined from the integral of the transient capacity current (I C, leak subtracted) evoked by a series of 15-ms hyperpolarizing voltage-step commands applied within −10 mV of resting potential, using ∫I C =Q M at each command potential (V M).C M is determined from the slope of the plot of Q M versus ΔV M for the series of step commands. Input resistance (R M) was determined via linear regression applied to the linear portion of the quasi-steady-state current-voltage (I-V) relationship generated by a slow voltage ramp (30 mV/s) initiated from −90 mV. In subsequent analyses we take the reciprocal ofR M as an estimate of the voltage-insensitive leak conductance (g Leak e.g., see Fig. 4). Series resistance (R S) was calculated from the decay-time constant of I C, since in voltage clamp τ ≅ R S C M, where τ is an exponential fit to the I C decay time. In general an adequate voltage-clamp requiresR M ≥10R S. Cells failing to meet this criterion were excluded from voltage-clamp analysis.
Voltage dependence and kinetics of whole-cell currents were analyzed from voltage-clamp data using Pulsefit (HEKA), Chart (ADInstruments), and Igor Pro (Wavemetrics) software. Regression analyses were performed with a nonlinear least-squares method in IDL (Research Systems) or Igor Pro. Voltage-ramp data were fit to Boltzmann functions:g/g max = [1 + exp([V M –V 1/2]/k)]−1, where g and g max represent whole-cell conductance at V M and the maximal conductance (for all V M), respectively. V M is membrane potential, V 1/2 is the voltage for half-maximal activation, and k is a slope factor. Kolmogorov–Smirnov tests were performed with Igor Pro. Monte Carlo-based statistical analyses were performed using Igor Pro and Resampling Statistics v5. Normality of data distributions was tested by a Shapiro–Wilk test (JMP software, SAS Institute).
Electrophysiological phenotypes of pre-BötC inspiratory neurons
The thin brain stem slice preparations (Fig. 1 A) spontaneously generate rhythmic inspiratory motor discharge from the XII nerve rootlets (shown as upward deflections of the integrated XII activity in Fig. 1, B and D), allowing respiratory cells to be identified in the context of network activity. We recorded 71 inspiratory neurons in the pre-BötC using whole-cell patch-clamp techniques. These cells were identified based on membrane depolarization or intracellular Ca2+transients (Koshiya and Smith 1999a) during the inspiratory phase. Shifting the membrane potential (V M) under current clamp revealed voltage-dependent intrinsic bursting behavior in a subset of inspiratory neurons (n = 22) defined as bursting-pacemaker cells (also see Koshiya and Smith 1999a; Smith et al. 1991; Thoby-Brisson and Ramirez 2001). At baselineV M of approximately −50 mV or greater, pacemaker neurons generated ectopic bursts during the interval between inspiratory phases of network activity (Fig. 1 B). Nonbursting inspiratory neurons (n = 49) discharged bursts of action potentials only during the inspiratory phase due to excitatory inspiratory synaptic drive. In contrast to pacemaker-type cells, these cells generated only tonic spiking without ectopic bursts between the phases of synaptically driven inspiratory discharge when the baseline V M was depolarized above −50 mV (Fig. 1 D).
To examine intrinsic behavior of isolated inspiratory cells, we blocked excitatory synaptic transmission using CNQX (Koshiya and Smith 1999a) or blocked all chemical synaptic transmission using low Ca2+ solution (with elevated Mg2+ and 100–200 μM Cd2+to block voltage-dependent Ca2+ channels). Either method stopped respiratory network activity and blocked rhythmic excitatory synaptic drive currents to inspiratory pre-BötC neurons as assessed under voltage clamp.
