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Ligation-Dependent Picosecond Dynamics in Human Hemoglobin as Revealed by Quasielastic Neutron Scattering Satoru Fujiwara, Toshiyuki Chatake, Tatsuhito Matsuo, Fumiaki Kono, Taiki Tominaga, Kaoru Shibata, Ayana Sato-Tomita, and Naoya Shibayama J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b05182 • Publication Date (Web): 04 Aug 2017 Downloaded from http://pubs.acs.org on August 13, 2017

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The Journal of Physical Chemistry

Ligation-Dependent Picosecond Dynamics in Human Hemoglobin as Revealed by Quasielastic Neutron Scattering

Satoru Fujiwara†*, Toshiyuki Chatake‡, Tatsuhito Matsuo†, Fumiaki Kono†, Taiki Tominaga§, Kaoru Shibata¶, Ayana Sato-Tomitaǁ, and Naoya Shibayamaǁ

†

Quantum Beam Science Research Directorate, National Institutes for Quantum and

Radiological Science and Technology, 2-4 Shirakata, Tokai, Ibaraki 319-1106, Japan ‡

Research Reactor Institute, Kyoto University, 2 Asashiro-Nishi, Kumatori, Osaka 590-0494, Japan

§

Neutron Science and Technology Center, Comprehensive Research Organization for Science and Society (CROSS), 162-1 Shirakata, Tokai, Ibaraki 319-1106, Japan ¶

Neutron Science Section, J-PARC Center, 2-4 Shirakata, Tokai, Ibaraki 319-1195, Japan ǁ

Division of Biophysics, Department of Physiology, Jichi Medical University, 3311-1 Yakushiji, Shimotsuke, Tochigi 329-0498, Japan

Corresponding author Satoru Fujiwara, Ph.D. Quantum Beam Science Research Directorate National Institutes for Quantum and Radiological Science and Technology 2-4 Shirakata, Tokai, Naka-Gun, Ibaraki 319-1106, Japan. Phone number: +81-70-3943-3436 FAX number:+81-29-287-1445 E-mail address: [email protected]

1 Environment ACS Paragon Plus


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Abstract Hemoglobin, the vital O2 carrier in red blood cells, has long served as a classic example of an allosteric protein. Although high resolution X-ray structural models are currently available for both the deoxy tense (T) and fully-liganded relaxed (R) states of hemoglobin, much less is known about their dynamics, especially on the picosecond to subnanosecond time scales. Here, we investigate the picosecond dynamics of the deoxy and CO forms of human hemoglobin using quasielastic neutron scattering under near physiological conditions, in order to extract the dynamics changes upon ligation. From the analysis of the global motions, we found that, whereas the apparent diffusion coefficients of the deoxy-form can be described by assuming translational and rotational diffusion of a rigid body, those of the CO form need to involve an additional contribution of internal large-scale motions. We also found that the local dynamics in the deoxy and CO forms are very similar in amplitude, but are slightly lower in frequency in the former than in the latter. Our results reveal the presence of rapid large-scale motions in hemoglobin, and further demonstrate that this internal mobility is governed allosterically by the ligation state of the heme group.


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Introduction Hemoglobin (Hb) is a tetrameric hemoprotein that transports O2 from lungs to tissues. Hb consists of two α and two β subunits, each containing one heme group to which O2 can bind reversibly. When an O2 molecule binds to the heme of one subunit, this information is propagated to other distant hemes through structural and dynamics changes in the tetramer, thereby increasing the O2 affinity of the whole molecule. Owing to this cooperative behavior, Hb has long served as a prototypical experimental system for the study of allosteric regulation in macromolecules. Since the seminal crystallographic work by Perutz1, Hb has been studied extensively by X-ray crystallography particularly in the 1970s and 1980s, accumulating a wealth of structural data on its fully-unliganded tense (T) and fully-liganded relaxed (R) states. The standard description based on those data was that Hb switches between a low-affinity T conformation and a high-affinity R conformation upon ligand binding2-4. Classical models of allosteric mechanisms were therefore greatly influenced by the static images of end-point crystal structures of Hb5-7.

However, it is now becoming apparent that proteins are in motion in order to function. Hb is no exception. For example, as evident in the crystal structures of Hb, the heme groups are buried deep inside the protein, with no static channel through which the ligand can move to its binding site. This implies that a rigid, static structure without conformational flexibility has no biological activity. Moreover, Mozzarelli and colleagues showed that the O2 affinity of single crystals of deoxyHb is much lower than that of deoxyHb in solution8, indicating that the crystal lattices hinder the protein motions that are essential to physiological function. Also, NMR studies show that the solution structure of COHb is in a rapid equilibrium between different quaternary structures that include the crystallographically observed R and R2 states9, indicating the occurrence of large-scale protein motions even in the end-point state. In



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addition, 6-ns molecular dynamics (MD) simulations suggest the presence of functionally significant tertiary motions in both the T and R states of Hb10. Thus, a full description of the allosteric mechanism of Hb requires information about dynamics as well as structure in both its deoxy (T) and fully-liganded (R) forms.

Proteins have a hierarchy of dynamics ranging from picosecond thermal fluctuations of atoms within a protein, through submillisecond diffusive motions of polypeptide chains and domains, to conformational changes that occur at millisecond or slower time scales11. This hierarchy of the dynamics has been shown to be correlated12. In particular, the dynamics at the picosecond time scale is known to work as a lubricant for the slower motions, without which the structural changes of the proteins do not occur13. Characterization of the dynamics at the picosecond time scale is thus important as an elementary process of the hierarchy of protein dynamics.

