Patrick G Blachly, Gregory M Sandala1, Debra Ann Giammona2, Donald Bashford2, J Andrew McCammon, Louis Noodleman3. 1. ‡Department of Chemistry and Biochemistry, Mount Allison University, 63C York Street, Sackville, New Brunswick E4L 1G8, Canada. 2. §Department of Structural Biology, St. Jude Children's Research Hospital, 262 Danny Thomas Place, Memphis, Tennessee 38105, United States. 3. #Department of Integrative Structural and Computational Biology, CB213, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, California 92037, United States.
Abstract
The recently discovered methylerythritol phosphate (MEP) pathway provides new targets for the development of antibacterial and antimalarial drugs. In the final step of the MEP pathway, the [4Fe-4S] IspH protein catalyzes the 2e(-)/2H(+) reductive dehydroxylation of (E)-4-hydroxy-3-methyl-but-2-enyl diphosphate (HMBPP) to afford the isoprenoid precursors isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP). Recent experiments have attempted to elucidate the IspH catalytic mechanism to drive inhibitor development. Two competing mechanisms have recently emerged, differentiated by their proposed HMBPP binding modes upon 1e(-) reduction of the [4Fe-4S] cluster: (1) a Birch reduction mechanism, in which HMBPP remains bound to the [4Fe-4S] cluster through its terminal C4-OH group (ROH-bound) until the -OH is cleaved as water; and (2) an organometallic mechanism, in which the C4-OH group rotates away from the [4Fe-4S] cluster, allowing the HMBPP olefin group to form a metallacycle complex with the apical iron (η(2)-bound). We perform broken-symmetry density functional theory computations to assess the energies and reduction potentials associated with the ROH- and η(2)-bound states implicated by these competing mechanisms. Reduction potentials obtained for ROH-bound states are more negative (-1.4 to -1.0 V) than what is typically expected of [4Fe-4S] ferredoxin proteins. Instead, we find that η(2)-bound states are lower in energy than ROH-bound states when the [4Fe-4S] cluster is 1e(-) reduced. Furthermore, η(2)-bound states can already be generated in the oxidized state, yielding reduction potentials of ca. -700 mV when electron addition occurs after rotation of the HMBPP C4-OH group. We demonstrate that such η(2)-bound states are kinetically accessible both when the IspH [4Fe-4S] cluster is oxidized and 1e(-) reduced. The energetically preferred pathway gives 1e(-) reduction of the cluster after substrate conformational change, generating the 1e(-) reduced intermediate proposed in the organometallic mechanism.
The recently discovered methylerythritol phosphate (MEP) pathway provides new targets for the development of antibacterial and antimalarial drugs. In the final step of the MEP pathway, the [4Fe-4S] IspH protein catalyzes the 2e(-)/2H(+) reductive dehydroxylation of (E)-4-hydroxy-3-methyl-but-2-enyl diphosphate (HMBPP) to afford the isoprenoid precursors isopentenyl pyrophosphate (IPP) and dimethylallyl pyrophosphate (DMAPP). Recent experiments have attempted to elucidate the IspH catalytic mechanism to drive inhibitor development. Two competing mechanisms have recently emerged, differentiated by their proposed HMBPP binding modes upon 1e(-) reduction of the [4Fe-4S] cluster: (1) a Birch reduction mechanism, in which HMBPP remains bound to the [4Fe-4S] cluster through its terminal C4-OH group (ROH-bound) until the -OH is cleaved as water; and (2) an organometallic mechanism, in which the C4-OH group rotates away from the [4Fe-4S] cluster, allowing the HMBPP olefin group to form a metallacycle complex with the apical iron (η(2)-bound). We perform broken-symmetry density functional theory computations to assess the energies and reduction potentials associated with the ROH- and η(2)-bound states implicated by these competing mechanisms. Reduction potentials obtained for ROH-bound states are more negative (-1.4 to -1.0 V) than what is typically expected of [4Fe-4S] ferredoxin proteins. Instead, we find that η(2)-bound states are lower in energy than ROH-bound states when the [4Fe-4S] cluster is 1e(-) reduced. Furthermore, η(2)-bound states can already be generated in the oxidized state, yielding reduction potentials of ca. -700 mV when electron addition occurs after rotation of the HMBPP C4-OH group. We demonstrate that such η(2)-bound states are kinetically accessible both when the IspH [4Fe-4S] cluster is oxidized and 1e(-) reduced. The energetically preferred pathway gives 1e(-) reduction of the cluster after substrate conformational change, generating the 1e(-) reduced intermediate proposed in the organometallic mechanism.
In 2012, the World
Health Organization documented 8.6 million cases of tuberculosis,
of which 450 000 were multidrug-resistant (MDR TB); of these,
171 000 cases were fatal.[1] In cases
of MDR TB, the use of alternative, less effectual therapies is required
when the first-line drugs are no longer effective.[1] The problem associated with drug resistance is not unique
to tuberculosis and, notably, also plagues efforts to curb malaria[2−5] and hospital-borne bacterial infections.[6,7] The
diminished efficacy of conventional therapies against the multidrug-resistant
organisms that cause these illnesses necessitates the development
of new drugs with novel modes of action.[8]Recently, the isoprenoid biosynthesis pathway discovered in
microorganisms has inspired the development of new antibacterial and
antimalarial drugs.[9,10] Isoprenoids comprise a wide selection
of essential biomolecules that includes sterols, chlorophylls and
quinones, all of which are synthesized from the precursors isopentenyl
pyrophosphate (IPP; 1 in Figure 1) and dimethylallyl pyrophosphate (DMAPP; 2 in Figure 1).[11,12] Rohmer and Arigoni independently
discovered the methylerythritol phosphate (MEP) metabolic pathway
(alternatively named the 1-deoxy-d-xylulose 5 phosphate [DOXP]
pathway) that is responsible for the synthesis of isoprenoids in most
eubacteria (including the pathogens Helicobacter pylori and Mycobacterium tuberculosis) and in apicomplexan
protozoa such as the malaria parasite Plasmodium falciparum.[13−16] Although isoprenoid synthesis is also essential in humans, all animals
obtain DMAPP and IPP through a mevalonate-dependent pathway that is
distinct from the MEP pathway,[12,17] which justifies the
pursuit of MEP inhibitors to treat bacterial and malarial infections.
The first step toward producing such drugs has recently been achieved
with the approval of fosmidomycin, an antimalarial drug that targets
1-deoxy-d-xylulose 5-phosphate reductoisomerase (DOXP reductase,
also referred to as Dxr or IspC), the second enzyme in the MEP pathway.[18−20]
Figure 1
Schematic
representation of the two disparate mechanisms used to explain IspH
catalysis. Both the Birch reduction and organometallic mechanisms
attempt to explain how IspH catalyzes the 2e–/2H+ reductive dehydroxylation of HMBPP
(3) to afford IPP (1) and DMAPP (2) in an approximate 5:1 ratio.
Schematic
representation of the two disparate mechanisms used to explain IspH
catalysis. Both the Birch reduction and organometallic mechanisms
attempt to explain how IspH catalyzes the 2e–/2H+ reductive dehydroxylation of HMBPP
(3) to afford IPP (1) and DMAPP (2) in an approximate 5:1 ratio.Following the success of fosmidomycin, multiple groups have
worked to structurally characterize and develop inhibitors for other
enzymes in the MEP pathway,[10] including
the IspH (LytB) protein.[21−27] In the final step of the MEP pathway, IspH catalyzes the 2e–/2H+ reductive dehydroxylation
of (E)-4-hydroxy-3-methyl-but-2-enyl diphosphate
(HMBPP; 3 in Figure 1) to produce
IPP and DMAPP in an approximate 5:1 ratio.[28−32] Various spectroscopic studies[21,26,29,31,33,34] and high-resolution
crystal structures[23,35,36] indicate the presence of a central [4Fe–4S] cluster in the
active form of IspH. In the Escherichia coli crystal
structure of IspH in complex with HMBPP (IspH:HMBPP),[35] three conserved cysteine residues (C12, C96, and C197)
tether the cluster to the protein, leaving a single iron site, labeled
Fe1 or the apical Fe, available for coordinating the C4–OH group of the substrate HMBPP (atom numbers are labeled
on 3 in Figure 1). The [4Fe–4S]
cluster not only anchors the HMBPP molecule in the active site but
also facilitates the transfer of 2e– to HMBPP.[28−31,34] Additionally, the nearby E126
residue is understood to be essential in IspH catalysis.[26,37] Kinetics experiments performed on an IspH E126A mutant give a Vmax that is over 40-fold lower than what is
observed for wild-type (WT) IspH, indicating that the E126A mutant
is nearly unable to catalyze the conversion of HMBPP to IPP and DMAPP.[26]Despite having reasonable knowledge of
the proton and electron sources for IspH catalysis, the detailed catalytic
mechanism is highly debated. Since a number of thorough review articles
have catalogued recent experimental progress toward understanding
IspH catalysis,[9,38−41] we briefly describe the two predominant
mechanisms currently under consideration—the Birch reduction
and organometallic mechanisms, borrowing the nomenclature used in
the review by Liu and co-workers.[40]Proponents of the Birch reduction mechanism (top route in Figure 1) suggest catalysis is driven by the ability of
Fe1 to act as a Lewis acid.[30,32,35,39,42,43] The first mechanistic step in this mechanism
is the reduction of the oxidized [4Fe–4S]2+ cluster
(3) to its [4Fe–4S]+ form (4). Once reduced, the [4Fe–4S]+ cluster transfers
an electron to HMBPP concurrent with the protonation and cleavage
of the HMBPP C4–OH group to generate a delocalized,
allyl radical intermediate (5). Product generation (1 and 2) then requires the addition of both a
proton and electron to the substrate intermediate. In this step, the
electron is transferred either from an external source or from the
[4Fe–4S]2+ cluster, which would then assume a [4Fe–4S]3+ (HiPIP-like[44−46]) oxidation state (6). While support
for the Birch reduction mechanism derives from biochemical studies
of HMBPP analogues,[42] which do not require
the formation of organometallic complexes, structures of the proposed
intermediates (4–6) have not been
directly observed.In contrast with the Birch reduction mechanism,
Oldfield and co-workers propose an organometallic mechanism for IspH
catalysis (bottom route in Figure 1),[26,35,41,47−49] in which the Fe1–OC4 bond breaks
and the C4–OH group rotates away from Fe1 when the
[4Fe–4S] cluster is reduced by one electron (7). Following this rotation, two electrons are transferred from the
[4Fe–4S]1+ cluster to the substrate, which, upon
proton transfer and water loss, forms an allyl anion species (8).[48,49] This [4Fe–4S]3+ HiPIP state is similar to the proposed intermediate in the Birch
reduction step (6), differing only in that it is formed
following bond rotation. The requirement of bond rotation proposed
in the organometallic mechanism is based on electron nuclear double
resonance (ENDOR) spectroscopy experiments performed on an E126A mutant
intermediate that showed hyperfine coupling between the HMBPPcarbon
atoms—likely the olefinic C2 and C3 atoms
(Figure 1, numbering shown on 3)—and the [4Fe–4S]1+ cluster.[26] It is unclear whether this intermediate exists
in wild-type (WT) IspH, as the 1e– reduced state has not been trapped when E126 is present.A
minor species identified in the X-ray structure of the WT IspH:HMBPP
complex,[36] obtained shortly after irradiation
of the crystals, contains HMBPP in an alternative conformation with
its C4–OH group rotated away from Fe1. In this
crystal structure, HMBPP weakly coordinates Fe1 through its olefinic
C2 and C3 atoms, and the C4–OH
group is positioned to form a hydrogen bond with the HMBPP PP (pyrophosphate) tail. Such HMBPP conformations are also observed in crystal structures
of [3Fe–4S] T167C, E126D, and E126Q mutants[36] and indicate that the properties of the IspH active site
can be tuned to induce HMBPP binding in a manner that is similar to
what is proposed in the organometallic mechanism. Separately, 13C feeding studies[47] have also
provided independent support for the organometallic mechanism.Further analysis is needed to establish which IspH catalytic mechanism
is preferred. Since the proposed binding modes of HMBPP in the Birch
reduction and organometallic mechanisms differ when the [4Fe–4S]
cluster is 1e– reduced,[40] this report uses broken-symmetry density functional
theory (BS-DFT) computations to study the geometries and energies
of the different 1e– reduced intermediates
implicated by these two distinct mechanisms. We perform these computations
on the same active-site model used previously to examine the different
IspH oxidized states.[50] This approach enables
us to obtain reduction potentials and explore the feasibility of identifying
different IspH reaction intermediates in the 1e– reduced state. We also extend our analysis of oxidized
states and related reaction pathways beyond that in previous work.[50]
Methods
Active-Site
Model Used to Probe 1e– Reduced States of IspH
The active-site quantum model employed in this work is identical
to that used previously to successfully compute geometries and Mössbauer
parameters for the IspH oxidized state.[50] Briefly, this large active-site model is constructed from the oxidized
[4Fe–4S] IspH:HMBPP crystal structure solved to 1.7 Å
resolution by Grawert et al. (PDB ID: 3KE8).[35] In addition
to the [4Fe–4S] cluster, its coordinating thiolates (C12, C96,
and C197), and the substrate HMBPP, we include the side chains of
various residues suggested to play roles in catalysis: T167, E126,
H41, and H124. Additionally, we include other residues that are ideally
positioned to stabilize the highly charged HMBPP PP tail: H74, S225, S226, N227, and S269. Further, the model
includes the backbones of A199/T200, P97/L98, and G14/V15, the side
chain of T200, and a crystallographic water that cumulatively donate
the only five hydrogen bonds to the cluster sulfides and thiolates
observed in the [4Fe–4S] IspH/HMBPP crystal structure.[35] The inclusion of all hydrogen bond donors to
the [4Fe–4S] cluster is necessary because of their collective
role in modulating the reduction potentials of [4Fe–4S] clusters.[51−54] Upon addition of hydrogen atoms and capping groups, as detailed
previously, the IspH active-site model contains 203–205 atoms,
depending on the protonation state of C4–O(H), E126,
and the PP tail.[50]
Practical Considerations for Broken-Symmetry Density Functional Theory
Computations of the 1e– Reduced States of IspH
In [4Fe–4S] clusters, the different Fe sites are spin-polarized
and spin-coupled, with two antiferromagnetically (AF) coupled Fe–Fe
pairs. Since conventional DFT methods are typically unable to obtain
AF-coupled states, we employ BS-DFT computations to obtain optimized
geometries and relative energies for the IspH active-site quantum
cluster in the 1e– reduced state.[55−57]Previously, we considered an active-site model of the IspH
oxidized state.[50] In these computations,
the AF-coupled oxidized state contains two Fe–Fe spin-coupled
pairs: one pair with a net spin of +9/2, and the other pair with a
net spin of −9/2. Collectively, these pairs combine to give
a system net spin of STot = 0. To generate
the AF-coupled 1e– reduced state,
we add a spin-α electron to the system to give STot = +1/2. (The plus sign indicates that the ẑ-component
of total spin, MS,Tot, equals +1/2 in
the BS state used; the majority spin is thus α for the quantum
cluster.) In practice, generating this AF-coupled 1e– reduced state is achieved from the optimized
geometries previously obtained for the oxidized state of the IspH
cluster. The AF-coupled BS state for the 1e– reduced state is found by first computing a ferromagnetically coupled
state, where all Fe atoms are high-spin with parallel net spins (STot = 9/2 + 8/2 = +17/2). Then, the spin vectors
on two of the four Fe atoms are rotated to generate the AF-coupled,
BS state with STot = +1/2, which is used
as the starting point for geometry optimizations of the 1e– reduced states.When the [4Fe–4S]
cluster is 1e– reduced, the spin-coupled
Fe–Fe pair whose net spins are aligned with the total system
spin (STot) formally corresponds to a
delocalized, mixed-valence pair (two Fe2.5+, S = +9/2); the Fe–Fe pair whose net spins are aligned opposite
to STot is a ferrous pair (two Fe2+, S = −8/2). Because of the non-equivalency
of these two Fe–Fe pairs, computations are performed on different
valence isomers of the 1e– reduced
[4Fe–4S]1+ cluster; that is to say, different Fe–Fe
spin-coupling combinations were examined in this study. Consistent
with our recent study of the IspH oxidized state,[50] we consider four of the six possible valence isomers in
the 1e– reduced state, which are
named according to the net spin on each specific iron site (Fe1–Fe4):
αββα, ααββ, βαβα,
and βααβ (Figure 2).
