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Biophys J, June 2002, p. 3224-3245, Vol. 82, No. 6
Laboratoire de Modélisation et Ingénierie des Protéines, Institut de Biochimie et de Biophysique Moléculaire et Cellulaire, Centre National de la Recherche Scientifique, Unité Mixte de Recherche 8619, Université Paris-Sud, 91405 Orsay cedex, France
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ABSTRACT |
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 TOP
 ABSTRACT
 INTRODUCTION
METHODS
RESULTS
DISCUSSION
CONCLUSION
REFERENCES
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It is still difficult to obtain a precise structural
description of the transition between the deoxy T-state and oxy R-state conformations of human hemoglobin, despite a large number of
experimental studies. We used molecular dynamics with the Path
Exploration with Distance Constraints (PEDC) method to provide new
insights into the allosteric mechanism at the atomic level, by
simulating the T-to-R transition. The T-state molecule in the absence
of ligands was seen to have a natural propensity for dimer rotation, which nevertheless would be hampered by steric hindrance in the "joint" region. The binding of a ligand to the 
subunit would prevent such hindrance due to the coupling between this region and the
proximal histidine, and thus facilitate completion of the dimer
rotation. Near the end of this quaternary transition, the "switch"
region adopts the R conformation, resulting in a shift of the 
proximal histidine. This leads to a sliding of the -heme, the effect
of which is to open the -heme's distal side, increasing the
accessibility of the Fe atom and thereby the affinity of the protein.
Our simulations are globally consistent with the Perutz strereochemical mechanism.
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INTRODUCTION |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
CONCLUSION
REFERENCES
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Human hemoglobin (Hb A) is an allosteric
oxygen-binding protein that adopts two distinct conformations: the
low-affinity deoxygenated T state and the high-affinity fully liganded
R state. A mechanism for the transition from one conformation to the
other upon ligand binding has been proposed by Perutz
(1970)
, Perutz et al. (1998), and Baldwin
and Chothia (1979). In this mechanism, the binding of a ligand
to one subunit modifies the position of the proximal histidine (F8)
with respect to the heme, inducing a movement of the FG segment (the
segment that connects helices F and G), which forms a part of the
12 interface. The adjustment of this interface causes dimer
rotation and modifies the network of hydrogen bonds and salt bridges at
the 12 interface. This decreases the strain on the proximal
histidine of the facing subunit and modifies the ligand accessibility
to the heme iron atom in the subunit by "opening" its distal
side. These structural modifications result in an increase of the
protein affinity. The Perutz mechanism provides the best framework for
understanding much of the experimental results on oxygen binding,
although several points remain unclear. One is the role played by the
11 interface. This interface is not referred to in this
mechanism, but several experimental results (Levy et al.,
1992; Tsai et al., 1999, 2000; Mihailescu and Russu, 2001)
suggest that its role is not negligible. There is also an aspect of the
proposed mechanism that is difficult to explain, in that the binding of
ligand to the subunits is supposed to induce the quaternary
transition, as is seen experimentally in solution (Ogawa and
Shulman, 1972; Fujii et al., 1993; Kiger
et al., 1993; Unzai et al., 1998), whereas the
conformational changes seen in these subunits are minimal as compared
to the chains.
A tremendous number of experiments have been carried out to study the
allosteric transition and to try to trap intermediate structures along
this path. Most solution studies suggest that, under physiological
conditions, Hb passes through a quaternary R-like intermediate state
(Ogawa and Shulman, 1972; Murray et al.,
1988; Eaton et al., 1991; Henry et al.,
1997). However, crystal structures of partly liganded Hb have
indicated a quaternary T-like structure (Luisi and Shibayama,
1989; Luisi et al., 1990; Waller and
Liddington, 1990; Liddington et al., 1992;
Bruno et al., 2000), but this may reflect the
experimental constraints (such as the presence of allosteric effectors,
low temperature, etc.). It also might be noted that even a fully
liganded Hb has been crystallized in the T structure under certain
conditions (Paoli et al., 1996). Moreover, a mutant
carbonmonoxyHb (Hb Ypsilanti, 99Asp
Tyr) (Smith et al.,
1991), and a wild-type carbonmonoxyHb (R2) that was
crystallized at low salt concentration (Silva et al.,
1992) were first described as being in an intermediate state
between T and R. However, computer simulations, based on docking and
distance calculations, suggested that it is instead the R form that is
intermediate between T and R2 (Srinivasan and Rose,
1994), or between T and Hb Y (Janin and Wodak,
1993).
