The objectives of our modeling studies were to build a model of the spatially distributed brainstem respiratory network that could reproduce the above experimental findings and suggest an explanation for possible transformations of the rhythm-generating mechanism after sequential reduction of the network. The model has been developed based on a previous model (Rybak et al., 2004a
) and represents an extension of the “hybrid pacemaker-network model” proposed by Smith et al. (2000)
. All neurons were modeled in the Hodgkin–Huxley style (one-compartment models) and incorporated known biophysical properties and channel kinetics characterized in respiratory neurons in vitro. Specifically, the fast sodium (INa
) and the persistent (slowly inactivating, INaP
) sodium currents were described using experimental data obtained from the studies of neurons acutely isolated from the rat’s ventrolateral medulla (Rybak et al., 2003a
) at the level of the pre-BötC; the high-voltage activated calcium current (ICaL
) was described based on the data of Elsen and Ramirez (1998)
; the intracellular calcium dynamics was described to fit the data of Frermann et al. (1999)
; the description of potassium rectifier (IK
) and calcium-dependent potassium (IK,Ca
) currents and all other cellular parameters were the same as in the previous models (Rybak et al., 1997a
). Each neuronal type was represented by a population of 50 neurons with some parameters and initial conditions randomized within the population. The full description of the model and model parameters can be found in Appendix
The schematic of the full model is shown in . Three major medullary regions are considered (in the rostral-to-caudal direction): Bötzinger Complex (BötC), pre-Bötzinger Complex (pre-BötC) and rostral VRG (rVRG). The BötC compartment includes inhibitory populations, aug-E(1) and post-I, each of which serves as a source of expiratory inhibition widely distributed within the medullary respiratory network (Ezure, 1990
; Jiang and Lipski, 1990
; Tian et al., 1999
). In the model, these populations inhibit all populations in the pre-BötC and rVRG compartments and each other (see ). The BötC compartment also includes a second aug-E (aug-E(2)) inhibitory population, providing the additional control of the duration of expiration via inhibition of post-I activity, and an excitatory post-I (post-I(e)) population that provides the expiratory output (e.g., contributes to the cVN motor output). All neurons in the BötC compartment (in the post-I, post-I(e), aug-E(1) and aug-E(2) populations) have intrinsic adapting properties defined by ICaL
. Because of this, the post-I neurons exhibit decrementing discharge patterns during expiration. In contrast, the aug-E neurons (under normal conditions) start firing later in expiration and exhibit augmenting patterns because of the slow disinhibition from the adapting inhibitory post-I neurons.
Fig. 3 The schematic of the full (intact) model (A) and the reduced medullary (B) and pre-BötC–VGR (C) models. Neural populations are represented by spheres. Excitatory and inhibitory synaptic connections are shown by arrows and small circles, (more ...)
The pre-BötC compartment includes two neural populations: pre-I, and early-I(1) (see ). The pre-I population is the major source of inspiratory activity in the network. It projects to the pre-motor inspiratory ramp-I population of rVRG and also defines the XII motor output. The pre-I population in the model is comprised by excitatory neurons with INaP
-dependent endogenous bursting properties and mutual excitatory synaptic interconnections within the population. Under certain conditions (depending on total tonic drive, phasic inhibition, etc), this population can operate in a bursting mode and intrinsically generate rhythmic inspiratory activity (Butera et al., 1999a
; Smith et al., 2000
; Rybak et al., 2003b
) similar to that recorded in vitro (Koshiya and Smith, 1999
; Johnson et al., 2001
). However, in the model under normal conditions, most neurons of this population operate in a tonic spiking mode due to high tonic excitatory input, and are inhibited by expiratory neurons (post-I, aug-E(1)) during expiration. The early-I(1) population of pre-BötC is a population of inhibitory neurons with adapting properties (defined by ICaL
). This population receives excitation from the pre-I population and serves as a major source of inspiratory inhibition. In the model, this population inhibits all expiratory neurons during inspiration (see ).
The rVRG compartment contains ramp-I, and early-I(2) populations (). Ramp-I is a population of excitatory premotor inspiratory neurons that project to PN motor output, and contribute to cVN activity (see ). The major role of the inhibitory early-I(2) population (with adapting neurons containing ICaL and IK,Ca) is shaping the augmenting patterns of ramp-I neurons.
