hub:
  repo_type: generator
  builtin: okamoto-switch
  tags:
  - banzhaf-yamamoto
chemistries:
- id: okamoto-switch
  name: Okamoto's biochemical switch
  intuition: 'A biochemical flip-flop. Two enzyme cofactors interconvert, each conversion driven by one
    of two input-derived substrates, so whichever input dominates pushes the pair into the corresponding
    state and holds it there. The result is bistability with a sharp transition: the outputs swap within
    seconds of the inputs crossing, and how fast depends on how quickly inputs are converted. An early
    demonstration that chemistry can hold a bit.

    '
  origin: Okamoto, Sakai & Hayashi, 1987-1993
  book: 17.4.1
  refs:
  - '[632]'
  - '[633]'
  - '[634]'
  - '[635]'
  - '[631]'
  - '[386]'
  - '[387]'
  - '[539]'
  family: application
  kind: generator
  constructive: false
  S:
    repr: inputs I1, I2; substrates X1..X4; enzyme cofactors A and B (the outputs)
    definition: explicit
  R:
    definition: explicit
    arity:
    - 1
    - 2
    scheme: 'I1 -> X1 ; I2 -> X3 ; A + X3 --k2--> B + X4 ; B + X1 --k1--> A + X2 ; X2 --k3--> ; X4 --k4-->
      ; plus I1 -> I2 to drive the inputs across each other

      '
  A:
    reactor: ode
    dilution: X2 and X4 decay out
  params:
  - name: k1
    type: float
    default: 50000.0
    min: 0
    role: kinetic
    meaning: B + X1 -> A + X2
  - name: k2
    type: float
    default: 50000.0
    min: 0
    role: kinetic
    meaning: A + X3 -> B + X4
  - name: k3
    type: float
    default: 10.0
    min: 0
    role: kinetic
    meaning: decay of X2
  - name: k4
    type: float
    default: 10.0
    min: 0
    role: kinetic
    meaning: decay of X4
  - name: k_in
    type: float
    default: 1.0
    min: 0
    role: kinetic
    meaning: production of X1 from I1 and of X3 from I2
  - name: k_conv
    type: float
    default: 0.006
    min: 0
    role: kinetic
    meaning: conversion I1 -> I2; sets when the inputs cross and hence the switching time
  - name: I1_0
    type: float
    default: 100.0
    min: 0
    role: population
    meaning: initial concentration of input I1
  - name: I2_0
    type: float
    default: 80.0
    min: 0
    role: population
    meaning: initial concentration of input I2
  provides:
  - topology
  - stoichiometry
  - catalysts
  - rate-constants
  - initial-state
  fidelity: book+decisions
  decisions:
  - Inputs are 'controlled externally ... not affected although consumed' (book), so input reactions are
    written I1 -> I1 + X1 and I2 -> I2 + X3, with rate k_in (not given in the book; default 1).
  - 'The book''s I1/I2 profiles are reproduced as in its simulation: I1(0) = 100, I2(0) = 80 and an irreversible
    I1 -> I2. k_conv = 0.006 makes the inputs cross at about 17.5 s, as in figure 17.5 (top).'
  - 'Known discrepancy: with the reactions as printed, X1 (X3) is never lost while A (B) is saturated,
    so surplus substrate accumulates and the flip lags the crossing by ~18 s at the defaults, instead
    of ''a few seconds'' in figure 17.5. The original cyclic-enzyme model [633] has reversible enzyme
    steps and substrate influx/efflux that the book omits; the paper was not accessible, so the book''s
    scheme is kept.'
  - 'Other initial concentrations are the book''s: X1 = X3 = 0, X2 = X4 = 8, A = 1, B = 0.'
  phenomena:
  - 'bistability: A and B flip within seconds of the inputs crossing'
  - switching time tunable via the input conversion rate
  - composable into chemical neurons, logic gates, finite state machines and a Turing-universal chemical
    computer