Change in the phase of the second-order frequency in phosphorylated protein oscillation under varying circadian clock model parameters.
<p>(A) The parameters <i>k</i><sub>1</sub>, <i>k</i><sub>2</sub>, <i>k</i><sub>3</sub>, <i>p</i><sub>1</sub>, <i>p</i><sub>2</sub>, and <i>r</i> were randomly inc...
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2025
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| Summary: | <p>(A) The parameters <i>k</i><sub>1</sub>, <i>k</i><sub>2</sub>, <i>k</i><sub>3</sub>, <i>p</i><sub>1</sub>, <i>p</i><sub>2</sub>, and <i>r</i> were randomly increased from 1.1 to 1.9. The horizontal axis represents the arithmetic mean of the fast-case values of <i>k</i><sub>1</sub>, <i>k</i><sub>2</sub>, and <i>k</i><sub>3</sub> divided by the slow-case values. The parameters <i>p</i><sub>1</sub>, <i>p</i><sub>2</sub>, and <i>r</i> are omitted because they do not affect the period in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1013246#pcbi.1013246.e077" target="_blank">Eq (17)</a>. The vertical axis presents changes in the phase of the second-order frequency obtained via generalized harmonic analysis of numerically calculated periodic time series. When the period length is maintained (relative period within 0.85-1.0), the phase of of <i>x</i><sub>3</sub>(<i>t</i>) tends to decrease as the reaction rate increases. (B, C) Time series for the increased reaction rates (1.1-1.9) while maintaining the period. The red and blue lines represent the time series for increased reaction rates and those for the reference parameter set, respectively. The parameter values are provided in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1013246#pcbi.1013246.s014" target="_blank">S2 Table</a>. For comparison, the period length is standardized to 1. The time of the minimum value is set to 0, and the maximum phosphorylated protein oscillation is indicated by the dotted line. Increased reaction rates tend to advance the timing of the maximum oscillation.</p> |
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