chemart / repressilator

hub:
  repo_type: generator
  builtin: repressilator
  tags:
  - banzhaf-yamamoto
chemistries:
- id: repressilator
  name: Repressilator
  intuition: 'A synthetic oscillator that was actually built in bacteria. Three genes are arranged in
    a cycle so each represses the next, with repression modelled as cooperative binding and both mRNA
    and protein decaying. With enough cooperativity the loop cannot settle - the repression travels round
    the ring and the protein levels oscillate. With no cooperativity it simply relaxes, so the nonlinearity
    is doing the work, and the oscillation only exists inside a bounded region of parameter space.

    '
  origin: Elowitz & Leibler, 2000
  book: 19.3.2; appendix (Repressilator.py)
  refs:
  - '[256]'
  - '[518]'
  - '[926]'
  family: wet
  kind: generator
  constructive: false
  S:
    repr: 3 genes G_i, 3 gene-protein complexes C_i, 3 mRNAs M_i, 3 repressor proteins P_i (LacI, TetR,
      lambda-cI)
    definition: explicit
  R:
    definition: explicit
    arity: n+1, 1
    scheme: 'G_i + n P_{i-1} <-ke/kr-> C_i  (cyclic: P3 represses G1) ; G_i --km--> G_i + M_i ; M_i --kp-->
      M_i + P_i ; M_i --mu_m--> ; P_i --mu_p-->

      '
  A:
    reactor:
    - ode
    - ssa
    dilution: mRNA and protein decay
  params:
  - name: n
    type: int
    default: 2
    min: 1
    max: 10
    role: kinetic
    meaning: Hill coefficient (proteins per binding event); n=1 gives NO oscillations - the circuit needs
      a sigmoid response
  - name: ke
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: repressor binding
  - name: kr
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: repressor unbinding
  - name: km
    type: float
    default: 5.0
    min: 0
    role: kinetic
    meaning: transcription
  - name: kp
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: translation
  - name: mu_m
    type: float
    default: 0.5
    min: 0
    role: kinetic
    meaning: mRNA decay
  - name: mu_p
    type: float
    default: 0.1
    min: 0
    role: kinetic
    meaning: protein decay
  provides:
  - topology
  - stoichiometry
  - catalysts
  - rate-constants
  - initial-state
  fidelity: book
  decisions:
  - 'The SSA gene copy number m is not a parameter: it sizes a stochastic simulation (V = m/N_A), not
    the network.'
  - 'Binding is the elementary mass-action reaction of eqs. 19.1-19.3, not a lumped Hill rate law. Initial
    state is figure 19.18''s: G1 = C2 = C3 = 1, everything else 0.'
  reference_impl: PyCellChemistry Repressilator.py
  phenomena:
  - sustained oscillations inside a bounded parameter region (n=2 with the default rates)
  - no oscillations for n = 1
  - oscillations survive stochastic noise at low gene copy number
  - implemented in real E. coli