Only a few molecular simulations have been carried out for Hb because
of its large size, which makes them very time-consuming. Thus, some
simulations have been done with only a part of the protein, such as the
subunit (Gelin et al., 1983), the 12 interface
(Gao et al., 1989), or the 11 dimer
(Ramadas and Rifkind, 1999), or by using a rigid-body
docking approach (Janin and Wodak, 1985). However, in
the last decade, increases in the power of computers have made it
possible to study the entire protein (Shibayama et al.,
1995b; Mouawad and Perahia, 1996; Kim et
al., 2001). Still, to our knowledge, no simulation of the
transition path of Hb by molecular dynamics (MD) has been published.
The problem with studying large-scale conformational transitions by
traditional molecular dynamics is that, even in very long simulations,
the transition will occur rarely, if at all. Different methods have
been introduced to attack this problem. One approach involves
generating an initial guess for a trajectory leading from the starting
to the final conformation, and then optimizing this trajectory to
obtain the best transition pathway (Elber and Karplus,
1987; Ulitsky and Elber, 1990; El-Kettani
and Durup, 1992; Fischer and Karplus, 1992;
Olender and Elber, 1996; Ulitsky and Shalloway,
1997; Huo and Straub, 1997; Zaloj and
Elber, 2000). This approach requires the generation of a large
number of intermediate structures in the initial trajectory to properly
sample the conformational space. The computational penalty associated
with optimizing such a large number of intermediate structures
simultaneously can be limiting for a large protein such as Hb. A second
class of approaches is sequential, i.e., it involves inducing the
transition in a single molecule simulation from one conformational
state to the other (Harvey and Gabb, 1993;
Schlitter et al., 1994; Guilbert et al.,
1995; Csajka and Chandler, 1998;
Zuckerman and Woolf, 1999; Geissler and Chandler,
2000). In most of these latter methods, the length of the
simulation, or the number of the intermediate structures, is
predetermined, which may constitute a difficulty for large proteins
where some readjustments can be harder to attain than initially estimated.
We present here the first MD simulations of the T-to-R transition in
human Hb. For this we used a combination of MD with the path
exploration by distance constraint method (PEDC) (Guilbert et
al., 1995). The value of this method is that it is sequential but without predetermination of the length of the simulation, and also
that it gives the possibility of simulating a pathway by MD (i.e., not
only by energy minimization) at ambient temperature in presence of the
solvent. This method consists of the addition to the potential energy
of a constraint term that forces the protein (in our case the
deoxygenated T-state Hb A) to approach a reference conformation (here,
the fully oxygenated R-state Hb A), by decreasing the mass-weighted
root-mean-square (mrms) deviation between the two conformations by a
series of displacements, each consisting of several picoseconds of MD
(here ~10 ps, see Methods). Two separate trajectories (TrajI and
TrajII) of 200 ps each, corresponding to 16 intervals of displacement,
were performed to bring deoxygenated hemoglobin from the T state to the
R state.
The simulated pathways made it possible to predict the presence of
transient events, especially at the 11 interface, and resulted in
a mechanism consistent with the Perutz stereochemical mechanism, but
with a different chronology of events. This mechanism makes clearer the
difference in roles played by the and subunits in Hb affinity
and cooperativity.
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METHODS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
CONCLUSION
REFERENCES
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Description of the method
The PEDC method (Guilbert et al., 1995), which we
implemented in the CHARMM program (Brooks et al., 1983),
involves the addition of three constraint terms to the potential energy
usually used in MD simulations. The main constraint is the distance
constraint potential, Vdist, which forces the
system toward a given mrms deviation from a reference, whereas the
other two terms, Vtrans and
Vrot prevent the system from satisfying the
distance constraint by overall translation or rotation, respectively.
