Article Figures & Data
Figures
- Fig. 1.
Scatter plots of physiological parameters across different fLICs. Significant change of the parameters, evaluated by whether the slope of the regression line deviates from zero, is indicated by an asterisk(t test, p < 0.05).A, Whole nerve experiments. i, ii, No significant change across different fLICs is present in the mean arterial pressure (MAP) and PaO2 as fLIC varies.iii, iv, When fLIC is high and no CO2 is added (filled circles,solid line), respiratory alkalosis develops with low PaCO2 and high pH (t test for zero slope, p < 0.001 for both). The PaCO2 and pH do not change significantly across different fLICs in experiments in which CO2 is added (open circles, dotted line). B, Single PGN experiments.i, No significant change across differentfLICs is present in MAP asfLIC is changed. ii, A borderline negative trend (t test for zero slope,p = 0.048) in PaO2 is observed when fLIC is increased.iii, iv, Respiratory alkalosis develops with low PaCO2 and high pH (ttest for zero slope, p < 0.001 for both) during periods of high fLIC.
- Fig. 2.
Frequency-dependent entrainment of PGN activity to LICs. A, Real time data (left panel) and superimposed autospectra (right panel) of dual recorded PGNs (dotted anddashed lines) and TP (LIC,solid line). i, Both neurons show an intrinsic dominant rhythm (fINT forPGN1 and PGN2, 0.78 and 0.69 Hz, respectively) under free-run conditions whenfLIC is high (2.00 Hz).ii–iii, When fLIC is moved into fINT range (fLIC: 0.60–0.70 Hz), stable 1:1 entrainment results. iv, AtfLIC = 0.81 Hz, the PGN with the higherfINT (PGN1) still shows entrainment but the other unit (PGN2) fails to lock.v–vi, At higher fLICs (0.97–1.41 Hz) both units are not entrained to LICs. The small peak atfLIC (arrowheads iniv, v) indicates minor LIC-related rhythmical components, suggesting relative coordination. Calibration: 25 μV (PGN), 10 mmHg (TP).B, Real time data (left panel) and superimposed autospectra of the PGN population (VCN,dotted line) and TP (LIC,solid black line). i, During free-run conditions (fLIC: 1.97 Hz), the population PGN activity reveals a broad peak (modal frequency, 0.64 Hz) representing the spread of fINTs within the population. ii–iv, MovingfLIC into this range (fLIC: 0.59–0.78 Hz) results in a single narrow peak at fLIC indicating that activity of most PGNs is 1:1 entrained to LICs. v–vi, At higher ventilation frequencies (1.00–1.35 Hz, v–vi) a narrow peak at fLIC is still preserved although some PGNs escape 1:1 entrainment as indicated by minor peaks in the fINT range (v,vi, arrows). Calibration: 0.5 μV (VCN), 10 mmHg (TP).
- Fig. 3.
Frequency response of coupling strength between PGN activity and/or LICs. The strength of coupling is evaluated by the coherence spectrum. The neural and LIC activities are the same as those in Figure 2. fLICs are indicated byfilled circles. A, LIC→single PGN (dotted and dashed lines) and single PGN→single PGN (solid line) coherence spectra.i, During free-run (fLIC: 2.00 Hz), LIC→PGN and PGN→PGN coherence at fLIC is minimal, indicating weak coupling between them. ii–iii, WhenfLIC is moved close to thefINT of the PGNs (fLIC: 0.60–0.70 Hz), strong LIC–PGN coupling strength at fLIC emerges as revealed by the high coherence between them. iv, The strong coupling at fLIC is still preserved although the dominant frequency of one unit, PGN2, is different fromfLIC when fLIC is increased to 0.81 Hz (compare with Fig. 2Aiv), a phenomenon believed to arise from relative coordination.v–vi, When fLIC is increased further, the coherence and therefore the coupling strength atfLIC drop (fLIC: 0.97–1.41 Hz).B, LIC→VCN (population PGN) coherence spectra.i, Under free-run conditions (fLIC: 1.97 Hz), the LIC→VCN coherence at fLIC is low, suggesting that most single PGNs are not coupled through LICs.ii–v, WhenfLIC is moved into the range of PGNfINT, high coherence emerges and is maintained through a wide fLIC range (0.59–1.00 Hz). vi, Although a moderate drop is observed, the coherence remains high althoughfLIC is above thefINT range (fLIC: 1.35 Hz).
