Fig 1.
INaP-dependent intrinsic bursting in a pre-BötC neuron model.
(A) Voltage trace illustrating the dependence of simulated neuronal activity patterns on excitability. Inset (bottom left) shows burst shape. Excitability was varied by linearly increasing the tonic excitatory synaptic conductance (gTonic) from 0.25 nS to 0.45 nS over the course of the simulation (bottom grey ramp). (B) Phase plane plot illustrating the relationship between the slow, voltage-dependent INaP inactivation variable hNaP and the membrane potential Vm during the bursting activity displayed in (A). Other model variables are not displayed in this view.
Fig 2.
Effects of simulated TTX and RZ blockade on INaP under steady-state conditions.
(A1 & B1) Effects of simulated TTX and RZ blockade on voltage-dependent steady-state activation (m∞(V)) and inactivation (h∞(V)) for INaP. Notice that simulated RZ blockade shifts inactivation in the hyperpolarizing direction and simulated TTX blockade induces no change. (A2 & B2) Effect of simulated TTX and RZ blockade on the I-V curves for INaP. Notice that simulated TTX and RZ blockade have nearly indistinguishable effects. (C) Peak INaP current as a function of the extent of simulated TTX and RZ blockade. TTX and RZ blockade are simulated by reducing INaP conductance (gNaP) and shifting its half-inactivation (h1/2) in the hyperpolarizing direction, respectively.
Fig 3.
Activity patterns in a model pre-BötC neuron as a function of tonic excitatory synaptic drive (gTonic) and (A) level of gNaP and (B) Δh1/2, which are reduced to simulate TTX and RZ block of INaP, respectively.
Burst frequency (top) and burst duration (bottom) are indicated by color within the bursting regions. Both TTX and RZ effectively abolish intrinsic bursting (colored region): bursting does not occur for gNaP < 2.7nS nor for Δh1/2 < −8.0mV.
Fig 4.
Phase plane representation of simulated TTX and RZ block of INaP in an isolated pre-BötC neuron.
(A) Vm- and hNaP-nullclines (black and gray, respectively) projected to the (Vm, hNaP)-plane under control conditions (gNaP = 5.0 nS) in a bursting regime, along with a projection of the bursting trajectory (blue). Note that this view does not represent the INaP activation variable mNaP. (B) Increasing TTX blockade of INaP moves the left knee of the Vm-nullcline to larger values of hNaP, which also abolishes bursting by creating a stable fixed point on the left branch of the Vm-nullcline via a SNIC (saddle-node on an invariant circle) bifurcation. (C) Increasing RZ blockade of INaP shifts the h-nullcline to the left, abolishing intrinsic bursting by creating a stable fixed point left branch of the Vm-nullcline, also via a SNIC bifurcation. gTonicE = 0.35 nS in all panels.
Fig 5.
Hyperpolarized holding potential (Vhold) and duration (color-coded) required to elicit rebound bursting as a function of simulated (A) TTX or (B) RZ blockade of INaP.
Here, gTonic = 0.35 nS.
Fig 6.
A transient hyperpolarizing perturbation fails to elicit rebound bursting after simulated (A) TTX but not (B) RZ blockade of INaP.
(A & B) Top Panels: Vm- and hNaP-nullclines during baseline, hyperpolarization, and release from hyperpolarization. Arrows indicate the direction of the trajectory. (A & B) Bottom Panels: voltage trace of Vm during baseline hyperpolarization and release. Initial conditions that generate transient bursting trajectories are indicated by the filled red regions and only appear in the RZ case. For simulated TTX blockade in (A) gNaP = 1.25 nS. In this case, after hyperpolarization (middle panel), the equilibrium point (open circle) lies at an hNaP value that is too low to allow clearance of the left knee after release (right panel). For simulated RZ blockade in (B), Δh1/2 = −12 mV. Here, in the red region, and hence any hyperpolarization that allows the trajectory to enter the red region (e.g., center panel) will yield a burst upon release (right panel). For both simulations, gTonicE = 0.35 nS.
Fig 7.
Simulated pre-BötC network activity.
(top) Raster plots showing (A) intrinsic bursting in a subset of neurons in the synaptically uncoupled network and (B) synchronized network bursts in the synaptically coupled network. (bottom) Integrated population activity for the (C) uncoupled and (D) coupled network.
Fig 8.
Effects of simulated (A) TTX and (B) RZ block of INaP as well as (C) RZ block of ISynE on network amplitude and frequency of network oscillations in the pre-BötC pre-I neuron population.
Fig 9.
Comparison of experimental (colored) and simulated (black) effects of (A) TTX and (B) RZ application in the pre-BötC on the amplitude and frequency of pre-I network oscillations.
