From IBM Research, Zurich Research Laboratory, 8803 Rüschlikon, Switzerland
Received for publication, November 27, 2002, and in revised form, December 18, 2002
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ABSTRACT |
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Divalent metal ions are essential to many
enzymatic reactions involving nucleic acids, but their critical and
specific role still needs to be uncovered. Restriction endonucleases
are a prominent group of such metal-requiring enzymes. Large scale
accurate simulations of Mg- and Ca-BamHI elucidate the
mechanism of the catalytic reaction leading to DNA cleavage and show
that it involves the concerted action of two metal ions and water
molecules. It is also established that what is decisive for the
dramatically different behavior of magnesium (a cocatalyst) and
calcium (an inhibitor) are kinetic factors and not the properties of
the prereactive states of the enzymes. A new perspective is opened for
the understanding of the functional role of metal ions in biological processes.
Many enzymatic reactions involving nucleic acids are known to
critically rely on the cooperative action of divalent metal cofactors,
such as magnesium, that are incorporated into the protein as positively
charged ions (1). Although quite well established, their functional
role has not yet received a satisfactory explanation and is still a
matter of debate and speculation. Among these reactions, the ones more
often investigated experimentally pertain to the family of enzymes
called type II restriction endonucleases. These enzymes are highly
site-specific; their biological function is that of cleaving DNA at
both strands (2), and they all require metal cofactors. This is a
process of primary biochemical importance. For example, this
process provides protection to bacterial cells against
bacteriophage infection, occurs naturally during programmed cell death (apoptosis), and has been exploited in genetic engineering.
The experimental information accumulated over the years (see
e.g. Refs. 1-10) mostly concerns the structural properties
of the protein-DNA complexes and the effect of mutations on their activity. More is needed to unravel the precise mechanism driving the
cleavage of the phosphodiester bond at the DNA strands (11). Although
there is little doubt that the reaction takes place via a concerted
nucleophilic substitution, it is still unclear whether the attacking
nucleophile is a water molecule or a hydroxide ion. More importantly
the activity of these enzymes crucially depends on the presence and
identity of the metal ions,1
but simple features, such as ionic size, electronegativity, or average
coordination number, do not simply correlate with it. Other issues
concern the extent to which the characteristics of the initial state of
the reaction or the presence of water molecules can affect its
development. Here we make definitive progress toward answering all
these questions with the aid of accurate computer simulations that
provide the so far missing insight into the mechanism of the catalytic
reaction and a reliable evaluation of its energetics.
The validity of any computational approach to enzymatic processes
critically relies on a quantum mechanical description of the active
site, but the modeling often suffers from the size limitation typical
of ab initio calculations. To overcome this restriction, combined quantum-classical approaches have been proposed for a long time (12-14) that partition the system into two subsystems: the close environment of the reaction site, treated quantum
mechanically (QM),2 and the
outer region described with a molecular mechanics model (MM). However,
only recently has this method started to provide the required level of
accuracy (15-17). Our QM/MM approach combines two well established
methodologies, namely density functional theory (DFT) (18) and the
GROMOS force field (19), and includes a new careful treatment of the
electrostatic interactions (20).
We apply this method to the study of the restriction endonuclease
BamHI (1, 4-6) and focus on the comparison of the
activities of magnesium and calcium, which are experimentally known to
act as cocatalyst and inhibitor, respectively, of the DNA cleavage reaction. This drastically different behavior of magnesium and calcium
is quite common, and the reasons for it are largely unknown. The
advantage that this specific system provides for a thorough investigation consists in the availability of x-ray structures that
could be used as reference for our simulations: these structures refer to the complexes obtained by cocrystallizing the protein-DNA complex with calcium and with
manganese3 and can be
considered as representative of the pre- and postreactive states,
respectively. In particular, by comparing the two states, the
structure of the protein appeared to be largely insensitive to the
reaction as evidenced by the overall root mean square
displacement of only 0.33 Å between the C The QM subsystem was treated in the framework of DFT (18) using
Becke's approximation (21) for the exchange energy functional and the
Lee-Yang-Parr approximation (22) for the correlation energy
functional. The QM calculations were performed with the Car-Parrinello
molecular dynamics (CPMD)
code4 using a plane-wave
basis set for the description of the valence electron wave functions
(energy cut-off 70 Rydberg) and norm-conserving angular
momentum-dependent pseudopotentials for the description of
the core-valence interaction. The MM subsystem was treated within the
GROMOS force field (19), which is well established (see e.g.