To effectively manage the number of computations needed to characterize
the different protonation and electronic states available in the 1e– reduced state of our active-site quantum
model, we omit the αβαβ and ββαα
states from our analysis, which were found to be either intermediate
or higher in energy than all other states performed on a smaller active-site
model.
Figure 2
Illustration of the different valence isomers considered in this
study. Atom numbering applied to [4Fe–4S] cluster irons and
sulfides are used throughout this report. The naming of each valence
isomer corresponds to the alignment of the net spin on each Fe atom
(1–4): (a) αββα, (b) ααββ,
(c) βαβα, and (d) βααβ.
Illustration of the different valence isomers considered in this
study. Atom numbering applied to [4Fe–4S] cluster irons and
sulfides are used throughout this report. The naming of each valence
isomer corresponds to the alignment of the net spin on each Fe atom
(1–4): (a) αββα, (b) ααββ,
(c) βαβα, and (d) βααβ.
Geometry Optimizations
of the IspH 1e– Reduced States
BS-DFT computations
are performed using the Amsterdam Density Functional (ADF) 2009 program.[58] We choose to perform all geometry optimizations
and single-point energy computations with the OLYP exchange-correlation
(XC) functional,[59,60] since its use has been shown
to produce good-quality geometries, spin-state energetics, and spectroscopic
parameters for various Fe complexes,[61−63] including the oxidized
IspH active site.[50] Geometry optimizations
are performed on all valence isomers considered in this study and
employ the Slater-type triple-ζ plus polarization (STO-TZP)
basis set with core electrons frozen and a numerical integration accuracy
of 4.0. To ensure the active-site geometry in our computations best
matches that of the IspH protein, the Cα atoms of
all residues, with the exception of the thiolate residues, are constrained
to their crystallographic positions. All the thiolates are capped
at the Cβ atom, constraining one hydrogen atom attached
to the Cβ atom to lie along the Cβ–Cα bond vector. Further details pertaining
to the preparation of the model active site can be found in ref (49).In all geometry
optimizations, solvent effects are approximated using the Conductor-like
Screening Model (COSMO)[64,65] with a dielectric constant
(ε) of 20. This choice for ε has been validated in BS-DFT
studies of ribonucleotide reductase intermediate X,[66] the oxidized states of the [4Fe–4S]-containing adenosine
5′-phosphosulfate reductase (APS reductase),[67] and IspH.[50] When energies are
obtained from these geometry optimizations with COSMO solvation (ε
= 20), we refer to the results as having been obtained with the DFT/COSMO
method.
Single-Point Energy Calculations Using the DFT/SCRF Method
Following geometry optimizations in COSMO solvation (ε =
20), we perform single-point self-consistent reaction field (SCRF)
computations (henceforth referred to as DFT/SCRF computations) on
all BS states considered. In these DFT/SCRF computations, the optimized
geometry obtained for the active-site region is subjected to a multi-dielectric
environment that also includes the permanent charges and dipoles generated
by the surrounding IspH protein point charges through a finite-difference
solution to the Poisson equation.[68]To generate the protein/solvent environment included in the DFT/SCRF
method, the optimized geometry of each 1e– reduced state is embedded in the oxidized [4Fe–4S] IspH:HMBPP
crystal structure.[35] Atoms present in both
the active-site model and the protein crystal structure are omitted
from the electrostatic protein region to ensure that they are represented
only once—in the region described by DFT. All other protein
atoms are assigned fixed point charges and atomic radii from the PARSE
charge set.[69] The DFT/SCRF method then
assigns different dielectric constants to describe the active-site
region (ε = 1), its surrounding protein environment (ε
= 4), and the solvent region outside the protein (ε = 80).Following system preparation, DFT/SCRF computations are performed
using the standard interface between a developmental version of ADF2011
and Bashford’s Macroscopic Electrostatics with Atomic Detail
(MEAD)[70,71] program. (We note that all computations
reported here give results that are identical to those obtained using
the official release of ADF2012.[72]) In
practice, the DFT/SCRF computations are conducted iteratively, whereby
the following steps are taken: (1) a gas-phase single-point energy
calculation is performed on the active-site geometry obtained from
an optimization using COSMO; (2) following the gas-phase single-point
energy computation, point charges are obtained for the active-site
atoms by fitting to the DFT-derived molecular electrostatic potential
(ESP) using the CHELPG algorithm[73] combined
with singular value decomposition;[74] (3)
the total (electronic plus nuclear) charge density obtained for the
active site quantum cluster is subjected to two potentials obtained
by a finite-difference solution of the Poisson equation: a protein
potential arising from the protein point charges screened by different
dielectric media (ε = 1 for the quantum region, ε = 4
for the protein region, and ε = 80 for the solvent region) and
a reaction field potential generated by the response of the different
dielectric regions to the ESP charges in the quantum region; (4) the
sum of the protein and reaction field potentials are then added to
the Coulomb operator in the DFT scheme, and a single-point energy
calculation is performed, taking into account the polarization of
the quantum region by protein/solvent environment; (5) the electronic
energy obtained from the single-point energy calculation is added
to the protein and reaction field energies to obtain a total DFT/SCRF
energy; (6) steps 1–5 are iterated until the DFT/SCRF energy
does not deviate between cycles by more than 0.1 kcal mol–1.[68]
Naming Scheme for the Different
Oxidized and Reduced IspH States
To facilitate the discussion
of the different active-site protonation states of IspH, we adopt
a naming scheme introduced previously, ROXPYEZ, where X, Y, and Z are assigned either a minus sign
“–” or the letter “H” to signify
whether or not a proton resides on the HMBPP C4–O(H)
group, the HMBPP PP moiety, or E126,
respectively (Table 1).[50] For example, in the state named ROHP–E–, HMBPP possesses a protonated C4–O(H)
group and a fully deprotonated PP group
(giving the ligand a net charge of −3), whereas E126 is deprotonated. Combined with the 1e– reduced [Fe4S4Cys3]2 cluster and
the two charged imidazoles (of which each has = +1), the model active site of the ROHP–E– state carries a total charge of
−4 (Table 1). We stress that the “–”
sign does not specify the net charge of the PP group within this naming scheme, which has a −3 charge
when it is deprotonated (P–) and a −2 charge
when it is singly protonated at an oxygen on the terminal phosphate
group of HMBPP (PH).
Table 1
A Description of
the Nomenclature Used Throughout This Reporta
protonation state
q
C4–O(H)
PPi
E126
RO–P–EH
–4
–
–
H
RO–PHEH
–3
–
H
H
ROHP–E–
–4
H
–
–
ROHPHE–
–3
H
H
–
ROHP–EH
–3
H
–
H
ROHPHEH
–2
H
H
H
This nomenclature is identical to the scheme used previously
to describe the IspH oxidized state.[50] Unless
indicated with an H, the titratable moiety is assumed to be fully
deprotonated and is marked by a “–”. The total
charge () of the active-site quantum
cluster when the [4Fe–4S] cluster is 1e– reduced is also given for each state.
This nomenclature is identical to the scheme used previously
to describe the IspH oxidized state.[50] Unless
indicated with an H, the titratable moiety is assumed to be fully
deprotonated and is marked by a “–”. The total
charge () of the active-site quantum
cluster when the [4Fe–4S] cluster is 1e– reduced is also given for each state.Additionally, since the results
presented here consider different binding modes of HMBPP to Fe1, we
indicate the coordinating group of HMBPP in parentheses following
its protonation state when the coordination mode is ambiguous. For
example, when the ROHP–E– state coordinates Fe1 through its ROH group, it is denoted by ROHP–E–(ROH). When the same
protonation state is considered but with the HMBPP olefinic C2 and C3 atoms coordinating Fe1, the state is instead
labeled ROHP–E–(η2).
Computing Relative Energies in the 1e– Reduced State
The relative
free energy of deprotonation at pH = 7, ΔGdeprot, is obtained for an arbitrary number of titrating protons n (eq 1):When using the DFT/COSMO method, E(A) and E(HA) are the “total”
energies of the geometry-optimized BS states (ε = 20), computed
with respect to a sum of atomic fragments (spin-restricted atoms).[75] Alternatively, ΔGdeprot is computed with the DFT/SCRF method using the total
free energies of the active site described by DFT plus the effects
of the protein/solvent environment, as obtained by a finite-difference
solution of the Poisson equation.[68]We approximate the difference in zero-point energy (ZPE) between
the protonated and deprotonated states, ΔZPE (eq 1), as the difference in ZPE upon deprotonation of all fragments
that are titrated (e.g., the carboxylate of E126, the C4–O(H) group of HMBPP, or the PP tail of HMBPP), obtained from OLYP frequency calculations performed
on the two protonation states of each individual fragment. These values
are computed to be −8.7, −10.4, and −8.8 kcal
mol–1 for E126, the HMBPP C4–O(H)
group, and the HMBPP PP moiety, respectively,
using the OLYP/STO-TZP level of theory.[50]In eq 1, ΔGref(H+) is the free energy associated with the titrated
proton(s), as defined by eq 2:In eq 2, the energy of a proton, E(H+), is 292.7 kcal mol–1, which is obtained
from an empirically corrected, gas-phase OLYP calculation with respect
to a spin-restricted hydrogen atom.[50,76,77] For ΔGsol(H+, 1 atm), the solvation free energy of a proton, we use the
value of −264.0 kcal mol–1, which is an experimental
value derived from analysis of cluster-ion solvation data.[78,79] The translational entropy of a proton, −TΔSgas(H+), is chosen
to be −7.76 kcal mol–1, its value computed
theoretically at 298 K and 1 atm.[80] The
final term in computing the free energy of the titrating proton, 5/2 RT (1.5 kcal mol–1), arises from the sum
of the proton translational energy (3/2 RT) and the
work term PV = RT.[78,80]Finally, the term ΔEcorr corrects ΔGdeprot for a neutral
solvent environment (pH = 7), equal to −2.303 × kBT × pH (equivalent to
−9.6 kcal mol–1 at pH 7). When multiple protons
are titrated, the number of protons exerts a multiplicative effect
on ΔGref(H+) and ΔEcorr, whereas if two states are tautomers, the
variable n in eq 1 is equal
to zero, and the difference in energy between states is only corrected
for ΔZPE.
Computing Reduction Potentials in the 1e– Reduced State
Reduction potentials are obtained
for the general process:All reduction potentials are obtained with respect to the
standard hydrogen potential (ΔSHE = −4.34 V),[51,78,81] computed in the absence of proton
coupling using eq 4:where IPred(ROXPYEZ) is the computed ionization potential that includes
solvent effects, obtained using either the DFT/COSMO or DFT/SCRF methods.[51]
Results
Geometries
in [4Fe–4S]1+ IspH with HMBPP Bound via C4–O(H)
Because protonation of the C4–O(H)
group is required for catalysis, we will focus most of our discussion
on the lowest-energy valence isomers computed for each protonation
state having HMBPP bound to the [4Fe–4S]1+ cluster
via its C4–OH group (i.e., ROH-bound states). Across
three different charge states for the active-site clusters, namely,
ROHP–E– ( = −4), ROHPHE– ( = −3),
and ROHPHEH ( = −2), the Fe1–OC4 distance increases
by ∼0.02–0.05 Å following 1e– reduction of the [4Fe–4S] cluster (Figure 3, Table 2). For instance,
in the oxidized state,[50] the Fe1–OC4 distance is 2.13 and 2.21 Å for the ROHPHE– and ROHPHEH states, respectively; however, these respective distances
become 2.15 and 2.26 Å following 1e– reduction of the [4Fe–4S] cluster (Table 2).
Figure 3
Optimized geometries of the lowest-energy ROH-bound states when
the [4Fe–4S] cluster is 1e– reduced with different total system charges: (a) ROHP–E–, = −4; (b) ROHPHE–, = −3; (c) ROHP–EH, = −3; (d) ROHPHEH, = −2.
