Circadian Rhythmicity by Autocatalysis
Figure 5
Parameter Sensitivities and Temperature Compensation
(A–D) Period sensitivity analyses by varying the following selected rate constants (A) k1, (B) k3, (C) k4, and (D) k7. As ki is varied, the other rate constants are kept constant at their initial values as described in Figure 2.
(E) Temperature dependence of the period. Open circles show calculations, and solid circles show experimental results replotted from [1]. Each rate constant obeys the Arrhenius equation, ki = Ai exp (−Ei/RT), where Ei is the activation energy, R is the gas constant, and T is the temperature in Kelvin. Ai is the pre-exponential factor, which is also treated as a constant. Initial values of rate constants (Figure 2) are defined at 25 °C, and the period lengths are calculated for temperatures between 25 °C and 35 °C. (1) Temperature compensation (Q10 = 1.06) using the following activation energies: E1 = 40 kJ/mol, E2 = 35 kJ/mol, E3 = 28 kJ/mol, E4 = 43 kJ/mol, E5 = 40 kJ/mol, E6 = 25 kJ/mol, and E7 = 25 kJ/mol. (2) All activation energies have the average value (34 kJ/mol) from the calculation in (1) showing a Q10 of 1.58. (3) All activation energies are 80 kJ/mol, and the oscillator shows a Q10 of 2.85.
(F) Dependence of period and P-KaiC ratio as a function of KaiABC* stability mimicking KaiC mutant behaviors. (1) Rate constants are as in Figure 2 (“wild-type behavior”); (2) Decreased P-KaiC ratios amplitudes and shorter periods (“short period KaiC mutant behavior”) are observed for a more stable KaiABC* complex relative to (1): k4 = 2.3 μM−1 h−1, k5 = 4.5 h−1, k6 = 1.0 h−1; and (3) Long-period KaiC mutant behavior is observed when the KaiABC* complex is more stable compared to (1): k4 = 4.0 μM−1 h−1, k5 = 1.5 h−1, and k6 = 0.8 h−1.