An external substrate pool S feeds a branched pathway: R1 draws S into intermediate M1; R2 converts M1 into M2 along the main route while R4 siphons M1 away into a Byproduct; R3 turns M2 into the target Product, and R5 exports/consumes it. Every reaction follows Michaelis-Menten kinetics, v = Vmax·[substrate]/(Km+[substrate]), and each metabolite's concentration is integrated forward with a small Euler step every frame: d[M]/dt = Σ(inflows) − Σ(outflows).
v = Vmax·[S]/(Km+[S])
d[M1]/dt = v1 − v2 − v4
d[M2]/dt = v2 − v3
d[P]/dt = v3 − v5
- Vmax sliders — model over- or under-expressing each enzyme; raising R2/R3 or lowering R4 pushes carbon toward the product.
- KO — a full gene knockout: forces that reaction's flux to zero, the classic metabolic-engineering move to eliminate a competing branch.
- Yield fraction — v3/(v3+v4), the share of flux leaving M1 that reaches the product branch rather than the byproduct branch; the quantity a metabolic engineer tries to maximize.
- Particles flowing along each arrow are drawn at a rate proportional to that reaction's instantaneous flux, so a starved or knocked-out edge visibly goes quiet.