Resolution:
## Figure 4.
Equilibrium deviations and orbit structure changes caused by enzyme deletions. Impacts of enzyme deletions on dynamical stability are shown in terms of equilibrium
deviations and orbit structure changes. The curves are drawn under the principle of
topology conjugacy. They show the qualitative dynamics but they are not real-value
trajectories. Lines in different colors represent different curves initiated at different
values (init 1-3). In each subfigure, the 3 dimensions represent the metabolites that
differ most from the original kinetics. (A) The original equilibrium (X), denoted by (0,0,0). All trajectories converge to it. (B) The unstable equilibrium
after deleting TKb. The dimension _{eq}sed7p is divergent, (ribu5p, xyl5p) form an unstable limit cycle. The 3 colored orbits initiated from different values
lead to convergence, limit cycle and divergence on the 2D plane (ribu5p, xyl5p). (A) and (B) are separately drawn in order to show the limit cycle clearly. Orbits
are centred at (0,0,0) to achieve a better visual effect. (C) Deleting R5PI causes
a long-distance equilibrium deviation and alters the system stability. The source
and target ends of the grey arrow mark Xand the re-established equilibrium (_{eq }X) respectively, with the distance (in the metric unit of the state space) marked in
the box. Initiated from identical values, _{d}Xattracts the orbits and _{eq }Xrepels the orbits along the dimensions _{d }fdp and 3pg. (D) Deleting TIS causes the equilibrium to deviate an even larger distance. Legends
are the same. (E) Deleting PGK makes the system have no equilibrium. The deviation
is denoted as infinite (∞). (F) Deleting PGI does not cause obvious changes in system
dynamics. The re-established equilibrium is also asymptotically stable and it is very
near to X. See Additional file 6 for abbreviations of metabolite names.
_{eq}Li and Liu |