Mechanisms Leading to Rhythm Cessation in the Respiratory PreBötzinger Complex Due to Piecewise Cumulative Neuronal Deletions

Cumulative cellular ablations in the model preBötC network. Running time spike histogram (top, red) and plots of rhythmic burst frequency and six discrete network metrics (global and local). The simulated experiment where a total of 100 neurons were deleted (one per 25 simulated seconds) in sequence was repeated 15 times. The running time spike histogram is shown for one representative simulation. The top trace shows inspiratory-like burst frequency (Hz) for all 15 simulations. The abscissa (percentage of total cellular ablations) is the same for frequency and all discrete network metrics. LCC, CC, and BC are plotted for each neuron in the deletion sequence. The number of SCCs, K-core and in-degree are plotted for neurons in the remaining network during the ablation sequence. Blue symbols show the average metric (for 15 simulations) during the deletion sequence; these quantities were no longer computed after the 100th ablation. Red symbols show the scattered data points for all individual 15 simulations.

Model network bursts do not diminish during ablations sequences. Running time spike histogram (top, red) for one experiment. Time calibration (1 min) is displayed. a, The fifth network-wide burst. b, A network-wide burst after 21 deletions. c, The last network-wide burst after 31 deletions. The running time spike histogram (vertical calibration 10 spikes/ms) and average membrane potential (V_M, vertical calibration 20 mV) for all remaining neurons in the network for network-wide bursts (a, b, and c) are shown at higher sweep speed. Cells 190, 42, and 271 from the model system are shown individually. Baseline membrane potential (–60 mV) and time calibration (1 s) apply to all traces.

Active subnetwork properties for a sequence of inspiratory-like bursts given different I_CAN thresholds. A, Active subnetwork size (number of neurons) for five representative I_CAN thresholds (indicated above each trace) plotted versus sequential burst indices (1–213) for one simulation. Color represents different threshold values. Arrows indicate deletions 0, 4, 10, and 20. B, Active subnetwork size (number of neurons) for five representative I_Na-P thresholds (indicated above each trace) plotted versus sequential burst indices (1–213) for one simulation. C, Active subnetwork size (number of neurons) for five representative I_syn thresholds (indicated above each trace) plotted versus sequential burst indices (1–213) for one simulation. D, Active subnetwork size (number of neurons) for five representative s thresholds (indicated above each trace) plotted versus sequential burst indices (1–213) for one simulation.

Poincaré maps of instantaneous burst frequency and active subnetwork size. Each panel shows the map for frequency or active subnetwork size for the cycle i + 1 plotted versus the prior cycle (i). Frequency maps are at left (black to yellow). Active subnetwork size maps are at right (cyan to magenta). Each Poincaré map features an inset of the time series, where temporal relations are color-coded to points in the map. Vertical calibrations are given in A. A, Poincaré maps without any neuron deletions. B, C, and D show the same information for the same network realization as A, where the ablation tally was frozen after 4, 10, or 20 ablations, respectively.

Group data for instantaneous frequency and active subnetwork size. Instantaneous frequency (Hz) and active subnetwork size (number of neurons) at threshold θ₇ = –3.5 pA are plotted for cumulative neuron deletion simulations on six different network realizations. Black traces show instantaneous frequency (Hz); red traces show active subnetwork size (number of neurons) for each cycle period, plotted versus the percentage of total cellular ablations (%).

In-degree correlates with normalized I_CAN ordering and targeted ablation tallies. A, Linear regression between in-degree (unitless) and normalized I_CAN ordering among neurons in the same network. I_CAN order was computed based on the maximum number of appearances in the active subnetwork given 15 different thresholds. Blue symbols show the scattered distribution of in-degrees and normalized I_CAN ordering. Linear fit is shown by a dotted line. B, Ablation tallies (number of neurons) for three deletion strategies on different network realizations (n = 8). X-symbols mark the tally from eight different simulations where low I_CAN-order neurons were selectively ablated. Triangles mark when high I_CAN-order neurons were selectively ablated. Circles mark the tally for random neuron deletions (control default strategy).

Latency rank order of all constituent neurons in the network at four specific time points in a simulation. Top (red), The running time spike histogram for a random neuron deletion simulation. a, b, and c indicate three cycles leading to network-wide bursts (at time points 16, 557, and 814 s, respectively). d, The time after the last burst. The middle shows the latency rank order (defined in Results) for cycles a, b, and c, and after rhythm termination (d) plotted versus cycle time (in seconds). The dotted line indicates latency rank order (unitless) of the neuron after which the curve inflects upward, leading to a network-wide burst. The lower panel shows the same data as the middle, but where cycle time is limited to 0–4 s, emphasizing the similarity of b, c, and d.

Rate of recurrent excitation (neurons/ms) plotted at four specific time points in a simulation (same time points as Fig. 8). Dotted line in each panel indicates the threshold rate (1 neuron/ms); see text for details.