hub:
  repo_type: generator
  builtin: bagley-farmer
  tags:
  - banzhaf-yamamoto
chemistries:
- id: bagley-farmer
  name: Bagley & Farmer autocatalytic metabolism
  intuition: 'What Kauffman''s autocatalytic sets look like once you give them kinetics. Polymers split
    and join, and any polymer can catalyse a reaction, multiplying both directions of it. Run in a chemostat
    - food flows in, everything washes out - and mass concentrates onto a small mutually-catalysing core.
    The crucial detail is that catalysis alone cannot do this: at equilibrium a catalysed and an uncatalysed
    network reach the same place, so the focusing only appears away from equilibrium, driven by the flow.

    '
  origin: Bagley & Farmer, 1992; Bagley, Farmer & Fontana, 1992
  book: 6.3.1, 7.3.1
  refs:
  - '[49]'
  - '[50]'
  family: origin-of-life
  kind: generator
  constructive: true
  S:
    repr: polymers = strings over an alphabet of 1-4 letters (a, b for the paper's binary chemistry) up
      to max_length; water H; with saturation, one bound pool x_bound per polymer (sum of the enzyme complexes
      x is part of, eq. 26)
    definition: implicit
  R:
    definition: implicit
    arity:
    - 1
    - 2
    - 3
    scheme: 'A + B <-> C + H for every split of every polymer (kf forward, kr backward). A catalytic link
      E multiplies both directions by (1 + nu E) (eq. 9): A + B + E -> C + H + E at nu kf and C + H +
      E -> A + B + E at nu kr. With saturation (appendix, eqs. 22-29): A + B + E -> C_bound + E_bound
      + H at nu kf, C + H + E -> A_bound + B_bound + E_bound at nu kr, and x_bound -> x at ku.

      '
    notes: links are drawn with probability p per (reaction, catalyst) pair, the paper's random artificial
      chemistry (section 3.1.1); the string-matching rule (3.1.2) is not implemented
  A:
    reactor:
    - ode
    dilution: 'chemostat: each food species enters at flux delta, every species leaves at first-order
      rate K = delta * (monomers in the food set) / m0 (eqs. 10-12)'
    notes: 'optional deterministic metadynamics (section 3.2): only species at or above a concentration
      threshold react; the graph is updated at each dynamical fixed point until it stops changing'
  params:
  - name: alphabet_size
    type: int
    default: 2
    min: 1
    max: 4
    role: structural
    meaning: number of distinct monomers m (letters a, b, c, d); the paper's simulations use 2
  - name: max_length
    type: int
    default: 5
    min: 2
    max: 8
    role: structural
    meaning: longest polymer in the network (at most 512 polymers); the paper has no hard bound and relies
      on the threshold instead
  - name: food_set
    type: list
    default:
    - a
    - b
    range: Figures 5-12 use {a, b}; Figure 3 uses {a, b, ab, ba}
    role: population
    meaning: polymers supplied from outside at flux delta each
  - name: p
    type: float
    default: 0.01
    min: 0
    max: 1
    range: Figure 13 varies the number of links from 0 to 200 on a 15-reaction network
    role: structural
    meaning: probability that a given polymer strongly catalyses a given condensation/cleavage pair (ignored
      when links is given)
  - name: links
    type: list
    default: []
    role: structural
    meaning: explicit catalytic links 'A + B <-> C | E' (e.g. 'a + b <-> ab | bb'); when non-empty they
      replace the random draw
  - name: nu
    type: float
    default: 897000.0
    min: 0
    range: 'Table 2: 8.97e5 (network a), 5.26e5 (network b); Figure 3: 1e4'
    role: kinetic
    meaning: 'catalytic efficiency: a catalyst E multiplies both rate constants by (1 + nu E)'