Bursting behavior in inspiratory pacemaker neurons was voltage dependent, as previously shown (Del Negro et al. 2001;Koshiya and Smith 1999a; Smith et al. 1991; Thoby-Brisson and Ramirez 2001). To confirm that our sample of inspiratory pacemaker neurons exhibited intrinsic voltage-dependent bursting, we progressively depolarized cells in current clamp in the absence of network activity and phasic synaptic drive (Fig. 1 C). Depolarizing bias current application caused cells to move from quiescence at hyperpolarized potentials to bursting, where the cells alternate between phases of rapid subthreshold depolarization with spike discharge (i.e., bursts), followed by repolarization and quiescence. Cells transitioned to the tonic spiking state at highly depolarized levels (above approximately −45 mV). Nonbursting inspiratory cells subjected to similar protocols progressed from quiescence to steady tonic spiking as baselineV M was progressively depolarized (not shown) (Thoby-Brisson and Ramirez 2001).
Distribution of membrane and synaptic properties in inspiratory neurons
We used voltage-clamp protocols before and after blocking synaptic transmission to analyze the intrinsic membrane and synaptic properties of pre-BötC inspiratory neurons. Voltage-ramp commands were used to measure the quasi-steady-state I-V relationship with a ramp speed of ≤100 mV/s (see Figs. 1, 3, and 4). All inspiratory neurons examined showed nonmonotonic N-shaped I-V curves (e.g., Fig. 1 F) with the negative slope region at potentials above −60 mV under the slow voltage ramps after subtraction of the “leak” current (below), suggesting the presence of a common non- or slowly inactivating inward current in these cells.
We assessed the basic properties of our sample from the inspiratory cell population, using input resistance (R M), whole-cell capacitance (C M), peak inward current (I peak, measured between −40 and −30 mV in the quasi-steady-state I-V curve, see Figs.1 F, 3 A, and 4, A and B), and synaptic charge transfer (Q syn) computed from the integral of rhythmic inspiratory drive currents measured under voltage clamp (below). These measurements are displayed in histograms for the pooled sample in Fig.2 (top) and as cumulative probability histograms that compare bursting pacemaker and nonbursting inspiratory neuron phenotypes (bottom).
The distributions are skewed for R M,I peak, andQ syn, with most cells clustering below sample means (Fig. 2). Therefore we comparedR M,C M,I peak, andQ syn between pacemaker and nonpacemaker phenotypes using a nonparametric Kolgomorov–Smirnov test. Except C M, which showed a statistical difference in distributions between the phenotypes (pacemaker or not,P < 0.01), all other properties (R M,I peak, andQ syn) distributed indistinguishably between the phenotypes and were therefore pooled for further analyses.R M,I peak, andQ syn showed significant deviation from normal distributions (P < 0.05, Shapiro–Wilks test). Mean pooled R M was 380 ± 32 MΩ: pacemaker neurons (n = 20) had a meanR M of 430 ± 56 MΩ and nonpacemaker cells had a mean R M of 348 ± 40 MΩ (n = 32) (Fig. 2 A), which was not statistically different.C M was significantly different between pacemaker (n = 21) and nonpacemaker (n= 29) cells: 32 ± 3 versus 48 ± 3 pF, respectively (P < 0.01). The pooled sample mean forI peak, which measures the peak persistent inward current (after leak current subtraction) in the quasi-steady-state I-V curve, was 118 ± 23 pA (Fig.2 C) (n = 9 pacemaker cells, 30 nonpacemaker cells).
Q syn was computed from the integral of the envelope of inspiratory drive currents (I syn) (see Fig. 1 E) measured under voltage clamp at V M = −70 mV. I syn was collected for five or more cycles and averaged. Q syn was 11.6 ± 3.0 pC for pacemaker cells (n = 11) and 12.8 ± 2.0 pC for nonpacemaker neurons (n = 28), which was not significantly different between phenotypes (P = 0.75). The pooled sample mean was 12.4 ± 2.0 pC for Q syn (Fig. 2 D).
These results suggested that inspiratory bursting-pacemaker and nonpacemaker neurons cannot be reliably distinguished by any single intrinsic parameter, other than C M.