The distance constraint potential Vdist is
harmonic,
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d and carrying
out MD or energy minimization (EM) runs. Thus, step by step, the system
reaches the reference structure by the least energetically costly path
consistent with the constraints.
However, this harmonic potential, which is very satisfactory for EM, is
less suitable for MD. Indeed, driving the system toward the reference
structure requires a relatively large force constant for the constraint
potential, which may restrain the normal fluctuations of the system. We
therefore adopted a flat-bottomed-well potential. Thus, in this study,
Vdist was of the form (Fig.
1),
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d, was
set at a value a little larger than the average rms fluctuations of
hemoglobin at 300 K, i.e., 2d = 0.8 Å. The
force constant, which, in the case of a harmonic potential, must be
small to prevent damping of the fluctuations, should, in the case of
the flat-bottomed-well potential, be very large to confine the system
to the well. We used kdist = 106 kcal/mol/Å2. Such a large value
does not perturb the system when it is inside the desired well, but is
nevertheless not suitable for displacement of the system from one well
to another, because it will induce large forces. Hence, the
displacement phase is divided into two parts: the driving phase, in
which the force constant is increased gradually from 200 to
106 kcal/mol/Å2 (see the transition
pathways in the Procedure) to move the system into the energy well, and
the confinement phase, in which MD is carried out using the constraint
(Vdist) described above, with a force constant
equal to 106 kcal/mol/Å2, to keep the
system within the well.
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Procedure
This study was carried out on hemoglobin in a box of water with periodic boundary conditions.
The force field
The force field parameters were set as follows: the QUANTA/CHARMm21 parameter set for extended atoms (with polar hydrogens explicitly represented) was used for amino acids and TIP3 water, and the all-hydrogens CHARMM22 parameter set was used for heme, to prevent artefactual distortions of this prosthetic group.The water box
It was important to choose the truncation functions for electrostatic and van der Waals energies that yielded a radial distribution function of water g(r) that best fitted experimental data. Several MD trajectories of 10 ps each were calculated for boxes of water of different dimensions, with different combinations of truncation functions and cutoff distances. The combination that yielded the best radial distribution of water was the shift function for electrostatic energy with a cutoff distance of 11 Å and the switch function for the van der Waals energy with cuton and cutoff values of 10.5 and 11 Å, respectively. The water box considered was cubic, with the length of each side equal to the largest diameter of the protein in either state plus two times the cutoff distance. Thus, the length of the side of the box was 92 Å. Such dimensions were necessary to prevent direct interactions between the protein (or even the first layer of water) and its images, because movements of large amplitude were expected to be observed. This water box was constructed and equilibrated at 300 K. In all that follows, the MD was carried out in a microcanonical ensemble (constant volume and energy) with the Verlet algorithm (Verlet, 1967); the time step was equal to 1 fs with the use of the
SHAKE algorithm (Ryckaert et al., 1977) applied to all
covalent bonds involving hydrogen atoms. Because water molecules are
considered explicitly, the value of the dielectric constant was set
equal to 1.
The protein
The structure of the deoxy T-state Hb A used in this study was derived from PDB (Bernstein et al., 1977) entry 2HHB (Fermi et
al., 1984). A rigorously symmetric mean structure was generated for both dimers to start the simulations, as described in
Mouawad and Perahia (1996). In the oxy R state of Hb A,
the PDB structure designated 1HHO (Shaanan, 1983) shows
only one dimer, the other being obtained by symmetry. We point out that
symmetry was not maintained artificially in the MD calculations and the
structure was therefore free to evolve in a different way for each
dimer. In both T and R structures the tautomeric forms of the
histidines were assigned in a way that favored the formation of
hydrogen bonds. None of them was protonated.
