BIOMD0000000233
type: SBMLModel
occurs in: http://identifiers.org/taxonomy/131567
curated: true
created:
  W3 CDTF: Tue Jun 30 18:26:59 BST 2009
species: 825148
species: 825151
length unit: length
creator:
  ORG:
    orgname: IFR, Norwich, UK
  n:
    given: Thomas
    family: Wilhelm
volume units: metaid_0000004
is version of: GO:0042221
substance units: 094936
area units: metaid_0000005
species: 825150
reaction: 825154
time units: metaid_0000003
notes: This a model from the article: The smallest chemical reaction system with bistability Thomas Wilhelm BMC Systems Biology 2009;Sep 8;3:90. 19737387 , Abstract: Background Bistability underlies basic biological phenomena, such as cell division, differentiation, cancer onset, and apoptosis. So far biologists identified two necessary conditions for bistability: positive feedback and ultrasensitivity. Results Biological systems are based upon elementary mono- and bimolecular chemical reactions. In order to definitely clarify all necessary conditions for bistability we here present the corresponding minimal system. According to our definition, it contains the minimal number of (i) reactants, (ii) reactions, and (iii) terms in the corresponding ordinary differential equations (decreasing importance from i-iii). The minimal bistable system contains two reactants and four irreversible reactions (three bimolecular, one monomolecular). We discuss the roles of the reactions with respect to the necessary conditions for bistability: two reactions comprise the positive feedback loop, a third reaction filters out small stimuli thus enabling a stable 'off' state, and the fourth reaction prevents explosions. We argue that prevention of explosion is a third general necessary condition for bistability, which is so far lacking discussion in the literature. Moreover, in addition to proving that in two-component systems three steady states are necessary for bistability (five for tristability, etc.), we also present a simple general method to design such systems: one just needs one production and three different degradation mechanisms (one production, five degradations for tristability, etc.). This helps modelling multistable systems and it is important for corresponding synthetic biology projects. Conclusion The presented minimal bistable system finally clarifies the often discussed question for the necessary conditions for bistability. The three necessary conditions are: positive feedbac…
species: 825149
reaction: 825156
reaction: 825153
name: Wilhelm2009_BistableReaction
modified:
  W3 CDTF: Fri Apr 20 23:19:37 BST 2012
compartment: 825146
reaction: 825155
is: MODEL2425356597
is described by: http://identifiers.org/pubmed/19737387

825148
type: Species
constant: true
is: SBO:0000285
initial amount: NaN
substance units: 094936
initial concentration: 1.0
has only substance units: false
name: S
in compartment: 825146
boundary condition: true

825146
type: Compartment
is: SBO:0000290
constant: true
units: metaid_0000004
size: 1.0
spatial dimensions: 3.0
name: batch

825151
type: Species
constant: false
boundary condition: false
substance units: 094936
initial amount: NaN
has only substance units: false
is: SBO:0000285
in compartment: 825146
initial concentration: 1.0
name: Y

825150
type: Species
substance units: 094936
constant: false
has only substance units: false
in compartment: 825146
initial amount: NaN
boundary condition: false
is: SBO:0000285
name: X
initial concentration: 1.0

825154
type: Reaction
kinetic law: 111593
product: 111581
product: 111569
reactant: 111557
is: SBO:0000182
fast: false
reversible: false
name: r2

825160
type: LocalParameter
is: SBO:0000036
value: 1.0

111581
type: SpeciesReference
stoichiometry: 1.0
species: 825151

111569
type: SpeciesReference
stoichiometry: 1.0
species: 825150

111557
type: SpeciesReference
stoichiometry: 2.0
species: 825150

825149
type: Species
substance units: 094936
has only substance units: false
in compartment: 825146
constant: true
name: P
boundary condition: true
initial concentration: 1.0
is: SBO:0000285
initial amount: NaN

825156
type: Reaction
kinetic law: 111690
product: 111678
reactant: 111665
is: SBO:0000182
fast: false
reversible: false
name: r4

825163
type: LocalParameter
is: SBO:0000154
value: 1.5

111678
type: SpeciesReference
stoichiometry: 1.0
species: 825149

111665
type: SpeciesReference
stoichiometry: 1.0
species: 825150

825153
type: Reaction
kinetic law: 111545
product: 111533
reactant: 111521
reactant: 111509
is: SBO:0000182
fast: false
reversible: false
name: r1

825158
type: LocalParameter
is: SBO:0000036
value: 8.0

111533
type: SpeciesReference
stoichiometry: 2.0
species: 825150

111521
type: SpeciesReference
stoichiometry: 1.0
species: 825151

111509
type: SpeciesReference
stoichiometry: 1.0
species: 825148

825155
type: Reaction
fast: false
reactant: 111605
kinetic law: 111653
reversible: false
product: 111641
is: SBO:0000182
reactant: 111617
product: 111629
name: r3

111605
type: SpeciesReference
stoichiometry: 1.0
species: 825150

825161
type: LocalParameter
is: SBO:0000036
value: 1.0

111641
type: SpeciesReference
stoichiometry: 1.0
species: 825151

111617
type: SpeciesReference
stoichiometry: 1.0
species: 825151

111629
type: SpeciesReference
stoichiometry: 1.0
species: 825149