Table 2
Geometric Parameters for the Lowest-Energy Valence
Isomers of Three Representative Protonation States when the [4Fe–4S]
Cluster Is Both Oxidized[50] and Reduced
by One Electron
ROHP–E–(ROH)
ROHPHE–(ROH)
ROHPHEH(ROH)
exp
ox
red
Δa
ox
red
Δa
ox
red
Δa
cluster bond lengths
Fe1–S5
2.344
2.218
2.227
0.01
2.215
2.272
0.06
2.209
2.251
0.04
Fe1–S6
2.393
2.301
2.313
0.01
2.298
2.290
–0.01
2.280
2.268
–0.01
Fe1–S7
2.364
2.328
2.338
0.01
2.317
2.319
0.00
2.313
2.325
0.01
Fe2–S5
2.217
2.323
2.304
–0.02
2.324
2.340
0.02
2.333
2.343
0.01
Fe2–S6
2.186
2.203
2.253
0.05
2.201
2.209
0.01
2.210
2.215
0.00
Fe2–S8
2.181
2.362
2.392
0.03
2.359
2.390
0.03
2.353
2.391
0.04
Fe3–S5
2.319
2.313
2.306
–0.01
2.317
2.333
0.02
2.305
2.333
0.03
Fe3–S7
2.281
2.236
2.299
0.06
2.237
2.255
0.02
2.238
2.255
0.02
Fe3–S8
2.306
2.357
2.358
0.00
2.350
2.372
0.02
2.360
2.382
0.02
Fe4–S6
2.308
2.314
2.325
0.01
2.319
2.308
–0.01
2.325
2.325
0.00
Fe4–S7
2.217
2.320
2.326
0.01
2.324
2.305
–0.02
2.326
2.310
–0.02
Fe4–S8
2.276
2.245
2.265
0.02
2.242
2.312
0.07
2.242
2.296
0.05
Fe2–SC12
2.283
2.263
2.312
0.05
2.258
2.314
0.06
2.257
2.311
0.05
Fe3–SC197
2.285
2.283
2.337
0.05
2.274
2.337
0.06
2.271
2.324
0.05
Fe4–SC96
2.264
2.295
2.357
0.06
2.290
2.348
0.06
2.291
2.353
0.06
HMBPP bond lengths
Fe1–OC4
2.046
2.108
2.161
0.05
2.133
2.148
0.01
2.254
2.282
0.03
Fe1–C3
3.039
3.627
3.639
0.01
3.551
3.629
0.08
3.399
3.431
0.03
Fe1–C2
2.913
3.267
3.306
0.04
3.266
3.310
0.04
3.220
3.241
0.02
HMBPP bond lengths
OC4–OT167
2.702
2.816
2.880
0.06
2.914
2.843
–0.07
3.179
3.161
–0.02
OT167–OE126
2.761
2.770
2.799
0.03
2.771
2.795
0.02
2.667
2.654
–0.01
OE126–OW1
2.578
3.133
3.131
0.00
2.907
3.051
0.14
3.711
3.740
0.03
OW1–OPPi
2.548
2.746
2.753
0.01
3.006
2.989
–0.02
2.836
2.841
0.01
OC4–OE126
3.526
4.337
4.473
0.14
4.358
4.472
0.11
4.200
4.155
–0.05
OC4–OPPi
4.782
4.958
4.970
0.01
4.890
4.944
0.05
4.874
4.861
–0.01
HMBPP angle
C2–C3–C4–OC4
2.046
–104.6
–103.7
0.9
–101.8
–103.7
–1.9
–99.1
–99.3
–0.2
The differences
in bond length (Å) or angle (deg) between the oxidized and 1e– reduced states are given under the
column labeled Δ.
Optimized geometries of the lowest-energy ROH-bound states when
the [4Fe–4S] cluster is 1e– reduced with different total system charges: (a) ROHP–E–, = −4; (b) ROHPHE–, = −3; (c) ROHP–EH, = −3; (d) ROHPHEH, = −2.The differences
in bond length (Å) or angle (deg) between the oxidized and 1e– reduced states are given under the
column labeled Δ.The Fe–S2– (iron–sulfide) bond lengths
are similar between the oxidized[50] and
1e– reduced geometries within the
same protonation state and valence isomer; however, all Fe–thiolate
distances are elongated by ∼0.05 Å in the 1e– reduced state (Table 2). Nevertheless, identically protonated, oxidized, and 1e– reduced geometries possess similar hydrogen-bond
networks and orientations of the second- and third-sphere ligands
(i.e., protein residues). These results lead to a maximum heavy atom
root-mean-square deviation (RMSD) of 0.12 Å over all heavy atoms
in the full quantum cluster. Additionally, there is little difference
in geometry for the different valence isomers of the same protonation
state when the [4Fe–4S] cluster is 1e– reduced (RMSD < 0.18 Å).While the results
from our geometric analysis focus on three representative protonation
states in the 1e– reduced state,
the other protonation states considered in this study show similar
geometry changes upon reduction (Supporting Information,
Table S1).
Distribution of Spin Density
and Charge in the Oxidized and 1e– Reduced States of IspH with HMBPP Bound to Fe1 through its C4–OH Group
By tracking net spin populations
(NSPs) using Mulliken analysis and the ESP partial charges using DFT/SCRF
calculations, we can better understand how the electronic structure
of the active-site quantum cluster changes following a 1e– reduction of the [4Fe–4S] cluster. For
a representative protonation state (e.g., ROHPHE–), we present the NSPs and ESP charges computed
for the lowest-energy valence isomers having the net spin on Fe1 aligned
either with (net spin-α) or opposite (net spin-β) the
overall net spin of the full active-site quantum cluster (STot = +1/2). In all RO(H)-bound protonation
states, the lowest-energy state having Fe1 net spin-α is the
αββα state; analogously, all lowest-energy
states with Fe1 net spin-β are βααβ
valence isomers (Supporting Information, Table
S4). The important physical distinction between these spin
isomers is that they are also different valence isomers. When one
adds an α-spin electron to the oxidized cluster, this process
is a minority spin addition for each Fe site with net-β spin
and has little effect on the net-α spin sites. This result follows
because all Fe sites are high-spin and have greater than (or equal
to) a half-filled Fe 3d shell in the starting oxidized state.NSPs and ESP charges for the ROHPHE– state are reported for the oxidized and 1e– reduced states of the [4Fe–4S] cluster in Tables 3 and 4, respectively. Additionally,
we report the changes in NSPs and ESP charges (ΔNSP and Δ, respectively) following from the 1e– reduction of the [4Fe–4S] cluster
to elucidate where the charge and spin density associated with the
reducing electron resides.
Table 3
NSPs Given for Atoms
in the [4Fe–4S] Cluster, Its Coordinating Thiolates, and HMBPP
from Two Representative Valence Isomers of the ROHPHE–(ROH) State When the [4Fe–4S] Cluster
Is Oxidized[50] and Reduced by One Electron
ROHPHE–(ROH)
αββα
βααβ
ox
red
ΔNSPa
ox
red
ΔNSPa
Fe1
3.241
3.324
0.083
–3.247
–3.032
0.215
Fe2
–3.174
–2.904
0.270
3.170
3.284
0.113
Fe3
–3.181
–3.112
0.069
3.196
3.316
0.120
Fe4
3.206
3.272
0.066
–3.212
–3.069
0.143
sum
0.092
0.580
0.488
–0.092
0.499
0.591
S1
–0.034
0.018
0.053
0.026
0.194
0.168
S2
0.084
0.270
0.186
–0.083
–0.016
0.067
S3
0.096
0.183
0.087
–0.093
–0.036
0.056
S4
–0.047
0.007
0.054
0.049
0.157
0.108
sum
0.099
0.478
0.379
–0.101
0.299
0.399
C12
–0.224
–0.106
0.118
0.224
0.161
–0.062
C96
0.199
0.137
–0.062
–0.198
–0.086
0.112
C197
–0.191
–0.111
0.080
0.192
0.134
–0.058
sum
–0.215
–0.080
0.135
0.218
0.210
–0.008
cluster
–0.024
0.978
1.002
0.025
1.007
0.982
OC4
0.019
0.012
–0.007
–0.019
–0.012
0.008
C3
0.003
0.001
–0.001
–0.003
–0.001
0.001
C2
0.000
0.002
0.001
0.000
0.002
0.002
HMBPP
0.023
0.016
–0.007
–0.023
–0.013
0.011
cluster + HMBPP
–0.001
0.994
0.995
0.002
0.994
0.993
The difference
in NSP (ΔNSP) between the oxidized and 1e– reduced atoms is indicated.
Table 4
ESP Charge Distributions Given for Atoms
in the [4Fe–4S] Cluster, Its Coordinating Thiolates, and HMBPP
from Two Representative Valence Isomers of the ROHPHE–(ROH) State When the [4Fe–4S] Cluster
Is Oxidized[50] and Reduced by One Electron
ROHPHE–(ROH)
αββα
βααβ
ox
red
Δqa
ox
red
Δqa
Fe1
0.527
0.549
0.022
0.515
0.516
0.001
Fe2
0.472
0.528
0.056
0.472
0.559
0.087
Fe3
0.548
0.617
0.069
0.575
0.698
0.123
Fe4
0.440
0.502
0.062
0.444
0.490
0.046
sum
1.987
2.196
0.209
2.007
2.263
0.257
S1
–0.491
–0.636
–0.145
–0.495
–0.678
–0.183
S2
–0.293
–0.362
–0.069
–0.278
–0.340
–0.062
S3
–0.348
–0.505
–0.156
–0.357
–0.514
–0.157
S4
–0.591
–0.798
–0.206
–0.605
–0.825
–0.220
sum
–1.724
–2.301
–0.577
–1.735
–2.357
–0.622
C12
–0.266
–0.413
–0.148
–0.261
–0.387
–0.125
C96
–0.332
–0.478
–0.146
–0.334
–0.499
–0.165
C197
–0.380
–0.539
–0.159
–0.404
–0.567
–0.162
sum
–0.977
–1.430
–0.452
–1.000
–1.453
–0.453
total cluster
–0.714
–1.534
–0.820
–0.728
–1.546
–0.817
OC4
–0.386
–0.412
–0.026
–0.388
–0.418
–0.030
C3
0.013
0.024
0.010
0.019
0.028
0.009
C2
–0.213
–0.237
–0.024
–0.241
–0.269
–0.029
total HMBPP
–0.296
–0.370
–0.075
–0.317
–0.418
–0.101
cluster + HMBPP
–1.010
–1.905
–0.895
–1.046
–1.964
–0.918
The difference
in charge (Δ) between the
oxidized and 1e– reduced atoms
is indicated.
The difference
in NSP (ΔNSP) between the oxidized and 1e– reduced atoms is indicated.The difference
in charge (Δ) between the
oxidized and 1e– reduced atoms
is indicated.In the ROHPHE–(ROH) αββα
1e– reduced state, Fe1 and Fe4
(numbering illustrated in Figure 2) have NSPs
of +3.32 and +3.27, respectively, which is slightly more positive
than their respective values of +3.24 and +3.21 in the oxidized state
(Table 3). In contrast, Fe2 and Fe3 have spin
densities of −2.90 and −3.11 in the 1e– reduced state—values that are significantly
more positive than their corresponding values in the oxidized state
(−3.17 and −3.18, respectively). The net spin-β
Fe2–Fe3 pair has site NSPs that are reduced in magnitude relative
to Fe1 and Fe4, because the spin-α electron added in the broken-symmetry
scheme falls largely on Fe2 and Fe3. The magnitudes of these site
NSPs support the formal assignment of the Fe1–Fe4 spin-coupled
pair as being a delocalized, mixed-valence pair (S = +9/2), whereas Fe2 and Fe3 form a ferrous pair (S = −8/2). Comparing the NSPs summed over all Fe atoms in the
ROHPHE– αββα
1e– reduced state relative to the
ROHPHE– αββα
oxidized state, it is evident that approximately half of the reducing
electron spin density falls on the Fe atoms (ΔNSP = 0.49, Table 3). The remaining reducing net-α spin density
indicates there is significant Fe–S covalency in the system;
indeed, the cluster sulfides give a ΔNSP of +0.38, and the cluster
thiolates give a ΔNSP of +0.14 (Table 3).In both the oxidized and 1e– reduced states, it is apparent that each thiolate possesses significant
net spin density that is aligned with the majority spin density on
the iron to which it is coordinated. For instance, C12 (Cys12) is
attached to Fe2, which has NSPs of −3.17 and −2.90 in
the oxidized and 1e– reduced states,
respectively. When the [4Fe–4S] cluster is oxidized, C12 possesses
an NSP of −0.22, which shifts to −0.11 (decreases in
magnitude) following 1e– reduction
of the [4Fe–4S] cluster (Table 3). In
both the oxidized and 1e– reduced
states, the NSP of C12 is aligned with that on Fe2, and the shift
in the NSP accompanying reduction indicates that the electron density
on the Fe2–Fe3 pair decreases the spin and (negative) charge
transfer from C12 and C197 to the ferrous Fe2–Fe3 pair. This
result is analogous to the mixed-valence Fe2–Fe3 pair in the
oxidized cluster.In the ROHPHE– αββα state, there is very little spin density
on HMBPP in either the oxidized or 1e– reduced state (both having NSPs of 0.02). Consequently, nearly all
of the spin density associated with the reducing electron (net-α)
is localized on the [4Fe–4S] cluster and is involved in bonds
to the cysteine side chains.In the ROHPHE–(ROH) βααβ 1e– reduced state, Fe1 and Fe4 couple with lower
magnitude net spins (−3.03 and −3.07, respectively,
for the ROHPHE– state) than
Fe2 and Fe3 (+3.28 and +3.32, respectively; Table 3). Analogous to the αββα states, these
NSPs indicate that Fe1 and Fe4 form a Fe2+–Fe2+ pair, whereas Fe2 and Fe3 formally correspond to a delocalized,
mixed-valence pair (Fe2.5+–Fe2.5+). In
all βααβ states, and much like the αββα
states, most of the reducing net-α spin is localized on the
[4Fe–4S] cluster and the coordinating thiolates (total ΔNSP
= +0.98), and there is little net spin localized to HMBPP (ΔNSP
= +0.01, Table 3).Similar trends in
spin density distributions, including a dependence on the net spin
of Fe1, are observed for all other protonation states considered for
the system that is reduced by one electron when HMBPP coordinates
Fe1 through its C4–O(H) group (Supporting Information, Table S2).The charge distribution
in the ROHPHE–(ROH) βααβ
state is nearly identical to that of the αββα
for both the oxidized and 1e– reduced
states (Table 4). Furthermore, ESP charges
on the [4Fe–4S] cluster and HMBPP are largely similar among
all valence isomers for a given protonation state (RMSDs < 0.03),
indicating that charge distributions have less dependence on a given
valence isomer. The effects of charge transfer are directly observed,
specifically, the charges on the irons, inorganic sulfides, thiolates,
and ligand molecule in the ROHPHE– oxidized and 1e– reduced states.
In particular, the partial charges on all Fe atoms slightly increase
(i.e., become more positive) upon 1e– reduction, whereas the inorganic sulfides, thiolates, and ligand
molecule all become more negative. In the ROHPHE– αββα and βααβ
states, the sum of the partial charges on the Fe atoms increases by
0.21 and 0.26, respectively, whereas the sum of the partial charges
on the S2– and thiolate groups decrease (i.e., become
more negative) by 1.03 and 1.08, respectively (Table 4, Δ). From these
values, it is apparent that ∼0.82 e– charge is transferred to the [4Fe–4S] cluster and its coordinating
thiolates following 1e– reduction
of the cluster. The net charge of HMBPP changes less upon reduction,
becoming only 0.08–0.10 e– more negative in the ROHPHE– αββα and βααβ states.
