A ketoreductase (KRED) reduces a prochiral ketone to a chiral alcohol, but every turnover consumes one molecule of the cofactor NADPH and releases spent NADP⁺. Buying cofactor stoichiometrically (1 mole per mole of product) is far too expensive for industrial synthesis, so real processes add only a catalytic trace and recycle it in place with a second, coupled enzyme.
Here that partner is glucose dehydrogenase (GDH), which oxidizes glucose to gluconolactone while reducing NADP⁺ straight back to NADPH — closing the loop so each cofactor molecule turns over hundreds of times before the reaction is done:
KRED: Ketone + NADPH --k1--> Alcohol + NADP+
GDH: Glucose + NADP+ --k2--> Gluconolactone + NADPH
v1 = k1(T)·[NADPH]·[S] / (Km_S + [S])
v2 = k2(T)·[NADP+]·[G] / (Km_G + [G])
k(T) = k_base · 2^((T-37)/10) (Q10 = 2 rate–temperature rule)
d[S]/dt = -v1 d[P]/dt = +v1
d[NADPH]/dt = -v1 + v2 d[NADP+]/dt = +v1 - v2
d[G]/dt = -v2 + feed d[Lactone]/dt = +v2
- Cofactor loading — how much NADP(H) is charged in up front, as mol% of substrate. Lower loading means each molecule must turn over more times, raising the total turnover number (TTN) but relying more heavily on the recycling enzyme keeping pace.
- GDH:KRED ratio — the recycling enzyme's activity relative to the productive enzyme. Too low and NADPH runs out mid-reaction, stalling conversion even with substrate left; too high wastes GDH capacity.
- Temperature — both enzymes speed up with temperature following a Q10≈2 rule, until real enzymes would denature; this model keeps both rates coupled to one Arrhenius-like factor.
- Glucose feed — continuous glucose addition (fed-batch) keeps the recycling half-reaction supplied; without it, glucose depletes and NADPH regeneration halts.
- Cofactor TTN — cumulative product formed divided by the cofactor charged at loading. A TTN well above 1 is the entire economic point of coupling a recycling enzyme instead of buying stoichiometric NADPH.
Verified numerically against the stated ODE system: cofactor mass ([NADPH]+[NADP⁺]) stays exactly conserved at every loading level, a low GDH:KRED ratio measurably stalls conversion (NADPH runs out before substrate does), and low loading correctly drives up turnover number — the source kinetics are internally consistent, so this 2D model reuses them unchanged.
The circular loop between the two enzyme sites is the shared cofactor pool: cyan beads are reduced (NADPH, ready to react at KRED), amber beads are oxidized (NADP⁺, ready to be regenerated at GDH) — the split point tracks the live NADPH fraction below. Drag the loop to tilt the diagram; the strip chart beneath plots every pool over time.