The quest for a functional substrate access tunnel in FeFe
The quest for a functional substrate access tunnel
in FeFe hydrogenase
Juan C. Fontecilla-Camps§
May 24, 2010
We investigated di-hydrogen transport between the solvent and the active site
of FeFe hydrogenases. Substrate channels supposedly exist and serve various functions in certain redox enzymes which use or produce O2 , H2 , NO, CO, or N2 , but
the preferred paths have not always been unambiguously identified, and whether
a continuous, permanent channel is an absolute requirement for transporting diatomic molecules is unknown. Here, we review the literature and we use sitedirected mutagenesis and various kinetic methods (based on protein film voltammetry and isotope exchange assays) to test the putative “static” H2 channel of FeFe
hydrogenases. We designed 8 mutations in attempts to interfere with intramolecular diffusion by remodeling this putative route in Clostridium acetobutylicum FeFe
hydrogenase, and we observed that none of them has a strong effect on any of the
enzyme’s kinetic properties. We suggest that H2 may diffuse either via transient
cavities, or along a conserved water-filled channel. Nitrogenase sets a precedent
for the involvement of a hydrophilic channel to conduct hydrophobic molecules.
∗ Université de Toulouse; INSA,UPS,INP; LISBP, 135 Avenue de Rangueil, F-31077 Toulouse, France.
INRA, UMR792 Ingénierie des Systèmes Biologiques et des Procédés, F-31400 Toulouse, France.
CNRS, UMR5504, F-31400 Toulouse, France
† CNRS. Laboratoire de Bioénergétique et Ingénierie des Protéines. UPR 9036. Institut de Microbiologie de la Méditerranée, 31 chemin Joseph Aiguier, 13402 Marseille Cedex 20. Aix-Marseille Université.
‡ CEA, Institut de Biologie Environnementale et Biotechnologie, Laboratoire de Bioénergétique et
Biotechnologie des Bactéries et Microalgues, F-13108 Saint-Paul-lez-Durance, France;
CNRS UMR Biologie Végétale et Microbiologie Environnementales, F-13108 Saint-Paul-lez-Durance,
§ Laboratoire de Cristallographie et Cristallogenèse des Protéines, Institut de Biologie Structurale JeanPierre Ebel, CEA, CNRS, Université Joseph Fourier, 41 Rue Jules Horowitz, F-38027 Grenoble, France
¶ E-mail: [email protected]
Intramolecular mass transport is an essential aspect of biological catalysis. This is because many enzymes are large molecules, whose “business end” is buried in the protein
interior, rather than exposed to the solvent. In some cases, the protein that surrounds
the active site has well defined cavities (which we will call tunnels or channels herein)
whose role is to select the right substrate and/or guide it toward the active site. 1,2 There
are also multi-functional enzymes in which catalytic intermediates are transferred between active sites without escaping to the solvent: 3,4 the channel that guides indole in
tryptophan synthase is 25Å long, 5,6 whereas carbamoyl phosphate synthetase (CPS)
transfers ammonia and carbamate along two tunnel segments that traverse a distance of
nearly 100Å. 7–9
The enzyme tunnels that transport indole or ammonia are rather large (about 3.3Å
in CPS 9 ), which facilitated their identification in crystal structures, 5 but the situation is
less clear regarding biological intramolecular transport of small, diatomic molecules,
like O2 and CO. Small heme proteins, like myoglobins, have been extensively studied
in this context, both experimentally and theoretically, because time-resolved methods
for characterizing the kinetics of intramolecular diffusion of these ligands were already
available in the mid 1920’s (cf ref 10 and refs therein), and because the molecular
weight of these proteins makes computational investigations affordable. In the most
common experiment, a CO molecule is photo-dissociated from the heme and wanders
in the globin interior for tens to hundreds of nanoseconds before it either recombines
or escapes to the solvent, and UV-vis spectroscopy is used to monitor the kinetics of
rebinding. In combination with site-directed mutagenesis, 11,12 these experiments have
led to a clear picture of the ligand pathways. The protein does not harbor a permanent
tunnel. Instead, it has several cavities, identified as empty spaces or Xe-binding sites
observed by X-ray crystallography. The ligand accesses the distal pocket by a histidine
gate, and diffuses within the protein by “hopping” from one cavity to another, taking
advantage of the conformational fluctuations of the protein side chains. Myoglobin has
also been used as a model system for developing numerical methods. Approximations,
known as “locally enhanced sampling” (LES) 13 or “implicit ligand sampling” (ILS), 14
have been introduced to increase the efficiency of molecular dynamics (MD) simulations; they rely on the hypothesis that the fluctuations of the proteins are either weakly
coupled to, or fully independent of, the motion of the ligands. These methods usually
predict pathways and activation energies, but not rates (see however ref 15). Only very
recently did brute-force MD simulations make it possible to estimate the macroscopic
rate constants for both bi-molecular recombination and exit-to-solvent, from a statistics over many individual CO migration trajectories. 16 The agreement with reported
experimental values was fair, but Elber recently emphasized that no simulation so far
could predict the dominant escape pathway though the histidine gate of myoglobin. 15
The source of this disagreement between simulations and experiments is unknown.