The remaining difference in charge between the oxidized and reduced
states is transferred to various groups that donate hydrogen bonds
either to the [4Fe–4S] cluster or to the imidizolium groups
of H41 and H74 that coordinate HMBPP. Consequently, we find that most
of the reducing electron charge in the RO(H)-bound states is localized
on the [4Fe–4S] cluster and HMBPP molecule, with large amounts
of charge transfer occurring between the cluster irons and their coordinating
sulfides and ligands. ESP charges obtained for the lowest-energy valence
isomers of all other protonation states considered when HMBPP binds
Fe1 through its C4–OH group are presented in Supporting Information, Table S3.
Relative Energies of the ROH-Bound 1e– Reduced
States
To assess which protonation state is favored in the
1e– reduced state, we apply eq 1 to obtain the relative energies of the various RO(H)-bound
states considered, using both COSMO solvation with ε = 20 (DFT/COSMO)
and a finite difference solution to the Poisson equation for the active-site
quantum cluster embedded in the IspH protein (DFT/SCRF). The energies
of the lowest-energy valence isomer for each protonation state considered
along with their corresponding relative energies in the oxidized state
are given in Table 5.[50] Energies for all other valence isomers considered are tabulated
in the Supporting Material (Table S4).
Table 5
Relative Energies (kcal mol–1) of
the Different RO(H)-Bound States Considered in This Study When the
[4Fe–4S] Is Oxidized[50] and Reduced
by One Electron
oxidizeda
reduceda
state (charge)
qox/qred
DFT/COSMO
DFT/SCRF
DFT/COSMO
DFT/SCRF
RO–P–EH (RO–)
–3/–4
7.9
0.0
29.5
13.0
RO–PHEH (RO–)
–2/–3
0.0
2.2
16.6
10.3
ROHP–E– (ROH)
–3/–4
8.4
0.0
17.6
4.1
ROHPHE– (ROH)
–2/–3
5.3
6.1
5.8
0.0
ROHP–EH (ROH)
–2/–3
2.9
5.5
5.3
0.3
ROHPHEH (ROH)
–1/–2
0.0
13.3
0.0
4.5
Energies are given relative to the
lowest-energy state and are presented only for the lowest-energy valence
isomer for each protonation state. The relative energies of all valence
isomers are given in Supporting Information, Table
S4.
Energies are given relative to the
lowest-energy state and are presented only for the lowest-energy valence
isomer for each protonation state. The relative energies of all valence
isomers are given in Supporting Information, Table
S4.Using the DFT/COSMO
method, the lowest-energy 1e– reduced
state computed at pH = 7 is the ROHPHEH state with a net charge () of
−2. The ROHP–EH and
ROHPHE– states (both = −3) are higher in energy than
the ROHPHEH state by 5.3 and 5.8
kcal mol–1, respectively. In contrast, the structure
in which both the PP and E126 groups
are deprotonated and the C4–O(H) group is protonated
( = −4) is highly unfavorable.
This so-called ROHP–E– state lies 17.6 kcal mol–1 higher in energy than
the ROHPHEH state. All states having
HMBPP bound to Fe1 through a deprotonated C4–O(H)
group are significantly higher in energy than their ROH-bound counterparts
(>15 kcal mol–1 above the energy of the ROHPHEH state, Table 5).The ROHPHE– state
is lowest in energy using the DFT/SCRF method, but it is only 0.3
kcal mol–1 lower in energy than the ROHP–EH state. The proximity in energy
between these isoelectric ( = −3)
tautomers suggests that proton transfer between the PP and E126 groups is facile. The ROHP–E– ( = −4) and ROHPHEH ( = −2) states are higher in energy
than the ROHPHE– state by
4.1 and 4.5 kcal mol–1, respectively. Similar to
what is observed with the DFT/COSMO method, the RO–PHEH and RO–P–EH states are the highest-energy 1e– reduced states computed with the DFT/SCRF method,
which lie 10.3 and 13.0 kcal mol–1 above the ROHPHE– state, respectively.The two lowest-energy states found using the DFT/SCRF method, namely,
ROHPHE–(ROH) and ROHP–EH(ROH), both have a total charge
of −3 and are thus more negatively charged than the active
site preferentially stabilized by the DFT/COSMO method (ROHPHEH, q = −2). The
stabilization of 1e– reduced states
having q = −3 by the DFT/SCRF method is consistent
with the results obtained for active-site models of oxidized IspH,
where the RO–P–EH and
ROHP–E– states (both
having q = −3) are preferred energetically
(Table 5, column 4).
Reduction
Potentials of the C4–OH Bound States
All
reduction potentials are tabulated in Table 6 for processes where an electron is added to an oxidized state that
has HMBPP bound to Fe1 through its C4–O(H) group.
It will be recalled that all reduction potentials are computed relative
to the standard hydrogen electrode (ΔSHE, eq 4). Using the DFT/COSMO method, it is clear that the addition
of an electron to states having a deprotonated C4–O(H)
group is very unfavorable in the absence of proton coupling, as E° = −2.39 and −2.14 V for the RO–P–EH(ROH) and RO–PHEH(RO–) states, respectively
(Table 6). The reduction potentials obtained
with the DFT/COSMO method for the ROH-bound states are also very negative
but increase (i.e., shift toward positive values) as the number of
bound protons increases. For comparison, reduction of the ROHP–E–(ROH) state (q = −3/–4 for oxidized/reduced states) can be achieved
with a reduction potential of −1.82 V, whereas the reduction
potential for the ROHPHEH(ROH) state
(q = −1/–2 for oxidized/reduced states)
is −1.42 V. The lowest reduction potential calculated using
the DFT/COSMO method is found for the ROHPHEH state.
Table 6
Reduction
Potentials (E°, V) Computed for RO(H)-Bound
States. When Applicable, Redox Potentials Coupled to Proton Transfer
(E°′, V) Are Indicated in Parentheses
state
DFT/COSMO
DFT/SCRF
RO–P–EH(RO–)
–2.39
–1.86 (−1.29)a
RO–PHEH(RO–)
–2.14 (−1.42)
–1.64 (−1.19)c
ROHP–E–(ROH)
–1.82
–1.47 (−1.29)b
ROHPHE–(ROH)
–1.44
–1.03
ROHP–EH(ROH)
–1.52
–1.07 (−1.06)c
ROHPHEH(ROH)
–1.42
–0.91c
Electron transfer accompanies proton addition and a proton shift
to generate the ROHPHE–(ROH)
1e– reduced state.
Electron transfer accompanies proton
addition to generate the ROHPHEH(ROH)
1e– reduced state.
Electron transfer accompanies an internal
proton transfer to generate the ROHPHE–(ROH) 1e– reduced state.
Electron transfer accompanies proton addition and a proton shift
to generate the ROHPHE–(ROH)
1e– reduced state.Electron transfer accompanies proton
addition to generate the ROHPHEH(ROH)
1e– reduced state.Electron transfer accompanies an internal
proton transfer to generate the ROHPHE–(ROH) 1e– reduced state.Using the DFT/COSMO method, we found
that the RO–PHEH and ROHPHEH states are isoenergetic and of
lowest energy when the [4Fe–4S] cluster is oxidized, whereas
the ROHPHEH state is the lowest-energy
1e– reduced state. Reduction can
thus occur in one of three thermodynamically equivalent processes:
(1) reduction via the RO–PHEH protonation state (E° = −2.14 V), followed
by protonation of the C4–O(H) group in the 1e– reduced state (ΔE = −16.6 kcal mol–1); (2) protonation of
the C4–O(H) group in the oxidized state that requires
1.6 kcal mol–1, followed by reduction through the
ROHPHEH state (E° = −1.42 V); or (3) proton-coupled electron transfer
(following eq 5), which gives an effective reduction
potential of E°′ = −1.42 V (calculated
from eq 6).Regardless of the path taken, all reduction
potentials calculated with the DFT/COSMO method for states having
HMBPP bound to Fe1 through its C4–O(H) group are
too negative, lying outside the range expected for [4Fe–4S]
ferredoxin (Fdx) proteins (−700 to −280 mV).[51,82]All reduction potentials computed in the absence of proton
coupling with the DFT/SCRF method are shifted by 0.35–0.55
V in the positive direction relative to those obtained with the DFT/COSMO
method (Table 6). For example, the reduction
potentials obtained with DFT/SCRF for the ROHP–E– and ROHPHEH states are −1.47 and −0.91 V, respectively, which
we can see are more positive than their analogous values of −1.82
and −1.42 V obtained with DFT/COSMO. Although the reduction
potential obtained for the addition of an electron to the ROHPHEH state is closer to the expected range
for [4Fe–4S] Fdx proteins,[51,82] the ROHPHEH state is 13.3 kcal mol–1 above the lowest-energy ROHP–E– and RO–P–EH states when the [4Fe–4S] cluster is oxidized. This
energy barrier, which is obtained using the DFT/SCRF method, likely
prohibits reduction of the ROHPHEH state. The more likely candidate for reduction in the absence of
proton coupling is the ROHPHE– state, which can be reached following protonation of the ROHP–E– oxidized state at
a cost of 6.1 kcal mol–1 and reduction at E° = −1.03 V (Tables 5 and 6).Since the protonation states
of the lowest-energy oxidized states (i.e., ROHP–E– and RO–P–EH) and the lowest-energy 1e– reduced state (i.e., ROHPHE–) differ by a single proton using the DFT/SCRF method, the addition
of an electron to the system may be coupled to protonation of one
of the active-site residues. Starting from the ROHP–E– oxidized state, coupling reduction
to the protonation of the PP moiety (eqs 7 and 8) gives an effective
reduction potential of E°′ = −1.29
V, which is positively shifted by 0.18 V relative to its uncoupled
reduction potential. Alternatively, protonation of the PP moiety in the RO–P–EH oxidized state, which requires 2.2 kcal mol–1, can precede reduction and coupled to an internal proton transfer
from E126 to the C4–O(H) group (eqs 9 and 10, E°′
= −1.19 V).While both the reduction potentials
and effective reduction potentials that consider proton coupling indicate
that reduction is more favorable when the energies used to compute
the reduction potentials are calculated with the DFT/SCRF method,
rather than the DFT/COSMO method, all relevant reduction potentials
obtained using the DFT/SCRF method are still more negative than the
typical values associated with [4Fe–4S] Fdx proteins.[51,82] This conclusion leads us to consider alternative routes for the
one-electron reduction of the IspH active site.
Geometries of [4Fe–4S]1+ IspH with HMBPP Bound
via C2 and C3 (η2-Complex)
In addition to the mechanism involving RO(H)-bound intermediates
in the reduction of IspH, we performed geometry optimizations of 1e– reduced states that are consistent
with the organometallic mechanism,[26] which
have HMBPP coordinate Fe1 through its olefinic C2 and C3 atoms (η2-binding). The starting points
for these computations are generated by rotating the C2–C3–C4–OH dihedral angle
(henceforth referred to as ϕ) from its C4–O(H)
bound value, which ranges from −105 to −95° in
all 1e– reduced RO(H)-bound optimized
geometries, to values of either ca. +100° (Figure 4A,B) or −160° (Figure 4C,D). When ϕ ≈ +100°, the HMBPP C4–OH
group is fully rotated away from the [4Fe–4S] cluster, forming
a ring conformation in which it participates in (charged) hydrogen-bond
interactions with the PP tail of HMBPP
(Figure 4A,B). This conformation is similar
both to the minor species observed in the X-ray crystal structure
of the [4Fe–4S] IspH:HMBPP complex after irradiation and to
various [3Fe–4S] mutants in complex with HMBPP.[36] When ϕ ≈ −160°, the
C4–OH group is rotated under the plane of the [4Fe–4S]
cluster and assumes a trans-like conformation that allows the C4–OH group to form a hydrogen bond with the carboxylate
of E126 (Figure 4C,D). Geometry optimizations
of both the “ring” and “trans” η2-bound states (henceforth referred to as η2-ring and η2-trans) reveal two distinct energy minima
when the C4–O(H) group is protonated: (1) a weak
complex in which the olefinic C2 and C3 atoms
are ∼2.5–2.8 Å from Fe1, and (2) a tight coordination
in which the C2 and C3 atom are close to Fe1
(with Fe1–C distances of ∼2.1 Å). In cases where
the C4–O(H) group is deprotonated, no local minima
corresponding to η2-bound states are present.
Figure 4
Optimized geometries
of the lowest-energy η2-bound states computed with
DFT/SCRF when the [4Fe–4S] cluster is 1e– reduced. For comparison, the lowest-energy valence
isomers having Fe1 net spin-α and net spin-β are considered.
(A) The ROHP–EH(η2-ring) ααββ state; (B) the ROHP–EH(η2-ring)
βααβ state; (C) the ROHP–EH(η2-trans) ααββ
state; (D) the ROHP–EH(η2-trans) βααβ state.
Optimized geometries
of the lowest-energy η2-bound states computed with
DFT/SCRF when the [4Fe–4S] cluster is 1e– reduced. For comparison, the lowest-energy valence
isomers having Fe1 net spin-α and net spin-β are considered.
(A) The ROHP–EH(η2-ring) ααββ state; (B) the ROHP–EH(η2-ring)
βααβ state; (C) the ROHP–EH(η2-trans) ααββ
state; (D) the ROHP–EH(η2-trans) βααβ state.To illustrate the characteristics of the computed
η2-bound geometries, we use the ROHP–EH protonation state as a representative
case (Table 7, Figure 4), with particular consideration given to valence isomers having
different net spins on Fe1. In the optimized geometry of the ROHP–EH(η2-ring)
ααββ valence isomer, ϕ is equal to +95.2°,
which is rotated over 180° from its value when HMBPP is bound
through its C4–OH group (−101.4°, Table 7). The Fe1–OC4 bond is broken
in the η2-ring state, as the C4–OH
group is displaced >2 Å from Fe1. However, the olefinicHMBPP
atoms, namely, C2 and C3, weakly coordinate
Fe1, with Fe1–C2/C3 distances of ∼2.5
Å (Figure 4A). These distances suggest
that the complex is stabilized mainly through weak interactions between
Fe1 and the olefin, and these interactions are enhanced relative to
those present in RO(H)-bound states.[35] With
an OC4–OPPi distance of 2.68 Å,
a charged hydrogen bond between the C4–OH group
and the HMBPP PP group further stabilizes
the ααββ η2-ring conformation
(Figure 4A, Table 7).