The maintenance of normal breathing at the appropriate homeostatic level depends on a variety of afferent inputs to different clusters of respiratory neurons within the brainstem. These inputs are viewed as “excitatory drives” that carry state-characterizing information provided by multiple sources distributed within the brainstem (pons, RTN, raphe, NTS, etc.), including those considered to be major chemoreceptor sites (sensing CO2
/pH), and activated by peripheral chemo-receptors (sensing CO2
/pH and low O2
) (Nattie, 1999
; Guyenet et al., 2005
). Although currently undefined, these drives appear to have a certain spatial organization with specific mapping on the spatial organization of the brainstem respiratory network. In our model, these drives are conditionally represented by three separate sources located in different compartments (pons, RTN/BötC, and pre-BötC) and providing drives to different respiratory populations (see ).
shows the performance of the intact model. The activity of each population is represented by the average spike frequency histogram of population activity. The post-I population of BötC shows decrementing activity during expiration. This population inhibits all other populations (except post-I(e)) during the first half of expiration (post-inspiratory phase). Because of the reduction of post-I inhibition with the adaptation in the post-I activity, the aug-E(1) and then the aug-E(2) population start activity later in expiration forming a late expiratory (E2) phase. At the very end of expiration, the pre-I population of pre-BötC is released from inhibition and activates the early-I(1) population, which inhibits all expiratory populations of BötC. As a result, the ramp-I (and early-I(2)) populations of rVRG release from inhibition (with some delay relative to pre-I) giving the start to the next inspiratory phase (onset of inspiration). During inspiration, the activity of early-I(2) population decreases providing the ramp increase of ramp-I population activity (and PN burst). The activity of early-I(1) population of pre-BötC decreases during inspiration providing a slow disinhibition of the post-I population of BötC. Finally, the post-I population fires and inhibits all inspiratory activity completing inspiratory off-switching. Then the process repeats. In summary, the respiratory rhythm (with a typical three-phase pattern) is generated in the intact model by the neuronal ring comprising the early-I(1), post-I, and aug-E(1) inhibitory populations with the pre-I population participating in the onset of inspiration.
Fig. 4 Performance of the intact model (network architecture shown in ). (A) Activity of each neural population (labeled on the left) is represented by the histogram of average neuronal spiking frequency (number of spikes per second per neuron, bin = (more ...)
The motor output patterns of the model (PN, XII, and cVN) are shown in and may be compared with the integrated activities of the corresponding nerves obtained from our experimental studies (). A comparison clearly demonstrates that the model reproduces all major characteristics of the respiratory pattern recorded under normal conditions from the intact preparation: (i) an augmenting shape of the PN bursts; (ii) a delay in the onset of the PN bursts relative to the XII bursts; and (iii) a decrementing post-I component in cVN bursts. However, the shape of XII busts in the model is slightly different which suggests that the neural organization of the pre-BötC and/or the hypoglossal motor output in the real system is more complicated (more heterogeneous) than that in our model.
shows a schematic of the reduced (“medullary”) model used for simulation of a reduced experimental preparation remaining after medullary transections removing the pons or the pons together with an adjacent part of the medulla (e.g., a part of Facial nucleus and RTN). The performance of this model is shown in . Based on indirect evidence about a strong excitatory influence of the pons on the post-I neurons (Rybak et al., 2004a
; Dutschmann and Herbert, 2006
), we have suggested that with the removal of the pons and adjacent medullary regions, all post-I populations of BötC lose a significant portion of the excitatory drive (see ), whereas the drive to aug-E(2) is less dependent on these regions. As a result, a balance of mutual inhibitory interactions between aug-E(1) and post-I shifts to the domination of aug-E. The latter now demonstrates a “natural” decrementing pattern (see in ) and completely inhibits all post-inspiratory activity in the network ( and ). The respiratory oscillations in this state are generated by a half-center mechanism based on the mutual inhibitory interactions between the adapting early-I(1) and aug-E(1) populations (see and ). The model now generates a typical two-phase rhythm (lacking the post-I phase). In addition, elimination of the drive from more rostral compartments reduces excitability and firing frequency of the pre-I and ramp-I populations, which reduces the amplitudes of all motor outputs of the model (PN, XII, and cVN, see ). Also, because of this drive reduction, the early-I(2) population becomes silent and does not influence the ramp-I population activity, which changes the shape of ramp-I () and PN () bursts from an augmenting to a square-like pattern. Finally, the patterns of motor outputs in the model (PN, XII, and cVN, ) are very similar to the integrated activities of the corresponding nerves obtained in our experimental studies (). This reduced model reproduces all major characteristics of the respiratory pattern recorded in the corresponding reduced preparations: (i) an apneustic “square-like” shape of the PN bursts; (ii) a synchronized activities in all three nerves; and (iii) a lack of the post-I component in the cVN bursts.
