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BIOMD0000000257 - Piedrafita2010_MR_System

 

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Reference Publication
Publication ID: 20700491
Piedrafita G, Montero F, Morán F, Cárdenas ML, Cornish-Bowden A.
A simple self-maintaining metabolic system: robustness, autocatalysis, bistability.
PLoS Comput. Biol. 2010; 6(8): 861-864
Departamento de Bioquímica y Biología Molecular I, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Madrid, Spain.  [more]
Model
Original Model: BIOMD0000000257.origin
Submitter: Lukas Endler
Submission ID: MODEL1008090000
Submission Date: 09 Aug 2010 16:14:44 UTC
Last Modification Date: 04 Apr 2014 17:44:16 UTC
Creation Date: 09 Aug 2010 16:31:52 UTC
Encoders:  Lukas Endler
set #1
bqbiol:hasTaxon Taxonomy cellular organisms
set #2
bqbiol:isVersionOf Gene Ontology regulation of catalytic activity
Notes

This is the self maintaining metabolism model described in the article:
A Simple Self-Maintaining Metabolic System: Robustness, Autocatalysis, Bistability.
Piedrafita G, Montero F, Morán F, Cárdenas ML, Cornish-Bowden A, PLoS Computational Biology 2010, 6(8):e1000872. doi:10.1371/journal.pcbi.1000872
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

As this is a theoretical model and no units are given in the article, the standard units (mol, seconds and litre) are used for the parameters. k8 and k11 are set equal to k4.

Originally created by libAntimony v1.4 (using libSBML 3.4.1)

Model
Publication ID: 20700491 Submission Date: 09 Aug 2010 16:14:44 UTC Last Modification Date: 04 Apr 2014 17:44:16 UTC Creation Date: 09 Aug 2010 16:31:52 UTC
Mathematical expressions
Reactions
reaction1 reaction2 reaction3 reaction4
reaction5 reaction6 reaction7 reaction8
reaction9 reaction10 reaction11  
Rules
Assignment Rule (variable: k8) Assignment Rule (variable: k11)    
Physical entities
Compartments Species
environment S U T
STU STUS STUST
STUSU SU ST
SUST SUSTU  
Global parameters
k1 k1r k2 k2r
k3 k3r k4 k5
k5r k6 k6r k7
k7r k8 k9 k9r
k10 k10r k11  
Reactions (11)
 
 reaction1 [S] + [STU] ↔ [STUS];  
 
 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];  
 
 reaction10 [STUSU] ↔ [STU] + [SU];  
 
 reaction11 [ST] → ;  
 
Rules (2)
 
 Assignment Rule (name: k8) k8 = k4
 
 Assignment Rule (name: k11) k11 = k4
 
 environment Spatial dimensions: 3.0  Compartment size: 1.0
 
 S
Compartment: environment
Initial concentration: 4.0
 
 U
Compartment: environment
Initial concentration: 1.0
 
 T
Compartment: environment
Initial concentration: 2.0
 
 STU
Compartment: environment
Initial concentration: 5.0
 
 STUS
Compartment: environment
Initial concentration: 0.0
 
 STUST
Compartment: environment
Initial concentration: 0.0
 
 STUSU
Compartment: environment
Initial concentration: 0.0
 
 SU
Compartment: environment
Initial concentration: 0.0
 
 ST
Compartment: environment
Initial concentration: 0.0
 
 SUST
Compartment: environment
Initial concentration: 0.0
 
 SUSTU
Compartment: environment
Initial concentration: 0.0
 
Global Parameters (19)
 
 k1
Value: 10.0   (Units: per_time_per_M)
Constant
 
 k1r
Value: 10.0   (Units: per_time)
Constant
 
 k2
Value: 10.0   (Units: per_time_per_M)
Constant
 
 k2r
Value: 10.0   (Units: per_time)
Constant
 
 k3
Value: 2.0   (Units: per_time)
Constant
 
 k3r
Value: 1.0   (Units: per_time_per_M)
Constant
 
 k4
Value: 0.3   (Units: per_time)
Constant
 
 k5
Value: 1.0   (Units: per_time_per_M)
Constant
 
 k5r
Value: 1.0   (Units: per_time)
Constant
 
 k6
Value: 1.0   (Units: per_time_per_M)
Constant
 
 k6r
Value: 1.0   (Units: per_time)
Constant
 
 k7
Value: 0.1   (Units: per_time)
Constant
 
 k7r
Value: 0.1   (Units: per_time_per_M)
Constant
 
  k8
Value: NaN   (Units: per_time)
 
 k9
Value: 0.1   (Units: per_time_per_M)
Constant
 
 k9r
Value: 0.05   (Units: per_time)
Constant
 
 k10
Value: 0.05   (Units: per_time)
Constant
 
 k10r
Value: 0.05   (Units: per_time_per_M)
Constant
 
  k11
Value: NaN   (Units: per_time)
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000257

Curator's comment: (updated: 09 Aug 2010 17:30:23 BST)

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.

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