% Science example: competitive enzyme inhibition.
%
% Michaelis-Menten kinetics with a competitive inhibitor:
%   Km_effective = Km * (1 + Inhibitor / Ki)
%   rate = Vmax * Substrate / (Km_effective + Substrate)

% Output declarations: query/1 selects the relations written to this example's golden output.
query(effectiveKm_uM(X0, X1)).
query(uninhibitedRate_uM_s(X0, X1)).
query(inhibitedRate_uM_s(X0, X1)).
query(inhibitionFraction(X0, X1)).
query(status(X0, X1)).
query(reason(X0, X1)).

% Program structure: facts set up the scenario, and rules derive the queried conclusions.
assay(assay1, vmax_uM_s, 120.0).
assay(assay1, substrate_uM, 50.0).
assay(assay1, km_uM, 30.0).
assay(assay1, inhibitor_uM, 10.0).
assay(assay1, ki_uM, 5.0).
threshold(assay1, significant_inhibition_fraction, 0.25).

% Derivation rules: each rule below contributes one logical step toward the displayed results.
competitive_multiplier(Assay, Multiplier) :-
  assay(Assay, inhibitor_uM, Inhibitor),
  assay(Assay, ki_uM, Ki),
  div(Inhibitor, Ki, Ratio),
  add(1.0, Ratio, Multiplier).

effective_km(Assay, Effectivekm) :-
  assay(Assay, km_uM, Km),
  competitive_multiplier(Assay, Multiplier),
  mul(Km, Multiplier, Effectivekm).

uninhibited_rate(Assay, Rate) :-
  assay(Assay, vmax_uM_s, Vmax),
  assay(Assay, substrate_uM, Substrate),
  assay(Assay, km_uM, Km),
  mul(Vmax, Substrate, Numerator),
  add(Km, Substrate, Denominator),
  div(Numerator, Denominator, Rate).

inhibited_rate(Assay, Rate) :-
  assay(Assay, vmax_uM_s, Vmax),
  assay(Assay, substrate_uM, Substrate),
  effective_km(Assay, Effectivekm),
  mul(Vmax, Substrate, Numerator),
  add(Effectivekm, Substrate, Denominator),
  div(Numerator, Denominator, Rate).

inhibition_fraction(Assay, Fraction) :-
  uninhibited_rate(Assay, Uninhibited),
  inhibited_rate(Assay, Inhibited),
  sub(Uninhibited, Inhibited, Delta),
  div(Delta, Uninhibited, Fraction).

significant_inhibition(Assay) :-
  inhibition_fraction(Assay, Fraction),
  threshold(Assay, significant_inhibition_fraction, Limit),
  gt(Fraction, Limit).

effectiveKm_uM(Assay, Effectivekm) :-
  effective_km(Assay, Effectivekm).

uninhibitedRate_uM_s(Assay, Rate) :-
  uninhibited_rate(Assay, Rate).

inhibitedRate_uM_s(Assay, Rate) :-
  inhibited_rate(Assay, Rate).

inhibitionFraction(Assay, Fraction) :-
  inhibition_fraction(Assay, Fraction).

status(Assay, significant_inhibition) :-
  significant_inhibition(Assay).

reason(Assay, "competitive inhibitor raises effective Km and lowers reaction rate") :-
  significant_inhibition(Assay).