In addition to this HMBPP intramolecular hydrogen bond, the hydrogen-bond
network observed in the ROHP–EH(ROH) state (Figure 3C) is largely preserved
in the ααββ η2-ring state:
E126 donates a hydrogen bond to T167, which directs the proton from
its side chain OH group toward the cluster sulfide S3 atom (Table 7, Figure 4A). The internal
geometry of the 1e– reduced [4Fe–4S]1+ cluster in the ROHP–EH(η2-ring) ααββ state is
quite similar to that of the ROHP–EH(ROH) ααββ state, with cluster bond
lengths from the two states giving an RMSD value of 0.02 Å. Despite
this similarity, a superposition of the two states reveals that the
position of the [4Fe–4S] cluster in the ROHP–EH(η2-ring) ααββ
state is shifted down toward the HMBPP olefin group relative to its
position in the ROHP–EH(ROH)
ααββ state (Supporting
Information, Figure S1). In other words, the position of HMBPP
in the ROHP–EH(ROH) ααββ
state is largely unchanged from that in the ROHP–EH(η2-ring) ααββ
state. For the η2 interaction to exist, the [4Fe–4S]
cluster must translate toward HMBPP to bring Fe1 in proximity of the
olefin (Figure S1).
Table 7
A Comparison of Key Bond Lengths (Å) and Angles (deg) between
the ROH- and η2-Bound Structures in the 1e– Reduced ROHP–EH State
binding mode
ROH
η2-ring
η2-trans
valence isomer
ααββ
βααβ
ααββ
βααβ
ααββ
βααβ
cluster bond lengths
Fe1–S1
2.282
2.245
2.307
2.285
2.309
2.289
Fe1–S2
2.279
2.267
2.284
2.291
2.279
2.299
Fe1–S3
2.229
2.324
2.241
2.384
2.238
2.375
Fe2–S1
2.336
2.333
2.330
2.316
2.332
2.321
Fe2–S2
2.298
2.213
2.302
2.194
2.307
2.200
Fe2–S4
2.283
2.395
2.270
2.373
2.277
2.370
Fe3–S1
2.260
2.328
2.248
2.311
2.250
2.313
Fe3–S3
2.312
2.258
2.340
2.271
2.331
2.259
Fe3–S4
2.368
2.382
2.362
2.367
2.364
2.366
Fe4–S2
2.272
2.321
2.270
2.312
2.273
2.316
Fe4–S3
2.314
2.307
2.332
2.307
2.327
2.302
Fe4–S4
2.339
2.301
2.343
2.246
2.343
2.252
Fe2–SC13
2.335
2.309
2.310
2.285
2.314
2.292
Fe3–SC197
2.297
2.330
2.300
2.364
2.302
2.356
Fe4–SC96
2.337
2.356
2.295
2.314
2.297
2.315
HMBPP bond lengths
Fe1–OC4
2.340
2.257
4.552
4.287
3.751
3.593
Fe1–C3
3.363
3.304
2.541
2.144
2.615
2.143
Fe1–C2
3.603
3.573
2.496
2.118
2.531
2.112
H-bond lengths
OC4–OT167
3.178
3.174
4.397
4.384
3.424
3.370
OT167–OE126
2.653
2.649
2.693
2.687
2.655
2.634
OE126–OW1
3.686
3.677
3.733
3.598
3.687
3.633
OW1–OPPi
2.730
2.734
2.782
2.774
2.732
2.723
OC4–OE126
4.156
4.154
3.620
3.621
3.149
3.137
OC4–OPPi
4.838
4.852
2.683
2.722
4.541
4.593
HMBPP angle
C2–C3–C4–OC4
–101.4
–101.9
95.2
90.3
–154.8
–158.4
The orientation of
HMBPP in the IspH active site observed in the ROHP–EH(η2-ring) βααβ
state is largely similar to that observed in the ααββ
valence isomer, although the olefinic C2 and C3 atoms bind Fe1 more tightly in the βααβ
valence isomer (with respective bond lengths of 2.12 and 2.14 Å).
Relative to the ROHP–EH(ROH)
βααβ state, the geometry of the [4Fe–4S]
cluster in the ROHP–EH(η2-ring) state is distorted at Fe1: all Fe1–S2– distances are elongated 0.03 to 0.06 Å (Table 7). In particular, the Fe1–S3 bond is lengthened in
the ROHP–EH(η2-ring) βααβ state (2.38 Å) compared
with its ROH-bound counterpart (2.32 Å). This distortion of the
[4Fe–4S] cluster allows for a closer interaction between Fe1
and C2/C3, as well as better interaction between the −OH group
of T167 and the cluster sulfide S3. Distances between hydrogen bond
partners in the ROHP–EH(η2-ring) βααβ state are nearly identical
to those in the ROHP–EH(η2-ring) ααββ state; consequently, the
“tight” and “loose” η2-complexes observed in these respective states appear to differ only
in the position of the [4Fe–4S] cluster and in the local environment
of the Fe1–C2/C3 bonds.In geometry-optimized
η2-trans states, the HMBPP C4–OH
group is rotated under the plane of the [4Fe–4S]1+ cluster (Figure 4C,D). This η2-trans conformation involves a rotation of ϕ by ca. −50°
from its ROH-bound value to give ϕ = −154.8° and
−158.4° in the ROHP–EH(η2-ring) ααββ and
βααβ states, respectively. In η2-trans states, the C4–OH group does not
accept a hydrogen bond from T167 as is observed in the ROH-bound state;
instead, T167 forms a hydrogen bond with the carboxylate of E126 (OC4–OE126 distance of ∼3.15 Å,
Table 7). Similar to the ROHP–EH(η2-ring) ααββ
state, the C2 and C3 atoms form a weak van der
Waals complex with Fe1 in the ROHP–EH(η2-trans) ααββ valence
isomer (Fe1–C2/C3 distance of ∼2.55 Å). Alternatively,
the olefinicHMBPP atoms in the ROHP–EH(η2-trans) βααβ
state tightly coordinate Fe1 (Fe–C distances of ∼2.1
Å), which is similar to what is observed in the ROHP–EH(η2-ring) βααβ
state (Table 7).Although our discussion
has focused on the ROHP–EH state as a representative protonation state, similar η2-ring and η2-trans geometries are also observed
for the ROHPHEH protonation state
(Supporting Information). We note that
η2-bound states having a deprotonated E126 group
are significantly higher in energy than their protonated counterparts;
for this reason, we omit them from further discussion.
Distribution of Charge and Spin in [4Fe–4S]1+ IspH
with HMBPP η2-Complex
From the geometric
data obtained for the η2-bound states, it is apparent
that two possible orientations of the C2–C3–C4–OH dihedral angle exist: η2-ring and η2-trans. The strength of Fe1–C2/C3 coordination, however, depends only on the
spin isomer considered and is independent of whether the geometry
is η2-ring or η2-trans. An inspection
of the Mulliken spin populations on the Fe atoms in these different
η2-bound states shows that there is correlation between
the alignment of the net spin on Fe1 and the Fe1–C2/C3 distances. Specifically, when the net spin on Fe1
is aligned with the system net spin STot = +1/2, as is the case with the ααββ and
αββα valence isomers, the observed η2-bound geometries have elongated Fe1–C2/C3 distances. In contrast, when Fe1 possesses
a net spin-β and is thus aligned opposite to STot (e.g., the βααβ and βαβα
valence isomers), the Fe1–C2/C3 distances are much shorter (Table 7).We consider the ROHP–EH states
as representative cases for comparing the NSPs and partial charges
in the η2-ring and ROH-bound states following reduction
(Tables 8 and 9). Specifically,
we track the dependence of these electronic properties on the net
spin of Fe1 by considering the αββα and βααβ
states. In the ROHP–EH(η2-ring) αββα state, Fe1 possesses a
net spin-α. This Fe atom has an NSP of +3.17 and couples with
Fe4 (NSP = +3.30) to form a delocalized, mixed-valence (Fe 2.5+ −Fe 2.5+) pair. The Fe2–Fe3 spin pair
carries reduced (in magnitude) NSPs of −3.00 and −2.88,
which are characteristic of a ferrous pair (Table 8). From summing the NSPs of the Fe atoms in the ROHP–E H(η2-ring) αββα
state, it is evident that most of the system’s net spin falls
on the [4Fe–4S] cluster iron atoms (+0.59). Significant spin
density is also found on the cluster sulfides (+0.44) and thiolates
(−0.07). Similar to what is observed in the ROH-bound states,
however, there is little spin density found on HMBPP (+0.02, Table
8).
Table 8
NSPs Given for Atoms
in the [4Fe–4S] Cluster, Its Coordinating Thiolates, and HMBPP
from Two Representative Valence Isomers of the ROHP–EH(η2-ring) State When
the [4Fe–4S] Cluster Reduced by One Electron Compared with
the NSPs from the Same Valence Isomers in the ROHP–EH(ROH) State When the [4Fe–4S] Cluster
Is Oxidized
ROHP–EH
αββα
βααβ
ox (ROH)
red (η2-ring)
ΔNSPa
ox (ROH)
red (η2-ring)
ΔNSPa
FE1
3.205
3.173
–0.032
–3.206
–2.879
0.327
FE2
–3.175
–3.000
0.175
3.174
3.204
0.030
FE3
–3.197
–2.880
0.317
3.195
3.328
0.132
FE4
3.222
3.297
0.075
–3.222
–3.194
0.029
sum
0.055
0.590
0.535
–0.059
0.459
0.519
S1
–0.013
0.050
0.062
0.014
0.218
0.204
S2
0.086
0.160
0.074
–0.085
–0.036
0.049
S3
0.101
0.220
0.119
–0.101
–0.022
0.079
S4
–0.037
0.014
0.052
0.038
0.048
0.009
sum
0.137
0.443
0.306
–0.133
0.208
0.341
C12
–0.233
–0.119
0.114
0.233
0.187
–0.046
C96
0.207
0.143
–0.064
–0.207
–0.145
0.062
C197
–0.185
–0.092
0.093
0.185
0.137
–0.048
sum
–0.211
–0.068
0.143
0.212
0.179
–0.033
total cluster
–0.019
0.965
0.984
0.019
0.846
0.827
OC4
0.013
0.006
–0.007
–0.013
0.003
0.015
C3
0.002
0.011
0.008
–0.002
0.055
0.058
C2
0.000
0.001
0.001
0.000
0.109
0.109
total HMBPP
0.019
0.020
0.001
–0.019
0.155
0.174
cluster + HMBPP
–0.001
0.985
0.985
0.000
1.000
1.001
The difference in NSP (ΔNSP) between the oxidized and 1e– reduced atoms is indicated.
Table 9
ESP Charges Given
for Atoms in the [4Fe–4S] Cluster, Its Coordinating Thiolates,
and HMBPP from Two Representative Valence Isomers of the ROHP–EH(η2-ring) State
When the [4Fe–4S] Cluster Reduced by One Electron Compared
with the Charges from the Same Valence Isomers in the ROHP–EH(ROH) State When the [4Fe–4S]
Cluster Is Oxidized[50]
ROHP–EH
αββα
βααβ
ox
red (η2-ring)
Δqa
ox
red (η2-ring)
Δqa
FE1
0.404
0.373
–0.030
0.404
0.307
–0.097
FE2
0.490
0.533
0.043
0.491
0.512
0.021
FE3
0.599
0.645
0.045
0.599
0.692
0.093
FE4
0.477
0.515
0.038
0.477
0.494
0.018
sum
1.969
2.065
0.096
1.970
2.005
0.035
S1
–0.440
–0.583
–0.143
–0.440
–0.592
–0.152
S2
–0.302
–0.328
–0.026
–0.302
–0.267
0.035
S3
–0.412
–0.597
–0.186
–0.412
–0.570
–0.158
S4
–0.600
–0.740
–0.140
–0.600
–0.691
–0.091
sum
–1.753
–2.248
–0.495
–1.754
–2.119
–0.365
C12
–0.267
–0.396
–0.129
–0.268
–0.346
–0.078
C96
–0.332
–0.434
–0.102
–0.332
–0.398
–0.066
C197
–0.393
–0.486
–0.093
–0.393
–0.460
–0.068
sum
–0.993
–1.316
–0.324
–0.993
–1.205
–0.212
total cluster
–0.777
–1.499
–0.723
–0.777
–1.319
–0.542
OC4
–0.119
–0.309
–0.189
–0.119
–0.328
–0.209
C3
–0.036
–0.016
0.020
–0.035
–0.038
–0.003
C2
–0.142
0.049
0.191
–0.142
0.068
0.210
total HMBPP
–0.430
–0.636
–0.205
–0.430
–0.784
–0.354
cluster + HMBPP
–1.207
–2.135
–0.928
–1.207
–2.103
–0.896
The difference
in charge (Δq) between the oxidized and 1e– reduced atoms is indicated.
The difference in NSP (ΔNSP) between the oxidized and 1e– reduced atoms is indicated.The difference
in charge (Δq) between the oxidized and 1e– reduced atoms is indicated.From a direct comparison between
the NSPs computed for the oxidized ROHP–EH(ROH) αββα state and the 1e– reduced ROHP–EH(η2-ring) αββα
state (ΔNSP, Table 8), it is clear that
the reducing electron is almost entirely localized on the [4Fe–4S]
cluster and its coordinating thiolates (ΔNSP ≈ 0.98)
and not on HMBPP (ΔNSP < 0.01).The distribution of
spin densities in the 1e– reduced
ROHP–EH(η2-ring) βααβ state differs from the αββα
valence isomer in the amount of spin density localized on the [4Fe–4S]
cluster and HMBPP. In the 1e– reduced
ROHP–EH(η2-ring) βααβ state, Fe2 and Fe3 couple with
NSPs that are larger in magnitude (+3.20 and +3.33, respectively)
than either member of the Fe1–Fe4 spin-coupled ferrous pair
(−2.88 and −3.19, respectively). The NSPs summed over
all iron atoms is +0.46, which is ∼0.1 less than what is observed
for the αββα state (Table 8). Spin density found on the cluster sulfides (+0.21) and
thiolates (+0.18) in the βααβ valence isomer
do not compensate for the lower spin density found on the iron atoms
relative to what is observed in the αββα valence
isomer. Instead, HMBPP has a total NSP of 0.16 in the ROHP–EH(η2-ring) βααβ
state, which is indicative of majority (α) spin transfer from
the [4Fe–4S] cluster to HMBPP. This spin, which is parallel
to the system net spin (STot = +1/2) but
opposite to the net spin on Fe1 (β), is largely localized on
the olefinic C2 and C3 atoms (+0.11 and +0.06,
respectively; Table 8).The greater net
spin density found on HMBPP in the βααβ valence
isomer is also accompanied by higher negative charge localized on
HMBPP (Table 9). In the 1e– reduced ROHP–EH(η2-ring) αββα and
βααβ states, the total charge summed over
the [4Fe–4S] cluster, its coordinating thiolates and HMBPP
are nearly equivalent (−2.14 and −2.10, respectively,
Table 9). However, the distribution of charge
on these different groups depends on the valence isomer. For example,
the charge on the [4Fe–4S] cluster and its coordinating thiolates
is −1.50 in the αββα isomer, whereas
the charge on HMBPP is −0.64 (Table 9). In contrast, the βααβ isomer possesses
less negative charge on its [4Fe–4S] cluster and coordinating
thiolates (q = −1.32); however, significantly
more charge is found on the HMBPP ligand (q = −0.78,
Table 9).Combining the geometric analyses
of 1e– reduced ROHP–EH(η2-ring) states with
a tabulation of their NSPs and ESP charge distributions, it is clear
that the alignment of the net spin on Fe1 correlates with the type
of coordination of HMBPP and the amount of spin and charge transfer
from the [4Fe–4S] cluster to the ligand. When the net spin
of Fe1 (α) is aligned with the total spin of the system (α),
the HMBPP olefin coordinates Fe1 loosely, and very little spin density
is transferred to HMBPP. In contrast, when the net spin of Fe1 (β)
is aligned opposite the system net spin (α), the HMBPP olefin
forms a tight, metallacycle complex with Fe1 and significant α
spin density, and relatively more charge is transferred to HMBPP.
