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Synchronization-induced rhythmicity of circadian oscillators in the suprachiasmatic nucleus.

Bernard S, Gonze D, Cajavec B, Herzel H, Kramer A - PLoS Comput. Biol. (2007)

Bottom Line: The authors simulated different experimental conditions and found that: (1) in normal, constant conditions, coupled circadian oscillators quickly synchronize and produce a coherent output; (2) in large populations, such oscillators either synchronize or gradually lose rhythmicity, but do not run out of phase, demonstrating that rhythmicity and synchrony are codependent; (3) the number of oscillators and connectivity are important for these synchronization properties; (4) slow oscillators have a higher impact on the period in mixed populations; and (5) coupled circadian oscillators can be efficiently entrained by light-dark cycles.Based on these results, it is predicted that: (1) a majority of SCN neurons needs periodic synchronization signal to be rhythmic; (2) a small number of neurons or a low connectivity results in desynchrony; and (3) amplitudes and phases of neurons are negatively correlated.The authors conclude that to understand the orchestration of timekeeping in the SCN, intracellular circadian clocks cannot be isolated from their intercellular communication components.

View Article: PubMed Central - PubMed

Affiliation: Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece. samubernard@gmail.com

ABSTRACT
The suprachiasmatic nuclei (SCN) host a robust, self-sustained circadian pacemaker that coordinates physiological rhythms with the daily changes in the environment. Neuronal clocks within the SCN form a heterogeneous network that must synchronize to maintain timekeeping activity. Coherent circadian output of the SCN tissue is established by intercellular signaling factors, such as vasointestinal polypeptide. It was recently shown that besides coordinating cells, the synchronization factors play a crucial role in the sustenance of intrinsic cellular rhythmicity. Disruption of intercellular signaling abolishes sustained rhythmicity in a majority of neurons and desynchronizes the remaining rhythmic neurons. Based on these observations, the authors propose a model for the synchronization of circadian oscillators that combines intracellular and intercellular dynamics at the single-cell level. The model is a heterogeneous network of circadian neuronal oscillators where individual oscillators are damped rather than self-sustained. The authors simulated different experimental conditions and found that: (1) in normal, constant conditions, coupled circadian oscillators quickly synchronize and produce a coherent output; (2) in large populations, such oscillators either synchronize or gradually lose rhythmicity, but do not run out of phase, demonstrating that rhythmicity and synchrony are codependent; (3) the number of oscillators and connectivity are important for these synchronization properties; (4) slow oscillators have a higher impact on the period in mixed populations; and (5) coupled circadian oscillators can be efficiently entrained by light-dark cycles. Based on these results, it is predicted that: (1) a majority of SCN neurons needs periodic synchronization signal to be rhythmic; (2) a small number of neurons or a low connectivity results in desynchrony; and (3) amplitudes and phases of neurons are negatively correlated. The authors conclude that to understand the orchestration of timekeeping in the SCN, intracellular circadian clocks cannot be isolated from their intercellular communication components.