Experimental data was adapted from [9] and shows the progressive change in amplitude and frequency of network oscillations (monitored by integrated hypoglossal nerve activity) relative to baseline following bilateral microinfusion of TTX or RZ at different concentrations into the pre-BötC. The experimental data points represent the network frequency and amplitude plotted at successive 1 minute intervals after TTX or RZ application. The corresponding data points from simulated TTX and RZ application represent network frequency and amplitude for increasing levels of blockade. Simulated RZ application affects INaP and excitatory synapses whereas TTX only affects INaP. In the simulations, the relevant values at the end points (where network oscillations stop) are as follows: (A) gNaP = 3.52; (B) (top trace) Δh1/2 = −5.0 mV, WmaxE = 0.0255 nS, (bottom trace) Δh1/2 = −4.5 mV, WmaxE = 0.0224 nS. Notice that TTX only affects frequency, whereas RZ affects frequency and amplitude. (a1, b1, b2) Effect of simulated TTX and RZ (tunings 1 & 2) blockade on the peak INaP, peak ISyn, and the INaP inactivation threshold () required to initiate bursting.
was defined as the maximal value of the mean population hNaP prior to burst initiation.
Fig 10.
Simulated progressive nonuniform INaP block in the isolated pre-I network.
(A,B,C) From left to right: network burst with neurons color-coded as pacemakers (red) or non-pacemakers (blue) and numbered based on order affected from 1 (first affected) to 50 (last affected); amplitude and frequency of isolated pre-I population oscillations as a function of the percentage of the pre-I population where INaP is completely blocked. For a given neuron, INaP is considered completely blocked when gNaP = 0 nS in the case of TTX (A1,B1,C1) or when Δh1/2 = −15 mV and ISynE is attenuated by 25% for RZ (A2,B2,C2), see Figs 2 and 8. Error bars in C1 and C2 indicate the ±SEM of ten trials where INaP is progressively blocked across the network in random order.
Fig 11.
Simulated intact respiratory network.
(A) Circuit diagram of the intact respiratory network composed of the inhibitory (post-I, aug-E early-I) and excitatory (pre-I) subpopulations. (B) Integrated subpopulation spiking activity. Amplitudes of each subpopulation were normalized. (C) Spiking in example neurons from each subpopulation.
Fig 12.
Characterization of the intact respiratory network behavior.
(A) Identification of INaP and/or network dependent regimes of pre-I population bursting as a function of tonic excitatory drive (gTonic). Effect of post-I inhibition strength and gTonic on (B) post-inspiratory phase hyperpolarization, (C) hNaP dynamic range, and (D) the peak inspiratory phase INaP in the pre-I population. Notice that the INaP level is strongly affected by the magnitude of post-I inhibition and gTonic. Strong post-I inhibition increases the magnitude of post-inspiratory phase hyperpolarization, which decreases INaP inactivation and increases the peak INaP. In contrast, strong gTonic decreases post-inspiratory phase hyperpolarization, which increases INaP inactivation and decreases the peak INaP. Dashed lines in C indicate the dynamic range of hNaP in the isolated pre-I population under baseline conditions used in Fig 7.
Fig 13.
Predicted effect of blockade of INaP in the intact network.
Relative effects of “complete” blockade of INaP by simulated (A) TTX and (B) RZ application on the amplitude (left) and frequency (right) as a function of tonic excitatory drive (gTonic) and the strength of post-I inhibition. Oval shape indicates parameters capable of matching the maximal relative changes in amplitude and frequency seen with experimental application of RZ. The points labeled C and D indicate the gTonic and post-I inhibition values used in panels C and D. (C) Comparison of experimental and simulated RZ blockade of INaP. Simulated RZ application closely matches experimental data when gTonic = 0.4 and post-I inhibition = 0.82. Experimental data is adapted from [13]. (D) Predicted effect of experimental TTX blockade of INaP in the intact network under identical conditions to panel C.
Fig 14.
Sketch of proposed distribution of pacemaker and non-pacemaker neurons within the pre-BötC as well as the the direction and depth of TTX and RZ penetration in thick and thin in vitro slice preparation containing the pre-BötC.
The direction of diffusion and maximal diffusion depth in the thin and thick slice sketches are indicated by arrows and vertical dashed lines. Notice that in a thick slice non-pacemaker neurons are affected first and TTX and RZ fail to fully penetrate the thick slice.
Table 1.
U(a, b) indicates a uniform distribution from a to b.
Table 2.
Neuronal type specific parameters.
U(a, b) indicates a uniform distribution from a to b.
Table 3.
Maximal weight of excitatory (WMaxE) and inhibitory (WMaxI) synaptic connections in nS.