Kinetics of batch-wise enzymatic cycling system for mass production of chiral compound

Kinetics of batch-wise enzymatic cycling system (oxidoreductase-catalyzed reaction system involving enzyme-coupled cofactor regeneration) has been studied covering a broad range of the conserved total cofactor concentration, C]₀ (=NAD(P)⁺?+?NAD(P)H), based on reasonable several assumptions. It is composed of two elementary reactions, i.e. product synthesis reaction and cofactor regeneration reaction, both of which have been expressed by Michaelis–Menten type rate equations. A novel dimensionless variable, r, has been introduced, which is defined as the concentration of one of the two cofactor components, X] (NADH⁺ or NADPH⁺), divided by C]₀, i.e. r .eX]/C]₀. The following results have been obtained. (1) The fundamental equation of the batch-wise enzymatic cycling system has been transformed to a differential equation whose formula is: dr/dT?=?N(r)/D(r) (N(r) and D(r) are quadratic equations of r having different coefficients). (2) It has been elucidated that the batch-wise enzymatic cycling system has two phases, an early short transient phase followed by a long phase in quasi-steady state (QSS). (3) In the enzymatic cycling system, r converges to a definite level regardless of any initial value of r. (4) In QSS, the definite level of r nearly equals the singular solution, r_singular, of the differential equation. (5) The actual rate of the targeted product (chiral compound) formation can be calculated by Michaelis–Menten equation in which the cofactor concentration is C]₀×r_singular instead of C]₀. r_singular has been proposed to name “redistribution factor”. (6) It is recommended that the “unit” of the cofactor regeneration enzyme be 2–3 times more used than the “unit” of the synthesis enzyme and that C]₀ be 15–25 times more than the K_m value. Four special cases relating to the batch-wise enzymatic cycling system have been discussed.