Figures
There are errors in the legend for Figure 2, “Time-course of the fluctuation of the signaling molecules displays a chaos-like oscillation.” Please view Figure 2 and its complete, correct legend here.
Diffusion of active cofactor binding signaling molecule (X) and of inactive cofactor binding signaling molecule (Z). The Appendix S1 presents the simulation parameters, with the notation of Eqs. (3.9). p is (a) 0.795, (b) 0.81, (c) 0.84, (d) 0.88, (e) 0.96, (f) 1.00, (g) 1.12, and (h) 1.16. The upper graph shows two parametric plots of X, and Z. Red, and blue lines in the lower graph represent the concentrations of X, and Z, respectively. The horizontal axis represents time (0 ≤ t ≤ 200) and the vertical axis represents the concentrations of X, and Z, respectively. When p exceeds 0.80, chaos-like oscillation is observed. Mathematica cord when p = 0.795 (a) is shown below. Below is the simulation program when p = 1.0253: D1 = 0.28 k2 = 0.00034580 a = 800 b = 656 c = 100 d = 100 e = 100 f = 100 p = 1.0523 D4 = 156 D5 = 156 R = 1 X = k2/D1 Z = (k2 (D1∧2 R+ D4 k2))/(D1 (D1 p - D5 k2)) NDSolve[{Derivative[1][x][t] = = -(R (D1 - a X) + 2 X D4 + D5 Z) x[t] + (R a - D4 + 2 c X + e Z) x[t]∧2 + (p - D5 X - b X - d X∧2 - f X Z) z[t] - (D5 + R b - e X + f Z) x[t] z[t] - (f X) z[t]∧2, Derivative[1][z][t] = = (2 X D4 + D5 Z - c X∧2 - e X Z) x[t] + (D4 - 2 c X - e Z) x[t]∧2 + (D5 + 2 X d - e X + f Z) x[t] z[t] + (D5 X - p + d X∧2 + f X Z) z[t], x[0] = = 1.’*∧-6, z[0] = = 1.’*∧-6}, {x, z}, {t, 0, 30000}, MaxSteps -> 50000] g001 = Plot[{X + x[t]}/. %, {t, 0, 200}, PlotRange -> All, PlotStyle -> {RGBColor[1, 0, 0]}, PlotRange -> ALL] g003 = Plot[{Z + z[t]}/. %%, {t, 0, 200}, PlotRange -> All, PlotStyle -> {RGBColor[0, 0, 1]}, PlotRange -> All] g004 = ParametricPlot[Evaluate[{X + x[t], Z + z[t]}/. %%%], {t, 0, 2000}, PlotRange -> All, AxesLabel -> {"X", "Z"}] Show [g001, g003, AxesLabel -> {"t", "X, Z"}].
In the Results, there is an error in last equation before the “Evaluation of the stability of the model around the equilibrium state” subsection. This equation should be numbered 4.3. Please view the complete, correct equation here: (4.3)
There is an error in the first sentence of the “Evaluation of the stability of the model around the equilibrium state” subsection of the Results. The correct sentence is: For mathematical analysis of stability around the critical point, Eq. (3.9) (4.3) was formulated.
There is an error in the first sentence of the last paragraph of the Discussion. The correct sentence is: The simulation allowed us to define the formula (4.3) mentioned above.
Reference
Citation: The PLOS ONE Staff (2014) Correction: A Model of Cell Biological Signaling Predicts a Phase Transition of Signaling and Provides Mathematical Formulae. PLoS ONE 9(11): e112993. https://doi.org/10.1371/journal.pone.0112993
Published: November 4, 2014
Copyright: © 2014 The PLOS ONE Staff. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.