Instead of animating individual particles, this version numerically integrates the actual rate equations of both routes with a 4th-order Runge-Kutta stepper, every frame, using the real elapsed time. The catalytic lane follows Michaelis-Menten enzyme kinetics — substrate binds catalyst reversibly, then turns over to product while the catalyst returns unchanged:
dS/dt = R − v, v = kcat·[E]·S / (Km + S)
dP/dt = v
TON(t) = P(t) / [E]
The stoichiometric lane follows ordinary second-order kinetics between substrate and activator — no regeneration step exists, so the activator is a second consumable reactant:
dS/dt = R − r, dA/dt = R − r, r = k₂·S·A
dP/dt = r
Both lanes are fed substrate at the same real molar rate R. Waste mass and product mass are integrated forward alongside the kinetics — not looked up from a formula — so the live E-factor is a genuine mass balance:
E = ∫waste-mass-rate dt / ∫product-mass-rate dt
Atom Economy = MW(product) / Σ MW(reactants) × 100%
- Catalyst loading — sets [E], the catalyst pool size relative to the unit substrate scale. A smaller pool saturates (v → kcat·[E]) sooner, so the catalytic lane can become rate-limiting at low loading — watch [S] climb instead of leveling off when that happens.
- Activator molar mass — the stoichiometric lane consumes one activator per product molecule outright; the catalytic lane only needs a trace, amortized at the loading fraction, matching the mean-field limit of one catalyst molecule serving many turnovers.
- Leaving-group buttons — change the reaction's intrinsic byproduct mass; atom economy shifts identically in both lanes because it is a property of the balanced equation, not of how the promoter is supplied.
- Feed rate — scales R, the real molar feed rate into both lanes; push it past what the catalyst pool can turn over and the catalytic curve saturates while the stoichiometric one keeps pace (it isn't concentration-limited the same way).
Because the E-factor here is measured from integrated mass flow rather than assumed, it converges to — and cross-checks — the same analytic ratio a steady-state mass balance predicts: E ≈ [LG + loading·MW(activator)] / MW(product) for the catalytic route, and E ≈ [LG + MW(activator)] / MW(product) for the stoichiometric one.