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piedrafita1

piedrafita1

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reaction1

S + STU = STUS

reaction10

STUSU = STU + SU

reaction11

ST > ∅

reaction2

T + STUS = STUST

reaction3

STUST = ST + STU

reaction4

STU > ∅

reaction5

SU + ST = SUST

reaction6

U + SUST = SUSTU

reaction7

SUSTU = STU + SU

reaction8

SU > ∅

reaction9

U + STUS = STUSU

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Global parameters

Fixed species

Initial values

Functions and Rules

Assignment rules

k11 = k4

k8 = k4

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Note that constraints are not enforced in simulations. It remains the responsibility of the user to verify that simulation results satisfy these constraints.


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A simple self-maintaining metabolic system: robustness, autocatalysis, bistability.

  • Gabriel Piedrafita
  • Francisco Montero
  • Federico Morán
  • María Luz Cárdenas
  • Athel Cornish-Bowden
PLoS Comput. Biol. 2010; 6 (8):
Abstract
A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts.
The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000257) Biomodels notes: Reproduction of the figures 2 b) and c) and figure 3 of the original article. Figures a) and b) show simple time-courses with different initial concentrations for STU - 5 in a) and 20 in b). The initial concentrations of all other dependent metabolites were set to 0. Calculations were performed using SBW 2.8.1 Figure c) is a bifurcation diagram calculated with the Auto2000 tool of SBW (see http://frank-fbergmann.blogspot.com/2009/02/simplifying-bifurcation-analysis.html), with the initial concentrations for STU set to 20 and to 10 for all other dependent metabolites. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.