The above methods have all been used to study the ins and outs of various enzymes
which use or produce O2 , CO, NO, N2 or H2 . Well-defined diffusion pathways may
provide advantages in terms of catalytic efficiency, protection against harmful products or inhibitors, or selectivity. In acetyl-CoA synthase / CO dehydrogenase (ACSCODH), CO is produced from CO2 at the so-called C cluster and transferred to the A
cluster, where it is used for acetyl-CoA synthesis, without being released to the solvent; 17,18 CO is not toxic for several microorganisms that use ACS-CODH, and the
function of the tunnel identified by X ray crystallography 19,20 may only be to ensure
that no CO molecule goes to waste. 21 In NiFe hydrogenase, there is experimental evidence that the shape of the tunnel, near the active site, partly restricts access of the
inhibitor O2 , 22–25 and an active area of research concerns the putative O2 egress tunnel in Photosystem II, which is supposed to prevent singlet oxygen production at the
P680+ Pheo− pair by directing away the O2 produced. 26 In soybean lipoxygenase-1, a
tunnel directs O2 towards a certain carbon of the substrate (an Ile to Phe substitution in
the channel affects this selectivity 27–29 ), just like in certain flavoproteins it appears to
determine how O2 reacts with the active site. 30,31
Putative tunnels are most easily identified as hydrophobic cavities in (static) X-ray
structures, either by visual inspection or by using softwares (such as CAVER, 32 MOLAXIS 33 or CASTP 34 ) which perform automatic searches. Xenon is often used as a
probe in crystallographic studies, because it is supposed to prefer hydrophobic environments, like O2 ; it is of similar size as O2 but it is more electron-rich, thereby facilitating its detection with X-rays. 35 Indeed, crystals of NiFe hydrogenase and ACS-CODH
flash-cooled after exposure to pressurized xenon house a number of Xe atoms which
lie along the predicted channels; 20,21,36 this confirms the accessibility of these cavities
from the solvent, and suggests that sites that stabilize and sequester Xe atoms in the
crystal also facilitate the transit of other small hydrophobic molecules at room temperature. However, the ideal situation encountered with NiFe hydrogenase and ACS-CODH
is rare, and Xe-binding experiments sometimes gave puzzling results. For example, in
Photosystem II, the numerous Xe binding sites do not match the putative O2 channels, 37,38 and the Xe sites are not conserved in four structures of copper-containing
amine oxidases. 39,40
MD simulations have been employed to probe ligand transport within enzymes
(see ref 41 for a recent review focusing on O2 -biocatalysis). The permanent channel
observed in the structure of NiFe hydrogenase, 36,42 which binds xenon, is indeed used
“in silico” by H2 . 36,43 Its functional character was recently demonstrated using sitedirected mutagenesis and various kinetic measurements. 24,44 Regarding heme-copper
oxidases, the results of MD simulations, 45 Xe-binding 46 and mutagenesis studies 47
also agree with the existence of a conserved, 48 permanent O2 tunnel. In other cases,
the results of MD simulations supported the idea that small ligands may use transient
pathways, rather than permanent channels. For example, from the results of LES calculations and the experimental finding that most of the mutations intended to fill a Xe
cavity near the active site of copper amine oxidase do not affect the bimolecular rate of
reaction with O2 , it has been inferred that O2 uses multiple dynamic pathways. 40 In the
case of FeFe hydrogenases, a conserved permanent tunnel was identified by analysing
the structure of the enzyme from D. desulfuricans, 49 and Cohen and coworkers suggested that H2 may also transit via a distinct path, predicted from the protein’s dynamics, which may actually be the dominant route for O2 . 50,51
The wetlab approach for testing putative diffusion pathways, which we favor, uses
site-directed mutagenesis to try to alter the main routes. Most commonly, this consists
in increasing the bulk of the side chains that point in the channels. In bi-functional
enzymes, mutations in the channel may uncouple the two active sites, 7,52–55 but information about the kinetics of channeling is rare. 56 When the tunnel connects the
active site to the solvent, determining how the mutations affect the rates of transport
proved challenging. The kinetics of oxygen binding to cytochrome c oxidase mutants
has been studied using the flash flow method, whereby the reduced enzyme inhibited
by CO is mixed with O2 in the dark and the reaction is initiated by photo-dissociating
the bound ligand. 47,57 Time-resolved FTIR has also been used in this respect. 58 We
recently proposed two quantitative methods for probing the rate of intramolecular diffusion in hydrogenases. 24,44 One uses protein film voltammetry (PFV) 59–61 to resolve
the kinetics of binding and release of the competitive inhibitor CO; 62,63 the other is
based on interpreting the yield in the isotope exchange assay. Indeed, HD is an intermediate along the reaction pathway from D2 to H2 , and because the egress of HD
competes with its transformation into H2 (scheme 1 page 10), the slower intramolecular
transport, the less HD dissociates from the enzyme and the less it can be detected in the
solvent. Modeling the change in HD concentration against time returns the ratio of rate
of HD dissociation over H+ /D+ exchange at the active site. 44 We also demonstrated a
quantitative relation between rate of diffusion within NiFe hydrogenase and Michaelis
constant for H2 . 24 This result has broad relevance because a variation of Km or kcat /Km
is often the main — and sometimes the only — indication that intramolecular transport
is impaired in channel mutants. We used an expression of Km in terms of the maximal
turnover rate at infinite concentration of H2 (kcat ), the second order rate of substrate
transport to the active site (k1 2 ), and the 1st order rate of H2 release (k−12 ):
Km = (kcat + k−12 )/k1 2
This equation shows that a change in Km reveals the reciprocal variation of k1 2 provided
intramolecular transport is slow (k−12 kcat ) and on condition that the mutation does
not affect kcat . If k−12 kcat , a mutation that slows diffusion in both directions (to and
from the active site) has no effect on Km . The rate constant k1 2 cannot be measured
directly, but in a series of NiFe hydrogenase mutants whose channel is obstructed, we
observed that Km was proportional to the reciprocal of the rate of inhibition by CO,
showing that the rates of diffusion of H2 and CO are proportional to each other (we
found that the ratio of the two approximately equates 30). 24 We also showed that O2
and CO diffuse within NiFe hydrogenase at about the same rate, consistent with earlier
experiments carried out with myoglobin. 64 An increase in Km or a decrease in kcat /Km
has been observed in channel mutants of NiFe hydrogenase, 24,44,65 nitrogenase, 66 and,
regarding enzymes that use O2 , cytochrome c oxidase, 57,67 lipoxygenase, 68 copper
amine oxidase 40 and type-1 cholesterol oxidase. 69
Site-directed mutagenesis studies of enzyme channels have given information about
structure/function relationships, but the properties of channel mutants cannot always be
anticipated: as expected, the width of the hydrophobic channel is an important parameter, 70 but hydrophilicity is also very influential, and unexpected structural rearrangements may occur; 8 in this respect, it is remarkable that very few structures of channel
