Landscape, Flux, Correlation, Resonance, Coherence, Stability, and Key Network Wirings of Stochastic Circadian Oscillation  Chunhe Li, Erkang Wang, Jin Wang  Biophysical Journal  Volume 101, Issue 6, Pages 1335-1344 (September 2011) DOI: 10.1016/j.bpj.2011.08.012 Copyright © 2011 Biophysical Society Terms and Conditions

Figure 1 Core wiring diagram for the circadian rhythms network. Biophysical Journal 2011 101, 1335-1344DOI: (10.1016/j.bpj.2011.08.012) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 2 Landscape and flux for V = 200. (A) Three-dimensional landscape for variable Mp (mRNA in nucleus) and PN (per protein in nucleus). (B) Two-dimensional landscape and corresponding probabilistic flux. (Arrows) Curl flux vector. Biophysical Journal 2011 101, 1335-1344DOI: (10.1016/j.bpj.2011.08.012) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 3 (A) Barrier height versus the molecular number V. (B) Coherence versus the molecular number V. (C) Entropy production rate versus the molecular number V. Biophysical Journal 2011 101, 1335-1344DOI: (10.1016/j.bpj.2011.08.012) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 4 (A1) Trajectories of variables PN and Mp for V = 100. (A2) Autocorrelation function versus interval time Δt when V = 100. (A3) Power spectrum of the autocorrelation function in panel A2. (Solid line) Mp (mRNA), (dashed line) PN (nuclear protein). (B1–B3) Trajectories, autocorrelation function, and the corresponding power spectrum for V = 200, respectively. (C1–C3) Trajectories, autocorrelation function, and the corresponding power spectrum for V = 300, respectively. (A4, B4, and C4) Height of peak of power spectrum of autocorrelation function versus barrier height, coherence, and entropy production rate, respectively. Biophysical Journal 2011 101, 1335-1344DOI: (10.1016/j.bpj.2011.08.012) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 5 (A and B) Three-point autocorrelation function: x(t0), x(t0 + t1), and x(t0 + t1 + t2) and its time reversal x(t), x(t − t1), and x(t − t1 − t2) for variable Mp (mRNA) when V = 200. From the contour map, it can be seen that the results of correlation function in panels A and B are obviously different, which can also be found in panel C. (C) Difference between panels A and B. It should be noticed that the scales of difference of panels A and B are between −0.1 and 0.1, which approximate the scales of these two correlation functions themselves; they are obviously different. Biophysical Journal 2011 101, 1335-1344DOI: (10.1016/j.bpj.2011.08.012) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 6 (A) Distribution of escape time of jumping to outside from closed ring for different molecular number V. (B–D) Barrier height, the phase coherence, and the height of power spectrum of autocorrelation function versus the average of escape time, respectively. Biophysical Journal 2011 101, 1335-1344DOI: (10.1016/j.bpj.2011.08.012) Copyright © 2011 Biophysical Society Terms and Conditions

Figure 7 Sensitivity analysis. (A) Effects of parameters on the barrier height at the same perturbation. The x axis represents: 1, vs; 2, a1; 3, a2, 4; a3, 5, a41; 6, d1; 7, d2; 8, d3; 9, d4; 10, km1; 11, km2; 12, km3; 13, ks; 14, k11; 15, k12; 16, k13; 17, k21; 18, k22; 19, k23; 20, k31; 21, k32; 22, k33; 23, k41; 24, k42; 25, k43; 26, kd1; 27, kd2; 28, kd3; 29, k1; and 30, k2. (B) Effect of parameter a4 on barrier height. Δa4/a4 = percent of parameter increased. Biophysical Journal 2011 101, 1335-1344DOI: (10.1016/j.bpj.2011.08.012) Copyright © 2011 Biophysical Society Terms and Conditions