The potential energy of the protein was slightly minimized in vacuum,
using the conjugate gradient algorithm of CHARMM, to eliminate
unfavorable interactions due to crystal imprecision. In the first 300 steps, harmonic constraints (not to be confused with PEDC constraints)
were applied to heavy atoms to allow smooth minimization without any
abrupt deviations from the crystal structure. The harmonic force
constant was decreased every 50 steps, taking the values of 250, 100, 50, 25, 10, and 5 kcal/mol/Å2. We then carried
out free minimization for 300 steps.
The protein in the water box
Hemoglobin, along with the crystallographic water molecules, was immersed in the center of the water box. All water molecules that overlapped either protein or crystallographic water molecules (i.e., distance between heavy atoms less than 2.8 Å) were deleted, leaving a system of 66,723 atoms, 5,598 of which corresponded to the protein itself. The protein's temperature was close to 0 K because its energy was minimized, whereas the temperature of the water was 300 K. To homogenize the system, the protein was fixed and the temperature of water was decreased to 0 K in 5 ps. The whole system was then heated to 300 K in 50-K intervals over 7 ps. This procedure was applied to both T and R structures. The oxygen ligands were kept in the heating phase for the R-state structure. The resulting R structure was used as the reference R in the PEDC method to compute the transition pathway. For comparison, two transition pathways were calculated; both used the same reference structure and started from the same minimized T structure but were heated with different Gaussian assignments of velocities. We refer here to these two trajectories as I and II.The transition pathways
The same procedure was applied for both trajectories. The system was equilibrated at 300 K for 10 ps, then the mrms between the obtained structure of Hb in the T-state and the reference structure in the R-state was calculated: mrms(I) = 3.15 Å and mrms(II) = 3.05 Å, (the mrms between the T and R crystal structures is 2.66 Å). The oxygen molecules (O2) of the reference (R) were not taken into account. Then followed 10 ps of productive dynamics simulations in which the PEDC constraints were applied to maintain the structure at approximately the same mrms distance from the reference (Fig. 1). However, because the protein was always inside the flat bottom of the potential well during these simulations and therefore did not "feel" the constraint at all, this phase of the calculations, which we will call displacement 0 (J = 0, where d
10 kcal/mol/Å2, respectively,
and the width of the potential well 2d = 0.8 Å.
For the first displacement (J = 1), the mrms was
decreased by d = 0.3 Å, such that
d
d from 0.3 to 0.15 Å
for subsequent displacements, the rest of the procedure remaining the
same. Throughout both trajectories, the PEDC constraint energy in the
confinement phase (as opposed to the driving phase) was maximally
103 kcal/mol per degree of freedom of the protein, when
the system reached one of the walls of the well. Thus, 16 displacement
phases (or intervals) were used to bring the protein within d of the R state (d
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RESULTS |
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TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
CONCLUSION
REFERENCES
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In a MD simulation, the movements of the protein appear rather chaotic. Thus, we considered significant only the results relative to events taking place in both dimers (although not necessarily at the same time) and in both trajectories. The time indicated throughout the article refers to our simulation time, and not to the real time of the T-R transition, because the dynamics were carried out under constraints.
Potential energy profile
It is difficult to straightforwardly calculate an energy profile
of the transition pathway of a protein calculated by MD in explicit
solvent. The strategy generally used is to apply an implicit solvent
model to configurations of the protein taken from the trajectories
(Duan et al., 1998). We present in this section the potential energy profile of Hb in which the solvent effects are taken
into account by using a distance-dependent dielectric constant. Such an
implicit solvent representation can overestimate electrostatic energies, but our purpose here is only to present a rough estimation of
the potential energy along the transition trajectories to see whether
the use of PEDC has introduced artefactual energy barriers.
In Fig. 2, we can observe that, for both trajectories, the potential energy of the protein is almost stable until ~57 ps (corresponding to the end of displacement J = 3), at which point it starts to increase, reaching a plateau at ~100 ps (end of J = 7). The large energy difference between these two points is mainly due to the overestimation of electrostatics as mentioned above. At the end of the trajectories (t > 165 ps, corresponding to the last 3 intervals of displacements), one can see that, in each driving phase leading to the next interval (see Methods), the potential energy of the protein increases and then decreases as it relaxes during the confinement phase. At this stage of the trajectories, it would appear that the confinement phase is not long enough to allow a complete relaxation of the protein. However, this is of no consequence for the structural analyses that follow, because, in the last three displacements (J = 14-16) the protein is already within fluctuation distance from the reference structure.