mutants have been determined by X-ray crystallography. 8,44,69,71–73 Regarding nitrogenase, the larger the substrate, the more significant is the increase in Km caused by
mutations in the channel (e.g. acetylene > dinitrogen), although the polarity of the
substrate also appears to be significant (the greatest effects are observed with azide). 66
In NiFe hydrogenase, the sides chains of L122 and V74 define a bottleneck in the channel, near the active site. We initially found no relation between rates of diffusion and
the estimated diameters of the channels of NiFe hydrogenase variants (L122F-V74I,
L122M-V74M, V74M, pdb entries 3CUR, 3CUS 44 and 3H3X 74 ); this may indicate
that the limited resolution of the structures makes geometrical characterization inaccurate, or that fluctuations of the side chains of the position 122 and 74 amino acids are
significant. 44 In contrast, we recently established that increasing the length of the position 74 residue side chain by one CH2 slows the diffusion rate about 30-fold irrespective
of the nature of the position 74 amino acid (V74D to V74E, or V74N to V74Q). 24 The
polarity of this amino acid also matters: replacing a carboxylic acid with an amide,
keeping the van der Waals volume constant (V74E to V74Q, or V74D to V74N), slows
diffusion about ten-fold. 24 This may reveal the stabilization of a water molecule that is
part of the barrier to ligand entry, as observed for the V68T mutant of myoglobin. 75,76
Such mutation-induced repositioning of water molecules is difficult to predict, and can
strongly impact function. For example, certain mutations in the channel of catalase
affect the presence of water molecules that are remote from the mutation site, which
inactivates the mutants. 72,73 On the basis of MD simulations, it has been proposed that
a water molecule (rather than a bulky side chain) blocks the channel of the L367F
mutant of lipoxygenase. 68 The opposite occurs in dehalogenase: MD simulations suggest that a certain polyaromatic replacement (I135F/C176Y/V245F/L246I/Y273F) increases kcat by shielding the active site from bulk solvent, despite the fact that product
release is slowed to the point of becoming rate limiting. 2
We embarked on a search of the substrate channel in Clostridium acetobutylicum
FeFe hydrogenase, by using site-directed mutagenesis and the methods that proved useful for characterizing H2 , O2 and CO transport in NiFe hydrogenase. 24,44 We designed
8 mutations that were expected to significantly modify the rate of diffusion along a
channel found in the X-ray structure. We purified the mutants and determined their
properties by using isotope-exchange assays, by measuring in vitro specific activity for
H2 uptake coupled to methyl viologen reduction, by measuring the Michaelis constant
relative to H2 and the rates of binding and release of the inhibitors CO and O2 . Protein film voltammetry (PFV), which consists in measuring the turnover rate by having
the enzyme directly exchanging electrons with the electrode onto which it is adsorbed,
proves very useful for precisely characterizing the kinetics of inhibition. We observed
that none of the mutations has a strong effect. We discuss the possibility that alternative
The putative channels of FeFe hydrogenase
The enzymes that catalyse the oxidation and production of H2 come in two main flavors, 77 with an active site consisting of either a dinuclear NiFe cluster or a dinuclear
FeFe subsite covalently bound to a 4Fe4S cluster (the so-called “H cluster”). 78 FeFe
hydrogenases are found in anaerobic bacteria, archae and green algae. The algal FeFe
hydrogenase from Chlamydomonas reinhardtii (Cr) houses the H cluster and no other
cofactor. 79 In the enzyme from D. desulfuricans (Dd, pdb accession code 1HFE 49 ) and
C. pasteurianum (Cp, 1FEH 80 and 3C8Y 81 ), electrons are transferred to or from the
redox partner by 2 or 4 FeS clusters, respectively. Supplementary figure 1 shows a
complete alignment of the amino acid sequences of these enzymes, together with those
of the catalytic subunits of the complex NADP-dependent hydrogenases of Thermotoga
maritima (Tm) 82 and D. fructosovorans (Df). 83 Figure 1A shows the overall arrangement of the cofactors in Cp FeFe hydrogenase, which is very similar to the enzymes
from C. acetobutylicum (Ca) we study (the percentage of identity equates 71%).
Figure 1 depicts three putative channels in Cp FeFe hydrogenase. The grids are the
surfaces of tunnels calculated by exploring the “dry” (internal water removed) enzyme
using the program CAVER. 32 Figure 1B is rotated about 90◦ .
We call “A” the elongated, “static” cavity that was first found by some of us in
the structure of Dd hydrogenase. 49 It has the same overall shape and position in the
enzymes from Cp. In Dd, it stabilizes a single Xe atom, 77,84 which appears to be
blocked by the site chains of A306, F372 and F160 (A427, F493 and L283 in Cp). Its
location is marked by a blue ball on the structure of Cp hydrogenase in figs 1B and 2.
Channel “B”, depicted as a cloud of sticks in Figure 1, is the “dynamic” path that has
Figure 1: Side and top views of the structure of C. pasteurianum FeFe hydrogenase (pdb
3C8Y), 81 showing the cofactors and the putative channels. The “static” hydrophobic
channel, and the water-filled channel are shown as calculated by the program CAVER. 32
We indicate the position of the “dynamic” channel by showing as sticks the amino acids
that define the corresponding path. 50 Red balls are water molecules stabilized in the
structure of Cp FeFe hydrogenase; the blue ball indicates the location of the Xe binding
site in the homologous enzyme from Dd. 77,84
been identified from the MD simulations of Cohen and coworkers. 50 The two channels
meet in a central cavity called “C”, slightly closer to the active site than the Xe binding
site in the Dd structure. Channel “W” is hydrophilic and stabilizes ten water molecules
in both structures of Cp hydrogenase 80,81 (red balls in figs 1 and 2). Water molecules
are also present at the protein surface, near the entrances of channels A and B.
The three channels (A, B and W) and the central cavity C extend across the portion
of the protein that is common to all FeFe hydrogenases. Tables 1 to 3 show alignments
of the amino acids that define cavity C and channels A and B according to the study of
Cp FeFe hydrogenase in ref 50.
Table 4 lists the amino acids around channel W.
Table 1 shows that the amino acids which line the central cavity are identical in
the 6 enzymes, except for the T-to-V and I-to-A substitutions in the sequence of the
Tm enzyme. In contrast, the cavities A and B are not fully conserved (cf Tables 2 and
3), and the buried amino acids do not seem to be more conserved than those that are
surface exposed. The amino acids that define the position of the wet channel are very
conserved, which suggested that some of them (marked by a superscript h in Table 4)
(a) We list hereafter, using Cp numbering, the amino acids that are close to the pathway A+C calculated
with CAVER and shown in figs 1 and 2 (they are not exactly those listed by Cohen et al., 50 although some
of them, marked with a star hereafter, belong to the list of Cohen et al.): T275, I276, E279, A280∗ , L283∗ ,
V284∗ , I287∗ , C299, P324, F417, V423, A427∗ , L428∗ , A431∗ , A435, I461∗ , N462, N464, F493∗ . We
found that amino acids F293, M295, M424, V459, Y466, N467, V468, H492, identified by Cohen et al. as
part of path A, are actually remote from the channel identified by CAVER.