Persistent Na+ current in pre-BötC inspiratory neurons
Inspiratory pacemaker neurons in neonatal rat slices depend on a persistent Na+ current (I NaP), since bursting continues in low Ca2+ solution (Del Negro et al. 2001; Johnson et al. 1994) and bursting ceases in the presence of TTX (Thoby-Brisson and Ramirez 2001). Here, we tested for the presence ofI NaP in neonatal rat inspiratory pacemaker neurons using a voltage-clamp ramp protocol (n = 9 neurons tested) with ramps generated over the voltage interval −80 to +10 mV with ramp speeds that were slow enough (≤100 mV/s) in some neurons to maintain space clamp sufficiently to prevent activation of the transient fast action potential-generating Na+ current (see Fig. 4 A). We identified bursting pacemaker-type inspiratory neurons based on ectopic bursts in the context of network activity (e.g., Fig. 1 B) (Del Negro et al., 2001; Koshiya and Smith 1999a) and then isolated the cells for voltage-clamp analysis in low Ca2+ solution containing Cd2+ (100–200 μM) to block chemical synaptic transmission and voltage-dependent Ca2+ currents. The inward current in the quasi-steady-state I-V curve was completely blocked by 1 μM TTX (Fig.3 A), indicating the presence of a TTX-sensitive I NaP, obtained by subtraction of I-V curves.
To characterize the voltage dependence of activation, we fitted a Boltzmann function (see methods) to conductance-voltage data (Fig. 3 B and see Fig.4 D), where the conductance was calculated from the I-V relationships and a Na+ reversal potential of +50 mV (based on bathing and pipette solutions). I NaPwas consistently (n = 9 pacemaker neurons) activated starting at −60 mV and reached half-maximal activation at approximately −40 mV, with a slope factor k of approximately 5 (e.g., Fig. 3, B and C, Fig.4 D). Since all inspiratory neurons examined exhibited an N-shaped, quasi-steady-state I-V relationship with a negative-slope region with similar voltage dependence, we hypothesized that I NaP was commonly expressed in all inspiratory cells. Therefore we applied TTX to nonbursting inspiratory neurons (n = 4) and obtained identical results. TTX blocked the subthreshold-activating inward current, and activation curves for the subtracted current (I NaP) fitted with a Boltzmann function for nonbursting inspiratory neurons were indistinguishable from those obtained for pacemaker cells (Fig. 3, B andC).
Ramp-rate dependence of INaP
Using the voltage-clamp ramp protocol, we quantified the voltage-activated inward membrane current in three pacemaker-type neurons at different ramp speeds (e.g., 100, 33, 10, and 3.3 mV/s, Fig.4) under conditions in which Ca2+ currents were blocked with Cd2+ (100–200 μM). The voltage-activated inward current was extracted (Fig. 4 A, solid curve) by subtracting the passive leak currentI Leak, extrapolated from linear regression fits to the I-V curve at membrane voltages between −80 and −60 mV. Consistent with the I-Vrelationships obtained from the TTX protocol, the inward current activated at approximately −60 mV. The multispeed voltage ramp protocol revealed that the amplitude of this inward current was attenuated progressively at slower ramp speeds (Fig. 4, Band C), reflecting the slow inactivation kinetics ofI NaP. The conductance corresponding to each current was calculated using the Na+reversal potential (+50 mV) and normalized to the peak conductance to compare activation characteristics at different ramp rates. The normalized activation conductance-voltage relationship was essentially identical for different ramp speeds over the membrane voltage range −80 to −30 mV. A single Boltzmann function fitted to the data set from one of the neurons (not shown) gave aV 1/2 of –44.7 mV and k = −4.4 mV, similar to the values obtained for the two other pacemaker cells studied with this protocol and similar to values obtained for the TTX-sensitive I NaP described above.
