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Fig. 2 | BMC Systems Biology

Fig. 2

From: Kinetic stability analysis of protein assembly on the center manifold around the critical point

Fig. 2

Time-course of the fluctuation in monomer concentrations displays a oscillation. Diffusion of active cofactor binding monomer (X) and of inactive cofactor binding monomer (Z). p is (a) 0.000, (b) 0.001, (c) 0.002, (d) 0.004, (e) 0.008, (f) 0.009, (g) 0.01000, (h) 0.010705, (i) 0.011000. The graphs show plots of X (black), Y(red), and Z (blue). Lines represent the concentration of X and Z. The horizontal axis represents time (0 ≤ t ≤ 1000) and the vertical axis represents the concentration of X and Z. When p exceeds 0.01, oscillations are observed. The Mathematica (version 9, Wolfram Research, Inc., Champaign, IL) code for p = 0.01 is as follows: p = 0.01 X = ((D2 M p)/(D2 k + D2 p + D1 D2 W + D1 p W)) Y = ((D1 M p W)/(D2 k + D2 p + D1 D2 W + D1 p W)) Z = ((D2 M (k + D1 W))/(D2 k + D2 p + D1 D2 W + D1 p W)) M = 0.1 W = 1 D1 = 0.28 D2 = 0.012061855670103093` a = 150 b = 156 k = 0.005 c = 0.1 d = 0 NDSolve[{Derivative[1][x][t] == − (D1 - a X) x[t] + a x[t]^2 + (p - b X) z[t] - b x[t] z[t] - k x[t], Derivative[1][z][t] == k x[t] + c x[t]^2 + d x[t] z[t] - p z[t], x[0] == 1.`*^-6, z[0] == 1.`*^-6}, {x, z}, {t, 0, 3300}, MaxSteps - >50000] g001 = Plot[{X + x[t]} /. %, {t, 0, 1000}, PlotRange - > All, PlotStyle - > {RGBColor[0, 0, 0]}] g002 = Plot[{Y - x[t] - z[t]} /. %%, {t, 0, 1000}, PlotRange - > All, PlotStyle - > {RGBColor[1, 0, 0]}] g003 = Plot[{Z + z[t]} /. %%%, {t, 0, 1000}, PlotRange - > All, PlotStyle - > {RGBColor[0, 0, 1]}, PlotRange - > All] Show[g001, g002, g003]

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