3.2.1 Analysis of the LmSucP reaction
Reaction of Lm SucP with sucrose and glycerol is described very
well by the base mechanism M1 (see the values of \(R^{2}\) in Figure 3,
panels A1 – E1). Dependence of \(v_{X}\) on [Suc] is of the
Michaelis-Menten type, with a \(K_{\text{GlcXH}}\) that increases to\(K_{\text{GlcX}}\) when glycerol is present, as expected. Dependence of\(v_{X}\) on [GOH] is a straight line as is the dependence of\(\frac{v_{X}}{v_{H}}\) on [GOH]. The \(v_{H}\) is largely
unaffected by [GOH], and the experimental dependence is reproduced
in excellent quality by the model with parameters estimated from the
data in panels A1, B1, C1 and E1.
Using G1P (50 mM) as the donor, the transfer coefficient from the
dependence of \(\frac{v_{X}}{v_{H}}\) (TC = 3.3
M-1 ± 0.1 M-1; determined from
linear regression of the data) was 1.4-fold smaller than theTC (= 4.7 M-1 ± 0.1 M-1)
obtained from the corresponding \(\frac{v_{X}}{v_{H}}\) dependence using
sucrose as the donor (Figure 3, panel E1). Mechanism M1 is unable to
account for this difference. Best fits based on mechanism M2 required
that \(k_{+7}\) be effectively zero. For conditions of \(k_{+7}\) = 0,
mechanism M2 is reduced to mechanism M1 (Figure 2), thus eliminating it
from consideration.
Using mechanism M3, excellent fit of the full set of data was obtained,
as shown in Figure 3 (panels A2 – E2). Characteristic features of the
reaction are captured precisely: the substrate inhibition by G1P (panel
B2) and the dependence of \(\frac{v_{X}}{v_{H}}\) on [GOH]. The
internal control (dependence of \(v_{H}\) on [GOH]) was reproduced
very well using parameter estimates from the fit. Most importantly in
view of mechanism discrimination, however, the mechanism M3 predicts
that at low concentrations of G1P (here: 5 mM) that prevent formation of
the inhibitory complex between E-Glc and G1P (Figure 2), the dependence
of \(\frac{v_{X}}{v_{H}}\) on [GOH] should become close to what it
was with sucrose as the donor substrate. The TC determined at
5 mM G1P was 4.8 M-1 ± 0.1 (Figure 3, panel E3) in
perfect agreement with the TC obtained from the sucrose data.
Mechanism 3 also captured the appearance of curvature in the dependence
of \(v_{X}\) on [GOH] recorded at 5 mM G1P (Figure 3, panel C3).
This was not present in analogous dependencies determined at 50 mM G1P
(Figure 3, panel C2) or using sucrose (Figure 3, panel C1). Finally,
decrease of \(v_{X}\) at high [GOH] was predicted with excellent
accuracy for the conditions of 5 mM G1P.
Boundaries of first- and second-order rate constants for the enzymatic
half-reaction with sucrose or G1P leading up to the E-Glc intermediate
can be derived from steady-state apparent kinetic parameters
(\({}^{\text{app}}V_{X}\),\(\frac{{}^{\text{app}}V_{X}}{{}^{\text{app}}K}_{\text{GlcX}}\))
of Lm SucP reported in the literature (Mueller & Nidetzky, 2007).
Details are given in the Supporting Information Table S2-S4. We assessed
the obtained results for consistency by calculating the equilibrium
constant (\(K_{\text{eq}}\)) for the reaction, sucrose + phosphate ↔
fructose + G1P. Values obtained from the model parameters
(\(K_{\text{eq}}\) = 11.3 – 38.4) are in reasonable agreement with
experimentally determined \(K_{\text{eq}}\) values in the range of 3.6
– 14.4 (Wildberger, Luley-Goedl, & Nidetzky, 2011) and 17.6 – 70.4
(Goedl et al., 2007).
Rate constants for the half-reaction of E-Glc with glycerol and water
must be independent of the donor substrate used. However, high deviation
in the rate of GG release (\(k_{+4}\)) was observed in the best fit
results for sucrose (195.15 s-1) and G1P
(>105 s-1).
Consequently, influence of \(k_{+4}\) on fit quality was investigated
within the observed lower (195.15 s-1) and upper
boundaries (105 s-1). The observed
solution spaces on kinetic rate constants and kinetic parameters are
shown in the Supporting Information (Tables S5 and S6). The effects on
fit quality are shown in Figure 2 (red areas). The glycerol binding
constant to E-Glc (\(k_{+3}\)) estimated from sucrose (0.013 – 0.012
s-1M-1) or G1P data (0.016 – 0.016
s-1M-1) was fully consistent. The
rate constant for hydrolysis of E-Glc (\(k_{+5}\)) was similar as
estimated from sucrose (2.72 – 2.68 s-1) and G1P data
(3.37 – 3.32 s-1). Hydrolysis of the complex of E-
Glc and G1P occurred with a similar rate (\(k_{+7^{\prime}}\) = 3.0 – 3.0
s-1). The complete sets of rate constants and
calculated kinetic parameters are summarized in Tables S5 and S6 of the
Supporting Information. As shown, fits of the data were rather
insensitive to changes in the rate constant for release GG (\(k_{+4}\))
(see Figure 3). Constancy of \(k_{+4}\) for reaction with sucrose and
G1P can thus be assumed. The \(k_{+4}\) estimate of 195
s-1 obtained from the sucrose data was therefore used
in further analyses.
We show in Table 1 that employing the rate constants from Table S5
(\(k_{+4}\) = 195 s-1), mechanisms M1 and M3 show
excellent capability to reproduce the apparent kinetic parameters of,
respectively, the reaction with sucrose and G1P for given substrate
conditions. This immediately suggests practical utility of the models
for prediction and optimization purposes (see Discussion).