Ref. 23) for the determination of both the structure and the dynamics
of proteins in aqueous solutions (24). The parametrization used
corresponds to the 43A1 version of the force field. The interface
between the two subsystems was modeled using the link-atom method (14).
The QM subsystem was enclosed in a box (of edges 43.36, 48.55, and
39.21 atomic units) and treated as an "embedded cluster"
namely using the Hockney method (25) and accounting for the influence
of the MM subsystem via explicit calculations of van der Waals and
electrostatic interactions. The electrostatic potential of the MM atoms
was calculated in the QM region exactly within a cut-off radius of 15 Å and including a Poisson-Boltzmann reaction field correction (26)
outside. The influence of the QM atoms on the MM atoms was accounted
for via the electrostatic interaction. The QM region was represented by
a distribution of effective charges, which we obtained from fitting to
the ab initio electrostatic potential using a novel and
suitable procedure that avoids common errors due to inconsistency between quantum mechanically derived parameters and the rest of the
force field (20).
The initial structure is taken from the x-ray structure of the calcium
complex (6) (Protein Data Bank entry 2BAM), and hydrogen atoms are
added as required by the force field (19). The system was solvated in a
rectangular box of 14,819 simple point charge water molecules (24).
Sodium ions were added in proximity of the DNA chain to provide charge neutralization.
The optimization procedure (of the electronic and geometric variables)
consisted of three consecutive steps. First the structure of the QM
system was optimized keeping the positions of the MM atoms fixed,
consistent with the experimental observation of a minor difference
between pre- and postreactive states. Next the MM geometry was relaxed
with molecular dynamics runs and optimized. The interaction with
the QM system (fixed) was modeled as discussed above. Finally
the structure of the QM subsystem was optimized again. Only minor
changes were observed in these last two steps.
In our simulations, the system is immersed in water to provide a
realistic model (see Fig. 1) for the
study of the enzymatic reaction. As the starting configuration, we used
the crystallographic structure of the BamHI-DNA complex with
calcium and optimized its structure (Fig. 2b) in water; we
then repeated this procedure after replacing calcium with magnesium
(Fig. 2a). As attacking agent, we considered a hydroxide
generated either by a water molecule (4, 6) deprotonated in
situ (intrinsic mechanism) or by an external source (extrinsic
mechanism) (27). Fig. 2 refers only to
the modeling of the latter reaction. In this case, only minor
geometrical differences emerged in the initial states of the two
enzymes apart from the expected decrease of the metal-oxygen distances
(on average from 2.6 to 2.2 Å) on passing from calcium to magnesium.
Water molecules are part of the metal coordination shell and are
crucial to guarantee the preferred coordination number for both the A
and B ions. If the hydroxide is replaced by a water molecule as
attacking species, more significant differences between the A and B ion
environments in the initial state as well as between those of calcium
and magnesium are observed. For example, the magnesium B ion loses the
phosphate O-2 oxygen as binding partner in a 5-fold
coordination. However, the structural discrepancies we have detected in
the prereactive states of the two metal-requiring proteins are minor
and do not reflect a significantly different propensity of calcium and
magnesium to donate electrons or polarize the surrounding bonding
pattern. This is best illustrated by the spatial distribution of the
charges obtained from the topological analysis of the electron density
along the lines of Bader's theory (28) (Fig.
3). The atomic charges associated with
the A and B ions are the same, and only a small difference is found
between calcium and magnesium. Both A and B ions help stabilize a
cluster distribution of negative charges localized at the active site. This is in agreement with the experimental observation of an
enhancement of the stability of the protein-DNA complex in the presence
of divalent ions (5). In the two-metal atom mechanism suggested in Ref.
6, the role of the A ion is that of stabilizing hydroxyl ions generated
by the Glu-113-driven deprotonation of water, and the failure of
Ca2+ to act as cocatalyst was interpreted as failure to
provide the concentration of metal-hydroxyl ions necessary for the
nucleophilic attack because of an acidity lower than that of either
Mg2+ or Mn2+. The stabilizing role of the A ion
is confirmed by our calculations for magnesium, but the same is true
for calcium. From our analysis, it has become clear that the active
site does not contain any relevant feature in the initial state of the
binding that could provide a simple explanation for the dramatically
different behavior of magnesium and calcium.
INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
COMPUTATIONAL METHOD
RESULTS AND DISCUSSION
REFERENCES
positions of the
pre- and postreactive states. Two metal atoms (A and B) were observed
at the active site, corroborating earlier proposals for a two-metal
mechanism (4), the nature of which will emerge clearly from our results.
COMPUTATIONAL METHOD
TOP
ABSTRACT
INTRODUCTION
COMPUTATIONAL METHOD
RESULTS AND DISCUSSION
REFERENCES
RESULTS AND DISCUSSION
TOP
ABSTRACT
INTRODUCTION
COMPUTATIONAL METHOD
RESULTS AND DISCUSSION
REFERENCES
View larger version (35K):
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Fig. 1.
a, model used for the
BamHI-DNA complex. The QM subsystem (represented by
sticks) consists of 297 atoms: the scissile phosphate of DNA
with the DNA backbone connecting it to two other adjacent phosphates,
all the residues as far as 11 Å from the scissile P-O bond, two metal
ions (green spheres), and 10 crystallographic water
molecules. The surrounding solvent and counterions are omitted here for
sake of clarity. b, more detailed view of the active site.
Arrows mark the positions of the scissile P-O bond and of
the attacking hydroxide.
View larger version (31K):
[in a new window]
Fig. 2.
Schematic representation of the optimized
geometries in the close neighborhood of the scissile phosphate in the
initial and transition states of the magnesium (a and
c) and calcium (b and
d) complexes. All distances are in Å.
View larger version (34K):
[in a new window]
Fig. 3.
Prereactive states of both magnesium
(a) and calcium (b) complexes.
The atomic charges obtained using Bader's approach (28) are shown in
the range 2.0 (deep blue) to +2.0 (deep red).
Values outside this range were condensed in the extremes for sake of
clarity, and aliphatic hydrogen atoms were omitted. Also displayed is
the charge distribution projected onto a plane containing the scissile
bond. Note the strong similarity all over the region of the active
site. Bader's atomic charges may differ only slightly from the nominal
ionic charges, e.g. they are +2.0 for magnesium and +1.9 for
calcium.
We proceeded to investigate the reaction mechanisms and evaluate the energy profiles. For the phosphodiester cleavage by the hydroxide, be it extrinsic or intrinsic, we chose its approach distance to the phosphate as reaction coordinate. For the deprotonation of the water molecule, we selected its distance from the protonating amino acid (Glu-113 in Fig. 2). In the case of magnesium, the mere bond breaking induced by the hydroxide costs 14 kcal/mol in the extrinsic and 29 kcal/mol in the intrinsic process. Substantially higher energy barriers are obtained when magnesium is replaced by calcium, namely 31 and 52 kcal/mol, respectively. The presence of calcium instead of magnesium also increases, although to a lesser extent, the energy barrier relative to deprotonation of water in situ, namely from 20 to 26 kcal/mol. On the other hand, the cost to transfer a hydroxide from the bulk solution to the metal coordination shell, which is not explicitly calculated here, is expected to be only slightly different in the two cases. An estimate of the free energy change involved in this process can be obtained (29) from the difference between the pKa of the metal ion-bound water and the experimental external pH (30). This amounts to about 5 kcal/mol for magnesium and 7 kcal/mol for calcium. In conclusion, our results unambiguously show that the kinetics of the reaction is decisive for the dramatically different behavior of the two divalent ions. Our calculations also show that the extrinsic mechanism is the most plausible one, which is consistent with recent model calculations of the free energy gain in the presence of the enzyme for the formation of the hydroxide in the two cases (27). An activation free energy of ~18 kcal/mol was derived from the measured value of the rate constant of the phosphodiester bond cleavage reaction (30) catalyzed by the magnesium enzyme. If we subtract the amount due to the inclusion of the hydroxide in the system from it, we obtain a value of ~13 kcal/mol. Comparison with our calculated value of ~14 kcal/mol for the energy barrier indicates that the entropy contribution is minor.
