Cycle-by-cycle assembly of respiratory network activity is dynamic and stochastic

Abstract

Rhythmically active networks are typically composed of neurons that can be classified as silent, tonic spiking, or rhythmic bursting based on their intrinsic activity patterns. Within these networks, neurons are thought to discharge in distinct phase relationships with their overall network output, and it has been hypothesized that bursting pacemaker neurons may lead and potentially trigger cycle onsets. We used multielectrode recording from 72 experiments to test these ideas in rhythmically active slices containing the pre-Bötzinger complex, a region critical for breathing. Following synaptic blockade, respiratory neurons exhibited a gradient of intrinsic spiking to rhythmic bursting activities and thus defied an easy classification into bursting pacemaker and nonbursting categories. Features of their firing activity within the functional network were analyzed for correlation with subsequent rhythmic bursting in synaptic isolation. Higher firing rates through all phases of fictive respiration statistically predicted bursting pacemaker behavior. However, a cycle-by-cycle analysis indicated that respiratory neurons were stochastically activated with each burst. Intrinsically bursting pacemakers led some population bursts and followed others. This variability was not reproduced in traditional fully interconnected computational models, while sparsely connected network models reproduced these results both qualitatively and quantitatively. We hypothesize that pacemaker neurons do not act as clock-like drivers of the respiratory rhythm but rather play a flexible and dynamic role in the initiation and stabilization of each burst. Thus, at the behavioral level, each breath can be thought of as de novo assembly of a stochastic collaboration of network topology and intrinsic properties.

Fig. 1.

Schematic of multielectrode recording and analysis of in vitro rhythmic activity. Example spike time raster of 13 neurons recorded during several inspiratory population bursts under baseline conditions (A) and after synaptic isolation (B). Average population burst phase-dependent firing activity is parameterized on multiple features (C), which are tested for correlation with endogenous activity after synaptic block. For this comparison, a burstiness metric based on a characteristic pattern of long and short interspike intervals (D), and exemplified in a bimodal interspike interval histogram (E), is comprised of a log₁₀ sum of the ratio of longest to shortest intervals (F). ISI, interspike interval.

Fig. 2.

Comparison of in-network firing patterns with two characterizations of intrinsic rhythmicity derived from recordings made in synaptic isolation. An intrinsic burstiness metric produces a broad unimodal distribution (Aiii) that is uncorrelated with the first principle component decomposition of in-network firing behavior (Aii) and only weakly related to manual categorization of control activity (Ai; *P < 0.05 for nonrespiratory vs. inspiratory). Manual score of intrinsic behavior also produces a unimodal distribution (Biii) that is not clearly related to in-network behavior as defined by manual classification (Bi) or principal component analysis (PCA; Bii). Non-resp., nonrespiratory; Insp., inspiratory; Exp., expiratory; Post-Insp., postinspiratory; a.u., arbitrary units.

Fig. 3.

Correlations between features of firing patterns during control epochs and subsequent behavior during synaptic blockade. Kendall tau shows prominent correlations between an algorithmic metric of burstiness (A) and manually scored burstiness classes (B) for features related to spike rate and variability, although not for features associated with the timing of burst-triggered single unit activity. A and B: Mean Spike Rate, average spike rate across all phases of population burst activity; Exp. Spike Count, spike count during expiratory phases of population activity; Insp. Spike Count, count during inspiratory phases; Post Spike Count, count during post-inspiratory period; Insp. Modulation, difference between inspiratory and expiratory phase spike counts; Exp./Insp./Post Count Std., standard deviations of spike counts during indicated phases; Pre-insp. Slope, slope of the firing rate function during the preinspiratory phase; Insp. Slope, slope during the inspiratory burst onset; Post Slope, slope during the inspiratory burst offset; Quart. Over Time, relative timing of the quarter-amplitude threshold crossing during the inspiratory phase; Half Over Time, relative timing of the half-amplitude threshold crossing. C: mean (solid lines) and quartile bounds (dashed) of firing rate function for the most (purple) and least (orange) bursty 25% of cells. Means and interquartile bounds are shown after amplitude normalization and detrending in D.

Fig. 4.

Cycle-by-cycle activation of individual units in relation to population activity is stochastic. Spike rasters for 18 simultaneously recorded neurons (B), ordered along the ordinate axis by degree of burstiness exhibited in synaptic block, and color-coded for instantaneous firing rate (shown against population burst activity, background line in gray), and probability of anticipating population burst activity for each recorded cell calculated over entire control epoch (A). C: burst initiation probability (log₁₀ transformed) of 688 cells is strongly related (Kendall tau = 0.60; P < 0.0001) to overall spike rate in control epochs and more weakly (although significantly; tau = 0.24; P < 0.0001) correlated with interspike interval metric of burstiness in synaptic block (D).

Fig. 5.

Burst onset timing is variable in individual neurons. Burst onset timing variability (A) is weakly, although significantly, anticorrelated with subsequent endogenous bursting (Kendall tau = −0,16; P < 0.0001). B: periburst first nth (for n = 1, 3, and 5; second axis) spike times for 10 randomly selected strong pacemakers confirms that burst onset in individual bursters can follow the population burst onset on many cycles.

Fig. 6.

Population activity and single cell onset variability are dependent on network sparsity. A: 4 measures of variability in simulated population activity from sparsely connected (1% connection probability) networks of different sizes illustrate importance of larger networks in simulating physiological variability. Networks with only 50 cells produce overly irregular population rhythms (i) while networks with 500 units are unphysiologically regular (ii). B: same metrics applied to population recordings from 21 in vitro experiments (example in i) indicate that the simulation experiments shown in A reach similar levels of irregularity at population sizes of 200–300 cells. In 300-cell models, variability in single cell burst onset timing (C) with respect to the population burst varies with network sparsity and approaches mean levels from 21 in vitro experiments (left) only when the connection probability is near 1%.