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Global analysis
Analysis of the structural modifications along the trajectories
showed that the T-R transition could be divided into two major steps:
the first step involving the quaternary transition (i.e., the rotation
of one dimer with respect to the other), and the second step
being the tertiary transition (i.e., the internal modifications of each
or chain to give the R-state). Indeed, as shown in Fig.
3, the rotation of the dimers was almost
completed (i.e., dimer rotation angle 
relative to R reduced almost
to 0°) when the rms deviation of the subunits from their tertiary R
structures started to decrease
at 67 ps (beginning of interval J = 5) for the chains and a bit later (77 ps,
beginning of interval J = 6) for the chains.
However, this does not mean that the chains behaved as rigid bodies in
the first part of the transition. Indeed their rms with respect to the
T structure increased from the beginning of the transition, but their
internal modifications did not start to bring them close to the R
structure until the quaternary transition was almost completed.
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In TrajI, rotation of the dimers started spontaneously. The system did
not feel the energy of constraint in the first displacement (J = 1, 27 ps < t 
37 ps)
because it had already reached the first intermediate mrms window in
the unconstrained step (J = 0). In addition, for the
next displacement (J = 2), the energy of constraint to
bring the system into the window (see Fig. 1) did not exceed 7 kcal/mol. This constraint energy, which is global (i.e., not localized
in any particular part of the protein) represented a negligible
perturbation for the protein as it corresponded to less than one
thousandth of its total energy (4 × 104 kcal/mol
per degree of freedom), and it lasted less than half a picosecond. This
shows that the quaternary transition may take place easily in the T
state, confirming the results obtained previously by normal-mode (NM)
calculations, which yielded a single low-energy mode corresponding
mainly to the quaternary rotation (Mouawad and Perahia,
1996).
In contrast, in TrajII, in the free dynamics phase (J = 0, 17 ps < t 27 ps), dimer rotation began in
the opposite direction from that required for the R structure. Thus, in
the first displacement phase (J = 1), constraint was
necessary to bring the structure closer to the reference. Indeed, in
this trajectory, the energy of constraint was greater than zero during
the whole driving phase (1.2 ps), although with a maximum of only about
103 kcal/mol per degree of freedom. However, as seen in
Fig. 2, for both TrajI and TrajII, the overall energy profile, up to
~60 ps, is essentially flat.
Movement of the helices
Visually, it is clear that the axis of rotation of one dimer is
very close and parallel to the axis of its G helix (Fig. 4). This was confirmed by projection of
the axis of the G helix onto the rotation axis of the corresponding
dimer. This projection, after normalization of the two vectors, was
close to unity along both trajectories.
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To describe the movement of the helices of the protein over time, we
calculated the angle between each helix axis at time t
relative to its corresponding axis in the T structure (here, the 7-ps
structure at the beginning of free equilibration) after superimposition
of the relevant chain (results not shown). In the chains, the C
helix underwent the largest movement, which started in the beginning of
the transition. The F helix moved to a lesser extent, and the other
helices did not move significantly. In the chains, the amplitude of
the movement of the D and F helices was greater than that of the C
helix, and the movement of the other helices was not significant.
Interestingly, in the chains, the system behaved as if the
amplitude of the C helix movement was diminished by the presence of the
D helix, which has no equivalent in the chains.
Comparison with rigid-body rotation
We investigated possible factors impeding or favoring simple
rigid-body rotation of the dimers. Independently of the calculated PEDC-MD trajectories, we carried out a rigid-body rotation (RBR) of one
dimer with respect to the other and calculated, for each degree of
rotation, the distances between the C
atoms of the
contact residues at the 12 and 21 interfaces. More
precisely, the rigid-body movement consisted of rotation of one dimer
with respect to the other, accompanied by a small translation of that dimer to bring the quaternary T structure close to the R form. For the
sake of simplicity, however, this rigid-body movement will be referred
to as rotation.
