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Figure 3 | BMC Systems Biology

Figure 3

From: Characterizing criticality of proteins by systems dynamics: Escherichia coli central carbon metabolism as a working example

Figure 3

The asymptotically stable equilibrium point. The stable equilibrium (X eq ) is illustrated by trajectories and phase orbits in the 18D space with 10% perturbations. The red line: the original curve with respect to the experimental initial value [5]; the yellow/blue lines: the curves whose initial value has a -10%/+10% perturbation from the experimental one; the triangular spots: projections of X eq on the corresponding dimensions. (A) Asymptotical stability shown by trajectories. Each subplot represents a dimension in the 18D space, i.e. the kinetics of a metabolite. All trajectories eventually and consistently converge to the X eq (projection on the corresponding dimension) although a 10% perturbation is in the initial value. The x-axis: time (s); y-axis: concentration (mM). (B) Asymptotical stability shown by phase orbits. Stability is more clearly illustrated in such presentation. We randomly chose 2 state variables (metabolites #7 and #8 in the plot) to form the phase orbit in the 2D subspace. Arrows denote the directions of orbits and they eventually and consistently converge to X eq (projection on the 2D subspace, marked by the triangular spot). For other 2D subspaces, the orbit profiles are the same.

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