Introduction

Complex processes of signaling in the living cell are comprised of many allosteric interactions between proteins1. Thus controlling the allostery is emerging as a promising approach for pharmaceutical drug discovery and allosteric ligands for G protein-coupled receptors have been approved as medicines2. Allosteric regulation is assumed to be triggered by site-specific ligand binding to allosteric sites, which are distinct from the orthosteric ligand binding site. As a paradigm of such allosteric regulation, allostery of human hemoglobin (HbA), which is an oxygen transport protein composed of two α and two β subunits, has long been thoroughly studied3,4,5. Under the circumstances, it is widely accepted that O2 acts as a “site-specific” homotropic allosteric effector, or the successive O2 binding to the four subunit hemes triggers quaternary change from the low O2 affinity T state to the high affinity R one. The MWC model6 is one of the most successful models to explain the sigmoidal oxygen binding curve on the basis of the homotropic allosteric mechanism. From the molecular point of view, the homotropic allostery was additionally explained by including the interaction energies of intersubunit contacts which stabilize the T state structure7; when O2 binds to the heme, the tertiary structural change of the HbA subunit is triggered by the heme deformation from the domed structure to the planar one and, as a result, those contacts are destabilized to drive the T to R transition3. In fact, in HbA subunit analogous protein, myoglobin (Mb), it has been elucidated that the heme deformation by the ligand (O2 or CO) binding or dissociation triggers structural relaxation in the whole protein8,9,10,11,12,13. However, our current molecular dynamics (MD) simulation revealed that, even without site-specific O2 binding to the heme, the solution environment of high O2 partial pressure enhances the quaternary structural change from T to R, suggesting the “non-site-specific” allosteric effect of O2.

Using the statistical ensemble MD approach11,12,13,14, we executed 128 independent 8 nanosecond (ns) MD simulations starting from the T state deoxy-HbA crystal structure15 at the physiological condition (310 K and 1 atm) in both aqueous solvent (MDwat with ~12000 H2O molecules) and oxygen-rich aqueous solvent with [O2] = 0.55 mol/L (MDO2 with 120 O2 and ~12000 H2O molecules), which is about 500 times higher than that in the O2 saturation concentration at ambient conditions, ~1 mmol/L. This high partial pressure was applied to amplify the non-site-specific effect of O2. We artificially ignored the O2 binding to the heme and thus all the hemes were retained in the domed structure for the purpose to exclude the heme O2 binding effect.

Results

Global evidence of quaternary change: transition in intersubunit dihedral angle and RMSD

It was reported that spontaneous T to R quaternary transition reproducibly occurred in the submicrosecond MD simulations of HbA starting from the T state structure16,17. Our simulations also exhibited the T to R quaternary changes. Because the quaternary change is accompanied with α1β1 (α2β2) dimer rotation3,18, the temporal change of the intersubunit dihedral angle χ, defined by the four centers of mass (COMs) of subunits (see Fig. 1), is an index of the quaternary change; −99.5 and −89.0 degrees for T and R crystal structures (PDB ID: 2DN2 and 2DN115), respectively. Figs. 2 gives one of the typical trajectories of MDO2 in which the T to R quaternary change occurred. Until 3 ns, the HbA structure kept its initial T structure and later, χ changed during t = 3.0 to 4.5 ns and reached −87 degrees, strongly correlating with the decrease of RMSDR to 1.4 Å (Fig. 2a).

Figure 1
figure 1

T state crystal (initial MD) structure of HbA (PDB ID: 2DN2).

The dihedral angle χ defined by the four centers of mass, i.e., those of α1 subunit, α1β1 dimer, α2β2 dimer and α2 subunit, is shown as ball and stick drawing. The blue color drawing is the COMs of the initial T state structure with χ = −99.5 degrees. The red one is those from a typical T to R quaternary change trajectory at 4.584 ns with χ = −87.8 degrees.

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Figure 2
figure 2

T to R quaternary structural change.