A complete understanding of the difference in the calculated energy barriers can be obtained by investigating the active site in the region of the "transition state" (Fig. 2, c and d). These structures show the presence of a trigonal bipyramid for the reacting moiety with both the attacking and leaving groups in axial positions. This is consistent with the geometry of the transition state involved in the hydrolysis of phosphate esters (31). Here the structural differences between the calcium and magnesium environments are much more pronounced than in the initial state, and their role in increasing the barrier for the transition to happen can now be detected. From our simulations of the active magnesium enzyme, it becomes clear that the role of the B ion is crucial in stabilizing the pentacoordinated transition state of the phosphate. In doing this, the B ion reduces its coordination with oxygen from six to four. This is what allows a water molecule to exit the coordination sphere of the metal and position itself to stabilize, via hydrogen bonding, another water molecule, which drives the final step of the reaction, i.e. the protonation of the O-3' leaving group of the phosphate. An oxygen coordination shell of four is not so uncommon for magnesium. This is not the case for calcium, which tends to overcoordinate (with respect to a 6-fold coordination) rather than undercoordinate. In fact, when the system is forced to accommodate the pentacoordinated phosphate, resulting in a loosening of the bonding between the phosphate and the metal ion, the calcium B ion does not readjust its coordination but responds to keep all possible oxygen partners. Calcium thus fails to stabilize a situation that would be favorable for the transition to happen. As Fig. 2d shows, the A ion also tends to increase its coordination, resulting in a strained rearrangement of the atoms around it in contrast to the case of the magnesium enzyme in which the A ion keeps a quasisymmetric octahedral structure during the entire reaction (see Fig. 2, a and c). All this explains the much higher energy required by the calcium complex with respect to the magnesium complex in allowing the final reaction to take place.
These simulations have elucidated the mechanism by which magnesium ions
coadjuvate the BamHI enzyme in cleaving the phosphodiester bond in DNA strands and finally unraveled why calcium ions inhibit the
catalytic reaction. These findings have confirmed earlier suggestions
(6) that a crucial role in the reaction is played by water molecules as
well as by a second metal ion, beyond the one binding the attacking
agent, and elucidated their concerted mode of action. This leads to a
transition state with a configuration that perturbs the coordination
shell of the metal ions in a way that is compatible with the binding
mode of magnesium but not with that of calcium. On this basis, barriers
lower than those for the calcium complex can reasonably be expected for
complexes incorporating manganese, cobalt, zinc, and cadmium, which are more similar to magnesium and also act as cocatalysts (6). Calculations
from first principles were necessary to account for the
nontrivial difference of the electronic structure of the two enzymes
that drastically affects the kinetics of the reaction rather than the
static properties of the prereactive states. The success of this
investigation is largely due to our computational method, which relies
on a careful description of all relevant interactions and on a
sufficiently large size of the QM subsystem. In fact, as we have
verified, reducing the size of the QM subsystem (50-100 atoms)
drastically changes the nature of the frontier orbitals and thus the
chemical behavior of the system, and ignoring dominant interactions
with the MM region makes it unstable. The large discrepancy found in
the values of the energy barriers of the enzyme with the two different
metals (~20 kcal/mol) is such that future enhancements of the
accuracy of these calculations (e.g. an improvement of the
DFT functional or a dynamic search for the transition state)
will not alter the explanation we have provided here for their
different chemical behavior. These results also reveal a new
perspective on the large variety of enzymatic reactions relying on
metal ion cofactors (1) and offer an efficient and accurate method that
can now be confidently extended to verify several mechanistic
hypotheses and to calculate specific physical quantities such as
reaction activities.
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ACKNOWLEDGEMENTS |
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We are grateful to Andrea Califano and Ajay K. Royyuru for encouraging us to investigate this problem.
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FOOTNOTES |
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* The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
To whom correspondence should be addressed: IBM Research, Zurich
Research Laboratory, Säumerstr. 4, 8803 Rüschlikon,
Switzerland. Tel.: 41-1-724-8344; Fax: 41-1-724-8962; E-mail:
and@zurich.ibm.com.
Published, JBC Papers in Press, December 19, 2002, DOI 10.1074/jbc.C200664200
1 Between one and three metal binding sites have been observed in the crystallographic structures of different restriction endonucleases, but the correlation between number of ions and activity is unclear.
3 The use of manganese is often meant to provide information on the analog case of magnesium, which is essentially invisible in x-ray measurements but is the natural, and thus most interesting, cocatalyst.
4 CPMD: copyright IBM Corp. 1990, 1997, 2001 and Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany, 1997; see www.cpmd.org.
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ABBREVIATIONS |
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The abbreviations used are: QM, quantum mechanics; MM, molecular mechanics; DFT, density functional theory; GROMOS, Groningen molecular simulation.
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