1. Computational and Systems Biology
  2. Neuroscience
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Biophysical mechanisms in the mammalian respiratory oscillator re-examined with a new data-driven computational model

  1. Ryan S Phillips
  2. Tibin T John
  3. Hidehiko Koizumi
  4. Yaroslav I Molkov
  5. Jeffrey C Smith  Is a corresponding author
  1. National Institute of Neurological Disorders and Stroke, National Institutes of Health, United States
  2. University of New Hampshire, United States
  3. Georgia State University, United States
Research Article
Cite this article as: eLife 2019;8:e41555 doi: 10.7554/eLife.41555
11 figures, 1 table and 2 additional files

Figures

Manipulations of g-CAN in the CaV and CaSyn networks produce opposite effects on network activity amplitude (spikes/s) and frequency.

(A and B) Histograms of neuronal population activity amplitude in the CaV, and CaSyn networks with linearly increasing g-CAN. (C) Plot of g-CAN (% of the baseline mean value for the simulated population) vs. network activity amplitude for the CaV and CaSyn networks in A and B. (D) Plot of g-CAN (%) vs. network frequency for the CaV and CaSyn networks in A and B. CaV network parameters: g-Ca=1.0 (nS), PCa=0.0, PSyn=0.05 and Wmax=0.2 (nS). CaSyn network parameters: g-Ca=0 (nS), PCa=0.01, PSyn=0.05 and Wmax=0.2 (nS).

https://doi.org/10.7554/eLife.41555.002
Calcium source and g-CAN-dependent effects on cellular properties regulating network frequency for the simulations presented in Figure 1.

(A) Average magnitude of ICAN in pacemaker neurons during the interburst interval for the CaV (red) and CaSyn (blue) networks. (B) Average inactivation (hNaP ) of the burst generating current INaP in pacemaker neurons immediately preceding each network burst as a function of g-CAN (%) for the voltage-gated and synaptic calcium networks. CaV network parameters: g-Ca=1.0 (nS), PCa=0.0, PSyn=0.05 and Wmax=0.2 (nS). CaSyn network parameters: g-Ca=0 (nS), PCa=0.01, PSyn=0.05 and Wmax=0.2 (nS).

https://doi.org/10.7554/eLife.41555.003
Calcium source and g-CAN-dependent effects on cellular properties regulating network activity amplitude for the simulations presented in Figure 1.

(A) Number of recruited neurons in the modeled population of 100 neurons as a function of g-CAN (%) for voltage-gated and synaptic calcium sources. The number of recruited neurons is defined as the peak number of spiking neurons per bin during a network burst. (B) Average spiking frequency of recruited neurons as a function of g-CAN for the voltage-gated and synaptic calcium mechanism. Average spiking frequency is defined the number of spikes per bin divided by the number of recruited neurons. The parameters used in these simulations are: CaVg-Ca=1.0 (nS), PCa=0.0, PSyn=0.05 and Wmax=0.2 (nS)CaSyng-Ca=0 (nS), PCa=0.01, PSyn=0.05 and Wmax=0.2 (nS).

https://doi.org/10.7554/eLife.41555.004
Manipulations of synaptic strength (N·PSyn·12Wmax) and g-CAN have equivalent effects on network activity amplitude, frequency and recruitment of inspiratory neurons not involved in rhythm generation.

(A and B) Relationship between g-CAN  (mean values for the simulated populations), synaptic strength and the amplitude and frequency in the CaSyn network. Notice the symmetry about the X=Y line in panels A and B, which, indicates that changes in g-CAN and or synaptic strength are qualitatively equivalent. Synaptic strength was changed by varying Wmax. (C) Relationship between network activity amplitude and the reduction of g-CAN (blue) or synaptic strength (green). (D) Relationship between network frequency and the reduction of g-CAN (blue) or synaptic strength (green). (E and F) Decreasing g-CAN or synaptic strength de-recruits neurons by reducing the inspiratory drive potential, indicated by the amplitude of subthreshold depolarization, right traces. The solid blue and green lines in panels A and B represent the location in the 2D parameter space of the corresponding blue and green curves in C and D. The action potentials in the right traces of E and F are truncated to show the change in neuronal inspiratory drive potential. The parameters used for these simulations are CaSyng-Ca=[0,0], PCa=0.01, PSyn=1.0 and Wmax=var.

https://doi.org/10.7554/eLife.41555.005
Robustness of amplitude and frequency effects to changes in g-CAN and synaptic strength in the CaV network for ‘high’ (left), ‘medium’ (middle) and ‘low’ (right) conductance of the voltage-gated calcium channel ICa as well as ‘high’ (top) and ‘low’ (bottom) network connection probabilities.