A typical quaternary change trajectory of MDO2. (a) Changes of the RMSD to the T (RMSDT) and R (RMSDR) crystal structures and the intersubunit dihedral angle χ. (b) Structural rearrangement at the switch region of the α1β2 interface. Important residues are drawn at 3 ns (red) and 4.25 ns (blue) with the intermediate structure of β2His97 at 3.7 ns (white). (c) Distance changes between the COM of the βHis97 sidechain and the COMs of αThe38 and αPro44 at the two switch regions plotted with χ.

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Local evidence of quaternary change: switch region rearrangement

Furthermore, local structural changes in the α1β2 (α2β1) switch region were also consistent with the T to R change: β2His97 moves from the groove between α1Pro44 and α1Thr41 to that between α1Thr38 and α1Thr414,18. This rearrangement also occurred in this trajectory during t = 3 to 4.25 ns (Fig. 2b). The α1Thr38-β2His97 distance decreased from 11 to 5 Å and that of α1Pro44-β2His97 conversely increased from 5 to 11 Å (Fig. 2c). Other trajectories of MDO2 and MDWAT in which the quaternary change occurred also revealed the similar behaviors of the χ, RMSDR and switch region structural changes (Supplementary Figs. S1 and S2).

Other regions also revealed T to R quaternay change characteristics. Breakages of intersubunit salt bridges α1Lys40-β2His146 and α1Tyr42-β2Asp99 occur by the T to R quaternary change15. These breakages were also observed in the quaternary change trajectory (Supplementary Fig. S3). Meanwhile, in the α1β2 (α2β1) hinge region (also denoted as flexible joint region), the intersubunit contacts were retained and there were no significant structural rearrangements during the quaternary change (Supplementary Fig. S4) as crystallographically observed19.

Non-site-specific allostery emerged in the intersubunit dihedral angle distribution

To investigate the effect of high O2 partial pressure, statistical comparison between the 128 MD trajectories of MDO2 and MDwat was carried out. When the time average of χ over 7–8 ns is larger than −95 degrees, the trajectory is defined as a quaternary change trajectory. On this definition, the number of quaternary change trajectories were 10 and 4 for MDO2 and MDwat, respectively, suggesting that the high O2 partial pressure enhances the T to R quaternary change.

To obtain further structural insight, we investigated the χ distributions of MDO2 and MDwat during 7–8 ns (Fig. 3). The two distribution curves were well fitted by the sum of three Gaussian functions as

The fitted parameters (Ai, δχi, χMi) and the fitted curves are summarized in the Supplementary Table S1 and Fig. S5. For MDwat, the main distribution g1(χ) with the mean angle (χ1M) and width (δχ1) of −100.2 and 1.54 degrees was obtained. Meanwhile, for MDO2, the main distribution was −99.6 degrees mean angle and 1.75 degrees width.

Figure 3
figure 3

χ Distribution shift by high O2 partial pressure.

Distributions of the intersubunit dihedral angle χ calculated from 128 independent MD trajectories during 7–8 ns. The dihedral angles were sampled every 1 ps from 7 to 8 ns of each trajectory (in total 128,000 samples from 128 trajectories).

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The comparison of MDO2 and MDwat distributions allows us to conclude that the solution environment of high O2 partial pressure enhances the T to R quaternary change from the following two aspects. First, from the 0.6 degrees peak position shift of the main distribution toward the R state (from −100.2 (MDwat) to −99.6 (MDO2) degrees), the T state structure is biased toward the R state. Second, from the width increase from 1.54 (MDwat) to 1.75 (MDO2) degrees, the global structural fluctuation of the T state, which would contribute to the T to R quaternary change, is enhanced. The observed enhancement can be considered as the “non-site-specific” allosteric effect, or another allosteric regulation by O2 without binding to the heme.

Discussion

Our ensemble MD simulation revealed that, even without the heme deformation by the O2 binding to the heme, the solution environment of high O2 partial pressure itself enhances the quaternary structural change from T to R. This means that the traditional site-specific allosteric regulation by O2 binding to the heme is not necessarily the only one unique mechanism of O2 allostery and the additional non-site-specific regulation does exist. From a molecular point of view, we propose following two hypothetical mechanisms of the non-site-specific allostery of O2.