Similar trends in geometry, NSPs, and charge distributions are observed
for the ROHPHEH protonation state
and η2 -trans states (Supporting
Information, Tables S6 and S7).
Relative
Energies of the η2-Bound 1e– Reduced
States
The relative energies of the different η2-bound states in the 1e– reduced state are computed to further understand differences between
the tightly-bound complexes found when Fe1 possesses a net spin-β
(e.g., the βααβ valence isomer) and the loosely-bound
complexes found when Fe1 possesses a net spin-α (e.g., the ααββ
valence isomer). Considering only the lowest-energy valence isomers
having Fe1 with either net spin-α or net spin-β, we examine
the relative energies of the 1e– reduced ROHP–EH(η2-ring) state. Using the DFT/COSMO method, the βααβ
valence isomer is 7.8 kcal mol–1 lower in energy
than the ααββ state (Supporting
Information, Table S8). Similarly, using the DFT/SCRF method,
the ROHP–EH(η2-ring) βααβ state is 8.8 kcal mol–1 lower than the ααββ valence isomer. Indeed,
regardless of protonation and type of η2 coordination,
all η2-bound states having Fe1 net spin-β are
7–14 kcal mol–1 lower in energy than states
with net spin-α on Fe1 (Table S8).
From these results, it is apparent that the tightly-bound metallacycle
complexes formed when Fe1 is net spin-β are preferred energetically
over complexes with Fe1 having net spin-α that are stabilized
predominantly through van der Waals interactions.The energies
of all computed η2-bound states are further compared
to the energies of RO–- and ROH-bound states to
determine which conformations of HMBPP are preferred when the [4Fe–4S]
cluster is reduced by one electron (Table 10, Figure 5). We note that all relative energies
discussed here are given only for the lowest-energy valence isomers
computed for each protonation state and binding mode; a complete tabulation
of the relative energies of all valence isomers considered can be
found in Supporting Information, Table S9.
Table 10
Relative Energies
(kcal mol–1) of Different RO(H)- and η2-Bound States in Both the Oxidized and 1e– Reduced States
oxidizeda
reduceda
state (charge)
q
DFT/COSMO
DFT/SCRF
DFT/COSMO
DFT/SCRF
RO–P–EH(RO–)
–3/–4
7.9
0.0
29.5
13.0
RO–PHEH(RO–)
–2/–3
0.0
2.2
16.6
10.3
ROHP–E–(ROH)
–3/–4
8.4
0.0
17.6
4.1
ROHPHE–(ROH)
–2/–3
5.3
6.1
5.8
0.0
ROHP–EH(ROH)
–2/–3
2.9
5.5
5.3
0.3
ROHPHEH(ROH)
–1/–2
0.0
13.3
0.0
4.5
ROHP–EH(η2-ring)
–2/–3
5.4
6.0
0.7
–5.7
ROHPHEH(η2-ring)
–1/–2
6.7
19.3
–10.3
–3.4
ROHP–EH(η2-trans)
–2/–3
11.6
14.1
6.4
1.5
ROHPHEH(η2-trans)
–1/–2
6.2
19.6
–1.5
3.6
Energies are given relative to the lowest-energy
RO(H)-bound state.
Figure 5
Relative energies (kcal mol–1) of different RO(H)-
and η2-bound 1e– reduced states. Energies are given relative to the lowest-energy
state.
Relative energies (kcal mol–1) of different RO(H)-
and η2-bound 1e– reduced states. Energies are given relative to the lowest-energy
state.Energies are given relative to the lowest-energy
RO(H)-bound state.With
the DFT/COSMO method, the ROHPHEH (η2-ring) state is the lowest-energy η2-bound state when the [4Fe–4S] cluster is 1e– reduced. The energies of the isoelectric
ROHPHEH (η2-ring)
and ROHPHEH (η2-trans)
states are both lower than that of the lowest-energy RO(H)-bound state
(i.e., ROHPHEH) by 10.3 and 1.5 kcal
mol–1, respectively (Table 10). In contrast, we find the ROHP–EH(η2-ring) and ROHPHEH (η2-ring) states to be the lowest-energy
1e– reduced states computed using
the DFT/SCRF method, with energies that are, respectively, 5.7 and
3.4 kcal mol–1, lower than the lowest-energy RO(H)-bound
state ROHPHE–(ROH). In the
DFT/SCRF computations, the η2-trans states are disfavored
energetically, as the energies of the ROHP–EH (η2-trans) and ROHPHEH (η2-trans) states are, respectively,
1.5 and 3.6 kcal mol–1 higher than the energies
of the ROHPHE–(ROH) state
(Table 10, Figure 5).Relative energies obtained using both the DFT/COSMO and DFT/SCRF
methods thus indicate that η2-ring states are preferred
over all RO(H)-bound geometries when the [4Fe–4S] cluster is
1e– reduced. Similar to what was
observed with the RO(H)-bound states, we find the relative energies
of η2-bound states depend on the method used to calculate
the energy and the charge in the active site: the ROHPHEH (η2-ring) state, which has
a charge of −2, is preferentially stabilized with the DFT/COSMO
method, whereas the ROHP–EH(η2-ring) state, which has a charge of −3,
is the lowest-energy state when using the DFT/SCRF method.
Barrier to Rotation of the C4–OH Group in
the 1e– Reduced State
Clearly, η2-bound states are lower in energy than all RO(H)-bound states
upon 1e–reduction of the [4Fe–4S]
cluster. However, it is unclear from our computations whether these
η2-bound states are catalytically relevant. More
specifically, it is possible that η2-bound states
may not be accessible from ROH-bound states, despite being lower in
energy. To search for rotational barriers that would prevent an ROH-bound
HMBPP structure from accessing η2-type geometries,
we perform linear transit (LT) computations in the 1e– reduced state along the C2–C3–C4–OH dihedral angle (ϕ),
which distinguishes HMBPP geometries in ROH- and η2-bound states.LT computations are performed on the ROHP–EH βααβ
state since it is the lowest-energy η2-bound state
computed with the DFT/SCRF method. Two different starting points are
used to conduct the LT computations: (1) starting from the ROH-bound
conformation with ϕ set to −100°, which is its approximate
value in ROH-bound states; (2) starting from an η2-ring conformation with ϕ set to +100°. From these starting
points, the transit is stepped in 20° increments forward and
backward to complete the full range of the torsion. Geometry optimizations
are performed along ϕ, from which energies are obtained using
both the DFT/COSMO and DFT/SCRF methodologies (Figure 6A,B).
Figure 6
Linear transit computations performed along ϕ in
the 1e– reduced state starting
from an ROH-bound geometry (black) and an η2-ring
geometry (red). Energies (kcal mol–1) are obtained
using the DFT/COSMO (A) and DFT/SCRF (B) methods.
Linear transit computations performed along ϕ in
the 1e– reduced state starting
from an ROH-bound geometry (black) and an η2-ring
geometry (red). Energies (kcal mol–1) are obtained
using the DFT/COSMO (A) and DFT/SCRF (B) methods.Starting with the DFT/COSMO results, we observe two different
behaviors in the LT curves given in Figure 6A. When initiated from the ROH-bound state at ϕ = −100°
(Figure 6A, black curve), the system increases
in energy when ϕ is distorted from its approximate ROH-bound
value. HMBPP remains attached to Fe1 via its C4–OH
group in the range of −120° ≤ ϕ ≤
−40°. When ϕ < −120°, HMBPP adopts
its η2-trans conformation, although the geometries
obtained in the LT computation contain little interaction between
Fe1 and the olefiniccarbons, with Fe–C2/C3 distances of 3.3–3.5 Å. Similarly, only weakly-bound
η2-ring conformations are found at values of ϕ
> −40°, with similarly elongated Fe–C2/C3 distances. The only local minimum corresponding to
an η2-bound conformation is found at ϕ = +100°,
although neither this state nor the LT state obtained near the η2-trans value of ϕ (ca. −160°) are lower
in energy than the ROH-bound states found along the LT.LT computations
performed starting from the geometry-optimized η2-ring state (Figure 6A, red curve) permits
computation of η2-bound states along the full ϕ
reaction coordinate. In these calculations, the state computed at
ϕ = +80° represents a tightly-bound η2-complex with Fe–C2/C3 distances of
∼2.1 Å. This structure is the global minimum among all
LT states computed with the DFT/COSMO method.Combining the
LTs initialized from the ROH-bound (Figure 6A, black curve) and η2-ring (Figure 6A, red curve) states, we consider the relative energies of
transitioning from an ROH-bound conformation to an η2-ring complex. Starting from the ROH-bound conformation at ϕ
= −100°, the system moves along the black, ROH-bound curve
until ϕ = −60°. At this value of ϕ, the orientation
of HMBPP switches to an η2-type coordination of Fe1
and the system propagates along the red curve until it reaches the
global minimum η2-ring state at ϕ = +80°.
From these LT curves, the barrier to transition from the ROH-bound
state to the η2-ring state is approximately the energy
required to travel along the black curve from ϕ = −100°
to ϕ = −60°. From Figure 6A, this energy barrier is ∼3 kcal mol–1 when
using the DFT/COSMO method.From DFT/SCRF computations performed
on the optimized geometries obtained along the LT paths, we obtain
slightly different energies along ϕ (Figure 6B). Qualitatively, however, these DFT/SCRF LT curves are similar
to those obtained using the DFT/COSMO method. The energy required
to transition from the ROH-bound state to the η2-ring
state can be approximated as the difference in energy between the
ROH-bound state at ϕ = −100° and the point at which
the black and red curves in Figure 6B intersect.
This approximation gives a rotational barrier of ∼2 kcal mol–1. Consequently, both DFT/COSMO and DFT/SCRF methods
predict a small barrier that connects the ROH- and η2-ring states.
Geometries of [4Fe–4S]2+ IspH with HMBPP Bound via C2 and C3 (η2-Complex)
In previous sections, we
obtained reduction potentials for the one-electron reduction of RO(H)-bound
states (−1.4 to −1.0 V) that are more negative than
the reduction potentials expected for [4Fe–4S] Fdx proteins.[51,82] Additionally, we have located η2-bound structures
in the 1e– reduced state that are
both lower in energy than ROH-bound states and accessible from these
states. Building on these findings, we entertain the hypothesis that
the orientation of HMBPP switches from ROH- to η2-binding in the oxidized state to facilitate the 1e– reduction of the [4Fe–4S] cluster. Using
the η2-bound geometries computed in the 1e– reduced state as a starting point,
we perform geometry optimizations of oxidized active-site clusters
with the C4–OH group rotated away from Fe1. Our
discussion of these states focuses on η2-ring states
since they are lower in energy when the [4Fe–4S] cluster is
1e– reduced; however, analyses
of oxidized η2-trans states are provided in the Supporting Information.Regardless of valence
isomerism, all oxidized η2-ring states have elongated
Fe1–C2/C3 distances (Table 11). We are unable to obtain tightly-bound η2 complexes like those observed in the βααβ
η2-bound valence isomers when the [4Fe–4S]
cluster is 1e– reduced, even when
the geometry optimizations are initialized from these states. Giving
consideration to the lowest-energy states having Fe1 either net spin-α
or net spin-β, we find that both the αββα
and βααβ ROHP–EH(η2-ring) oxidized states have Fe1–C 2/C3 distances of ∼2.6 Å (Table 11, Figure 7). Indeed, these
two states are structurally similar (with an RMSD of 0.02 Å),
and both maintain the network of hydrogen bonds observed in the 1 e– reduced η2-ring states
(Table 11, Figure 7). For instance, the distance between the OC4 and OPPi atoms in both the oxidized and 1e– reduced η2-ring states is ∼2.70
Å, indicating that the intramolecular hydrogen bond stabilizing
the HMBPP ring conformation is not disrupted between the two oxidation
states considered.
Table 11
A Comparison of
Key Bond Lengths (Å) and Angles (deg) between the ROH- and η2-ring Structures in Both the Oxidized and 1e– Reduced ROHP–EH States
oxidized
reduced
binding mode
ROH
ROH
η2-ring
η2-ring
valence isomer
αββα
βααβ
αββα
βααβ
αββα
βααβ
cluster bond lengths
Fe1–S5
2.200
2.200
2.197
2.197
2.207
2.285
Fe1–S6
2.282
2.282
2.277
2.278
2.298
2.291
Fe1–S7
2.319
2.319
2.304
2.304
2.308
2.384
Fe2–S5
2.328
2.328
2.305
2.304
2.302
2.316
Fe2–S6
2.206
2.206
2.193
2.192
2.225
2.194
Fe2–S8
2.357
2.357
2.358
2.360
2.361
2.373
Fe3–S5
2.305
2.305
2.300
2.300
2.285
2.311
Fe3–S7
2.240
2.240
2.265
2.267
2.320
2.271
Fe3–S8
2.361
2.361
2.350
2.349
2.344
2.367
Fe4–S6
2.326
2.326
2.309
2.310
2.318
2.312
Fe4–S7
2.322
2.322
2.325
2.324
2.343
2.307
Fe4–S8
2.241
2.241
2.229
2.230
2.256
2.246
Fe2–SC12
2.256
2.256
2.241
2.238
2.290
2.285
Fe3–SC197
2.275
2.275
2.285
2.284
2.281
2.364
Fe4–SC96
2.295
2.295
2.279
2.279
2.338
2.314
HMBPP bond lengths
Fe1–OC4
2.214
2.214
4.514
4.516
4.525
4.287
Fe1–C3
3.531
3.531
2.603
2.604
2.552
2.144
Fe1–C2
3.272
3.272
2.571
2.569
2.485
2.118
H-bond lengths
OC4–OT167
3.189
3.189
4.334
4.342
4.380
4.384
OT167–OE126
2.661
2.661
2.700
2.702
2.684
2.687
OE126–OW1
3.687
3.688
3.703
3.685
3.717
3.598
OW1–OPPi
2.734
2.734
2.794
2.793
2.786
2.774
OC4–OE126
4.209
4.209
3.629
3.641
3.590
3.621
OC4–OPPi
4.875
4.875
2.695
2.695
2.703
2.722
HMBPP angle
C2–C3–C4–OC4
–101.5
–101.5
95.4
95.7
94.1
90.3
Figure 7
Optimized geometry of the lowest-energy η2-ring state, ROHP–EH(η2-ring), when the [4Fe–4S] cluster is oxidized.