Various pairwise residue distances at the interdimer interface were
calculated as a function of the RBR angle '. To compare the RBR
distances with those obtained along the calculated PEDC-MD trajectories, they are expressed as a function of time using the correspondence between angles ' and to obtain the equivalent time from Fig. 3 A. Some typical curves are shown in Fig.
5.
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As can be seen in Fig. 5 for the residue pair 1(2)Pro-44(CE2) and
2(1)His-97(FG4), several distance curves taken from the PEDC-MD
trajectories corresponded well, or with a short time-lag, to RBR,
suggesting that modification of the distance between these regions is
similar to that of a simple dimer rotation. Interestingly, some of the
other curves were very different, such as those referring to the
"flexible joint" region consisting of the FG corner and the C
helix (Fig. 6). More precisely, the
curves in Fig. 5, corresponding to the C distance
between 1(2)Asp-94(G1) and 2(1)Trp-37(C3), showed that the
RBR distance decreased to 3.5 Å, whereas the distance seen in PEDC
dynamics decreased only to 6 Å. Similar behavior was observed to a
lesser extent for other amino-acid pairs in the flexible joint region,
such as those involving residues 92, 93, and 95 in the chains, and
residues 40 and 43 in the chains. This implies that the residues in
this region, especially Asp-94 and Trp-37, are likely to impede
simple rotation of the dimers and that this could be overcome by
tertiary modifications of the subunits.
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Another interesting case in which RBR yielded a distance curve
significantly different from the corresponding PEDC result concerned
the residues 1Val-96(G3) and 2Val-96(G3). Indeed, whereas RBR
would increase the distance between the C atoms of these
residues, in the calculated trajectories, this distance decreased to a
minimum (at ~57 ps, J = 3) during dimer rotation and
then increased to the distance given by the RBR. At the minimum distance in the PEDC-MD results, contact between valine side chains occurred.
Interfaces 21 and 12
The major structural modifications in the T-to-R transition
described in the literature concern the C-termini of the and chains and the switch region, which consists of the C-helix of
2(1) and the FG segment of 1(2) (Figs. 5 D
and 6). In the switch region, during the T-R transition, the relative
position of 1His-97 (FG4) changes from between 2Pro-44(CE2) and
2Thr-41(C6) to the adjacent placement between residues
2Thr-41(C6) and 2Thr-38(C3). This movement is referred to here as
the "switch transition"; it is shown in Fig.
7, in which the -chain C helices of
several structures (at the ends of intervals J = 0 to
J = 16) are superimposed. However, this representation
can give the misleading impression that the 2C helix is static and
that only the 1His-97 moves. This is not the case because, as was
mentioned above, the C helices were shown to be very mobile during
the transition. Thus, Fig. 8 shows
another representation in which the 2C helix and its facing
1His-97 in the first half of the transition (snapshots taken at the
ends of intervals J = 0 through J = 7)
are represented on a grid in the absolute frame (i.e., with no
superimposition). This shows that, in the first part of the transition,
the 2C helix is mobile and deformable, possibly inducing the shift
of 1His-97(FG4). Indeed, in this representation, it is only in
interval J = 6 (between 78 and 88 ps) that 1His-97
started to change its absolute position.
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The distance between the centers of mass (CM) of side chains
1(2)His-97(FG4) and 2(1)Pro-44(CE2) (Fig. 9
A), started to increase at 67 ps (start of interval J = 5) due essentially to movement of the C helix itself. Note that, at this point, before the
relative position of 1(2)His-97(FG4) started to change, the dimer
had rotated by ~11° ( 
4°, see Fig. 3
A). At the end of the switch transition (J = 9, 120 ps), when dimer rotation was essentially complete ( < 2°),
the intrasubunit distance between the side chains CM of the
C-terminal residue His-146(HC3) and Asp-94(FG1) began to increase
significantly (Fig. 9 B). Finally, near the end of the
trajectories (130 ps, end of J = 10), the interdimer
residues 1(2)Trp-37(C3) and the C-termini
2(1)Arg-141(HC3) started to separate (Fig. 9 C).