First is the internal effect: O2 molecules enter the hydrophobic cavities inside HbA subunits20 and trigger the tertiary structural changes to enhance the T to R quaternary change. In MDO2 simulations, hydrophobic O2 molecules tended to escape from water and prefer the hydrophobic environment on the surface or inside HbA subunits14. The O2 migrations between inside cavities would bring about the tertiary structural changes of HbA subunits since it was observed that, in Mb, structural changes occur in response to the ligand migrations between cavities21,22,23. In particular, these reported structural changes in response to the CO transitions between the heme pocket and Xe4 cavity included displacements of the F helix, which forms the switch region of HbA β subunit22 and hence would affect the stability of the T state structure.

Second is the surface effect: the existence of O2 around the subunit interfaces weakens the contacts which stabilize the T state structure3 by affecting the surface residues directly and/or indirectly through perturbing the behavior of water molecules. In fact, there are obviously high O2 density locations in the vicinity of the switch region (Fig. 4). Thus it should be possible that the existance of O2 directly affects the switch region residues through steric hinderance to weaken the contacts, while O2 also influences surface water molecules to indirectly affect the switch region residues. In general, the characteristic constants of water molecules near the protein surfaces, such as diffusion constant24, can be different from that in bulk solvent. Moreover, it has been reported that the number of interfacial water molecules changes during quaternary changes in hemoglobins25,26,27,28, suggesting the important roles of the number of interfacial water molecules in the quaternary regulation. Thus, we can conjecture that the existence of O2 would perturb the behavior of water molecules, e.g., as the deviation of diffusion constants and the number of interfacial water molecules around the surfaces, and, as a result, indirectly weaken the intersubunit contacts to enhance the T to R quaternary change.

Figure 4
figure 4

Distribution of O2 oxygen atoms around switch region.

Distribution of O2 oxygen atoms calculated from 128 MD trajectories during 7 to 8 ns in the vicinity of the switch region at the α1β2-interface switch region. Locations with density >0.05 Å−3 and >0.1 Å−3 are drawn with red wire frame and solid surface, respectively. Since the average density in the bulk solvent region (distance to the nearest protein atom >4.0 Å) is about 0.005 Å−3, the wire frame and solid surface regions are 10 and 20 times denser than that in the bulk solvent, respectively. Four high density locations around the switch region are numbered in descending order of the peak density.

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The O2 partial pressure applied in this work (0.55 mol/L) is about 500 times higher than that in the O2 saturation concentration at ambient conditions (~1 mmol/L). We anticipate that the non-site-specific effects should be also observed under the ambient conditions for the following three reasons. First, our previous computational analysis with the same concentration 0.55 mol/L reproduced the rate constants of O2 entry into the binding sites of HbA subunits14. Assuming a kinetic model of O2 entry

where x denotes subunit (x = α or β) and is the situation of O2 in the binding site, the rate of O2 entry is and the rate constants and are calculated to be 45 and 99 (μmol/L)−1s−1, respectively. These values are consistent with experimentally observed values after temperature correction, 48–69 and 81–131 (μmol/L)−1s−1 for α and β subunits, respectively. This consistency indicates that the concentration 0.55 mol/L is within the linearly extrapolatable range by the O2 concentration, as the rate constants can be estimated by the formula . Second, the “effective” O2 concentration around HbA is higher than the bulk concentration. As discussed above, hydrophobic O2 molecules prefer the hydrophobic environment near the HbA surface and there are several high O2 density regions, whose density is an order of magnitude higher than that in the bulk solvent region (Fig. 4). Therefore, compared to the bulk concentration, the “effective” O2 concentration around HbA is higher. This should partially narrow the concentration gap between the current simulation conditions and ambient conditions. Third, a preliminary ensemble MD simulation at one-tenth concentration, 0.055 mol/L (MDlowO2 with 12 O2 and ~12000 H2O molecules) also revealed the non-site-specific effect. We executed 40 MD simulations for 8 ns at the 0.055 mol/L concentration and calculated the χ distribution during 7–8 ns (Supplementary Fig. S6). The MDlowO2 distribution is apparently shifted toward the R state as in MDO2.

