chemart / kauffman-autocatalytic-sets

hub:
  repo_type: generator
  builtin: kauffman-autocatalytic-sets
  tags:
  - banzhaf-yamamoto
chemistries:
- id: kauffman-autocatalytic-sets
  name: Kauffman autocatalytic sets (binary polymer model)
  intuition: 'The original argument that metabolism could precede genes. Polymers join and split, and
    any polymer may catalyse any such reaction with some probability. As polymers get longer the number
    of possible reactions grows faster than the number of molecules, so above a critical catalysis probability
    a mutually-catalysing set almost surely exists - order for free, from combinatorics rather than design.
    This entry gives the topology; the dynamics and the formal test for such sets live in bagley-farmer
    and raf.

    '
  origin: Kauffman, 1986; Farmer, Kauffman & Packard, 1986
  book: 6.3.1
  refs:
  - '[446]'
  - '[447]'
  - '[260]'
  family: origin-of-life
  kind: generator
  constructive: true
  S:
    repr: polymers = strings over an alphabet of size B (a, b for B = 2), up to a maximum length
    definition: implicit
  R:
    definition: implicit
    arity:
    - 1
    - 2
    - 3
    scheme: 'condensation A + B -> AB and cleavage AB -> A + B for every split of every polymer, each
      optionally catalysed by a polymer E: A + B + E <-> AB + E'
  A:
    reactor: n/a - static graph analysis
    dilution: food set inflow keeps the system out of equilibrium
    notes: the original analysis is graph-theoretic and static, with no kinetics
  params:
  - name: B
    type: int
    default: 2
    min: 2
    max: 4
    role: structural
    meaning: alphabet size
  - name: max_length
    type: int
    default: 5
    min: 2
    max: 8
    role: structural
    meaning: longest polymer in the network (at most 512 polymers in total)
  - name: P
    type: float
    default: 0.05
    min: 0
    max: 1
    range: critical value P_crit ~ B^(-2L) for a firing disk of polymers up to length L (eq. 6.3)
    role: structural
    meaning: probability that a given polymer catalyses a given condensation/cleavage pair
  - name: food_set
    type: list
    default:
    - a
    - b
    - aa
    - bb
    role: population
    meaning: the firing disk of polymers supplied from outside (book figure 6.12)
  provides:
  - topology
  - stoichiometry
  - catalysts
  - mass-conservation
  - flow
  - initial-state
  fidelity: book+decisions
  decisions:
  - 'Built as the binary polymer model: all polymers up to max_length, every split of every polymer as
    a reversible condensation/cleavage pair, and each polymer catalysing each pair (both directions) with
    probability P.'
  - 'Water (H in eq. 6.2) is left out, as in the usual formulation of the polymer model. No rates: the
    book''s analysis is static. The food set is recorded in extras.food_set, and monomer counts per letter
    are exact conservation laws (extras.conservation).'
  - The earlier parameter L (maximum food-set length) is replaced by an explicit food_set; the book's
    default food set is {a, b, aa, bb}.
  phenomena:
  - 'percolation transition at P_crit: above it, autocatalytic sets form almost surely'
  - larger B favours set formation, so proteins (B=20) beat RNA (B=4)
  notes: 'Topology only; see `bagley-farmer` for the dynamic version. RAF analysis (`raf`) applies directly
    to this network.

    '