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Effect of the Intrinsic Period on Amplitude and Phase(A) Resulting periods of two mixed populations of oscillators, one with a 24 h period and one with 20 h period (type 1 coupling; c0 = 0.1). The period was calculated with proportions of 24 h period cells of 0.0, 0.1, 0.2, 0.5, 0.8, and 1.0, and results of five runs for each proportion were averaged (total n = 100, [open circles] average period). The dashed line represents the average of the individual oscillators' periods.(B) Deviation of the resulting population periods shown in (A) from the average of the individual oscillator periods (the error bars are the standard deviations).(C) Three coupled oscillators with different intrinsic periods showing their phase and amplitude relationships: the short period oscillator (thick blue line) is phase-advanced and low amplitude compared with the average period oscillator (green line) and the long period oscillator (dashed red line).(D) Phase difference from the average Per/Cry mRNA concentration with respect to the intrinsic periods, from the simulations shown in Figure 3A and 3B (dark blue ×, left VL neurons; light blue, left DM neurons; dark red ×, right VL neurons; light red, right DM neurons). A positive phase difference means phase-advanced compared with the phase of the population.(E) Amplitude with respect to the intrinsic period from the simulations shown in Figure 3A and 3B (color code as in [D]).(F) Amplitude phase relationship for type 1 coupling (K = 0.9, c0 = 0.1, number of oscillators n = 100).
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pcbi-0030068-g006: Effect of the Intrinsic Period on Amplitude and Phase(A) Resulting periods of two mixed populations of oscillators, one with a 24 h period and one with 20 h period (type 1 coupling; c0 = 0.1). The period was calculated with proportions of 24 h period cells of 0.0, 0.1, 0.2, 0.5, 0.8, and 1.0, and results of five runs for each proportion were averaged (total n = 100, [open circles] average period). The dashed line represents the average of the individual oscillators' periods.(B) Deviation of the resulting population periods shown in (A) from the average of the individual oscillator periods (the error bars are the standard deviations).(C) Three coupled oscillators with different intrinsic periods showing their phase and amplitude relationships: the short period oscillator (thick blue line) is phase-advanced and low amplitude compared with the average period oscillator (green line) and the long period oscillator (dashed red line).(D) Phase difference from the average Per/Cry mRNA concentration with respect to the intrinsic periods, from the simulations shown in Figure 3A and 3B (dark blue ×, left VL neurons; light blue, left DM neurons; dark red ×, right VL neurons; light red, right DM neurons). A positive phase difference means phase-advanced compared with the phase of the population.(E) Amplitude with respect to the intrinsic period from the simulations shown in Figure 3A and 3B (color code as in [D]).(F) Amplitude phase relationship for type 1 coupling (K = 0.9, c0 = 0.1, number of oscillators n = 100).

Mentions: With this experimental observation in mind, we tested whether our model might be able to explain this nonintuitive result. We randomly mixed and connected a 24 h–period population with a 20 h–period population (total, n = 100; standard deviations of the periods, 0.1 h) in various ratios. The resulting period of the synchronized population was compared with the period that would have been expected from averaging the individual oscillator periods. For ratios between 0.2 and 0.8 (i.e., 20% and 80% wild-type cells), the resulting population period was systematically longer than expected (five runs per ratio, R > 0.8; Figure 6A and 6B). Thus, in mixed population, slow oscillators seem to have a higher impact on the period than the faster ones.


Synchronization-induced rhythmicity of circadian oscillators in the suprachiasmatic nucleus.

Bernard S, Gonze D, Cajavec B, Herzel H, Kramer A - PLoS Comput. Biol. (2007)

Effect of the Intrinsic Period on Amplitude and Phase(A) Resulting periods of two mixed populations of oscillators, one with a 24 h period and one with 20 h period (type 1 coupling; c0 = 0.1). The period was calculated with proportions of 24 h period cells of 0.0, 0.1, 0.2, 0.5, 0.8, and 1.0, and results of five runs for each proportion were averaged (total n = 100, [open circles] average period). The dashed line represents the average of the individual oscillators' periods.(B) Deviation of the resulting population periods shown in (A) from the average of the individual oscillator periods (the error bars are the standard deviations).(C) Three coupled oscillators with different intrinsic periods showing their phase and amplitude relationships: the short period oscillator (thick blue line) is phase-advanced and low amplitude compared with the average period oscillator (green line) and the long period oscillator (dashed red line).(D) Phase difference from the average Per/Cry mRNA concentration with respect to the intrinsic periods, from the simulations shown in Figure 3A and 3B (dark blue ×, left VL neurons; light blue, left DM neurons; dark red ×, right VL neurons; light red, right DM neurons). A positive phase difference means phase-advanced compared with the phase of the population.(E) Amplitude with respect to the intrinsic period from the simulations shown in Figure 3A and 3B (color code as in [D]).(F) Amplitude phase relationship for type 1 coupling (K = 0.9, c0 = 0.1, number of oscillators n = 100).
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC1851983&req=5