Table 1: Partial alignment of the amino acids that line the central cavity of FeFe hydrogenases. A complete alignment is shown in Supplementary Figure 1. Boldface indicates
the amino acids we substituted. The dagger († ) marks some of the amino acids whose
substitution is proposed in the patent application of King et al. 85 Ca = Clostridium acetobutylicum, Cp = Clostridium pasteurianum, Dd = Desulfovibrio desulfuricans, Cr =
Chlamydomonas reinhardtii HydA1, Tm = Thermotoga maritima, Df = Desulfovibrio
Table 2: Partial alignment of the amino acids that line pathway A. Boldface indicates
the amino acids we substituted. The dagger († ) marks some of the amino acids whose
substitution is proposed in the patent application of King et al. 85 The double dagger (‡ )
indicates an amino acid selected in the study of Tosatto et al. 86 The stared amino acids
are surface exposed. The superscript "X" marks the xenon binding site.
Table 3: Partial alignment of the amino acids that line pathway B, which Cohen and
Schulten identified from MD simulations using the structure of Cp FeFe hydrogenase. 50
The double dagger (‡ ) indicates an amino acid selected in the study of Tosatto et al. 86 .
Table 4: The “wet” pathway (W). Stars mark surface exposed amino acids. The superscripts indicate the number of contacts with water molecules in both structures of Cp
hydrogenase. 80,81 The superscript “h” marks amino acids that are part of a putative
proton-transfer pathway 49 that also includes K358 and Q366 (Cp numbering, equivalent to K237 and E245 in Dd).
are involved in a proton transport pathway. 49 The three water molecules close to the H
cluster (marked with a star in fig 2) are conserved in the structures of Cp and Dd FeFe
hydrogenase, however, CAVER does not find the wet channel in the latter.
Design of the mutants, purification and solution assays
The boldfaced amino acids in Tables 1 and 2 are those we targeted. They line the
“static” pathway A and the central cavity C, as shown in figure 2. We designed the following mutants (sorted in the order of decreasing distance from the H cluster): I460F
and A430I in attempts to narrow the channel at the surface of the enzyme, F492A and
A426L to alter the Xe-binding site in the middle of the putative channel, V422W and
F416W to obstruct the channel near the active site, and C298A, C298L to respectively
enlarge and narrow the entrance of the central hydrophobic cavity (we use Ca numbering hereafter, unless otherwise stated).
Site-directed mutagenesis was performed on hydA cloned into the pPHhydA1LL-Cstrep-tag vector earlier described by Girbal et al. 87 and improved based on the
study of Von Abendroth et al. 88 to generate the eight HydA mutants for expression in
Clostridium acetobutylicum. This expression system allows production and purification of large amounts of highly active FeFe hydrogenase under strict anaerobic conditions. An average amount of 0.8 mg of purified active protein was obtained for both
native and mutant enzymes. 89 The purity factor, based on the H2 uptake specific activity, is around 60 for most purifications. Since the specific activity of the enzyme
decreases over time, the production, purification, H2 uptake measurements and PFV
experiments were done promptly, and the enzyme samples were handled and stored at
4◦ C and never frozen (we observed that the specific activity decreases by a factor of
Figure 2: Side view of channel A in the enzyme from Cp (pdb 3C8Y), 81 showing the location of the 7 amino acids we targeted. We also indicate the nature of the homologous
amino acids in Ca and/or Dd. Red balls are water molecules stabilized in the structure of
Cp; those marked with a star are conserved in the structure of Dd FeFe hydrogenase. 49
The blue ball indicates the location of the Xe binding site in the enzyme from Dd. 77,84
two in each freeze/thaw cycle).
The in vitro H2 uptake specific activities were measured in the presence of oxidized
methyl viologen. Certain mutations (V422W and F416W) decrease the activity more
than 20-fold. All amino-acids substitutions affect the activity except those of I460 and
A430, which are remote from the active site. The turnover rates are collected in Table 5
(page 17), with all the other kinetic parameters we determined.
We previously introduced the isotope exchange assay as a mean of probing intramolecular transport in hydrogenases. 44 In this non-redox reaction, the enzyme transforms
heavy di-hydrogen (D2 ) into H2 according to scheme 1.
kin [HDout ]
Scheme 1: Mechanism of isotope exchange, and definition of the rate constants used in
the text. The assay is performed in the absence of redox partner.
The mechanism is the following: (i) D2 diffuses from the solvent to the active site,
where it is heterolytically cleaved; (ii) H+ from the solvent substitutes for D+ ; and (iii)
Figure 3: Isotope exchange assay
of the WT enzyme (panel A) and
the A426L variant (panel B). Initial
production of HD (black lines) and
H2 (red lines) after an aliquot of
stock solution of enzyme is injected
in a solution saturated with D2 . pH
7.2, T=30◦ C.
the D+ of the resulting HD species is eventually replaced with H+ , generating H2 . The
formation of H2 from HD can occur either right away or after HD has been transiently
released into the solvent where it can be detected by mass spectrometry.
Since HD production depends on the competition between HD-release and H+ /D+
exchange at the active site, the ratio of initial rates of production of HD and H2 (v0HD
and v0H2 , respectively) informs on the rate of intramolecular diffusion. Indeed, it is
where kout is the 1st order rate constants of HD diffusion to the solvent, and k is the
rate constant of H + /D+ exchange (scheme 1). Alternatively the ratio kout /k can be measured from the rates of decrease of [D2 ] and of the “itotopic content” ([D2 ]+[HD]/2)
and eq. 3 in ref 44 (method 3 in supplementary information therein); we used this
method because we found that the result is less dependent on the initial values of the
concentrations of H2 and HD when the assay is started.
To assay isotope exchange activity, we inject the enzyme in a solution saturated
with D2 , and we use mass spectrometry to monitor the changes in H2 and HD concentrations. 44 Figure 3A shows that the WT enzyme produces HD slightly more quickly
relation is simply obtained from the kinetic model which we introduced in the supplementary
information section of ref 44, by noting that v0HD = 2c0 (kD − kT ), v0H2 = c0 (2kT − kD ), and kT /kD = (1 +
k/kout )/(2 + k/kout ), using the notations defined therein.
than H2 , whereas the difference is less pronounced for the A426L mutant (panel B).
We collected in Table 5 the values of kout /k for the WT enzyme and the 8 mutants.