I NaP was further isolated in two pre-BötC pacemaker cells with K+conductances blocked with TEA, in addition to Ca2+ conductances blocked with Cd2+ (Fig. 4 C), to minimize voltage-dependent outward K+ currents and distortion of the ramp I-V relationship. Similar to the voltage-clamp data obtained under Ca2+ current blockade alone (Fig. 4 B), multirate ramps revealed rate-dependent attenuation of theI NaP, (with conductances as high as 4–5 nS at higher ramp speeds); essentially identical normalized conductance-voltage relationships were obtained at different ramp rates (Fig. 4 D). A single Boltzmann curve could be fit to the set of normalized conductance-voltage relationships as illustrated in Fig.4 D, with V 1/2 = −37.4 mV andk = −4.9 mV, very similar to the values obtained for the other data sets described above.
The gNaP/gLeak ratio differs between inspiratory neuron phenotypes
According to the model proposed by Butera et al. (1999a), bursting depends on dynamic interactions ofg NaP (which is voltage and time dependent) and the voltage-independent K+-dominated leak conductanceg Leak. Since the TTX-sensitiveI NaP was present in nonpacemaker as well as bursting-pacemaker neurons, we tested whether the ratio ofg NaP andg Leak was correlated to the pacemaker behaviors. If either parameter is considered alone, inspiratory pacemaker and nonbursting cells are indistinguishable (Fig. 2,bottom). However, when both parameters are considered simultaneously and are plotted for individual cells in a plane withg NaP andg Leak on the ordinate and abscissa, respectively, the spatial relationship shown in Fig.5 is obtained. Pacemaker cells (n = 7 analyzed) generally exhibited higherg NaP/g Leakratios than the sample of nonpacemaker neurons used for this analysis (n = 10).
In each pacemaker and nonpacemaker group,g NaP/g Leakratios were distributed normally: 0.78 ± 0.31 (mean ± SD) and 0.28 ± 0.03, respectively. Deviation from a normal distribution was not significant in both groups: P > 0.60 and P > 0.93, respectively. The distributions ofg NaP/g Leakwere significantly different between pacemaker and nonpacemaker groups:P < 0.0002 (Student's t-test). These data strongly suggested that pacemaker and nonpacemaker pre-BötC inspiratory neuron phenotypes were sampled from two distinct groups, each of which is normally distributed in terms of theg NaP/g Leakratios. We also used a Monte Carlo simulation (Manly 1991; Ripley 1981) to test whether the two phenotypes are spatially segregated in theg NaP-g Leakplane (Fig. 5), to further confirm that these phenotypes comprised significantly different subsets of inspiratory cells based on theg NaP/g Leakratio. This analysis also showed that the relationship between bursting-pacemaker phenotype and theg NaP/g Leakratio is statistically significant at P < 0.01.
Membrane and electrophysiological properties of pre-BötC inspiratory neurons
We have analyzed electrophysiological properties of inspiratory cells in the pre-BötC in vitro and demonstrated the existence of a persistent Na+ current with conductance values as high as 5 nS. These findings concur with our modeling studies (Butera et al. 1999a,b; Del Negro et al., 2001) that first postulated and demonstrated theoretically thatI NaP can function as a primary voltage-dependent burst-generating mechanism. We also confirmed previous studies (Del Negro et al. 2001; Johnson et al. 1994; Smith et al. 1991;Thoby-Brisson and Ramirez 2001) that inspiratory neurons can be divided into two phenotypes based on electrophysiological behaviors in the pre-BötC: bursting pacemaker-type and nonbursting inspiratory neurons. We analyzed a number of neuronal membrane and synaptic parameters that could contribute to or reflect these differences in cellular electrophysiological behavior. The sampled population revealed essentially no differences in properties such as R M,I peak, andQ syn. Our sample included neurons in the upper 60 μm of the slice near the caudal end of the pre-BötC—the region available to probing with neuron visualization-based methods for patch clamping (IR-DIC and IR-DIC combined with Ca2+ fluorescence imaging of cell activity). There have been no previous studies of membrane and synaptic properties of pre-BötC inspiratory neurons to quantify heterogeneity and to compare bursting pacemaker and nonbursting cell types. An important finding with our sampled population was that all identified inspiratory neurons expressed a range ofI NaP and the principal distinguishing property for the bursting pacemaker versus nonpacemaker behaviors was theg NaP/g Leakratios, which, as further discussed in the following text, reflects the basic biophysical mechanism for bursting.