pcbi-0030068-g006: Effect of the Intrinsic Period on Amplitude and Phase(A) Resulting periods of two mixed populations of oscillators, one with a 24 h period and one with 20 h period (type 1 coupling; c0 = 0.1). The period was calculated with proportions of 24 h period cells of 0.0, 0.1, 0.2, 0.5, 0.8, and 1.0, and results of five runs for each proportion were averaged (total n = 100, [open circles] average period). The dashed line represents the average of the individual oscillators' periods.(B) Deviation of the resulting population periods shown in (A) from the average of the individual oscillator periods (the error bars are the standard deviations).(C) Three coupled oscillators with different intrinsic periods showing their phase and amplitude relationships: the short period oscillator (thick blue line) is phase-advanced and low amplitude compared with the average period oscillator (green line) and the long period oscillator (dashed red line).(D) Phase difference from the average Per/Cry mRNA concentration with respect to the intrinsic periods, from the simulations shown in Figure 3A and 3B (dark blue ×, left VL neurons; light blue, left DM neurons; dark red ×, right VL neurons; light red, right DM neurons). A positive phase difference means phase-advanced compared with the phase of the population.(E) Amplitude with respect to the intrinsic period from the simulations shown in Figure 3A and 3B (color code as in [D]).(F) Amplitude phase relationship for type 1 coupling (K = 0.9, c0 = 0.1, number of oscillators n = 100).
Mentions: With this experimental observation in mind, we tested whether our model might be able to explain this nonintuitive result. We randomly mixed and connected a 24 h–period population with a 20 h–period population (total, n = 100; standard deviations of the periods, 0.1 h) in various ratios. The resulting period of the synchronized population was compared with the period that would have been expected from averaging the individual oscillator periods. For ratios between 0.2 and 0.8 (i.e., 20% and 80% wild-type cells), the resulting population period was systematically longer than expected (five runs per ratio, R > 0.8; Figure 6A and 6B). Thus, in mixed population, slow oscillators seem to have a higher impact on the period than the faster ones.

Bottom Line: The authors simulated different experimental conditions and found that: (1) in normal, constant conditions, coupled circadian oscillators quickly synchronize and produce a coherent output; (2) in large populations, such oscillators either synchronize or gradually lose rhythmicity, but do not run out of phase, demonstrating that rhythmicity and synchrony are codependent; (3) the number of oscillators and connectivity are important for these synchronization properties; (4) slow oscillators have a higher impact on the period in mixed populations; and (5) coupled circadian oscillators can be efficiently entrained by light-dark cycles.Based on these results, it is predicted that: (1) a majority of SCN neurons needs periodic synchronization signal to be rhythmic; (2) a small number of neurons or a low connectivity results in desynchrony; and (3) amplitudes and phases of neurons are negatively correlated.The authors conclude that to understand the orchestration of timekeeping in the SCN, intracellular circadian clocks cannot be isolated from their intercellular communication components.

View Article: PubMed Central - PubMed

Affiliation: Institute of Applied and Computational Mathematics, Foundation for Research and Technology-Hellas, Heraklion, Crete, Greece. samubernard@gmail.com

ABSTRACT
The suprachiasmatic nuclei (SCN) host a robust, self-sustained circadian pacemaker that coordinates physiological rhythms with the daily changes in the environment. Neuronal clocks within the SCN form a heterogeneous network that must synchronize to maintain timekeeping activity. Coherent circadian output of the SCN tissue is established by intercellular signaling factors, such as vasointestinal polypeptide. It was recently shown that besides coordinating cells, the synchronization factors play a crucial role in the sustenance of intrinsic cellular rhythmicity. Disruption of intercellular signaling abolishes sustained rhythmicity in a majority of neurons and desynchronizes the remaining rhythmic neurons. Based on these observations, the authors propose a model for the synchronization of circadian oscillators that combines intracellular and intercellular dynamics at the single-cell level. The model is a heterogeneous network of circadian neuronal oscillators where individual oscillators are damped rather than self-sustained. The authors simulated different experimental conditions and found that: (1) in normal, constant conditions, coupled circadian oscillators quickly synchronize and produce a coherent output; (2) in large populations, such oscillators either synchronize or gradually lose rhythmicity, but do not run out of phase, demonstrating that rhythmicity and synchrony are codependent; (3) the number of oscillators and connectivity are important for these synchronization properties; (4) slow oscillators have a higher impact on the period in mixed populations; and (5) coupled circadian oscillators can be efficiently entrained by light-dark cycles. Based on these results, it is predicted that: (1) a majority of SCN neurons needs periodic synchronization signal to be rhythmic; (2) a small number of neurons or a low connectivity results in desynchrony; and (3) amplitudes and phases of neurons are negatively correlated. The authors conclude that to understand the orchestration of timekeeping in the SCN, intracellular circadian clocks cannot be isolated from their intercellular communication components.

Show MeSH
Related in: MedlinePlus