Only the A426L mutation decreases this parameter; the effect is small (0.61 versus
0.75), but the results were very reproducible. Since A426 is remote from the active
site, it is unlikely that its substitution affects the properties of the H cluster, and the
observation that kout /k decreases a little suggests that the A426L mutation slightly
hinders intramolecular diffusion.
Michaelis constants for H2
We discussed in the introduction of this paper the relation between Michaelis constant
and diffusion kinetics. There are several methods for measuring the Michaelis constant
of hydrogenase. In one method, used by Hagen and coworkers, 90 the enzyme oxidizes
H2 with oxidized methyl viologen as the redox partner, the decrease in H2 against time
is monitored polarographically using a Clark electrode, and the progress of the reaction
is simulated by numerically integrating the one-substrate Michaelis-Menten equation.
This is more convenient than the conventional use of initial rates because the latter are
dependent on the activity of the sample, and because it is difficult to measure initial
rates in solution assays for discrete values of the hydrogen concentration.
The method which we use consists in measuring electrochemically the rate of H2
oxidation with the enzyme adsorbed onto, and exchanging electrons directly with, an
electrode, in a solution initially saturated with H2 and to vary the concentration of H2
by flushing the solution with Argon. The H2 concentration decreases exponentially
with time, 62 with a time constant τ of about 20 to 30s, and the change in activity
(current, i) against time can be modelled by using the Michaelis-Menten equation in
which we introduce a time-dependent concentration of H2 :
1 + [HKm] e τ
The time t is counted from the moment the cell is flushed with Argon, [H2 ]0 is the
initial concentration of H2 . Note that if Km is already larger than [H2 ] before the latter
starts to decrease, the change in current merely follows the change in H2 concentration,
and decreases exponentially with time according to:
imax [H2 ]0 − t
In this unfavorable situation, the value of Km cannot be evaluated. However, this is
not a limitation of the electrochemical method, since any evaluation of a Michaelis
constant requires that the rate be measured at a concentration of substrate that is of the
order of Km or greater, and the solubility of H2 (780µM at 25◦ C) sets an intrinsic limit
Figure 4: Measurement of the
Michaelis constant relative to H2
of the WT enzyme (panel A) and the
A426L variant (panel B). The activity is electrochemically measured
while the solution, initially saturated with H2 , is flushed by a stream
of Ar at t > 0. The data are shown
as black lines. The green dashed
lines are the best fit to eq 3, which
returned Km = 1.1 and 2.5 atm. of
H2 (panels A and B, respectively),
and the red dashed lines illustrate
the exponential decay that would be
obtained if Km were much greater
than the initial concentration of H2 ,
extrapolated from the end of the relaxation of the current using eq. 4.
E = −160mV, 30◦ C, pH 7, electrode
rotation rate ω = 3krpm.
to the greatest measurable value of Km .
Figure 4 shows a typical result obtained with WT Ca FeFe hydrogenase adsorbed
onto an electrode whose fast rotation minimises mass transport control. The H2 saturated solution was flushed with Ar at t > 0. The perfect fit of the data to eq. 3
(dashed green line) proves that the activity follows Michaelis-Menten kinetics. The
fact that the activity starts to decrease as soon as the concentration of H2 decreases
shows that the Michaelis constant is relatively high, which is typical of FeFe hydrogenases. 90 However, the data significantly depart from the exponential decay extrapolated
from the end of the relaxation of the current (dashed red lined), and the ratio Km /[H2 ]0
can be determined: we found Km = 1.1 atm. of H2 . The accuracy of this measurement
is intrinsically low; we estimate that the error on the value of Km is about ±30%.
The experiment in panel B was carried out with the A426L mutant. In this case, the
data hardly deviate from an exponential decay, showing that the Michaelis constant is
larger, of the order of 2.5 atm of H2 (the error on this parameter is large).
Table 5 collects the Michaelis constants of the WT enzyme and the 8 mutants we
tested. Each value is the average of at least four measurements. Only the Km of the
A426L mutant significantly differs from that of the WT enzyme (2.6 versus 1.1 atm of
Kinetics of inhibition by CO
We used the electrochemical method described previously 44,62,63 to measure the rates
of binding and release of the competitive inhibitor CO. The H2 -oxidation activity is
measured as a current, with the enzyme adsorbed onto an electrode immersed and
Figure 5: Kinetics of inhibition by
CO of WT Ca FeFe hydrogenase. The
blue line in panel A is the catalytic
current resulting from H2 -oxidation
by the enzyme adsorbed at a rotating
graphite disc electrode. The injections of CO are marked by arrows
above panel A. The black line is interpolated from the data and shows
the current that would have been
obtained in the absence of CO; the
downward trend is mainly caused
by protein desorption. Using this
black signal for normalization gives
the corrected data shown in black
in Panel B. The dashed green line
is a fit using the model depicted in
scheme 2. E = −160mV, pH 7, 40◦ C,
ω = 3krpm. The current is recorded
after a 300s equilibration period at
rotated in a solution continuously flushed with H2 , and small aliquots of a solution
saturated with CO are repeatedly injected in the cell. The concentration of CO instantly
increases after each injection (the mixing time is about 0.1s) and the resulting dilution
of H2 is negligible. The activity decreases after the addition of CO, and it is fully
recovered as CO is flushed away by the stream of H2 .
Figure 5 shows the result of this experiment carried out with the WT enzyme. Panel
A shows the change in current against time (blue line); the arrows above Panel A
indicate the injections of CO. The downward trend is caused by protein desorption;
this can be corrected by using a spline function to interpolate the data (black line) and
dividing the raw signal by this synthetic curve. 89 The result is shown in panel B (plain
line). To deduce the rate constants of CO binding and release from the data, we assume
that (i) the inhibition and reactivation are first- and zeroth- order in [CO], respectively,
and the concentration of CO decreases exponentially with time, with a time constant τ
(scheme 2), and (ii) the current is proportional to the instant coverage of active (COfree) enzyme.
CO [CO] e− τ
Scheme 2: Mechanism of inhibition by CO, and definition of the rate constants used in
We derived in ref 63 the analytical equation that can be used to fit the electrochem14
Figure 6: Oxidative inactivation
of Ca hydrogenase. The black line
in panel A is the decrease in current resulting from film desorption and anaerobic inactivation
recorded under anaerobic conditions at E = 190mV vs SHE, 30◦ C,
pH 7, ω = 3krpm. The dashed green
line is the best fit to a biexponential
decay. The blue line is the result of
an independent experiment (with a
fresh enzyme film), carried out under identical conditions, except that
aliquots of solution saturated with
O2 are injected at the times marked
by arrows above panel A. The black
line in panel B was obtained by dividing the latter signal by the control; 89 the dashed green line is the
fit to the model depicted in scheme 3.