This shows that there is a sequence of events that is well respected in
both dimers and in both trajectories. We will see later that, in these
trajectories, there appears to be a cause-and-effect relationship
between these events.
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Hydrogen bonds and salt bridges
In the switch region, the energy of the hydrogen bond between2(1)Thr-41(C6) and 1(2)His-97(FG4) was calculated along the
trajectories (Fig. 10). We found that,
in the 12 interface, a strong hydrogen bond formed between these
residues during the switch transition of 2His-97(FG4), whereas at
the corresponding 21 interface, this hydrogen bond formed only
after the relative transition of 1His-97 was completed. More
generally, during the transition of His-97 (i.e., between 67 and 120 ps), the interaction energy (and not only the hydrogen bond energy)
between this residue and Thr-41(C6) was always attractive at the
12 interface, whereas it was, at times, repulsive at the 21
interface (results not shown), suggesting that there are different ways
for the system to undergo this transition.
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2(1)Tyr-42(C7) and
1(2)Asp-99(G1), which is characteristic of the T-state,
largely resisted dimer rotation, although it did display
fluctuation. It broke definitively after the dimer rotation angle
decreased to less than 4°. Another T-state hydrogen bond, between
2(1)Asp-94(G1) and 1(2)Trp-37(C3) (in the joint region),
was much weaker but still resisted dimer rotation, at least at the
21 interface. The hydrogen bond between 2(1)Asp-94(G1) and
1(2)Asn-102(G4) is usually described as characteristic of the
R-state; Fig. 10 shows that it may exist at various stages of the
allosteric transition, even in the T-state, though it is more frequent
in the R-state. The strongest hydrogen bond (mean value 
1.5kcal/mol)
at this interface, which also resists dimer rotation, is between
2(1)Arg-141(HC3) and the backbone of 1(2)Val-34(B16).
Two salt bridges have also been described at this interface. In TrajI,
both salt bridges 2(1)Lys-90(FG2)-1(2)Glu-43(CD2) were
disrupted more or less as a function of dimer rotation (Fig. 11
a, left). In TrajII, this salt bridge
in the 12 interface broke very quickly because, during the first
half of this trajectory, 2Glu-43 interacted more strongly with the
neighboring 1Arg-92(FG4). In both trajectories and both dimers, when
the system was close to the R state, Lys-90(FG2) rotated and
established a hydrogen bond with one heme propionate of the same chain
(not shown).
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2(1)Lys-40(C5), which is in the
switch region, and the C-terminal carboxyl group of 1(2)His-146 (Fig. 11 A, right). It broke entirely after ~120 ps
(J = 9) because the C-terminal histidine moved away
from the -lysine (Fig. 11 b) as a result of the transition of
1(2)His-97(FG4) from the 2(1)Pro-Thr environment to the
2(1)Thr-Thr environment (Fig. 7). This transition also induced
the movement of 1(2)Asp-94(FG1), releasing the terminal histidine
(Fig. 9 B), which could then rotate easily to adopt its
position in the R structure. This is why the C-terminal histidine (Fig.
9 B) moved after the transition of His-97(FG4) in
the switch region (Fig. 9 A).
Interfaces 12 and 12
The 12 interface was not significantly modified during the
transition (Fig. 12), except that as
the R structure was neared, the Arg-141 C-termini rotated and filled
the space between the two chains. In contrast, the 12 interface
showed extensive modification during the transition. Indeed, in the T
structure, there is a wide cavity between the chains within which
2,3-diphosphoglycerate binds. This cavity closes upon dimer rotation,
as shown in the structure at the end of J = 6 (88 ps)
in which this rotation has already ended ( < 2°), but the
His-146 C-termini are still outside the cavity. Only after the
hydrogen bonds between the chain C-termini and the Lys-40(C5) in
the opposite dimer were broken at J = 9 (120 ps) did
the histidine residues rotate to fill the remaining space in the
cavity, as a consequence of the attraction by the N-terminal amino
group of the facing chain.