  - name: nu_distribution
    type: enum
    choices:
    - constant
    - uniform
    default: constant
    role: stochastic
    meaning: 'constant: every link has efficiency nu; uniform: each link draws its efficiency from U(0,
      2 nu)'
  - name: kf
    type: float
    default: 649.0
    min: 0
    range: 'Table 2: 6.49e2 (a), 3.02e4 (b); Figure 3: 1e2'
    role: kinetic
    meaning: condensation rate constant, the same for every reaction
  - name: kr
    type: float
    default: 2.5
    min: 0
    range: 'Table 2: 2.50 (a), 2.70 (b); Figure 3: 10'
    role: kinetic
    meaning: hydrolysis (cleavage) rate constant, the same for every reaction
  - name: ku
    type: float
    default: 50000.0
    min: 0
    range: 'Table 2: 5.00e4 (a), 7.11e4 (b); Figure 3: 1e4'
    role: kinetic
    meaning: unbinding rate of enzyme complexes (used only with saturation)
  - name: saturation
    type: bool
    default: true
    role: kinetic
    meaning: 'true: catalysis through bound complexes (appendix, eqs. 22-29), as in the paper''s simulations;
      false: the unsaturated approximation of eq. 9'
  - name: H
    type: float
    default: 1.0
    min: 0
    role: population
    meaning: water concentration, held constant (Figure 3 uses H = 1)
  - name: delta
    type: float
    default: 17.9
    min: 0
    range: 'Table 2: 1.79e1 (a), 1.41e2 (b); Figure 5 uses 0.01, 1e5 and 10^7.5'
    role: population
    meaning: inflow flux of each food species (mass flux driving the system from equilibrium)
  - name: m0
    type: float
    default: 2.0
    min: 1.0e-12
    range: 2.0 in Figures 5-14; 3 in Figure 3
    role: population
    meaning: total monomer concentration at the chemostat fixed point; sets the outflow rate K and the
      initial food concentrations
  - name: threshold
    type: float
    default: 0.0
    min: 0
    role: population
    meaning: metadynamics concentration threshold (one molecule in the reaction vessel); 0 keeps the whole
      bounded network, > 0 returns the graph at the metadynamical fixed point
  provides:
  - topology
  - stoichiometry
  - catalysts
  - rate-constants
  - mass-conservation
  - flow
  - initial-state
  - thermodynamic-consistency
  fidelity: reconstructed
  sources:
  - 'Bagley, R. J. & Farmer, J. D. (1992). Spontaneous emergence of a metabolism. In Langton, Taylor,
    Farmer & Rasmussen (eds.), Artificial Life II, SFI Studies in the Sciences of Complexity X, pp. 93-140.
    Addison-Wesley. Also LA-UR-91-1707. Scan: https://oms-inet.files.svdcdn.com/production/files/SpontaneousEmergence.pdf
    (listed at https://www.inet.ox.ac.uk/publications/spontaneous-emergence-of-a-metabolism)'
  - 'Bagley, R. J., Farmer, J. D. & Fontana, W. (1992). Evolution of a metabolism. Artificial Life II,
    pp. 141-158. Scan: https://oms-inet.files.svdcdn.com/production/files/EvolutionMetabolism.pdf (listed
    at https://www.inet.ox.ac.uk/publications/evolution-of-a-metabolism)'
  decisions:
  - 'Kinetics follow the paper: spontaneous A + B <-> C + H with the same kf, kr for all reactions (3.1.3),
    catalysis multiplying both directions by (1 + nu E) (eq. 9), and saturation through complexes that
    unbind at ku, aggregated into one bound pool per species (eqs. 22-29). All of it is mass action; the
    catalyst and nu are recorded in each catalysed rate dict.'
  - Eq. 24 routes the spontaneous flux through the complex CE; this looks like a typo (a spontaneous reaction
    uses no enzyme), so spontaneous reactions produce free species directly. Eqs. 10-11 and 25-29 agree
    with this reading.