From an experimental point of view, it is necessary to analyze the number of O2 molecules around or inside HbA subunits because the number of O2-bound heme in tetrameric HbA, which is the traditional index of O2 allostery and is easily observed by spectroscopy, cannot capture the non-site-specific O2 allosteric contributions. In particular, as Tomita et al. discussed in Mb case29, accurate measurement of the heme:O2 stoichiometry with modern instrumentation is desired to verify the traditionally employed stoichiometry 1:1, which assumes that only one O2 binds to the heme and there is effectively no O2 in the hydrophobic cavities or near the surfaces of HbA subunits. The stoichiometry greater than 1:1 is plausible by hydrophobic interactions between O2 and HbA and means that HbA subunits can carry excess O2 in their cavities and/or surfaces, or the “effective” O2 concentration around HbA is higher than bulk concentarion and support the existence of the non-site-specific effect.

The current non-site-specific effect should provide a complementary mechanism to account for the cleavages of intersubunit contacts during the T to R quaternary change of HbA in high O2 concentration environment from the molecular point of view. With respect to the displacements in the heme average strucutre, the O2-heme binding itself brings about very small structural rearrangements: a comparison of high resolution crystal structures of Mb revealed that the heme iron atom is 0.290 Å displaced by ligand binding10. Since the immediate displacements in the residues distant from the heme within 20 ps after ligand phosolysis are smaller than those neighboring to the heme because of the elastic behavior of Mb11, the immediate displacements propagated to the residues composing the intersubunit contacts must be smaller than the iron displacement. It is not obvious how such a small immediate displacements could cleavage the contacts, although it was in fact experimentally obserbed that the T to R quaternary change occurs after microseconds of ligand dissociation30. Meanwhile, by the dynamic non-equilibrium MD approach in Mb, it was shown that a large structural fluctuation in the FG-corner (that of β subunit forms the switch region in HbA) was brought about by the ligand dissociation and recombination to the heme31. Together with this structural fluctuation effect, O2 molecules located near the intersubunit contacts as in Fig. 4 can interact with the contacts, playing a complementary role in cleavage of the contacts.

The non-site-specific effect can also be an important factor in allosteric structural regulation in other proteins. For example, in muscarinic receptors, orthosteric ligands were observed to function as an allosteric modulator32 or weakly bind to the allosteric sites33, indicating that the ligands can interact with multiple sites; not only the orthosteric site but also allosteric sites. In particular, for allosteric proteins in which the distance between orthosteric and allosteric sites is so far-away that direct structural perturbation between the sites seems to be unlikely, the multiple interaction sites between proteins and ligands, most of which are invisible by the X-ray crystallography because of their small occupancy, can help the structural rearrangements at the orthosteric sites. The concept of non-site-specific allostery should facilitate further understanding of allosteric regulation process depending on the concentration of effectors from the atomistic point of view.

Methods

The MD simulation force field parameters were identical to our previous work14. All the MD simulations were executed by AMBER 9 pmemd module34. The initial HbA structure was retrieved from the T state deoxy-HbA crystal (PDB ID: 2DN2)15 and immersed in the periodic boundary TIP3P water box with 12023 water molecules and two chloride counterions, yielding the MDwat system. In addition, 120 water molecules were replaced by 120 O2 molecules to prepare MDO2 system. We executed 128 independent MD simulations for MDwat and MDO2 systems, respectively, according to the following procedure with different initial atomic velocities. First, we executed 300 ps high temperature NVT MD simulations at 700 K with the structure restraints on the protein. Second, equilibration NPT MD simulations for 200 ps at the target temperature 310 K and pressure 1 atm were executed with the protein restraint. Then production NPT MD simulations at 1 atm and 310 K were executed for 8 ns without any restraints. All the images of protein structures were drawn with VMD 1.9.135. The density map in Fig. 4 was calculated by “VolMap Tool” in VMD with the parameters 1.0 Å resolution and 1.0 × radius atom size.