3.1 Kinetic scenarios for SucP-catalyzed transglycosylation
To account for a transfer to hydrolysis rate ratio
(\(\frac{v_{X}}{v_{H}}\)) dependent on the donor substrate used, we
considered possible extensions of the base mechanism (M1) for enzymatic
trans-glycosylation, as shown in Figure 1 and more fully in Figure 2.
Mechanism M1 is a canonical Ping-Pong reaction with irreversible release
of GG (\(k_{+4}\)) and glucose (\(k_{+5}\)). Both extensions of
mechanism, M2 and M3, assume that not only does hydrolysis occur from
E-Glc, but it can also happen from a non-covalent complex of E-Glc,
still containing the leaving group expelled from the donor substrate
(M2; step \(k_{+7}\)) or having a second donor substrate bound (M3;
step \(k_{+7^{\prime}}\)). While able to undergo hydrolysis, these non-covalent
complexes of E-Glc are unreactive towards glycerol. Note: to avoid model
complexity not strictly necessary in the analysis, mechanism M2 was
formulated to consolidate two chemical reaction steps into one single
kinetic step \(k_{+7}\). One chemical step is the formation of E-Glc
with X still bound to the enzyme and the other is hydrolysis of the
complex to give free enzyme, glucose and X. The idea for mechanism M3
arose from experimental evidence of substrate inhibition in the reaction
of Lm SucP with G1P (see
later). Upon hydrolysis, these additional E-Glc complexes can regenerate
the free enzyme under release of glucose and the substrate leaving group
(M2; \(k_{+7}\)) or the substrate (M3; \(k_{+7^{\prime}}\)). For each proposed
mechanism, we derived mathematical expressions relating the observable
kinetic parameters, including \(\frac{v_{X}}{v_{H}}\) (Figure 2), to the
microscopic rate constants of the reaction. A detailed summary is given
in the Supporting Information (Table S1). Maximal rate (\(V\)) and
binding (\(K\)) parameters for formation of GG (\(V_{X},\)\(K_{\text{GlcX}}\), \(K_{\text{GOH}}\)) and hydrolysis
(\(V_{H}\), \(K_{\text{GlcXH}}\)) are thus defined
(Supporting Information Table S1; Figure 2, Eqs. 5, 7, 11). Substrate
inhibition (\(K_{i,GlcX}\)) is included in all mechanisms. Mechanism M3
involves additional parameters for hydrolysis (\(V_{H2}\)) and substrate
binding (\(K_{GlcXH2}\)), arising from donor substrate binding to the
E-Glc intermediate and hydrolysis via step \(k_{+7^{\prime}}\). With the help
of these expressions (Figure 2), important deductions can be made for
the experiment, which we then show, enable clear-cut mechanistic
discrimination.
In particular as demonstrated in Figure 2, mechanism M2 predicts\(\frac{v_{X}}{v_{H}}\) to exhibit curved dependence on [GOH] (Eq.
7), whereas in mechanism M1 \(\frac{v_{X}}{v_{H}}\) increases linearly
with [GOH] (Eq. 5). The dependence of \(\frac{v_{X}}{v_{H}}\) on
[GOH] derived from mechanism M3 is also linear (Eq. 11). However,
contrary to the other mechanisms, mechanism M3 involves a unique effect
of the donor substrate concentration [GlcX] on\(\frac{v_{X}}{v_{H}}\) dependent on [GOH], as can be easily
realized from the denominator term in Eq. 11. The\(\frac{v_{X}}{v_{H}}\) increases when the donor concentration
decreases, approaching a limiting value described by Eq. 12. Moreover,
Eq. 7 (mechanism M2) and Eq. 11 (mechanism M3) involve rate constants
from donor substrate-dependent steps, with the important implication
that the \(\frac{v_{X}}{v_{H}}\) for these mechanisms can exhibit
dependence on the type of donor substrate used. Eq. 5 for mechanism M1,
in contrast, involves only rate constants from steps after the E-Glc
intermediate, thus requiring the \(\frac{v_{X}}{v_{H}}\) to be
independent of the donor used. In mechanism M2, the\(\frac{v_{X}}{v_{H}}\) curve described by Eq. 7 reaches plateau at high
[GOH], with a maximum value equal to (\(\frac{k_{+2}}{k_{+7}}\) +
1) (Eq. 8). In the case that release of X (\(k_{+2}\)) is considerably
faster than the hydrolysis according to step \(k_{+7}\), Eq. 7 reduces
to Eq. 9 and M2 can no longer be distinguished from M1. Besides its
unique feature of \(\frac{v_{X}}{v_{H}}\) dependent on the donor
substrate concentration, as shown in Figure 2, the mechanism M3 can
additionally involve a characteristic deviation from Michaelis-Menten
behavior when initial rates dependent on the donor substrate
concentration are recorded in the absence of glycerol (compare Eq. 13
(M3) with Eq. 6 (M1) and Eq. 10 (M2)). Various scenarios are possible
from Eq. 13: one is inhibition at high [GlcX]; another is that the
initial rate does not reach saturation at high [GlcX]. Both have
relevance for the enzymatic reactions, as shown later.