- Fig. 4.
Phase relationships between single PGN activity and LICs. The neural and LIC activities are the same as those in Figures 2 and 3 (PGN1). The relative positions of the LIC occurrences are indicated by filled circles.A, Free-run. During free-run (fLIC: 2.00 Hz), the LIC→PGN cross-correlogram is essentially flat, suggesting noncorrelation (i). Constant phase-drift across time during these periods is indicated by the uniform distribution of PGN events in CRP (ii) and their cycle-spanning pattern in RCRP (iii) B, 1:1 entrainment. WhenfLIC is moved intofINT range (fLIC: 0.60 Hz), 1:1 entrainment emerges, and the cross-correlogram shows a pattern of rhythmical synchronization (i). A stationary fixed-phase relationship between PGN activity and LICs is revealed as stablevertical bands in both CRP (ii) and RCRP (iii). C, Relative coordination. WhenfLIC was moved away fromfINT (0.97 Hz), intermittent periods of phase-lock occurred, and it was manifested as LIC-related periodic peaks superimposed on a background level in the cross-correlogram (i). The dynamic nature of this phase-lock is indicated by intermittent vertical bands with variable density in CRP (ii) and vertical bands (arrows) superimposed on cycle-spanning bands in RCRP (iii). D, Asynchrony. WhenfLIC is moved farther away from PGNfINT(fLIC: 1.41 Hz), a pattern similar to that during free-run (compare with A), suggestive of complete asynchrony, appears. (i, cross-correlogram; ii, CRP; iii, RCRP). Event density in CRP and RCRP is indicated by the gray scale bar.
- Fig. 5.
High-order rational frequency-lock.A, 2:1 frequency-lock and B, 3:1 frequency-lock. The respective frequency-locking ratio is suggested by the alignment of the first peak in the PGN autocorrelogram (Ai, Bi) with the second and the third peak in the LIC autocorrelogram (Aii, Bii), respectively. A direct read-out of the 2:1 and the 3:1 frequency relationships is provided in their autospectra in which fLIC(LIC, solid line) coincides with the first harmonic frequency and the second harmonic frequency of PGN activity (dashed line), respectively (Aiii, Biii). Although the phase difference shows a stationary feature across time as revealed by the vertical bands in the CRP (Aiv, Biv; the relative positions of the LIC occurrences are indicated by filled circles), the RCRP demonstrates that the phase differences are grouped into two distinct clusters for 2:1 lock and three distinct clusters for 3:1 lock (arrowheads in Av and Bv, respectively). Event density in CRP and RCRP is indicated by thegray scale bar.
- Fig. 6.
Summary scatter plots showing entrainment of single PGNs (filled circles) and population PGN (open circles) to LICs (A–C) and the change of coherence between paired PGNs (D).A, Dominant frequency (fPGN) for single PGNs and population PGN plotted against fLICillustrates the difference in distribution offPGNs when fLICis changed. Although fPGN of single PGN activity remains close to the fINT range (shaded area) when fLIC is increased, fPGN of population activity can maintain 1:1 lock (dotted line) to LICs over a much wider range. B, The frequency ratio,fLIC/fPGN, plotted against the frequency difference,fLIC −fINT, provides evidence for frequency lock at 2:1 (top dotted line) as well as 1:1 (bottom dotted line). 1:1 entrainment for single PGNs is only possible when fLIC −fINT is less than ∼0.2 Hz (shaded area), whereas populationfPGN can followfLIC faithfully over a broader range.C, LIC→PGN coherence atfLIC plotted as a function offLIC −fINT shows the decline of coherence at the single neuron (solid line) and the population (dotted line) levels (t test for zero slope of the regression lines; single PGNs: p < 0.001, population PGNs: p < 0.001). The coherence drop is more moderate for population PGN activity than single PGN activity when fLIC is moved away fromfINT (t test for equal slope of the regression lines, p < 0.001).D, The drop of LIC→PGN coherence asfLIC is increased is accompanied by decline of PGN→PGN coherence (t test for zero slope of the regression line, p < 0.001). Higher coherence and therefore stronger coupling strength at fLICresult when both units are 1:1 entrained to LICs (filled triangles, both PGNs are entrained, vs open squares, at least one PGN is not entrained).
