2.3 Kinetic models
The King-Altman open-access tool (http://www.biokin.com/tools/king-altman/index.html) was used to derive mathematical equations for the kinetic schemes described under Results. Differential equations have the general form, \(v\) = N /D= d [X]/d t. The numerator (N ) and denominator (D ) contain coefficients (derived according to fundamental principles of enzyme kinetic theory (Segel, 1993) that group together the microscopic rate constants into kinetic parameters. For each kinetic scheme, an equation was additionally derived from the rate constants in order to express the dependence of the rate ratio on the glycerol concentration. A nomenclature is used in which microscopic rate constants for forward and reverse direction of reaction are indicated as\(k_{+i}\) and \(k_{-i}\), with i indicating the step in the reaction sequence. Net rate constants (Cleland, 1975) are also used and indicated as \(k^{\prime}\).
For data fitting, the Microsoft Excel 2019 add-in Solver was used. To determine estimates of each microscopic rate constant, dependencies of\(v_{X}\) (on [GlcX]), \(v_{X}\) (on [GOH]) and\(\frac{v_{X}}{v_{H}}\) (on [GOH]) were fitted simultaneously by maximizing the sum of respective coefficients of determination\(R^{2}\). Dependency of \(v_{H}\) on [GOH] was used to check quality and consistency of the estimated parameters. Constraints on the microscopic rate constants were derived from experimental (apparent) kinetic parameters of Lm SucP and their use is described in the Supporting Information (Table S2 – S4). Upper and lower boundaries forBa SucP rate constants were reasonably chosen for \(k_{-3}\)(Goedl, Sawangwan, et al., 2008).