  - The paper keeps the reaction graph finite with a concentration threshold and lumps the spontaneous
    background into per-length aggregates (eqs. 19-21). Here the chemistry is bounded by max_length and
    every spontaneous reaction is explicit, which is the exact system those aggregates approximate. The
    threshold metadynamics of section 3.2 is available with threshold > 0 (default off; the paper gives
    no numeric threshold).
  - In metadynamics a species is above threshold when its free plus bound concentration is; a reaction
    is in the graph when its free reactants and catalyst are above threshold (food is always above). Each
    round integrates the chemostat ODE of the current graph to its fixed point (t = 200/K) instead of
    the paper's algebraic solver. The final graph is returned with status truncated, and the fixed point,
    active species, rounds and outcome in extras.analysis.
  - 'Because every spontaneous reaction is explicit, a hard threshold can make the graph updates cycle:
    removing a species also removes the reactions that consume it, so it rises back above threshold. The
    paper reports a unique fixed point for its lumped background and says nothing about cycles. Here a
    repeated active set merges all sets in the cycle, and the merged graph''s fixed point is returned
    with outcome cycle-merged (''fixed'' when the updates stop, ''round-limit'' after 50 rounds).'
  - 'Outflow: eq. 12 writes dm/dt = N_f delta - K m. With polymers in the food set this is ambiguous,
    so K = delta * (total monomers in the food set) / m0, which makes m0 the true monomer mass at the
    fixed point and equals the paper''s rule for monomer food sets. The run starts with that mass in the
    food set, as in the paper (m(0) = m0).'
  - 'Eq. 15: solving eqs. 13-14 gives [ab]/[ba] = (1 + beta)/(1 + beta/gamma) with beta = K/(kr H). The
    printed beta = delta/(m0 kr H) matches only when m0 is the mass per food species (it is off by N_f
    = 2 otherwise); tests use K/(kr H).'
  - 'Defaults are Table 2 (a) / Figure 6: kf = 6.49e2, kr = 2.50, nu = 8.97e5, ku = 5.00e4, delta = 1.79e1,
    m0 = 2.0 (the caption of Figure 6 confirms delta = 1.79e1). H = 1 comes from Figure 3, since Figures
    5-14 do not state it. The paper gives no value of p, so the default p = 0.01 is a Chemart choice (about
    120 links on the default 62 polymers, close to the paper''s 118-link network).'
  - Table 2 (b) prints ranges nu in [<1, 1e4] and ku in [1e7, >1e10], which exclude their own optima (5.26e5
    and 7.11e4); the two ranges look swapped. Only the optima are used.
  - 'nu_distribution uniform draws U(0, 2 nu): the paper uses ''uniform within given maximum and minimum
    values'' without giving them. Any polymer, monomers included, may catalyse (the random rule of 3.1.1
    excludes nothing); the string-matching rule of 3.1.2 is not implemented.'
  - 'The v1 parameters firing_disk, food_influx, catalysis_probability, k_spontaneous, catalytic_enhancement
    and concentration_threshold became food_set, delta, p, kf, nu and threshold. mutation_rate (the stochastic
    metadynamics of the companion paper [50]) is dropped: it drives a simulation over fixed points rather
    than defining the network.'
  phenomena:
  - 'catalytic focusing: mass concentrates into a small core set, but only away from equilibrium (eq.
    15; Figures 5-8)'
  - 'catalysis does not change the equilibrium: at delta = 0 every catalysed and uncatalysed reaction
    reaches the same ratio C / AB = kf / (kr H)'
  - the steady-state profile falls off exponentially with length at equilibrium and flattens for the network
    at intermediate delta (Figures 5-7)
  - the deterministic metadynamics always reaches a unique fixed point
  - metabolisms jump between fixed points under spontaneous fluctuations, a first sign of evolution ([50])
  notes: 'Defines an autocatalytic metabolism dynamically: an autocatalytic set whose concentrations differ
    significantly from the uncatalysed case. The catalytic topology is the same as `kauffman-autocatalytic-sets`,
    so it is Chemart''s canonical demo of "same topology, different kinetics, different answer".

    '