The data are recorded after a 250 s
equilibriation period at −160mV,
followed by 50 s at E = 190mV.
CO [CO] , kCO and
ical data recorded after a single injection of CO, to determine kin,app
τ. We now find more convenient to simulate a single data set obtained by repeatedly
adding aliquots of CO-saturated solution (fig. 5). The green dotted line in fig 5B is the
CO , knowing
best fit calculated by adjusting a single set of rate constants kin,app
the four values of [CO]0 . Since CO is a competitive inhibitor of hydrogenases, H2
protects the active site against CO, all the more that the Michaelis constant is small.
Therefore, the rate of inactivation in the absence of H2 must be extrapolated using: 63
We repeated this analysis with the 8 variants, and collected the results in Table 5.
The apparent rate of CO binding is greater in the A426L mutant than in the WT enzyme, but this is a consequence of the value of Km being large: none of the mutations
CO or kCO .
significantly affects kin
We note that an alternative strategy for characterizing the kinetics of inhibition
by CO (or O2 ) consists in fitting the exponential relaxation of the catalytic current
that follows a step in inhibitor concentration. 91 This can be achieved by injecting an
aliquot of solution saturated with CO and simultaneously changing the composition of
the gas phase above the cell solution. In that case, the rate constant of the relaxation is
CO [CO] + kCO .
Kinetics of inhibition by O2
The procedure we use to quantify the aerobic inactivation of the enzyme 24,62,97 resembles the method for studying the inhibition by CO, except that the electrode potential
has to be high (greater than about 150mV vs SHE), or else O2 is directly reduced on
the electrode, which contributes to the current and decreases the concentration of inhibitor that is actually experienced by the enzyme. 91 The blue trace in fig 6A shows
the current recorded with the WT enzyme adsorbed onto a rotating electrode poised at
190mV, when aliquots of a solution saturated with O2 are repeatedly injected in the cell
solution saturated with H2 . The effect of film loss and anaerobic inactivation 92–96 can
be removed by dividing the blue trace by the control signal recorded in an independent
experiment carried out at the same electrode potential, but under anaerobic conditions
(black trace); 89 the result of the division is shown in black in fig. 6B.
This corrected trace is a clear readout of the effect of O2 . The current decreases
after each injection of O2 and then increases as O2 is flushed by the stream of H2 , which
reveals the reversible binding of the inhibitor, but the activity is not fully recovered as
the solution become anaerobic, because the O2 adduct slowly reacts to form a “dead”
enzyme, which cannot be reactivated.
The model we use to fit the data (scheme 3) accounts for the reversible binding of
O2 (apparent rates kin2 and kout2 ), followed by the irreversible reactivation of O2 at the
active site (rate kdead ).
[O2 ]0 e− τ
O2 − bound −−
Scheme 3: Mechanism of aerobic inhibition, and definition of the rate constants used in
The dashed green line in fig 6B shows the best fit of the corrected data, from which
the three rate constants in scheme 3 could be determined.
Similar experiments were carried out with all mutants, to obtain the values of the
rate constants collected in Table 5. The rates of O2 binding and release decreased
slightly in the A426L mutant. Remarkably, the 1st order reaction of O2 that follows the
formation of the adduct is twice faster in the F492A mutant than in the WT enzyme.
kout /k b
Km (atm. H2 ) c
CO (s−1 atm(CO)−1 ) d
CO (10−2 s−1 ) d
CO (s−1 atm(CO)−1 ) e
kin2 (s−1 atm(O2 )−1 )f
kdead (10−3 s−1 ) g
f Rate constants defined in scheme 3, and measured by fitting data such as those in fig. 6B, at pH 7, 30◦ C, 1 atm of H2 .
Table 5: Summary of the kinetic properties of Ca hydrogenase mutants (sorted in the order of decreasing distance from the H cluster) at 30o C, pH 7 (unless
otherwise stated). We used boldface for the values of the parameters which we think are significantly affected by the mutations. The dagger marks the amino
acids targeted in the patent of King et al. 85 Superscripts A or C indicate whether the amino acid line path A or the central cavity.
a Turnover rate in the H -oxidized methyl viologen assay. pH 7.2, 37◦ C.
b Value of the ratio k /k obtained by interpreting the results of isotope exchange experiments using eq. 3 in ref 44. pH 7.2, 30◦ C.
c Michaelis constant for H , in units of atm. of H , determined electrochemically by interpreting the results of experiments such as those in fig 4, with eq. 3;
pH 7, 30◦ C. The value of Km in units of atm. of H2 can be converted to a concentration of H2 using the Henry constant of 7.8 10−4 M/atm.
d Rate constants defined in scheme 2, and measured by fitting data such as those in fig. 5, at pH 7, 30◦ C, 1 atm of H .
e Rate constant of CO binding extrapolated to zero concentration of H using eq. 5 and the value of K .
kout2 (s−1 ) f
We have used site-directed mutagenesis and various kinetic methods to probe intramolecular diffusion in Ca FeFe hydrogenase mutants. Putative pathways that may guide H2
from the solvent to the active site of FeFe hydrogenases have been previously identified by performing cavity searches, 49 looking for Xe-binding sites in the crystals 84 or
using MD simulations. 50,51 The resulting picture was that H2 may use either of two
main pathways to enter the enzyme (fig. 1). Pathway A is called “static” because it
is detected as a permanent elongated cavity in the crystal. This channel houses the
only observed Xe-binding site. 84 Pathway B does not show up using programs which
search for cavities in the static structure. It consists of cavities that open transiently as
a consequence of the fluctuations of the protein. Molecular dynamics simulations suggested that this transient path is the dominant route for O2 . 50,51 The amino acids that
define pathways A and B are mostly hydrophobic. We have also described a conserved
“wet” channel connecting the active site to the solvent; it is lined by the hydrophilic
amino acids which interact with water molecules in the structures of Cp hydrogenase
(red balls in fig 2). These three paths end up in a central cavity called C, which leads
to the active site di-iron subcluster.