Amplitude and frequency are indicated by color (scale bar at right). Black regions indicate tonic network activity. Values of g-CAN indicated are the mean values for the simulated neuronal populations.

https://doi.org/10.7554/eLife.41555.006
Robustness of amplitude and frequency effects to changes in g-CAN and synaptic strength in the CaSyn network for ‘high’ (left), ‘medium’ (middle) and ‘low’ (right) calcium conductance in synaptic currents as well as ‘high’ (top) and ‘low’ (bottom) network connection probabilities.

Amplitude and frequency are indicated by color (scale bar at right). Black regions indicate tonic network activity. Values of g-CAN indicated are the mean values for the simulated neuronal populations.

https://doi.org/10.7554/eLife.41555.007
Experimental and simulated pharmacological blockade of ICAN by (A and C) 9-phenanthrol and (B and D) flufenamic acid (FFA).

Both voltage-gated and synaptic sources of intracellular calcium are included. Experimental blockade of ICAN (black) by 9-phenanthrol and FFA significantly reduce the (A and B) amplitude of network oscillations while having little effect on (C and D) frequency. The black line represents the mean and the gray band is the S.E.M. of experimental integrated XII output recorded from neonatal rat brainstem slices in vitro, reproduced from Koizumi et al., 2018. Simulated blockade of ICAN (red) closely matches the reduction in (A and B) amplitude of network oscillations and slight decrease in (C and D) frequency seen with 9-phenanthrol and FFA. Simulated and experimental blockade begins at the vertical dashed line. Blockade was simulated by exponential decay of g-CAN with the following parameters: 9-phenanthrol: ?Block=0.85tBlock=357s; FFA: ?Block=0.92tBlock=415s. The network parameters are: g-Ca=0.00175 (nS)PCa=0.0275, PSyn=0.05 and Wmax=0.096 (nS).

https://doi.org/10.7554/eLife.41555.008
INaP-dependent and Ca2+-sensitive intrinsic bursting.

(A) From left to right, intrinsic bursters (pacemakers) are first identified by blocking synaptic connections. Cells whose activity is elminated under these conditions are non-pacemaker neurons. Then, calcium sensitive neurons are silenced and identified by ICa blockade. The remaining neurons are identifed as sensitive to INaP block. Top traces show the network output and Cell ID vs. g-NaP scatter plots that identify silent and bursting neurons under each condition. (B) INaP blockade after synaptic blockade eleminates bursting in all neurons. Therefore, all intrinsic bursters are INaP dependent. (C) Identification of calcium-sensitive and INaP-dependent as well as calcium-insensitive and INaP-dependent intrinsic bursters. Notice that only the neurons with the highest value of g-NaP are intrinsic bursters and that a subset of these neurons are sensitive to calcium blockade but all are dependent on INaP. The network parameters are: g-Ca=0.00175 (nS), PCa=0.0275, PSyn=0.05 and Wmax=0.096 (nS). The values of g-NaP given in the scatter plots indicate the magnitude of g-NaP for each neuron in the network and show the range of the g-NaP distribution.

https://doi.org/10.7554/eLife.41555.009
ICAN blockade reveals an INaP-dependent rhythmogenic kernel.

The top traces show the network output at baseline, after ICAN blockade and INaP blockade. The bottom Cell ID vs. g-NaP scatter plots identify silent and bursting neurons in each conditon. Notice that only neurons with relitively high g-NaP remain active after ICAN block. The network parameters used are: g-Ca=0.00175 (nS), PCa=0.0275, PSyn=0.05 and Wmax=0.096 (nS). The values of g-NaP given in the scatter plots indicate the magnitude of g-NaP for each neuron in the network and show the range of the g-NaP distribution.

https://doi.org/10.7554/eLife.41555.010
Changes of network activity amplitude, average network intracellular calcium concentration Cai amplitude, and single model neuron Cai amplitude during simulated ICAN blockade.

