514
T. Borowski and M. Szaleniec
lax” the protein structure, i.e. allow it to attain a structure as in solution as opposed
to the situation in the crystal, (b) study ligand binding or dissociation, (c) study conformational freedom of a macromolecular system and many more. In the context
of metalloenzymes, the key issue is what kind of force field is used for the metal
with its ligands and where from its parameters can be obtained. One of the options
is to use a so-called non-bonded model for the metal ion, whereby the metal–ligand
interactions are described with non-bonded terms of classical force field, i.e. van der
Waals and electrostatic terms, the latter possibly also including ion-induced dipole
term [58]. The advantage of this approach is that it allows to simulate complexes of
a given metal ion with various coordination numbers and compositions of ligands
without the need to derive parameters for each particular coordination complex separately. Moreover, as this model does not specify explicit bonds between the metal
and the ligands, it permits to simulate the process of ligand binding or dissociation.
Up to quite recently, the disadvantage of classical non-bonded models was lack of
parameters for transition metal ions, so for example, quite often Mg
2+ ion was used
in simulations in place of Fe
2+ bound in the enzyme active sites [59, 60]. This situation has changed as parameters for many metal cations were derived by Merz and
co-workers [61, 62]. The alternative is a bonded model in which explicit bonds are
specified between the central metal ion and its ligands. The major disadvantages of
this approach are the need to derive bonded parameters for each specific complex
and the fact that bond cleavage/formation steps cannot be studied. There are several different ways in which one can derive such bonded metal–ligand parameters,
probably the most straightforward being those projecting the Hessian matrix, calculated at the QM (DFT) level, onto internal coordinates of the complex. This method
was originally suggested by Seminario [63, 64], but in its original form it suffers
from double counting of 1–4 interactions when the derived bonded parameters are
used together with atomic charges. A recent improvement proposed by Hirao and
co-workers to a large extent lifts this limitation (see Chapter “Applications of Computational Chemistry to Selected Problems of Transition-Metal Catalysis in Biological
and Non-biological Systems”). Recent advances in development of polarizable force
fields pave a way to more accurate description of electrostatic interactions in macromolecules including metal ion–ligand interactions. As writing this chapter, the first
works devoted to derivation and testing of polarizable force field parameters for
metal ions were already published. The preliminary results of molecular simulations
employing such force fields let us hope that in the near future such methods will be
used more routinely to study structure and dynamics of metalloenzymes [65–67].
A recent work on AsqJ dioxygenase may serve as a case study demonstrating
the value of relatively straightforward MD simulations for metalloenzymes [68].
The reaction mechanism for oxidative dehydrogenation (Fig. 5) was studied at the
QM/MM (ONIOM) level, yet the starting structures for these investigations were
derived from classical MD simulations performed for two reaction intermediates:
either for the enzyme–substrate complex, i.e. before O 2 activation and α-ketoglutarate
decarboxylation, or for the ferryl species, i.e. the state immediately before C–H bond
cleavage (S in Fig. 5). Interestingly, even though the QM/MM optimized structures
for species S looked very similar in these two cases, for the former model a lower
T. Borowski and M. Szaleniec
lax” the protein structure, i.e. allow it to attain a structure as in solution as opposed
to the situation in the crystal, (b) study ligand binding or dissociation, (c) study conformational freedom of a macromolecular system and many more. In the context
of metalloenzymes, the key issue is what kind of force field is used for the metal
with its ligands and where from its parameters can be obtained. One of the options
is to use a so-called non-bonded model for the metal ion, whereby the metal–ligand
interactions are described with non-bonded terms of classical force field, i.e. van der
Waals and electrostatic terms, the latter possibly also including ion-induced dipole
term [58]. The advantage of this approach is that it allows to simulate complexes of
a given metal ion with various coordination numbers and compositions of ligands
without the need to derive parameters for each particular coordination complex separately. Moreover, as this model does not specify explicit bonds between the metal
and the ligands, it permits to simulate the process of ligand binding or dissociation.
Up to quite recently, the disadvantage of classical non-bonded models was lack of
parameters for transition metal ions, so for example, quite often Mg
2+ ion was used
in simulations in place of Fe
2+ bound in the enzyme active sites [59, 60]. This situation has changed as parameters for many metal cations were derived by Merz and
co-workers [61, 62]. The alternative is a bonded model in which explicit bonds are
specified between the central metal ion and its ligands. The major disadvantages of
this approach are the need to derive bonded parameters for each specific complex
and the fact that bond cleavage/formation steps cannot be studied. There are several different ways in which one can derive such bonded metal–ligand parameters,
probably the most straightforward being those projecting the Hessian matrix, calculated at the QM (DFT) level, onto internal coordinates of the complex. This method
was originally suggested by Seminario [63, 64], but in its original form it suffers
from double counting of 1–4 interactions when the derived bonded parameters are
used together with atomic charges. A recent improvement proposed by Hirao and
co-workers to a large extent lifts this limitation (see Chapter “Applications of Computational Chemistry to Selected Problems of Transition-Metal Catalysis in Biological
and Non-biological Systems”). Recent advances in development of polarizable force
fields pave a way to more accurate description of electrostatic interactions in macromolecules including metal ion–ligand interactions. As writing this chapter, the first
works devoted to derivation and testing of polarizable force field parameters for
metal ions were already published. The preliminary results of molecular simulations
employing such force fields let us hope that in the near future such methods will be
used more routinely to study structure and dynamics of metalloenzymes [65–67].
A recent work on AsqJ dioxygenase may serve as a case study demonstrating
the value of relatively straightforward MD simulations for metalloenzymes [68].
The reaction mechanism for oxidative dehydrogenation (Fig. 5) was studied at the
QM/MM (ONIOM) level, yet the starting structures for these investigations were
derived from classical MD simulations performed for two reaction intermediates:
either for the enzyme–substrate complex, i.e. before O 2 activation and α-ketoglutarate
decarboxylation, or for the ferryl species, i.e. the state immediately before C–H bond
cleavage (S in Fig. 5). Interestingly, even though the QM/MM optimized structures
for species S looked very similar in these two cases, for the former model a lower