INaP and bursting pacemaker behavior of pre-BötC inspiratory neurons
VOLTAGE-DEPENDENT ACTIVATION OF INAP.
In many invertebrate and mammalian bursting neurons, the onset of bursting is caused by a subthreshold-activating inward cationic current. This current is responsible for maintaining the negative-slope region of the I-V curve in the subthreshold voltage range. Although Ca2+ imaging studies indicate that pre-BötC bursting pacemaker neurons have Ca2+ currents (Koshiya and Smith 1999a), bursting persists under low Ca2+conditions and accordingly we have proposed thatI NaP is the primary candidate mechanism for oscillatory burst generation (Butera et al. 1999a). Our data indicate thatI NaP in pre-BötC inspiratory neurons is TTX sensitive and activates at subthreshold potentials near −60 mV with a V 1/2 of approximately −40 mV. Errors in our estimates of the activation parameters could arise from voltage clamp errors due to inadequate space clamp and contamination of the measured inward current due to incomplete inactivation of the transient fast-activating, action-potential generating Na+ current at the slow voltage ramp speeds used for our analysis. Furthermore, in cases in which K+ currents were not blocked with TEA, the voltage-dependent outward K+ currents can distort the shape of the ramp I-V curve and reduce the amplitude of the measured inward current, although the Boltzmann function fits for the inward current activation were essentially identical with and without TEA. On the other hand, our I-Vplots are consistent in shape with other I-V characteristics estimated by slow voltage ramps: 2.33 to 70 mV/s (Fleidervish and Gutnick 1996). When using ramps of ≥35 mV/s,Fleidervish and Gutnick (1996) reported thatI NaP begins to activate around −60 mV and reaches a peak by −25 mV, similar to our data. Furthermore, our values of V 1/2 and k are essentially identical to the values used in our minimal pacemaker cell model (Butera et al. 1999a), which produces voltage-dependent bursting that closely mimics the experimentally observed behavior (Del Negro et al. 2001) whenI NaP interacts dynamically with the K+-dominated leakage conductance (see following text). Moreover, voltage-dependent bursting similar to that observed experimentally for pre-BötC neurons and predicted by our model can be produced by using the dynamic clamp to artificially incorporate in neurons I NaP with the voltage dependence of activation that we have modeled and found experimentally (Butera et al. 2001).
Currently we do not have information on the origin of the persistent current at the channel level in the inspiratory neurons studied. A type of persistent Na+ current in isolated cells has been attributed entirely to “modal gating” and late channel openings of the same Na+ channels that are responsible for the fast transient Na+ current generating action potentials (Alzheimer et al. 1993). TTX-sensitive persistent Na+ current has also been proposed to originate from subthreshold gating of the fast transient current in isolated tuberomammillary neurons (Taddese and Bean, 2002), implying that complex electrophysiological properties including pacemaker behavior arising from a persistent Na+ current could result from voltage-dependent gating properties of a single ubiquitous Na+ channel type. Regardless of the molecular mechanism, inspiratory cells have a persistent inward Na+ current that activates in the subthreshold voltage range to support voltage-dependent oscillatory bursting.
INACTIVATION PROPERTIES OF INAP.