(A and B) Effect of ICAN block on network activity amplitude, network calcium amplitude and frequency for network connection probabilities (A) P = 1 and (B) P = 0.05. (C and D) Effect of ICAN block on changes in the magnitude of peak cellular calcium transients for network connection probabilities (C) PSyn=1 and (DPSyn=0.05. (E) Maximum, minimum and average change in the peak intracellular calcium transient of individual neurons as a function of synaptic connection probability. All curves in A through E are normalized to their baseline values. Synaptic weight was adjusted to keep the average synaptic strength (N·PSyn·12Wmax=const) constant. Notice that lowering the synaptic connection probability increases the variability in the peak intracellular calcium concentration during ICAN blockade. Interestingly, for connection probabilities below approximately 5%, blocking g-CAN can increase the peak calcium transient in a small subset of neurons. The network parameters used are: g-Ca=0.00175 (nS) and PCa=0.0275 and Wmax=var.

https://doi.org/10.7554/eLife.41555.011
Comparison of experimental (black) and simulated (red) TRPC3 blockade (by CaSyn block) on network activity amplitude (A) and frequency (B).

Simulated and experimental blockade begins at the vertical dashed line. The black line represents the mean and the gray band represents the S.E.M. of experimental integrated XII output recorded from neonatal rat brainstem slices in vitro, reproduced from Koizumi et al., 2018. Blockade was simulated by exponential decay of PCa with the following parameters: 3-pyrazole: ?Block=1.0τBlock=522.5s. The network parameters are: g-Ca=0.00175 (nS), PCa=0.0275, PSyn=0.05 and Wmax=0.096 (nS).

https://doi.org/10.7554/eLife.41555.012

Tables

Table 1
Model parameter values.

The channel kinetics, intracellular Ca2+ dynamics and the corresponding parameter values, were derived from previous models (see Jasinski et al., 2013) and the references therein).

https://doi.org/10.7554/eLife.41555.013
ChannelParameters
INag-Na=150.0 nS, ENa=55.0 mV,Vm1/2=43.8mV, km=6.0 mV,Vτm1/2=-43.8 mV, kτm=14.0 mV, τmmax=0.25 ms,Vh1/2=67.5mV, kh=-10.8 mV,Vτh1/2=-67.5 mV, kτh=12.8 mV, τhmax=8.46 ms
IKg-K=160.0 nS, EK=-94.0 mV,
Aα=0.01, Bα=44.0 mV, κα=5.0 mV
Aβ=0.17, Bβ=49.0 mV, κβ=40.0 mV
ILeak

g-Leak=2.5 nS, ELeak=-68.0 mV

INaPgNaP[0.0,5.0]nS,
Vm1/2=47.1mV, km=3.1 mV,
Vτm1/2=-47.1 mV, kτm=6.2 mV, τmmax=1.0 ms,
Vh1/2=60.0mV, kh=-9.0 mV,
Vτh1/2=-60.0 mV, kτh=9.0 mV, τhmax=5000 ms
ICANgCAN[0.5,1.5]nS, ECAN=0.0 mV,
Ca1/2=0.00074 mM, n=0.97
ICag-Ca=0.01 nS, ECa=RT/FlnCaout/Cain,
R=8.314 J/(molK), T=308.0 K,
F=96.485 kC/mol, Caout=4.0 mM
Vm1/2=27.5mV, km=5.7 mV, τm=0.5 ms,
Vh1/2=52.4mV, kh=-5.2 mV, τh=18.0 ms
CainαCa=2.510-5mM/fCPCa=0.01, Camin= 1.010-10mM, τCa=50.0ms
ISyngTonic=0.31 nS, ESyn=-10.0 mV, τSyn=5.0 ms

Data availability

All data in this study are generated by computational simulations. All model parameters and equations are included in the manuscript and source code is included with this submission.

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