chemart / conrad-enzymatic

hub:
  repo_type: generator
  builtin: conrad-enzymatic
  tags:
  - banzhaf-yamamoto
chemistries:
- id: conrad-enzymatic
  name: Conrad's lock-and-key enzymatic / self-assembly processor
  intuition: 'Computation by molecular shape recognition. Ligands carry keys, an enzyme carries locks,
    and binding happens when shapes are complementary. Signal ions binding a modulator site switch the
    enzyme between conformations, each with different catalytic behaviour - so a single enzyme, in a milieu
    of two ion species, classifies input patterns by how much product it makes. Conrad''s argument was
    that this is what molecules are good at and digital logic is not: recognition of a whole pattern in
    one step, rather than a program over bits.

    '
  aliases:
  - enzymatic computing
  - conformation-based computing
  - lock-key paradigm
  origin: Conrad, 1985-1992; wet realisation by Zauner & Conrad, 2001
  book: 11.2.1; also 17.1.2 (emergence vs. programmability tradeoff)
  refs:
  - '[193] Conrad, On design principles for a molecular computer, CACM 28(5):464-480, 1985, doi:10.1145/3532.3533'
  - '[194] Conrad, Molecular computing: the lock-key paradigm, Computer 25(11):11-20, 1992, doi:10.1109/2.166400'
  - '[196] Conrad & Zauner, Conformation-based computing: a rationale and a recipe, in Sienko et al. (eds),
    Molecular Computing, MIT Press 2003, ch. 1, doi:10.7551/mitpress/4739.003.0003'
  - '[954] Zauner & Conrad, Enzymatic computing, Biotechnol. Prog. 17(3):553-559, 2001, doi:10.1021/bp010004n'
  - '[722] Rosen, Recent developments in the theory of control and regulation of cellular processes, Int.
    Rev. Cytology 23:25-88, 1968'
  family: bio-inspired
  kind: wet
  constructive: false
  S:
    repr: 'Molecules are 6-bit shapes: ligands (Mg2+, Ca2+ signal carriers, NAD+, L-malate, and the released
      NADH and oxaloacetate) carry a key, malate dehydrogenase carries three locks (coenzyme, substrate
      and modulator sites). One species per enzyme conformer (set of ions bound at the modulator site)
      and per binding state of its two catalytic sites.

      '
    definition: explicit
    notes: Species.structure holds the shape encoding and the occupied sites.
  R:
    definition: implicit
    arity:
    - 1
    - 2
    scheme: 'lock-and-key: a ligand binds a site when at least match_bits of the 6 shape positions are
      complementary (bit-inverted). Signal ions bind the modulator site and select a conformer; every
      conformer binds NAD+ then L-malate reversibly and turns the ternary complex over to oxaloacetate
      + NADH + H+.

      '
  A:
    reactor: well-stirred-multiset
    dilution: none
    notes: 'A batch spectrophotometric assay (1 cm cuvette, 29 C; glycine/NaOH buffer at pH 10 for the
      response surface, signal solutions in glycine/NaOH at pH 10.5 in the tabletop device): the response
      is the NADH absorbance at 339 nm read at a fixed time (300 s for the response surface, 10 s in the
      tabletop device) and thresholded to a logic output. Conrad''s reading of this as computation by
      free-energy minimisation is a description of the binding step, not a separate dynamics.

