chemart / michaelis-menten

hub:
  repo_type: generator
  builtin: michaelis-menten
  tags:
  - banzhaf-yamamoto
chemistries:
- id: michaelis-menten
  name: Michaelis-Menten enzyme kinetics
  intuition: 'The canonical enzyme mechanism, and a lesson about output formats. Written elementarily
    it is three mass-action reactions among four species: enzyme and substrate bind reversibly, then the
    complex releases product. Eliminate the complex and you get the familiar saturating rate law over
    just two species - fewer species and fewer reactions, but no longer mass action. The same chemistry
    thus has two faithful representations, and any schema that assumes mass action can only hold one of
    them.

    '
  book: 18.2.1; also 4.4 (as an abridgement method)
  refs:
  - '[42]'
  - '[81]'
  - '[503]'
  family: systems-biology
  kind: generator
  constructive: false
  S:
    repr: E, S, ES, P (elementary) or S, P (abridged)
    definition: explicit
  R:
    definition: explicit
    arity:
    - 1
    - 2
    scheme: E + S <-ka/ka'-> ES --kb--> E + P (irreversible product formation)
    notes: d[P]/dt = v_m [S] / (k_m + [S]), with v_m = kb [E0] and k_m = (ka' + kb)/ka
  A:
    reactor:
    - ode
    - ssa
    dilution: none
  params:
  - name: form
    type: enum
    default: elementary
    choices:
    - elementary
    - abridged
    role: structural
    meaning: elementary mass-action steps, or the single abridged reaction S -> P with a Michaelis-Menten
      rate law
  - name: ka
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: binding E + S -> ES
  - name: ka_rev
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: unbinding ES -> E + S
  - name: kb
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: catalytic turnover ES -> E + P
  - name: E0
    type: float
    default: 1.0
    min: 0
    role: population
    meaning: total enzyme, free + bound
  - name: S0
    type: float
    default: 10.0
    min: 0
    role: population
    meaning: initial substrate
  provides:
  - topology
  - stoichiometry
  - rate-constants
  - rate-law
  - initial-state
  fidelity: book+decisions
  decisions:
  - The book gives no numerical rates; all default to 1, with E0 = 1 and S0 = 10.
  - k_m is derived, not a parameter. In the extracted text of eq. 18.4 the prime on ka' is lost ('k_m
    = (k_a + k_b)/k_a'); the quasi-steady-state derivation gives k_m = (ka_rev + kb) / ka, which is used.
  notes: 'The abridged form has FEWER species and reactions than the elementary form but a NON-MASS-ACTION
    rate law; a schema that assumes mass action silently changes the model.

    '