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).