Research ArticleBIOLOGICAL RHYTHMS

Multicellularity enriches the entrainment of Arabidopsis circadian clock

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Science Advances  04 Oct 2017:
Vol. 3, no. 10, e1700808
DOI: 10.1126/sciadv.1700808
  • Fig. 1 Dependence of PRC on the oscillation amplitude.

    (A) Normalized bioluminescence of the plant with zeitgeber period of T = 24 hours (top) and 20 hours (bottom). (B) Phase difference ϕ between CCA1 and dark pulse for T = 24 hours (blue) and 20 hours (green). (C) Normalized amplitude for T = 24 hours (blue) and 20 hours (green). (D) PRC for all amplitudes. The dark pulse period ranged from T = 16 to 32 hours. (E) Dependence of the range of phase shift on amplitude. (F) PRC for the 2-hour dark pulse in large amplitude state (A ≥ 0.5). (G) PRC for the 2-hour dark pulse in small amplitude state (A ≤ 0.2). Here, θ and A represent the phase and amplitude, respectively, at the injection time of the 2-hour dark pulse. In (D), (F), and (G), the circles and crosses indicate the stable and unstable points of the PRC.

  • Fig. 2 PRC experimental data and theoretical plots.

    (A) Phase shift as a function of the phase and the amplitude was plotted from experimental data. (B) Phase shift as a function of the network phase and the network amplitude based on theoretical calculations.

  • Fig. 3 Dependence of entrainment range on the oscillation amplitude.

    (A and B) Period differences, T − <τ>, between dark pulse and CCA1 {mean ± SEM; n = 10 [at T = 18 hours in (B)], n = 39 [at T = 25 hours in (B)], and n = 40 [others]} plotted against dark pulse period, T. <τ> represents the mean period averaged over the peak-to-peak intervals excluding the interval, which exceeds max(T + 4, τ0 + 4), or falls below min(T − 4, τ0 − 4), for (A) tp(2)ttp(7) and (B) tp(9)ttp(14). The diagonal line represents the case without stimuli (τ = τ0). (C and D) Period differences T − <τ> obtained from Eq. 1. <τ> with an average period (C) 96 hours ≤ t ≤ 168 hours and (D) 264 hours ≤ t ≤ 336 hours.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/10/e1700808/DC1

    fig. S1. Schematic illustration of the PRC measurement.

    fig. S2. Verification of PRC measurement method by the van der Pol oscillator.

    fig. S3. Normalized bioluminescence for various dark pulse periods.

    fig. S4. Normalized amplitude for various dark pulse periods.

    fig. S5. Experimental data of phase response by dark pulse periods.

    fig. S6. PRCs for the 2-hour dark pulse obtained by the standard method (one-time stimulus) and our method (periodic stimuli).

    fig. S7. PRCs constructed from periodic stimuli with short and long periods of dark pulses.

    fig. S8. Phase distribution after the dark pulse was applied to the uniform distribution.

    fig. S9. Theoretical PRCs.

    fig. S10. PRC simulation using a phase oscillator model (Eq. 1).

    fig. S11. Range of entrainment in simulation using a phase oscillator model (Eq. 1).

    fig. S12. PRC of the 4-hour dark pulse.

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Schematic illustration of the PRC measurement.
    • fig. S2. Verification of PRC measurement method by the van der Pol oscillator.
    • fig. S3. Normalized bioluminescence for various dark pulse periods.
    • fig. S4. Normalized amplitude for various dark pulse periods.
    • fig. S5. Experimental data of phase response by dark pulse periods.
    • fig. S6. PRCs for the 2-hour dark pulse obtained by the standard method (one-time stimulus) and our method (periodic stimuli).
    • fig. S7. PRCs constructed from periodic stimuli with short and long periods of dark pulses.
    • fig. S8. Phase distribution after the dark pulse was applied to the uniform distribution.
    • fig. S9. Theoretical PRCs.
    • fig. S10. PRC simulation using a phase oscillator model (Eq. 1).
    • fig. S11. Range of entrainment in simulation using a phase oscillator model (Eq. 1).
    • fig. S12. PRC of the 4-hour dark pulse.

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