We have not yet quantified the voltage dependence of steady-state inactivation nor the inactivation time constants ofI NaP in pre-BötC inspiratory neurons. This information is important for understanding mechanisms of burst termination and the dynamics of the oscillatory bursting cycle. As shown by the present data and our previous modeling studies, initiation and termination of bursting are accompanied by a rapid transition between the silent phase and the subthreshold depolarization with firing of action potentials and vice versa. From theoretical studies of mechanisms generating oscillatory bursting behavior, a minimal mechanism for bursting requires a slow recovery process, such as a slow voltage-dependent conductance inactivation mechanism. In our minimal models of pre-BötC pacemaker neurons, we concluded that this process is more likely related to slow inactivation of I NaP rather than slow activation of an outward K+ current, which would interact with a noninactivating I NaPfor burst termination. In the model,I NaP inactivation during a burst contributes to burst termination and the slow kinetics of recovery from inactivation controls the time course of the quiescent interburst interval. Slow voltage-dependent inactivation kinetics (on the order of seconds) are required to produce the bursting dynamics observed for the pre-BötC pacemaker cells. In the present experiments, the attenuation of the peak inward current that we observed as voltage-clamp ramp speed is reduced and the shape of the I-Vrelationships obtained experimentally is consistent with the kinetics/voltage-dependent time constants ofI NaP inactivation of our model. Simulations with voltage ramps show the reduction of the peakI NaP by over 50% as ramp speed decreases over the range of speeds used in our experimental protocols but persistence of the inward current at the lowest ramp speeds (3.3 mV/s) used due to very slow inactivation (R. J. Butera, unpublished observations). Fleidervish and Gutnick (1996) demonstrated a TTX-sensitiveI NaP in rodent neocortical neurons and reported the time constant for the onset of slow inactivation ofI NaP was approximately 2 s at +20 mV and the time constant for recovery from slow inactivation of 2.3 s at −70 mV, which are consistent with the values employed in our model (2–10 s) (Butera et al. 1999a).
Heterogeneity of subthreshold conductances
We found evidence for I NaP in both inspiratory neuron phenotypes (bursting pacemaker and nonbursting) in the pre-BötC. In our sample populations, we did not detect differences in the voltage dependence of activation, suggesting that the current was identical (although we did not analyze the voltage ramp-speed dependence of the peak I NaPin nonbursting cells). While the activation properties ofI NaP appeared identical, there was considerable heterogeneity in the peak inward current densities (measured at voltage-clamp ramp speeds of 30 mV/s) within each population. For pacemaker type neurons the current densities were 4.3 ± 2.2 versus 2.0 ± 0.4 pA/pF in nonpacemaker cells. We also found heterogeneity in the values of leak conductance. Similarly we have previously found (Del Negro et al. 2001) heterogeneity in bursting behavior of inspiratory pacemaker cells that theoretically would reflect cell-to-cell differences in current densities (Butera et al. 1999b). Our pacemaker network model of the pre-BötC kernel indicates that such heterogeneity ing NaP andg Leak is functionally important because it extends the dynamic range for population burst frequency control: robust synchronous bursting occurs across a much greater range of parameter space in terms of the range of depolarizing inputs that control neuron voltage-dependent bursting and regulate population burst frequency (Butera et al. 1999b).