      '
  params:
  - name: operation
    type: enum
    choices:
    - AND
    - OR
    - XOR
    - NAND
    - NOR
    - NXOR
    default: XOR
    role: structural
    meaning: which of the six commutative two-bit operations of Table 1 the milieu encoding is meant to
      realise; fixes the truth table, the active milieu states and the signal-strength formula in extras['analysis']
  - name: inputs
    type: enum
    choices:
    - '00'
    - '01'
    - '10'
    - '11'
    default: '11'
    role: population
    meaning: the two-bit input pattern presented; each 1-signal adds one encoding unit of every carrier
      ion to the cuvette, giving milieu state a (00), b (01/10) or c (11)
  - name: encoding_mM
    type: dict
    default:
      Mg: 72.38
    range: 'published encodings: {Mg: 20} realises OR, {Mg: 20, Ca: 40} realises XOR; the response surface
      spans 0-133 mM of each ion, i.e. encodings up to ~67 mM'
    role: population
    meaning: 'concentration (mM) that one 1-signal contributes for each signal carrier; the keys choose
      the carriers, and hence which enzyme conformers exist. Valid keys: Mg, Ca'
  - name: match_bits
    type: int
    default: 5
    min: 5
    max: 6
    role: structural
    meaning: minimum number of complementary positions (out of 6) for lock-and-key recognition; 6 admits
      only perfect complements and so drops Ca2+ as a signal carrier
  - name: malate_mM
    type: float
    default: 5.41
    min: 0
    role: population
    meaning: L-malate in the cuvette (mM); 7.1 mM in 2 x 0.8 mL of signal solution diluted into 2.1 mL
  - name: nad_mM
    type: float
    default: 1.29
    min: 0
    role: population
    meaning: NAD+ in the cuvette (mM); 5.4 mM in 0.5 mL of enzyme solution diluted into 2.1 mL
  provides:
  - topology
  - stoichiometry
  - initial-state
  - mass-conservation
  - sequence-structure-function
  fidelity: reconstructed
  sources:
  - 'K.-P. Zauner and M. Conrad. Enzymatic Computing. Biotechnology Progress 17(3):553-559, 2001. doi:10.1021/bp010004n.
    Full text used: https://eprints.soton.ac.uk/259138/1/ZaunerKP01EnzComp.pdf'
  - W. Banzhaf and L. Yamamoto. Artificial Chemistries. MIT Press, 2015, sections 11.2.1 and 17.1.2 (Figure
    11.10, adapted from Conrad 1992).
  - M. Conrad. On design principles for a molecular computer. CACM 28(5):464-480, 1985. doi:10.1145/3532.3533
    (paywalled; not obtained).
  - 'M. Conrad. Molecular computing: the lock-key paradigm. Computer 25(11):11-20, 1992. doi:10.1109/2.166400
    (paywalled; not obtained).'
  - 'M. Conrad and K.-P. Zauner. Conformation-based computing: a rationale and a recipe. In Sienko et
    al. (eds), Molecular Computing, MIT Press, 2003, ch. 1, pp. 1-31. doi:10.7551/mitpress/4739.003.0003
    (paywalled; not obtained).'
  decisions:
  - 'The book''s Figure 11.10 processor is a schematic, so the generated network is the in-silico network
    of the wet realisation the book points to ([954]): the signal ions are the input signals, the ion-loaded
    conformer is the recognising complex, its active site is the adaptor that binds NAD+ and L-malate,
    and NADH is the output. The amplifying signalling cascade of the figure has no counterpart in the
    2001 experiment and is not generated.'
  - The 6-bit keys and locks are a Chemart encoding of the lock-and-key criterion of book 11.2.1, not
    published data. NAD+, L-malate and Mg2+ are perfect complements of the coenzyme, substrate and modulator
    locks; Ca2+ is one bit off, which reproduces the paper's observation that the signal strength is stronger
    for MgCl2 alone than for CaCl2 alone; the released NADH and oxaloacetate are 2 bits off their locks
    and do not rebind at match_bits >= 5.
  - 'The paper is deliberately phenomenological (''our purpose here was not to investigate mechanism''),
    so the mechanism is the minimal ordered scheme consistent with the assay: reversible coenzyme then
    substrate binding on every conformer, one irreversible turnover, and modulator-ion binding on the
    free enzyme only. No kinetics are published, so every reaction rate is None.'
  - 'Response levels are measured, not modelled: Figure 1 is an interpolated surface picture and Figure
    9 a bar chart, so no absorbance value is reproduced. What the module computes is Table 1''s classification
    law: the milieu states that must be active, and the signal strength Delta s = min(r over active states)
    - max(r over the rest), which reproduces all six of the table''s formulas.'
  - 'Defaults are the tabletop device of Figures 8-9 with MgCl2 alone: 190 mM MgCl2 in a 0.8 mL 1-signal,
    7.1 mM L-malate in each 0.8 mL signal and 5.4 mM NAD+ in 0.5 mL of enzyme solution give, in the 2.1
    mL cuvette, 72.38 mM Mg2+ per 1-signal, 5.41 mM L-malate and 1.29 mM NAD+.'
  - The enzyme is dosed as 6 uL/mL of a commercial suspension, so its molar concentration is not published
    and it is absent from initial_state; the protocol string is kept in extras['experiment']. The proton
    released by the turnover is listed in extras['buffered'] (glycine/NaOH, pH 10).
  - The Results sentence 'The activity first increases to a maximum and then decreases as the concentration
    of ion decreases' contradicts itself and Figure 1; it is read as '... as the concentration of ion
    increases', consistent with the surface being described as convex (strictly nonmonotonic) along both
    ion axes.
  - Conrad's own papers [193], [194] and [196] are paywalled and were not obtained, so the conceptual
    reading (computation as downhill free-energy minimisation, programmability traded against evolvability)
    is taken from book 11.2.1 and 17.1.2 and no number is attributed to them. The v1 entry's origin 'Conrad,
    1974-1992' is corrected to the works the bibliography actually cites, 1985 and 1992.
  - Readout times are not parameters (they do not change the network); 300 s for the response surface
    and 10 s for the device are recorded in extras['experiment'].
  phenomena:
  - 'lock-and-key recognition: only shape-complementary key/lock pairs bind, and Ca2+ is the weaker key
    of the two signal carriers'
  - 'context-sensitive pattern classification: a single enzyme classifies two-bit input patterns by its
    catalytic activity'
  - a nonmonotonic (convex) response to a single signal ion turns the linearly inseparable XOR into a
    linearly separable problem, solvable with one threshold
  - AND, OR, XOR, NAND and NOR are all realisable at suitable encodings; NXOR is realisable at none, because
    a unimodal response has no interior minimum
  - the tabletop device classified all 135 presented two-bit patterns correctly (45 x 00, 46 x 01/10,
    44 x 11)
  notes: 'Wet: the network returned is the in-silico network of the published experiment, not a laboratory
    protocol. Its lasting contribution to Chemart is the emergence-vs-programmability tradeoff of 17.1.2:
    "a system cannot at the same time be effectively programmable, amenable to evolution by variation
    and selection, and computationally efficient."

    '