Optimized geometry of the lowest-energy η2-ring state, ROHP–EH(η2-ring), when the [4Fe–4S] cluster is oxidized.Further, comparing
the oxidized η2-ring complexes to their 1e– reduced equivalents, we observe high
similarity between the oxidized complexes and the αββα
1e– reduced state (Table 11). In the case of the ROHP–EH(η2-ring) αββα
valence isomer, the geometries obtained in the oxidized and 1e– reduced states show an RMSD of only
0.08 Å. From these geometric data, it is apparent that the olefiniccarbons of HMBPP can only weakly interact with Fe1 when the [4Fe–4S]
cluster is oxidized. Upon 1e– reduction,
however, the olefin coordination to Fe1 can either remain elongated,
as in the αββα and ααββ
states, or can form a more tightly-bound complex when Fe1 is net spin-β
(Table 11).
Distribution
of Spin and Charge in η2-Bound Oxidized States
The NSPs obtained in the oxidized and 1e– reduced states for representative valence isomers of the ROHP–EH(η2-ring)
state are given in Table 12. In the ROHP–E H(η2-ring)
αββα oxidized state, the NSPs on the Fe atoms
are similar in magnitude, which precludes an assignment of the spin-coupled
ferric/ferrous and delocalized, mixed-valence pairs. Summing the spins
on these Fe atoms reveals that the total NSP of ∼0.05 is localized
on the Fe atoms (Table 12). Taking into account
the spin densities that reside on the cluster sulfides and thiolates
from the Fe atoms, we obtain a total NSP of −0.03 on the full
cluster. Equal to and opposite to the spin density localized on the
cluster, we find a total NSP of +0.03 on HMBPP, with individual NSPs
of ca. +0.01 on each of the olefiniccarbons and OC4 (Table 12). When comparing oxidized and 1e– reduced ROHP–EH(η2-ring) αββα states,
we find the reducing electron spin density falls almost entirely on
the [4Fe–4S] cluster and its coordinating thiolates (summed
ΔNSP of 0.99), with very little spin density transferred to
the HMBPP ligand (NSP ≈ −0.01, Table 12).
Table 12
NSPs Given for Atoms in the [4Fe–4S]
Cluster, Its Coordinating Thiolates, and HMBPP from Two Representative
Valence Isomers of the ROHP–EH(η2-ring) State When the [4Fe–4S] Cluster
Is Oxidized and Reduced by One Electron
ROHP–EH
αββα
βααβ
ox (η2-ring)
red (η2-ring)
ΔNSPa
ox (η2-ring)
red (η2-ring)
ΔNSPa
FE1
3.146
3.173
0.028
–3.145
–2.879
0.266
FE2
–3.106
–3.000
0.105
3.104
3.204
0.100
FE3
–3.193
–2.880
0.313
3.190
3.328
0.137
FE4
3.198
3.297
0.099
–3.199
–3.194
0.005
sum
0.045
0.590
0.545
–0.049
0.459
0.509
S1
–0.006
0.050
0.055
0.008
0.218
0.210
S2
0.063
0.160
0.096
–0.062
–0.036
0.026
S3
0.102
0.220
0.118
–0.104
–0.022
0.082
S4
–0.029
0.014
0.043
0.030
0.048
0.017
sum
0.130
0.443
0.313
–0.127
0.208
0.335
C12
–0.239
–0.119
0.119
0.240
0.187
–0.053
C96
0.216
0.143
–0.073
–0.215
–0.145
0.070
C197
–0.181
–0.092
0.089
0.181
0.137
–0.045
sum
–0.204
–0.068
0.136
0.206
0.179
–0.027
total cluster
–0.029
0.965
0.994
0.029
0.846
0.816
OC4
0.007
0.006
–0.001
–0.007
0.003
0.009
C3
0.010
0.011
0.000
–0.011
0.055
0.066
C2
0.007
0.001
–0.006
–0.006
0.109
0.115
total HMBPP
0.026
0.020
–0.006
–0.025
0.155
0.180
cluster + HMBPP
–0.004
0.985
0.988
0.004
1.000
0.996
The difference
in NSP (ΔNSP) between the oxidized and 1e– reduced atoms is indicated.
The difference
in NSP (ΔNSP) between the oxidized and 1e– reduced atoms is indicated.Similar to the αββα valence
isomer, the summed NSP localized on the [4Fe–4S] cluster and
its coordinating thiolates in the ROHP–EH(η2-ring) βααβ
oxidized state is equal to +0.03; the NSP localized to HMBPP in this
state is equal to −0.03 (Table 12).
From these data, it is clear that there is very little transfer of
spin density from the [4Fe–4S] cluster to HMBPP when the system
is oxidized. In contrast, upon 1e– reduction of the ROHP–EH(η2-ring) βααβ state, significant
NSP (0.18) is transferred to HMBPP and, specifically, onto the olefiniccarbons C2 and C3 (ΔNSP = 0.12 and 0.07,
respectively; Table 12).The different
electronic properties of the valence isomers considered are further
magnified when the ESP charge distributions following reduction of
the η2-bound complexes are considered. In both the
oxidized ROHP–EH(η2-ring) αββα and βααβ
states and the 1e– reduced ROHP–EH(η2-ring)
αββα state, the total charge obtained for
the HMBPP molecule is ca. −0.65 e– (Table 13). In contrast, HMBPP has a total
charge of ∼ −0.78 in the 1e– reduced ROHP–EH(η2-ring) βααβ state. From these trends,
it is clear that the electronic properties of HMBPP in oxidized η2-ring states are similar to those of valence isomers in 1e– reduced η2-ring states
having Fe1 net spin-α. Differing from these states, the 1e– reduced ROHP–EH(η2-ring) βααβ
state prefers tight coordination of Fe1 by the olefiniccarbons and,
consequently, contains greater transfer of spin and charge from the
[4Fe–4S] cluster to HMBPP.
Table 13
ESP Charge Distributions
Given for Atoms in the [4Fe–4S] Cluster, Its Coordinating Thiolates,
and HMBPP from Two Representative Valence Isomers of the ROHP–EH(η2-ring) State
When the [4Fe–4S] Cluster Is Oxidized and Reduced by One Electron
ROHP–EH
αββα
βααβ
ox (η2-ring)
red (η2-ring)
Δqa
ox (η2-ring)
red (η2-ring)
Δqa
FE1
0.386
0.373
–0.012
0.387
0.307
–0.080
FE2
0.464
0.533
0.068
0.459
0.512
0.053
FE3
0.621
0.645
0.023
0.618
0.692
0.074
FE4
0.459
0.515
0.056
0.455
0.494
0.040
sum
1.930
2.065
0.135
1.919
2.005
0.087
S1
–0.458
–0.583
–0.125
–0.458
–0.592
–0.133
S2
–0.268
–0.328
–0.060
–0.268
–0.267
0.001
S3
–0.448
–0.597
–0.149
–0.446
–0.570
–0.124
S4
–0.566
–0.740
–0.173
–0.563
–0.691
–0.129
sum
–1.741
–2.248
–0.508
–1.735
–2.119
–0.385
C12
–0.243
–0.396
–0.153
–0.238
–0.346
–0.108
C96
–0.305
–0.434
–0.129
–0.305
–0.398
–0.093
C197
–0.369
–0.486
–0.117
–0.367
–0.460
–0.094
sum
–0.916
–1.316
–0.400
–0.910
–1.205
–0.295
total cluster
–0.727
–1.499
–0.773
–0.726
–1.319
–0.593
OC4
–0.334
–0.309
0.025
–0.333
–0.328
0.006
C3
–0.010
–0.016
–0.006
–0.013
–0.038
–0.025
C2
0.019
0.049
0.030
0.026
0.068
0.042
total HMBPP
–0.646
–0.636
0.010
–0.645
–0.784
–0.139
cluster + HMBPP
–1.372
–2.135
–0.763
–1.371
–2.103
–0.732
The difference
in charge (Δq) between the oxidized and 1e– reduced atoms is indicated.
The difference
in charge (Δq) between the oxidized and 1e– reduced atoms is indicated.
Relative Energies of the
η2-Bound States in the Oxidized State
The
energies of η2-bound oxidized states can be directly
compared to their ROH-bound counterparts to obtain their relative
energies (Table 10). Using the DFT/COSMO method,
the lowest-energy η2-bound oxidized state is the
ROHP–EH(η2-ring) state, which is 5.4 kcal mol–1 higher in
energy than the lowest-energy RO(H)-bound oxidized states RO–PHEH and ROHPHEH. The ROHPHEH(η2-trans) and ROHPHEH(η2-ring) states are, respectively, 6.2 and 6.8 kcal mol–1 higher in energy than the lowest-energy RO(H)-bound
states (Table 10).Using the DFT/SCRF
method, the preferred η2-bound oxidized state is
also the ROHP–EH(η2-ring) state, which lies 6.0 kcal mol–1 higher
in energy than the lowest-energy RO(H)-bound states RO–P–EH and ROHP–E–. All other η2-bound oxidized
states are >14 kcal mol–1 higher in energy than
the RO–P–EH(ROH) and
ROHP–E–(ROH) states.
From both the DFT/COSMO and DFT/SCRF computations, it is clear that
the ROHP–EH(η2-ring) state is moderately higher in energy than the lowest-energy
RO(H)-bound oxidized states. We thus reason that the ROHP–EH(η2-ring) state
can be accessed prior to 1e– reduction
of the [4Fe–4S] cluster, provided that no kinetic barriers
prohibit the C4–OH group rotation required to achieve
η2 binding.
Reduction
Potentials Computed for η2-Bound States
Having obtained the energies of η2-bound states
when the [4Fe–4S] cluster is oxidized and reduced by one electron,
we can obtain reduction potentials for the addition of an electron
to these alternative geometries (Table 14).
With the DFT/COSMO method, the computed reduction potential for the
lowest-energy η2-bound state, ROHP–EH(η2-ring), is −1.22
V, which is shifted ∼300 mV positive relative to the reduction
potential computed for the similarly protonated ROHP–EH(ROH) state (Table 6). Coupling the transfer of a proton to reduction of the ROHP–EH(η2-ring) state
(eq 11) generates the 1e– reduced ROHPHEH(η2-ring) state and effectively increases the reduction potential E°′ to −0.74 V.
Table 14
Reduction Potentials
(V) Obtained for the Addition of an Electron to the η2-Bound States
protonation state
binding mode
DFT/COSMO
DFT/SCRF
ROHP–EH
ROH
–1.52
–1.07
η2-ring
–1.22 (−0.74)a
–0.78
η2-trans
–1.20
–0.74
ROHPHEH
ROH
–1.42
–0.91
η2-ring
–0.68
–0.31
η2-trans
–1.09
–0.60
Electron transfer
accompanies proton addition to generate the ROHPHEH(η2-ring) 1e– reduced state. Redox potential coupled to proton transfer indicated
in parentheses.
Electron transfer
accompanies proton addition to generate the ROHPHEH(η2-ring) 1e– reduced state. Redox potential coupled to proton transfer indicated
in parentheses.Alternatively,
we can consider reduction to proceed through the ROHPHEH(η2-ring) oxidized state, which
is 1.3 kcal mol–1 higher in energy than the ROHP–EH(η2-ring)
oxidized state (Table 10). The reduction potential
in this scenario is calculated to be E° = −0.68
V. Regardless of the pathway, it is evident that reduction is preferred
through η2-bound states when using the DFT/COSMO
method.Using the DFT/SCRF method, the reduction potential for
the addition of an electron to the ROHP–EH(η2-ring) state is −0.78 V.
This value is ∼300 mV more positive than that computed for
the analogous ROHP–EH(ROH)
state and ∼600 mV more positive than the reduction potential
coupled to proton transfer through the lowest-energy ROH-bound state,
ROHP–E–. Thus, it is
easier to add an electron to the ROHP–EH(η2-ring) state than to RO(H)-bound
states.
Barrier to Rotation of C4–OH
Group in the 1e– Oxidized State
Computed
reduction potentials for η2-bound states are closer
to the values expected for [4Fe–4S] Fdx proteins.[51,82] For such redox processes to occur, however, these η2-bound states must be accessible when the [4Fe–4S] cluster
is oxidized. Using the DFT/COSMO method, the ROHP–EH(η2-ring) state is only 5.4 kcal mol–1 higher in energy than the lowest-energy RO(H)-bound
state; with the DFT/SCRF method, the ROHP–EH(η2-ring) state is 6.0 kcal mol–1 higher in energy than the lowest-energy RO(H)-bound
states (Table 10). The addition of an electron
through these η2-bound intermediates is thus thermodynamically
attainable. To probe whether such mechanisms are kinetically feasible,
we perform linear transit computations along ϕ, following the
framework applied earlier to the 1e– reduced states, to quantify the barriers to rotate the C4–OH group away from Fe1 in the ROHP–EH state when the [4Fe–4S] cluster is oxidized
(Figure 8). The protonation state is fixed
throughout the computation. LT computations using the DFT/COSMO and
DFT/SCRF methods give respective rotational barriers of 11.4 and 8.9
kcal mol–1 to reach the ROHP–EH(η2-ring) state when the [4Fe–4S]
cluster is oxidized. These values indicate that rotation of the C4–OH group to attain η2-bound states
is feasible.
Figure 8
Linear transit computation performed along ϕ in
the oxidized state. Energies (kcal mol–1) are obtained
using the DFT/COSMO (black) and DFT/SCRF (red) methods.
Linear transit computation performed along ϕ in
the oxidized state. Energies (kcal mol–1) are obtained
using the DFT/COSMO (black) and DFT/SCRF (red) methods.
