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hydrolysis and synthesis of oligogalactosides with all possible
linkages, particularly within the context of determining the rela-
tive thermodynamic stability of the products.
contains no terms for processes occurring after galactosyl-enzyme
formation. Product inhibition affects the distribution of the
different enzyme forms, and thus, influences the absolute rate of
hydrolysis and transglycosylation at different times, so the product
complex E.aGal needs to be included in Scheme 1 for kinetic mea-
surements other than those of initial rates.
In the presence of acceptors RiOH, which do not have a binding
site, the transglycosylation reaction is described by a bimolecular
rate constant kF (see an expression for the constant below), and
k3 in the expressions for kcat and Km can be replaced by
(k3 + kF[RiOH]). When the acceptor has a binding site, the possibil-
ity that the EbGal.RiOH complex may be in a steady state makes the
expressions very complex, although if there is no hydrolysis
(k3 = 0), the kinetic analysis simplifies to that of a ping-pong reac-
Traditionally, the thermodynamics of glycosidic linkages have
been analysed via hydrolysis reactions, calorimetry yielding
change in enthalpy,
lytic equilibrium giving change in Gibbs free energy,
early papers report differences between the hydrolysis enthalpies
of -1,4- and
-1,6-glycosidic linkages,11,12 and more detailed
D
H0 and measurements of positions of hydro-
D
G°. Some
a
a
studies of different oligosaccharide hydrolyses enabled both
enthalpy and entropy changes to be measured.13 In the present
paper, a novel approach to estimation of free energy differences
is suggested. Both transglycosylation and hydrolysis of three types
of
formation and hydrolysis of pNP-galactobiosides catalysed by
monomeric glycoside hydrolase family 36 (GH36) -galactosidase
a-galactosidic linkages were investigated using total kinetics of
tion, with A = aGalOR, B = RiOH (see Eq. (1)):
a
V ¼ Vmax½Aꢁ½Bꢁ=ðKB ½Aꢁ þ KA ½Bꢁ þ ½Aꢁ½BꢁÞ
ð1Þ
from Thermotoga maritima, a retaining exo-acting glycoside hydro-
lase.14 Both enzymatically and chemically synthesized substrates
were used for the complete analysis of regioselectivity and ther-
modynamics of galactosidic bonds.
m
m
When ½Aꢁ ꢂ KAm and B ꢃ KBm the physical situation corresponds
to the interception of the galactosyl-enzyme by small concentra-
tions of RiOH, described either by kF[E]0 [RiOH] of the Scheme 1
or Vmax½Bꢁ=KB of the ping-pong mechanism, which are thus seen
m
2. Results and discussion
to be equivalent.
A frequently ignored determinant of regioselectivity is the
relative thermodynamic stability of the products.16 The kinetic
parameters for the hydrolysis of a link are related to the kinetics
of its formation and its thermodynamic stability by Haldane rela-
tionships: those for a classic ping-pong reaction (equivalent to
transglycosylation without hydrolysis in the present system) have
been explicitly derived.17 The more complex purely algebraic anal-
ysis of a transglycosylation with accompanying hydrolysis, both of
EbGal and of EbGal.pNPGal complex, is not essential for our pur-
poses, since the equations we wish to use to determine regioisom-
er free energy differences become apparent from inspection of the
relevant free energy profiles (reaction coordinate diagrams, Fig. 1).
Figure 1A shows the first half of the profile, explicitly account-
ing for the generation of the glycosyl-enzyme with all the known
or suspected intermediates. However, the important free energy
differences are those between the highest transition state and
the free enzyme and substrate on one side (given by kH = kcat/Km
2.1. Theoretical background
In the well established chemical mechanism,15 the nucleophile
of the
a-galactosidase of Thermotoga maritima (GH family 36 in
CAZy; PDB code 1ZY9) has been identified as Asp 327 based on
the ability of the normally inactive Asp327Gly mutant to convert
p-nitrophenyl
a-galactopyranoside (pNPaGal) and azide ion to
pNP and b- -galactopyranosyl azide (bGalN3), as addition of azide
D
ions replaced the excised CH2COO- grouping. Likewise, the
acid-base catalyst was identified as Asp387 from the ability of
the Asp387Gly mutant to generate aGalN3 from pNPaGal and azide
ion. The b-galactosyl-enzyme intermediate was hydrolytically
stable as a result of the absence of general base catalysis but could
be directly attacked by azide ion. The available X-ray structure sug-
gests an anti-protonation trajectory, and a possible role for Asp 220
in stabilizing oxocarbenium-ion-like transition states.14
The minimal kinetic scheme for a retaining glycosidase also
acting as a transglycosylase is given by Scheme 1:
for hydrolysis of aGalOR1) and between the highest transition state
and the galactosyl-enzyme (given by kF) on the other. However,
Figure 1B shows that any number of these half-profiles can be fit-
ted together at the galactosyl-enzyme to generate the free energy
differences between galactosides (pathways to hydrolysis do not
affect free energy differences between glycosides).
Here E is the enzyme, TmGal36A, S is pNPGal, E.S is the
Michaelis complex of enzyme and pNPGal, EbGal is the b-galacto-
syl-enzyme covalent intermediate and
regioisomer. The index i (for -1,2-,
a
GalORi is a pNPdiGal
a
a
-1,3- and -1,6-isomers
a
i = 1, 2 and 3, respectively) enables the three pathways for hydro-
lysis and formation of different isomers to be included in brackets
on the left-hand side of Scheme 1. E.Xi is E.pNPdiGal Michaelis
complex for the hydrolysis of a pNPdiGal regioisomer or is
EbGal.pNPGal Michaelis complex for the i-isomer formation; E.aGal
is a complex of the enzyme with a product.
When acting as a hydrolase, the Michaelis–Menten parameters
are given by kcat ¼ k2k3=ðk2 þ k3Þ and Km ¼ k3ðk1 þ k2Þ=k1ðk2 þ k3Þ,
so that the bimolecular rate constant kcat=Km ¼ k1k2=ðkꢀ1 þ k2Þ
Inspection of Fig 1B reveals that the free energy difference
between GalOR2 and GalOR1 is given by Eq. (2):
n
o
D
G0ð1!2Þ ¼ ꢀRT ln kH1 k2F =ðk1F kH2 Þ
ð2Þ
However, kF values are equivalent to (kcat/Km)B values in a
ping-pong mechanism. It is axiomatic in enzyme kinetics that in
any situation representing a competition — whether different
between different sites in the same molecule or between different
molecules—the selectivity observed at any substrate concentration
is that dictated by the ratio of kcat/Km values.18 Therefore, the ratio
kF1/kF2 can be obtained by measuring the initial ratio of galactoside
regioisomers produced from EbGal at any concentration. It should
be noted that in the present scheme, the galactosyl-enzyme com-
plex EbGal is the key component since both hydrolysis and trans-
glycosylation pass via its formation.
Second order constants were derived from the Scheme 1 as
kiH ¼ ki1k2i =ðkꢀi 1 þ kꢀi 2Þ and kFi ¼ kꢀi 1kꢀi 2=ðkiꢀ1 þ kꢀi 2Þ. Here, kHi (equal
to kcat/Km) and kiF are second order rate constants for a pNPdiGal
regioisomer hydrolysis and formation.
Scheme 1.