The search for a substrate channel is crucial in the case of algal FeFe hydrogenases,
because these enzymes could be used for the photosynthetic production of H2 if they
resisted inhibition by O2 . 98,99 We 97 and others 100 have shown that the competitive inhibitor CO protects FeFe hydrogenases against aerobic inactivation, showing that O2
targets the active site. X-ray absorption spectroscopy measurements 100 on the enzyme
from Cr suggest that destruction of the 4Fe4S portion of the H cluster follows up this
initial attack of the 2Fe subsite; this mechanism has not yet been considered in theoretical studies. 101,102 Engineering hydrogenase to slow oxygen access to the H cluster may
increase the tolerance of the enzyme to oxygen. A patent application actually protects
the redesign of FeFe hydrogenases by increasing the bulk of amino acids that line the
putative A-C pathway; 85 the authors’ claims were supported by the observation that
the V296W mutant of Cr FeFe hydrogenase (c) (V422 in Ca) increases the oxygen tolerance of Cr hydrogenase. We note that this observation is in contrast with the proposal
that O2 mainly uses path B in Cp hydrogenase. 51
We have previously developed various methods for probing the effects of mutations on the kinetics of diffusion in hydrogenases, which we have recently applied to
a number of NiFe hydrogenase mutants. 24,44 We showed that certain mutations which
obstruct the channel of Df NiFe hydrogenase slow CO and O2 binding, diminish the
transient production of HD in the isotope exchange assay and increase the Michaelis
constant for H2 . Most importantly, we established quantitative relations between the
(c) In ref 85, the numbering of the sequence of Cr is shifted by 56 amino acids with respect to the sequence
we discuss here: V296 is called V240 in the patent application.
corresponding kinetic parameters, and we demonstrated that O2 and CO diffuse within
NiFe hydrogenases at the same rate, but the former reacts slowly at the active site. This
explained that the rate of inhibition by CO is always greater than the rate of binding of
O2 , unless diffusion is so slow that it limits both processes, in which case kin
CO are of the same order of magnitude (Table 1 in
In WT Ca hydrogenase, kin
ref 24 and Table 5 herein), and we therefore concluded that diffusion limits the rates
of inhibition by CO and O2 in this enzyme. We emphasized the difference between Ca
and Dd FeFe hydrogenases in this respect: transport appears to be faster in the latter
CO ). 24 Similar conclusions were reached by Armstrong and cowork(hence kin
ers 91 from independent experiments aimed at comparing the kinetic properties of the
hydrogenases form Ca, Dd and Cr; the authors also reasoned by examining which rate
constants depend on the redox state of the active site, which can be varied by tuning
the electrode potential.
If true, the above conclusion that diffusion limits the rates of inhibition by CO and
O2 in Ca FeFe hydrogenase should have made our investigation very easy, because any
variation of the rate of diffusion should result in a proportional variation of the rates
of inhibition. And if, as occurs in NiFe hydrogenases, 24 the mutations affect the rates
of diffusion of all diatomic molecules in the same manner,(d) we could also expect
an effect of the mutations on the Michaelis constant for H2 . The isotope-exchange
measurement gives a result that depends only on the ratio of rate of HD release to the
solvent over rate of H+ /D+ exchange at the active site; we expect a variation of this
ratio upon modifying the channel if HD diffusion is slower than HD dissociation from
the active site, and if the mutations have little effect on active site chemistry.
We have applied these methods to 8 mutants of Ca FeFe hydrogenase, designed in
attempts to alter diffusion along the putative A+C pathway (fig. 2). Four of the amino
acids we targeted are among the five amino acids mentioned in the patent application
of King et al.; 85 the latter are marked by a dagger in Tables 1 and 2(e) . Table 5 collects the results; we used boldface for the values of the parameters which we think are
significantly affected by the mutations.
We designed the I460F and A430I mutants in attempts to obstruct the channel at
a distance from the H cluster. The I460F mutant has the same phenotype as the WT
enzyme, despite the fact that the lateral chain of I460 points inside the putative channel.
Alanine 430 is more conserved than I460 (cf Table 2). Replacing A430 with isoleucine
is also expected to obstruct the channel, but the only effect we observed is an increase
(+30%) of the rates of both binding and release of O2 , which is difficult to reconcile
with the fact that the Michaelis constant for H2 and the kinetics of inhibition by CO are
not at all affected.
(d) The mutations have the same relative effect on the rates of diffusion of O , CO and H in NiFe hydro2
genase, although the latter diffuses about 30 times more quickly than do CO and O2 24 .
(e) The patent also mentions F308 (A435 in Cp).
Crystals of Dd hydrogenase exposed to xenon exhibit a single binding site defined
by the side chains of A306, F372 and F160 (A426, F492 and L283 in Cp). The mutation
A426L should make this binding site smaller, and indeed, we found that it decreases
slightly (−20%) but significantly the yield of HD in the isotope exchange assay, suggesting that either HD release (kout ) has decreased or that the rate of H+ /D+ exhange at
the active site has increased; we consider the first option as more likely, because A426
is remote from the active site. The mutation also increases the Michaelis constant about
two-fold, suggesting again that it slows down the diffusion of H2 , but the agreement
between the two measurements (Km and kout ) is only qualitative (ideally, these parameters should be proportional to each other, consistent with our observations with NiFe
hydrogenase mutants in ref 44). The mutation seems to significantly slow O2 binding
and release (−30 and −20%, respectively), but surprisingly, it has no effect on the rates
CO and kCO ).
of binding and release of CO (kin
The properties of the F492A mutant were unexpected. The mutation has no effect
on any of the parameters that depend on intramolecular diffusion kinetics, but it increases about two-fold the 1st order rate of reaction of O2 at the active site (kdead in
scheme 3); this is so despite the fact that F492 is remote (> 10Å) from the active site.