Determinants of bursting pacemaker behavior
Our model of the pre-BötC kernel postulates that voltage-dependent oscillatory bursting arises in a subset of rhythm-generating cells that express critical levels ofg NaP in relation tog Leak (Butera et al. 1999b). Bursting behavior at the cellular level depends on dynamic interactions of the whole-cell currents mediated by these two key conductances (Butera et al. 1999a). A largeg NaP will produce a steeper negative slope in the whole-cell I-V relationship that gives rise to bursting behavior and will result in a largerg NaP/g Leakratio for bursting pacemaker versus nonbursting neurons as illustrated in Fig. 5. Accordingly we also analyzedg Leak, which our data indicate is not voltage sensitive, as postulated in the model, and we analyzed the relationships between g NaP versusg Leak. The graphical form of theg NaP versusg Leak plot roughly resembles a pie wedge, in which bursting-pacemaker activity emerges for a set ofg NaP/g Leakcombinations. Cells do not exhibit oscillatory bursting behavior withg NaP/g Leakratios lower than those within the parameter regime for bursting. This pie wedge-shaped graph is theoretically predicted for our model inspiratory pacemaker neurons. In Fig. 6, we have plotted the graph of g NaPversus g Leak from pacemaker neuron model 1 of Butera et al. (1999a). This graph emphasizes that there are three intrinsic activity states of neurons determined by theg NaP/g Leakratio: silent, oscillatory bursting, and beating (tonic spiking), for which bursting behavior only occurs for a finite set ofg NaP/g Leakcombinations. Taken together, our experimental and theoretical data suggest that the empirical distribution of bursting-pacemaker and nonpacemaker cells depends on the ratio ofg NaP andg Leak, and the dynamic interaction ofg NaP andg Leak can control the expression of these behaviors (Butera et al. 1999a; Del Negro et al. 2001).
Thus the present results suggest that bursting pacemaker versus nonbursting behaviors can be distinguished by the g NaP/g Leakratio as in the minimal model of Butera et al. 1999a), even though the cells may have other subthreshold-activating conductances, such as transient outward currents, voltage-activated calcium currents, and hyperpolarization-activated mixed-cationic currents (Thoby-Brisson et al. 2000), which could contribute to the neuronal dynamic behavior. The dynamics of bursting reflects a complex interaction of multiple currents and even high-voltage-activated currents such as the delayed rectifier K+ current can affect bursting behavior. InButera et al.'s (1999a) simulations with model 1, for example, subthreshold oscillations can exist even if the fast, transient action potential-generating Na+ current is removed, but their period is slightly different, suggesting that the dynamics of the delayed rectifier K+ current may play a minor role in determining bursting properties such as burst duration. Nevertheless, the present results indicate that the core biophysical mechanism for rhythmic bursting in the pre-BötC inspiratory neurons expressing I NaP is the dynamic interaction of I NaP andI Leak as postulated by the models ofButera et al. (1999a).
We currently do not know the precise functional roles of the experimentally sampled inspiratory cells in rhythm generation with the pre-BötC network. The pre-BötC has a heterogeneous cellular composition, for which only a subpopulation of the excitatory interneurons may actually be responsible for generating the rhythm. According to our models that incorporate a heterogeneous distribution of g NaP andg Leak, many of the neurons may not actually be burst capable due to lowg NaP/g Leakratios; these neurons nonetheless can participate in generation of the population-level inspiratory burst through excitatory synaptic activity. Indeed our simulations (Butera et al. 1999b) show that synchronized rhythms can emerge at the population level when there is a mixture of burst-capable and nonburst-capable neurons with a very high fraction of nonburst capable neurons, as well as under conditions with lowg NaP/g Leakratios where none of the neurons in the rhythm-generating kernel express voltage-dependent bursting pacemaker behavior. Moreover, a recent report suggests that the voltage-dependent bursting mediated byI NaP may not be necessary for rhythm generation (Del Negro et al. 2002), requiring further experimental clarification of the role of voltage-dependent pacemaker bursting engendered at the cellular level byI NaP. Nevertheless,I NaP is a common property of pre-BötC inspiratory neurons. A similar conclusion thatI NaP is a widespread property has been reached by McCrimmon et al. (2001) who have identified a TTX-sensitive I NaP in many neurons dissociated in culture from the pre-BötC and neighboring reticular formation, although their neurons were not functionally identified as inspiratory cells. I NaPmay be particularly important because it endows cells with a subthreshold-activating inward current that can amplify synaptic drive, promoting synchronization of neuronal activity in the network that, combined with the tendency for intrinsic bursting in a subset of cells, leads to the emergence of population-level bursting (Butera et al. 1999b) and network rhythms.
↵* C. A. Del Negro and N. Koshiya contributed equally to this study.
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