Figure 5: Assessment of modulatory amplitude–phase coupling.

(a) Waxing and waning of electrical slow-wave activity in the presence of decanoic acid (1 mM); 2 min recording. MP, membrane potential. (b) Time–frequency contour plot of mean power (continuous wavelet transform analysis) of a shows high (~25 c.p.m.) and low-(~3 c.p.m.) frequency components. (c) Modulation index (MI) of the phase–amplitude coupling (see Methods). Modulation of the higher frequency (~25 c.p.m.) component’s amplitude by the phase of a lower frequency (~3 c.p.m.) component is measured, where higher values (towards red) indicate greater modulation. Areas within black lines indicate significance with an alpha value of 0.05 using surrogate methods. (d) Intracellular electrical activity of circular muscle in the absence of decanoic acid. MP, membrane potential. (e) Time–frequency contour plot of mean power shows the high-frequency (~30 cycles per min) signal without significant low-frequency signals throughout. (f) No modulation (see Methods) is apparent, as no low-frequency component is present in d. (g) Waxing and waning pattern of intestine diameter recorded at one point along the small intestine during segmentation activity (2 min recording). (h) Time–frequency contour plot of mean power of g. (i) MI carried out as in c. Highly significant modulation of the higher frequency (38 c.p.m.) component’s amplitude by the phase of a lower frequency (~4 c.p.m.) is seen. (j) Constant amplitude intestine diameter recorded at one point along the small intestine during propulsion activity (2 min recording). (k) Time–frequency contour plot of mean power shows the high frequency (~38 c.p.m.) signal amplitude without significant low-frequency signals throughout. (l) No significant modulation is seen because of lack of significant low-frequency components. (m) To further demonstrate the nature of the cross-frequency coupling in the segmentation waxing and waning pattern of g, part of g depicted here (0.9–1.7 min) was band-pass filtered between 0.5 and 5 cycles per min to obtain the low-frequency component as shown. (n) The higher frequency component from the signal in m was obtained by band-pass filtering from 30 to 50 cycles per min and was superimposed on the lower frequency signal. A clear relationship is seen between the phase of the lower frequency and the amplitude of the higher frequency.