Discussion
Before discussing the
computations performed in this study, we briefly summarize the results
from BS/DFT computations performed on the oxidized state of our IspH
active-site quantum cluster.[50] Exploring
only RO(H)-bound geometries in the oxidized state, we previously found
that the DFT/COSMO method favors states with less negative charge
in the active site (q = −2) than the DFT/SCRF
method, which preferentially stabilizes q = −3
states. More specifically, the lowest-energy RO(H)-bound states obtained
using DFT/COSMO are the RO–PHEH and ROHPHEH, whereas the RO–P–EH and ROHP–E– states are the lowest energy
in DFT/SCRF computations (Table 10). Furthermore,
we observed that the geometry optimized structures of the ROHPYE–(ROH) states, regardless of PP protonation, best match the active-site
geometry observed in the oxidized [4Fe–4S] IspH:HMBPP crystal
structure.[35] Moreover, Mössbauer
isomer shifts[21,33] computed for ROH-bound states
gave better agreement with experiment than those computed for RO–-bound states.[50]Shifting
focus to the 1e– reduced RO(H)-bound
states computed in this work, the lowest-energy state obtained using
the DFT/COSMO method is the ROHPHEH(ROH) state (q = −2), whereas the ROHPHE–(ROH) state (q = −3) is favored using the DFT/SCRF method (Table 10, Figure 5). The propensity
of these different methods to stabilize different charge states is
consistent with the observed preference for q = −2
and q = −3 states by the DFT/COSMO and DFT/SCRF
methods, respectively, when the [4Fe–4S] cluster is oxidized.[50] The energetic preference for maintaining certain
active-site charge states ensures that protons accompany electrons
when the latter are added to the system, as is required in IspH catalysis.Combining the energetic analyses of the oxidized and 1e– reduced RO(H)-bound states, we obtain reduction
potentials using both the DFT/COSMO and DFT/SCRF methods. In our previous
study of the IspH oxidized state, we proposed the preferred state
to be ROHP–E–(ROH).
Using this state as a starting point to consider the 1e– reduction of the IspH [4Fe–4S] cluster,
we obtain reduction potentials in the absence of proton coupling of
−1.82 and −1.47 V using the DFT/COSMO and DFT/SCRF methods,
respectively (Table 6). As illustrated by this
example, all reduction potentials computed using the DFT/SCRF method
are ∼0.30–0.50 V more positive than those computed using
the DFT/COSMO method (Tables 6 and 14). The tendency of the DFT/COSMO method to obtain
reduction potentials that are more negative than those determined
experimentally has been noted previously.[51,68] In contrast with DFT/COSMO, the DFT/SCRF method lends improvement
to the computation of reduction potentials through its inclusion of
the surrounding protein point charges in a multi-dielectric environment,
which better accommodates the addition of an electron to the active-site
cluster reduction than the simpler COSMO description of the active
site surroundings.[51,68] While both DFT/COSMO and DFT/SCRF
methods give reduction potentials that are too negative, those computed
using the DFT/SCRF method are significantly closer to the range of
reduction potentials expected for [4Fe–4S] Fdx proteins.[51,82] Combining this result with previous findings that the DFT/SCRF method
also better predicts the geometry and protonation of the HMBPPROH
group in the oxidized state, we choose to limit further discussion
to our results obtained using the DFT/SCRF method.Returning
to our discussion of how ROH-bound states may undergo reduction, we
begin with the ROHP–E–(ROH) state, which is one of the two lowest-energy oxidized states
obtained with the DFT/SCRF method. The reduction potential for this
state can be increased from −1.47 to −1.29 V with proton
transfer to the HMBPP PP moiety (Table 6); however, there are no clear titratable groups
available to donate this proton in our active-site model. Consequently,
it is more likely that, if protonation is required for the addition
of the reducing electron, the proton transfer occurs in the oxidized
state prior to reduction of the [4Fe–4S] cluster. In this scenario,
either E126 or the PP group of HMBPP
can be protonated in the oxidized state at a respective energetic
cost of 5.5 or 6.1 kcal mol–1 (Table 5). Subsequent reduction of the system can be achieved with
reduction potentials of −1.03 and −1.07 V for the ROHPHE– and ROHP–EH states, respectively (Table 6). While these reduction potentials are less negative,
they still fall outside the expected range for [4Fe–4S] Fdx
proteins.[49,78] To obtain reduction potentials in the −800
to −200 mV range,[51,82] it thus appears that
reduction likely occurs via an alternative pathway.We address
the possibility that reduction may occur through an alternative pathway
by considering the suggestions of others that HMBPP shifts to η2 binding of Fe1 in the 1e– reduced state. To this end, we find two η2-bound
HMBPP rotamers (i.e., “ring” and “trans”)
distinguishable by their respective C2–C3–C4–OH dihedral angle (ϕ ≈
+90 and −160°, respectively) and, consequently, the orientation
of the C4–OH moiety of HMBPP in the active-site
hydrogen-bond network (Figure 4). The η2-ring state is found to be the lower energy η2-bound state (Table 10), and the ROHP–EH(η2-ring) state
is 7.2 kcal mol–1 lower than the energy of the lowest-energy
η2-trans state, ROHP–EH(η2-trans).In both of the η2-ring and η2-trans states, two binding modes
are present that differ with respect to the NSP on Fe1: (1) tight
coordination of Fe1 by C2 and C3 with Fe–C
distances of ∼2.1 Å when Fe1 is net spin-β and aligned
opposite to STot; and (2) a loose coordination
of Fe1 by the olefin (Fe–C distances of ∼2.6 Å)
when Fe1 is net spin-α and aligned with STot (Tables 7–8). In both η2-ring and η2-trans states, the tighter coordination mode observed when the net
spin Fe1 is aligned opposite STot is favored
energetically by ∼7–11 kcal mol–1 (Supporting Information, Table S8).The
ROHP–EH(η2-ring) state is 5.7 kcal mol–1 lower in energy
than all ROH-bound 1e– reduced
states considered in this study, demonstrating a thermodynamic preference
for this alternative geometry in the 1e– reduced state (Table 10). Given this finding,
we restrict further discussion of η2-bound states
to η2-ring states. Linear transit (LT) computations
along the ϕ reaction coordinate are initiated from both ROH-
and η2-ring geometries. An analysis of energies along
these LTs indicate that, while ROH-bound geometries are favored at
ϕ values between −120 and −80°, η2-bound states become lower in energy at all values of ϕ
outside this range. From these data, the rotational barrier obtained
along the ϕ reaction coordinate that permits HMBPP to transition
from ROH- to η2-ring coordination of the [4Fe–4S]
cluster is only ∼2 kcal mol–1 (Figure 6B). Thus, η2-ring states are both
kinetically accessible and thermodynamically favored in the 1e– reduced state.The stabilization
of η2-bound 1e– reduced states corroborate the organometallic mechanism proposed
by Oldfield and co-workers for IspH catalysis.[9] Coupling our finding that η2-ring geometries are
favored in the 1e– reduced state
with the indirect support for the existence of such intermediates
from ENDOR[26] and crystallographic studies[36] led us to consider reduction through states
with HMBPP bound to Fe1 in these η2-binding modes.
To obtain reduction potentials through the η2-ring
state, it is necessary that such geometries preexist in the oxidized
state. Starting from the geometries optimized in the 1e– reduced state, we compute η2-bound states with the [4Fe–4S] cluster oxidized. All such
states are characterized by loose coordination of Fe1 by the HMBPPolefiniccarbons, similar to what is observed in 1e– reduced η2-bound states having
Fe1 net spin-α (Table 11, Figure 7). The loosely-bound ROHP–EH(η2-ring) state is the lowest-energy
η2-bound structure in the oxidized state at only
0.5 kcal mol–1 above the energy of the similarly
protonated ROHP–EH(ROH) state,
and it is 6.0 kcal mol–1 higher in energy than the
energy of the lowest-energy RO(H)-bound states ROHP–E– and RO–P–EH.Reduction via η2-bound states is possible given the similar energies of ROHP–EH(ROH) and ROHP–EH(η2-ring) states when the [4Fe-4S]
cluster is oxidized and the low energy of the ROHP–EH(η2-ring) state upon
1e– reduction. Indeed, the reduction
potential obtained through the ROHP–EH(η2-ring) falls near the lower bound of the
expected range for [4Fe–4S] Fdx proteins at −0.74 V
(Table 14). Compared to the −1.07 V
reduction potential obtained for reduction through the ROHP–EH(ROH) state (Table 6), reduction through the η2-ring state is
preferred by over 7 kcal mol–1. However, LT computations
on ROHP–EH states along the
ϕ reaction coordinate when the system is oxidized suggests a
rotational barrier of ∼8.9 kcal mol–1 between
ROH- and η2-ring states. This kinetic barrier required
to reach the ROHP–EH(η2-ring) oxidized state opposes the thermodynamic preference
for reduction through η2-bound states; however, it
is likely, though outside the scope of the calculations performed
in this work, that the free energy barrier between these states is
overestimated. The breaking of the Fe1–OC4 bond,
while shown to be enthalpically unfavorable by our DFT/SCRF LT computations,
likely increases the configurational entropy of the system. Such entropic
compensation, which is not quantified in this work, would lower the
barrier to rotation and render reduction through η2-bound states more favorable. Additionally, the reorientation of
the electric dipoles of the protein in response to this HMBPP conformational
change is omitted from our model, as all DFT/SCRF computations use
a static protein structure corresponding to the oxidized [4Fe–4S]
IspH:HMBPP crystal structure[35] in which
HMBPP is bound to Fe1 through its C4–O(H) group.
Thus, the rotational barrier of 8.9 kcal mol–1 provides
an upper bound to the “true” barrier separating ROH-
and η2-ring states when the [4Fe–4S] cluster
is oxidized.We note that the reaction barriers observed for
reduction through both of the RO(H)- and η2-bound
pathways are not unfounded for the IspH enzyme. More specifically,
kinetic studies of the IspH enzyme performed in vitro indicate that
IspH has low catalytic turnover (kcat =
604 s–1).[34,39] Applying simple transition-state
theory for heuristic purposes,[83] this turnover
rate implies IspH catalysis occurs with a barrier energy of ca. 16
kcal mol–1. Although simplistic, this view of IspH
kinetics suggests the energetic penalties associated with reduction
through both ROH-bound and η2-ring states are within
reason.Using Figure 9, we show how our
computational work affects previous proposals for the IspH catalytic
mechanism. In the oxidized state (left column, Figure 9), the HMBPP coordinates Fe1 through its C4–OH
group in the ROHP–E– protonation state (4, Figure 9). From this starting point, the simplest path to the reduced state
is through proton–coupled electron transfer to the ROHP–E–(ROH) state (4 → 5, Path I) with E°′
= −1.29 V. Two problems exist that lead us to discard Path
I: (1) the reduction potential is too negative, and (2) there is no protonated group in the active site available for this electron
transfer. Consequently, the active site must be protonated (either
at E126 or the HMBPP PP group) prior
to 1e– reduction of the [4Fe–4S]
cluster. In the oxidized state, the easiest site to protonate to generate
the ROHP–EH(ROH) oxidized
state is E126 (6), which requires 5.5 kcal mol–1. Electron addition to the ROHP–EH(ROH) state is achieved with E° = −1.07
V (Path II, Figure 9), which, although shifted
positive relative to the reduction potential computed for ROHP–E–(ROH), is still too negative
for ferredoxins.[49,78]
Figure 9
Modifications to the catalytic mechanism
proposed for IspH,[40] using energies obtained
in this study. ΔE‡ signifies
an estimate of the energy barrier; all other energies are the differences
in free energy between intermediates.
Modifications to the catalytic mechanism
proposed for IspH,[40] using energies obtained
in this study. ΔE‡ signifies
an estimate of the energy barrier; all other energies are the differences
in free energy between intermediates.Thus, consistent with the findings of others,[26,35,41,47−49] we suggest Path III is a likely alternative to Path
II. Instead of reduction occurring at a high cost with HMBPP bound
to Fe1 through its C4–OH group, the C4–OH group crosses a kinetic barrier with an upper bound of
9 kcal mol–1 to assume an η2-ring
conformation (8, at a thermodynamic cost of 0.6 kcal
mol–1). Through such an oxidized ROHP–EH(η2-ring) state, electron
addition is achieved with a significantly lower E° = −0.74 V (9, Figure 9). In Path III, this 1e– reduction is gated by a substrate rotation and shift in Fe binding
mode in the oxidized state. Then after 1e– reduction, the Fe–C=C π bond strengthens and
becomes shorter. Following 1e– reduction,
the terminal −OH group must be cleaved and an additional proton
and electron must be added to yield IPP (1) and DMAPP
(2).While Path III appears to us to be the most
likely mechanism, there may not be a single mechanism by which reduction
occurs. The possible diversity of mechanisms can be explored experimentally
by varying reductants, working to isolate intermediates, and examining
the resulting reaction kinetics. From our computations, the ROHP–EH(η2-ring)
state is the lowest-energy state when the [4Fe–4S] cluster
is reduced. It is possible that reduction is not gated, and instead,
electron addition to the [4Fe–4S] cluster may be achieved through
either ROH- or η2-bound states. Upon reduction, however,
the η2-ring state is favored energetically with a
much smaller rotational barrier separating it from the ROH-bound state;
consequently, it is likely that the η2-ring state
precedes all later steps in IspH catalysis, regardless of whether
reduction occurs through ROH- or η2-bound states.Omitted from consideration in these studies is the potential for
cleavage of the −OH group attached to C4 either
accompanying or following reduction of the [4Fe–4S] cluster.
While the transfer of an additional proton to the C4–OH
group (to make a C4–OH2 group) would
likely make electron addition to the [4Fe–4S] cluster more
favorable by reducing the anionic character in its immediate vicinity,
we reason that having this concerted proton transfer event to the
C4–OH group prior to reduction would incur an energetic
barrier greater than what is observed for the rotation of the C4–OH group. Consequently, we suggest that the cleavage
of the C4–OH bond occurs after the C4–OH group has rotated away from Fe1 in the 1e– reduced state to form the η2-ring conformation.The computations performed in this study
suggest that the η2-ring state is favored following
1e– reduction of the [4Fe–4S]
cluster. This finding lends further support to development of olefin–based
inhibitors.[9,24,26] It is worth noting that, in the case of IspH, olefin binding to
Fe1 is favored over RO–/ROH binding in the 1e– reduced state. In contrast, binding
through the HMBPP RO(H) group is preferred when the [4Fe–4S]
cluster is oxidized. Consequently, our results suggest that inhibitor
design may be considered redox-dependent. Furthermore, since the binding
mode of olefinic groups changes upon reduction, we propose that docking
and other structural studies must account for the different binding
modes of such groups, depending on the oxidation state of the [4Fe–4S]
cluster. Attempts to improve inhibitor design by leveraging structural
insight from these computational studies are ongoing.
Authors: Weixue Wang; Ke Wang; Ingrid Span; Johann Jauch; Adelbert Bacher; Michael Groll; Eric Oldfield Journal: J Am Chem Soc Date: 2012-06-28 Impact factor: 15.419
Authors: Felix Rohdich; Ferdinand Zepeck; Petra Adam; Stefan Hecht; Johannes Kaiser; Ralf Laupitz; Tobias Gräwert; Sabine Amslinger; Wolfgang Eisenreich; Adelbert Bacher; Duilio Arigoni Journal: Proc Natl Acad Sci U S A Date: 2003-02-05 Impact factor: 11.205
Figure 1
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Figure 6
Figure 7
Figure 8
Figure 9