Challenges in Modelling Metalloenzymes
521
ular enzyme is in the case of molybdenum enzyme rather an exception then a rule.
Molybdenum enzymes are also often air sensitive, and they are crystalized under
anaerobic atmosphere which exhibits reductive properties (5% of H 2 in N 2 ). As a
result, the enzyme can crystalize in the reduced state despite the oxidized state of
the protein was prepared. Secondly, the oxidized cofactor can change its oxidation
state due to photo-reduction in the very intense synchrotron beam. This leads to additional ambiguity in the actual oxidation state of the cofactor. Therefore, in order to
study reaction pathway, one has to carefully construct the working theoretical model,
usually from just one geometry (be it reduced or oxidized).
In the case of the EBDH, the reduced and catalytically inactive state was available,
and only from that point, the oxidized Moco geometry was inferred by geometry
optimization of the whole cofactor with constraints. Such cofactor model was then
truncated, constrained at the edges and used for modelling of the reaction pathway.
In this case, the S 1 -S 2 -S 3 -S 4 dihedral turned out to be −38.3°, whereas the same
angle calculated using a QM/MM approach, which presumably models interactions
between Moco and the protein more properly, was only −20.4° [82]. This resulted
with the calculated (E+ZPE) for the first transition state of C–H activation higher
by 3.0 kcal/mol for the cluster model than calculated with QM/MM.
A slightly different approach was chosen for modelling steroid C25
dehydrogenase (S25DH). More specifically, the oxidized geometry of
the enzyme was obtained through homology modelling, MD simulation,
which actually yielded pretty decent S 1 -S 2 -S 3 -S 4 dihedral of −21.3°,
followed by QM/MM geometry optimization, which gave a significantly more
relaxed geometry with dihedral angle of −39.2° [94]. The cluster model cut out
from this macromolecular structure and constrained in the analogous way as before
relaxed even further yielding the dihedral of −48.6°. As a result, the calculated
transition state energies are quite high (approx. 21.2 kcal/mol) and the reduced state
exhibits more twisted conformation of the pterin ligand (−17°) than that observed
for the EBDH crystal structure.
We decided to illustrate the influence of the way in which the constraints are
introduced into the model on the reaction energy profile. To achieve this, we have
selected a big model of Moco that contains whole pterin ligands. The constraints were
introduced either to the MD-relaxed oxidized model 1 (dihedral −21.3°) or to the
reduced homology model 2, which had Moco in geometry as in the reduced EBDH
crystal structure (dihedral −4.86°). After optimization, the S 1 -S 2 -S 3 -S 4 dihedral
angle for the oxidized Moco in model 1 was −43° and differed from the value
obtained for model 2, i.e. −35.8°. This resulted in only slight energy elevation of
model 2 ES with respect to model 1; by 0.8 kcal/mol. However, the influence on C–H
activation barrier was more pronounced—the barrier was lower by 1.4 kcal/mol for
model 2. The largest effect was observed for EP complex where model 2 gave energy
lower by 4.0 kcal/mol. Moreover, model 2 not only yielded more favourable reaction
energetics but also the geometry of the relaxed reduced cofactor, with the S 1 -S 2 -S 3 -
S 4 dihedral of −1°, is much closer to the experimental value of −4.8° than the value
observed for EP in model 1 (−17.5°).
521
ular enzyme is in the case of molybdenum enzyme rather an exception then a rule.
Molybdenum enzymes are also often air sensitive, and they are crystalized under
anaerobic atmosphere which exhibits reductive properties (5% of H 2 in N 2 ). As a
result, the enzyme can crystalize in the reduced state despite the oxidized state of
the protein was prepared. Secondly, the oxidized cofactor can change its oxidation
state due to photo-reduction in the very intense synchrotron beam. This leads to additional ambiguity in the actual oxidation state of the cofactor. Therefore, in order to
study reaction pathway, one has to carefully construct the working theoretical model,
usually from just one geometry (be it reduced or oxidized).
In the case of the EBDH, the reduced and catalytically inactive state was available,
and only from that point, the oxidized Moco geometry was inferred by geometry
optimization of the whole cofactor with constraints. Such cofactor model was then
truncated, constrained at the edges and used for modelling of the reaction pathway.
In this case, the S 1 -S 2 -S 3 -S 4 dihedral turned out to be −38.3°, whereas the same
angle calculated using a QM/MM approach, which presumably models interactions
between Moco and the protein more properly, was only −20.4° [82]. This resulted
with the calculated (E+ZPE) for the first transition state of C–H activation higher
by 3.0 kcal/mol for the cluster model than calculated with QM/MM.
A slightly different approach was chosen for modelling steroid C25
dehydrogenase (S25DH). More specifically, the oxidized geometry of
the enzyme was obtained through homology modelling, MD simulation,
which actually yielded pretty decent S 1 -S 2 -S 3 -S 4 dihedral of −21.3°,
followed by QM/MM geometry optimization, which gave a significantly more
relaxed geometry with dihedral angle of −39.2° [94]. The cluster model cut out
from this macromolecular structure and constrained in the analogous way as before
relaxed even further yielding the dihedral of −48.6°. As a result, the calculated
transition state energies are quite high (approx. 21.2 kcal/mol) and the reduced state
exhibits more twisted conformation of the pterin ligand (−17°) than that observed
for the EBDH crystal structure.
We decided to illustrate the influence of the way in which the constraints are
introduced into the model on the reaction energy profile. To achieve this, we have
selected a big model of Moco that contains whole pterin ligands. The constraints were
introduced either to the MD-relaxed oxidized model 1 (dihedral −21.3°) or to the
reduced homology model 2, which had Moco in geometry as in the reduced EBDH
crystal structure (dihedral −4.86°). After optimization, the S 1 -S 2 -S 3 -S 4 dihedral
angle for the oxidized Moco in model 1 was −43° and differed from the value
obtained for model 2, i.e. −35.8°. This resulted in only slight energy elevation of
model 2 ES with respect to model 1; by 0.8 kcal/mol. However, the influence on C–H
activation barrier was more pronounced—the barrier was lower by 1.4 kcal/mol for
model 2. The largest effect was observed for EP complex where model 2 gave energy
lower by 4.0 kcal/mol. Moreover, model 2 not only yielded more favourable reaction
energetics but also the geometry of the relaxed reduced cofactor, with the S 1 -S 2 -S 3 -
S 4 dihedral of −1°, is much closer to the experimental value of −4.8° than the value
observed for EP in model 1 (−17.5°).