Optimal adjustment of the human circadian clock in the real world
Fig 4
Optimal schedules for entrainment to 12-hr shifts are simulated with different types of noise for 30 hypothetical subjects. (A-C) Phase trajectories with other sources of error were individually studied. The human circadian pacemaker acts as a limit cycle oscillator formed by two variables, x, and xc. The variable x represents the core body temperature, a phase marker of the human circadian rhythm, and the variable xc is required to achieve a limit cycle mathematically. The noiseless, optimal trajectory is plotted in the dark dashed line, while noisy trajectories are plotted in a lighter gray. The start and end of the trajectories are marked in green and red, respectively. Three sources of error were considered: initial conditions (i.e., starting circadian state), light levels in lux, and switch time (the times at which light is either switched on or off). For each source of error, the noise was sampled randomly from a normal distribution with mean 0 and standard deviation σ, where the standard deviation in each case is σinitial condition = (σamplitude, σphase) = (0.1,1), σlight = 1000 lux, and σswitch time = 2 hours respectively. (D-F) 24-hour snapshots of the circadian phase with all different types of noise acting together. Graphs from left to right represent the increasing magnitude of noise added to switch times (σswitch time = 2, 3, 4 hours), with a fixed magnitude of noise added to initial conditions and light levels σinitial condition = (σamplitude, σphase) = (0.1,1), σlight = 1000 lux). Predicted core body temperature minima (CBTmin) are plotted against the schedule of optimal light exposure, where the color yellow and black represent bright light exposure (10000 lux) and darkness (0 lux), respectively. Predicted CBTmin under the optimal schedule without noise is marked in red circles, while predicted CBTmin of 30 hypothetical subjects under schedule with noise is plotted in blue circles.