Figure 1.
Circadian phase response behavior.
Phase response curves traditionally characterize the light pulse to induced phase mapping of the input admitted to a free-running circadian oscillator. Here, phase response dynamics of the four system parameters exhibiting greatest state sensitivity is depicted: νs (mRNA transcription), νm (mRNA degradation), ks (protein translation), and νd (protein degradation). The x-axis denotes the time at which the 2 hour pulse is given (where CT0 reflects dawn and CT12 dusk), and the y-axis describes the induced phase shift. A positive shift reflects a phase advance. Since light targets TIM specific protein degradation, νdT, the light-based PRC of the Drosophila model is represented via the dash-dotted line.
Figure 2.
Open-loop phase resetting dynamics are plotted as a function of the initial phase difference (x-axis) and the initial condition (y-axis). The intensity of the color reflects the amount of time required to reset a given phase via the light∶dark cycles calibrated to the initial condition: the lighter the color, the longer the recovery time. The mapping of color intensity to phase recovery times (in hours) is shown in the vertical color bar.
Figure 3.
Closed-loop phase resetting dynamics for single control targets (ordered according to their relative sensitivity) are described as a function of the initial phase difference (x-axis) and the initial condition (y-axis). The intensity of the color gradient reflects the amount of time required to recover from the given control conditions: the lighter the color, the longer the phase recovery. Each color bar is calibrated according to a minimum recovery time of 0 hours and maximum of 60 hours. (A) νs Single Control Target (B) νm Single Control Target (C) ks Single Control Target (D) νd Single Control Target.
Figure 4.
Closed-loop phase resetting dynamics for dual ((A) and (B)), and triple ((C) and (D)) control targets are shown with respect to the initial phase difference (x-axis) and the initial condition (y-axis). The phase recovery time is denoted by the intensity of the color at each given data point: the lighter the color, the longer the recovery time. The mapping of color intensity to the recovery time (in hours) is reflected in the color bar. Each color bar is calibrated according to a minimum recovery time of 0 hours and maximum of 60 hours. (A) νs and νm Dual Control Targets (B) νs and KI Dual Control Targets (C) νs, νm, and KI Triple Control Targets (D) νm, νd, and k2 Triple Control Targets.
Figure 5.
Continuous phase resetting for the short-period mutant phenotype (dotted lines) and long-period mutant phenotype (dashed lines) are depicted with respect to an initial condition of 0 and 12 hours. Upper subplots describe the observed state trajectory (cumulative PER-TIM protein complex concentrations) as a function of controlled light pulses, shown in the lower subplots. The nominal response (denoted by solid lines) is entrained via regular 24 hour light∶dark cycles. As expected, short-period mutants reset via daily light pulses that occur during the subjective night, forcing daily phase delays. Long period mutants reset via daily light pulses that occur during the subjective morning, forcing phase advances. (A) Mutant Response at IC0 (B) Mutant Response at IC12.
Figure 6.
The convergence of state dynamics (from an initial phase difference of 15 hours at IC12) is plotted (top) as a function time. The corresponding cumulative control input (determined by integrating the value of each multiplicative control target over time) is described in the lower subplot. The light-induced target, νd, shown via the dash-dotted line, requires the greatest amount of multiplicative control while exhibiting the greatest amount of state error. Conversely, the ks target corresponds to the least amount of state error and requires less admitted control.