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Interfaces 11 and 22
The 11(22) interface consists of helices B, G, and H
in the subunit facing helices H, G, and B in the subunit,
respectively. The angles between the axes of the different helix pairs
were calculated along the trajectories. Of these, the G-G,
G-H, and H-H helix angles showed significant transient
deviations during the T-R transition. These movements are shown in
Fig. 13. Although, in the other
contacting helix pairs (B-H and H-B), such movements were
less pronounced, they were still sufficiently large to induce transient
contacts between certain residues at this interface, especially between
1(2)Phe-36(C1) and 1(2)Gln-131(H9).
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Environment of the hemes
Distal environment of the hemes
In the chains, the iron atom is hidden by the distal histidine
(E7) and valine (E11) in the T state, which makes binding of the oxygen
molecule more difficult than in the chains (Fig. 14). In the R state (in which
O2 is bound but not shown in the Figure), these residues
are pushed away. To characterize this movement, which is parallel to
the heme plane, we calculated for both trajectories and for all chains
the distances between the C atoms of the distal side
residues and the normal to the best plane made by the four nitrogens of
heme, this line passing through the Fe atom. In the chains, these
distances are approximately the same throughout the T-to-R transition
(Fig. 15). In the chains, these
distances are modified, reflecting the change in iron accessibility. For His-E7 and Val-E11, the distance to the heme normal is ~3.5 Å in the T state and increases during the transition to reach 5-5.5 Å in the R state. More precisely, this value is seen
to increase at the end of dimer rotation (near 90-110 ps, or
J = 6-8).
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subunits, there is apparently very little relative movement
of the distal side residues with respect to the heme normal. In the subunits, the distances calculated for these residues showed an
apparent correlation during the transition, although in some cases with
opposite profiles. This indicates that either the distal side residues
move together parallel to the heme plane in the subunit frame or the
heme moves relative to them. In both cases, given the position of these
residues encircling the normal to the heme plane (see Fig. 14, where
this normal points from the Fe atom toward the reader), such a relative
movement would bring the normal closer to some residues and away from
the others. This explains why, in Fig. 15, the curve corresponding to
Val-E11 (and to His-E7) in the chains have a profile opposite from
that of their neighboring residues.
In fact, these curves reflect movement of the heme within the subunit, rather than movement of the whole set of distal side residues
in concert. This is seen by examining the movement of the Fe atom
itself relative to its position in the T state. In this analysis, for
each or subunit, the structures along the trajectories were
superimposed on the corresponding subunit of the T structure, and the
distance between the Fe atom at each timepoint and its position in T
calculated (curves in black in Fig. 15). The data show that, in the subunits, the displacements of the Fe atom (black curves) are very well
correlated with the distances of the distal residues from the normal of
the heme plane (gray curves). This is not the case for the subunits, where these distances are seen not to vary during the T-R
transition. The same analysis but carried out for the C
atoms of the different distal residues instead of the Fe atom showed no
such correlation for either the or chains (data not shown).
Therefore, from the results presented in this section, we can conclude
that, whereas in the chain the Fe atom is accessible to ligand even
in the T state, in the chain the Fe atom becomes accessible during
the transition not because of concerted movement of the distal side
residues, but because of movement of the heme itself within the subunit.
Analysis in the frame of the heme
To study in detail the motion of other residues around the heme in each subunit, each chain was considered independently, and the reference frame was modified to coincide with its heme. This treatment involved frame modification in the T structure, with each subunit rotated and translated to position the origin of the frame on the Fe atom (Fig. 16 a), the heme plane in the (X, Y) plane, the X axis approximately parallel to the F helix in the C- to N-terminal direction of the helix, and the Z axis pointing toward the distal side of the heme. In this representation, the Y axis points toward the interior of the subunit. As before, the instantaneous structures of each chain along a given trajectory were superimposed, using the C and Fe atoms, on the corresponding chain in
the T structure in the new frame, and the coordinate differences
calculated along the X, Y, and Z axes. The results are discussed below.
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