The mutations V422W and F416W were designed to block the central cavity but
they do not affect the parameters we measured, except the H2 -oxidation turnover rate,
which is decreased more than 20-fold by either mutation. This substitution of V422 in
Ca is equivalent to the V296W mutation that increases the resistance to oxygen of Cr
FeFe hydrogenase, defined in ref 85 as the fraction of H2 -production activity that remains after Cr cell extracts have been exposed to small amounts of O2 (1 to 4% O2 for
two minutes). We defined and quantified oxygen sensitivity differently, as the rate of inhibition during H2 -oxidation. This may be the reason we could detect no improvement
of the resistance to O2 , although it is possible that the improvement of O2 tolerance
observed with the Cr hydrogenase mutant does not result from hindered intramolecular
diffusion of O2 , or that the equivalent mutations in Cr and Cp do not have the same
effects (since the mutant of Cr was not purified, it is unknown whether the mutation in
Cr also has a detrimental effect on turnover rate). We have recently emphasized that
certain equivalent mutations carried out in homologous NiFe hydrogenases do not have
the same effect. 25
Phenylalanine 416 is downstream from channels A and B (but not W), and it is
therefore most surprising that the F416W mutation has no effect either. This suggests
that fluctuations play a major role even at this position, whereas, according to the values
of the B-factors in the crystal structure of Cp hydrogenase, the mobility of F417 is low
Cysteine 298 is a highly conserved residue in the vicinity of the di-iron subsite,
whose side chain points inside the cavity, downstream from all paths. We did not
attempt to insert bulky residues at this position, fearing that this may destabilize the
Figure 7: Coloring of the structure of Cp FeFe hydrogenase (panels A and B) and Dd
hydrogenase (panel C) by B-factor (pdb 3C8Y and 1HFE, respectively). Panel A shows
the complete structure of Cp hydrogenase, panel B shows only the amino acids that line
channel A. The orientations are the same as those in figs 1A and 2. The B-factors are
coded from blue (low) to red (high).
active site, but we found that this amino acid is not essential for activity. Its substitution
does not affect oxygen sensitivity either, whereas in NiFe hydrogenases, the presence
of methionines near the active site greatly improves oxygen resistance. 74,103
Overall, we observed that only the A426L mutation has an effect on the rates of intramolecular transport: it slows the production of HD, increases the Michaelis Menten
constant, and decreases the rates of binding and release of O2 , although, surprisingly,
the mutation has no effect on CO binding and release. It is also remarkable how small
these effects are in comparison with those observed in NiFe hydrogenase mutants. 24,44
The reason for this is, of course, unclear, but we can propose three distinct explanations.
The first option is that the amino acids we targeted are indeed along the main path,
but the mutations do not block the channel, possibly because fluctuations are significant. Figure 7A shows a coloring of the structure of Cp FeFe hydrogenase by B-factor.
Channel A is in a region of the protein that is highly disordered in the crystal. The
same observation can be made from the structure of Dd hydrogenase (fig 7C). The
entrance of channel A, near the protein surface, is particularly mobile, and it is may
not be so surprising that the channel cannot be blocked here, although Tosatto and
coworkers identified one amino acid at the surface of the protein in this region (H492,
Cp numbering), which may provide oxygen tolerance to Thermotoga neapolitana FeFe
Alternatively, one or several of the mutations we designed may obstruct the channel, but this creates an alternative route that bypasses the blocked channel. In this respect, we note that MD simulations suggest that a mutation that blocks the permanent
channel of haloalkane dehalogenase causes the product to use a different (transient)
path. 71 However, we consider as unlikely that this would have no detectable effect on
the kinetics of intramolecular transport.
Last, it may be that we did not target the right pathway. Four mutants out of 8 were
designed to alter channel A, and two others were expected to modify the central cavity, downstream from paths A and B. We have not yet targeted any amino acid that is
specific of channel W, and it is possible that this channel is actually functionnal for H2
and O2 transport. Hydrophilic channels are not usually considered for the transport of
small hydrophobic ligands. However, several results in the literature suggest that this
may be a misconception. For example, hydrophobic ligands are sometimes stabilized
in hydrophilic pockets: Prangé and coworkers observed that Xe 35 or O2 104 under pressure can displace water molecules in protein crystals, and in at least one structure of
copper amine oxidase, Xe atoms displace two water molecules. 40 Conversely, recent
MD simulations of Myoglobin have shown that two Xe binding sites in Mb transiently
house water molecules, 105 and the channel of both type-1 106 and type-2 107 cholesterol oxidase stabilizes water molecules, despite the fact that they are predominantly
lined by hydrophobic side chains. In catalase, the results of MD simulations suggest
that O2 , H2 O2 and H2 O share the same channel, 108 which stabilizes a chain of water
molecules in the crystal. 72 In ACS-CODH, although the channel that transports CO
has been identified, the path for CO2 access to the C-cluster is unknown, and, among
other options, it has been suggested that a hydrophilic channel is used in this respect. 52
Last, there is now evidence that in nitrogenase, a channel that stabilizes a string of
water molecules in the crystal is used for transporting the substrates N2 , 66 whereas the
V76I mutation, which was expected to disrupt the putative hydrophobic putative channel, has no effect. 109 However, we must note that N2 reduction of ammonia is slow,
and therefore a channel that allows fast diffusion of N2 in this enzyme may not be a
The introduction of this paper made it clear that only in very few enzymes have substrate channels for small ligands been unambiguously identified. It is unfortunate that
the experiments reported here do not clarify the case of FeFe hydrogenase, considering
the usefulness of hydrogenases that are engineered to resist inhibition by O2 . 85,103 Yet,
our work illustrates how difficult it may be either to prove the existence of a preferred
pathway or to establish that a single pathway does not exist. This is because mutations
that do change the rate of diffusion may have no effect on the kinetic properties that
can be measured (cf the discussion of eq. 1 or the discussion in ref 24). Therefore, the
fact that the substitutions we performed did not modify the enzyme’s properties does
not imply that the substituted amino acids do not line the prefered gas pathway. In our
recent study of NiFe hydrogenase, 24 we showed that substitutions that make the channel hydrophilic have a much stronger effect that any attempt to block the channel with
a bulky side chain. Therefore, we are now trying to substitute hydrophobic side chains
in channel A with charged groups. We now also wonder whether it may be possible
to prove that small ligands diffuse within FeFe hydrogenase through transient cavities
created by the fluctuations of the protein by designing mutations that make the protein
more rigid, possibly by introducing intramolecular disulfide bonds or salt bridges. We
also must explore the possibility that, in contrast with previous hypotheses, the wet
channel is used for guiding the substrate and inhibitors in FeFe hydrogenases.
We acknowledge Sébastien Dementin and Emilien Etienne (BIP, Université de Provence,
Marseille), Azat Gabdulkhakov (Institut fuer Kristallographie Freie Universitaet Berlin)
and Yvain Nicolet (IBS/LCCP, CEA, CNRS, UJF, Grenoble) for fruitful discussions.
Our work is funded by the CNRS, ANR, INSA, CEA, Université de Provence and
City of Marseilles. We also acknowledge support from the “pôle de compétitivité
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