Fig. 5 Neuronal population activities and motor output patterns of the medullary model (shown in ). (A) Activity (spike frequency histograms) of all neural populations (labeled on the left). See explanations in the text. (B) Integrated activity of motor (more ...)
represents a more reduced model used for simulation of behavior of the reduced pre-BötC–VRG preparation after a transection at the rostral end of pre-BötC. The performance of this model is shown in . As shown in previous modeling studies (Butera et al., 1999a
; Smith et al., 2000
; Rybak et al., 2003b
) a population of neurons with INaP
-dependent endogenous bursting properties and mutual excitatory connections (as the pre-I population of pre-BötC in the present model) can, under certain conditions, intrinsically generate a population bursting activity similar to that recorded in pre-BötC in vitro (Koshiya and Smith, 1999
; Johnson et al., 2001
). Specifically, increasing tonic excitatory drive switches the population from a quiescent state to rhythmic population bursting, and then to asynchronous tonic activity (Butera et al., 1999b
; Rybak et al., 2003b
). A relatively strong excitatory drive to this population causes inactivation of NaP channels and maintenance of tonic activity. Alternatively, a reduction of the excitatory drive may hence switch this population to the regime of endogenous bursting activity. In the intact and medullary models above, the pre-I population of pre-BötC receives the total excitatory drive, which is large enough to keep this population in the state of tonic activity. This tonic activity is interrupted by the phasic expiratory inhibition from the post-I (intact model) or aug-E(medullary model) population. Removal of all compartments located caudal to pre-BötC results in further reduction of the drive to the pre-I population (). In addition, phasic inhibition from expiratory populations of BötC is also eliminated. As described above, with the reduction of tonic excitatory drive and elimination of phasic inhibition, the behavior of pre-I population switches to the regime of endogenous bursting activity. This population now intrinsically generates oscillations with a decrementing burst shape (similar to those recorded in vitro) (see ). Moreover, the bursting activity of the pre-I population now drives the activity of the ramp-I population () and all motor outputs that now exhibit one-phase (inspiratory) oscillations with a decrementing burst shape (PN, XII, cVN, see ) similar to that recorded in the pre-BötC–VRG preparation (see ).
Fig. 6 Performance of the pre-BötC–VGR model (shown in ). (A) Activity of all neural populations (labeled on the left). See explanations in the text. (B) Integrated activity of motor (nerve) outputs (PN, XII, and cVN) in this model. (C) (more ...)
In order to investigate the role of the persistent sodium current (INaP
) in the intact () and sequentially reduced models () and compare model behaviors to the corresponding experimental data on the dose-dependent effect of the INaP
blocker riluzole (), the maximal conductance of NaP channel (NaP
) was sequentially reduced in all neurons of the model. The results are shown in . The progressive reduction of NaP
(up to zero) in the intact and medullary models does not affect the frequency of respiratory (PN) oscillations and causes only a small reduction of the amplitude of PN bursts (see ). This occurs because a relatively high total excitatory tonic drive produces membrane depolarization that holds the (voltage-dependent) INaP
current in a significantly inactivated state In contrast in the pre-BötC–VRG model, with a reduction of the total drive the INaP
essentially contributes to the cellular firing behavior and the reduction of NaP
progressively decreases the frequency of PN bursts and finally abolishes the rhythm when NaP
becomes less than 2.5 nS (). These modeling results are fully consistent with our experimental data ().
Fig. 7 Effect of reduction of maximum conductance for the persistent sodium channels (NaP) in all neurons of the pre-I population of pre-BötC on frequency (solid lines) and amplitude (dashed lines) of PN bursts in the intact (A), medullary (B), (more ...)
Recent studies in vitro and in vivo (Mellen et al., 2003
; Janczewski and Feldman, 2006
) have demonstrated that a blockade of activity of inspiratory neurons in the pre-BötC, e.g., by administration of opioids, can produce spontaneous deletions or “quantal” skipping of individual or series of inspiratory bursts in the pre-BötC and/or in PN, while a rhythmic activity persists in a more rostral compartment of the brainstem, the para-facial (pF) region. In this regard, it is interesting to consider the behavior of our model when the activity of the pre-I population of pre-BötC is suppressed. The results are shown in . The pre-I population activity was suppressed by setting the maximal conductance for fast sodium current to zero () for some period shown by a horizontal bar at the top of . During this period, the pre-I population of pre-BötC as well as the PN and XII nerves show no activity. At the same time, despite the complete blockade of the output inspiratory activity, “expiratory” oscillations persist in the network. This expiratory rhythm results from mutual inhibitory interactions between the post-I, aug-E(1) and early-I(1) populations (see marked by gray in ).
Fig. 8 Neuronal activity patterns in the intact model () when the activity of the pre-I population of pre-BötC is suppressed. Activity of pre-I population was suppressed by setting the maximal conductance for fast sodium current to zero for the (more ...)