Neutron scattering is one of the most powerful experimental techniques that can directly measure the picosecond dynamics in proteins14. In particular, incoherent techniques such as elastic incoherent neutron scattering (EINS) and incoherent quasielastic neutron scattering (QENS) allow internal protein motions to be quantified by measuring the dynamics of protein hydrogen atoms. Such methodology is based on the following features of hydrogen atoms: (i) the incoherent neutron scattering cross-section of hydrogen is much larger than that of any other atoms including deuterium15, (ii) the hydrogen atoms constitute about a half of all the atoms in proteins, and (iii) the hydrogen atoms are (pseudo-)uniformly distributed in proteins and their dynamics reflect those of the larger groups to which the hydrogen atoms are bound14. These incoherent techniques thus provide average dynamics of the entire protein molecule. Indeed, these techniques and other coherent neutron techniques have been used to investigate


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the various aspects of Hb dynamics, such as dynamics in red blood cells16,17, hydration dependence of dynamics18, mutational effects on dynamics19, oligomerization-dependence of dynamics (comparison between Hb and myoglobin)20, and dynamics changes by the addition of an allosteric effector21.

In this study, we report on the picosecond dynamics of human deoxyHb and COHb using QENS at 280-310 K. To date, no neutron scattering experiments have been performed to determine the ligation-dependent dynamics changes in Hb, with the exception of Caronna et al.22. In that previous study22, although EINS and QENS of deoxyHb and COHb were measured to extract the difference in dynamics between the two quaternary conformations, the experimental conditions in the presence of 65% glycerol (to cover the wide temperature range for the EINS measurements) are no longer physiological. Since water activity is known to influence the relative stability of the T and R states of Hb through ~60 extra water molecules that preferentially bind to the R state23, the previous experimental conditions (with a small water content) might affect the dynamics of each allosteric state. Moreover, in the previous study, no detailed analysis of the QENS spectra could be achieved due to insufficient statistical accuracy of the data. It is therefore of interest to re-investigate the dynamic properties of deoxyHb and COHb in D2O solutions (without glycerol) using QENS in order to make a quantitative comparison between their dynamics under near physiological conditions.

Experimental Methods Sample preparation Human adult Hb was prepared and purified in the CO form as described previously24. The bound CO was removed from Hb by photolysis under a stream of O2 at 0 ˚C. The oxyHb solution was diluted about tenfold with a D2O buffer and concentrated by ultrafiltration at 5˚C,



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using an Amicon Ultra-15 centrifugal unit equipped with a YM-10 membrane (Millipore). The buffer used was 50 mM potassium phosphate (pD 7.4) in D2O. The dilution and concentration were repeated until the free H2O decreased down to less than 0.1%. The deuterium-exchanged oxyHb sample was then deoxygenated by repeated evacuation and equilibration with pure N2 gas, followed by the addition of a small amount of dithionite to give a final concentration of about 5 mM. The final concentration of Hb was 100 mg/ml. About one-half of the deoxyHb sample was converted to the CO form by equilibrated with CO gas. Both the deoxyHb and COHb samples were put into double-cylindrical quartz cells with a thickness of 0.5 mm, which were then put into aluminum cans sealed with an indium wire gasket. This operation was performed in a glove box filled with pure N2.

Quasielastic neutron scattering experiments The QENS measurements were carried out using the near-backscattering spectrometer, BL02 (DNA)25, at the Materials and Life Science Facility at the Japan Accelerator Research Complex (J-PARC MLF), Tokai, Ibaraki, Japan. The measurements were done at the energy resolution of 12 µeV, at which atomic motions faster than 55 ps are accessible, and at several temperatures between 280 K and 310 K. The QENS spectra of the solution samples of deoxyHb and COHb and the D2O-buffer were measured.

The measured QENS spectra S(Q, ω), where Q (= 4πsinθ/λ, where 2θ is the scattering angle and λ is the wavelength of the incident neutrons) is the momentum transfer and ω is the energy transfer of neutrons, were corrected for the empty cell contribution and the detector efficiency, and normalized to the vanadium standard, which was also used for defining the instrumental energy resolution. Subtraction of the spectra of the D2O-buffer from those of the D2O-solution samples was done using the scaling factors calculated from the scattering


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cross-section of the samples26. Examples of the QENS spectra of the sample solutions, the buffer, and the difference between the spectra of the sample solutions and the buffer are shown in Fig. S1(a) and (b) in the supporting information. The spectra thus obtained were verified by the static structure factor, S(Q), calculated by integrating the S(Q, ω) along the ω-direction, examples of which are shown in Fig. S1(c) and (d). The QENS spectra of the D2O-solution samples and the D2O-buffer show increase in intensity at Q > ~1.4 Å-1, which arises from coherent scattering of D2O27,28. On the other hand, the spectra of the proteins do not contain such a contribution28,29. Proper subtraction of the D2O-buffer spectra should thus provide S(Q) with rather flat intensity at Q > ~1.4 Å-1. As shown in Fig. S1(c) and (d), whereas increase in intensity at Q ≥ 1.4 Å-1 is observed in the curves of the solution sample and the buffer, such increase disappears in the difference curves. This indicates that the solvent contribution is negligible in the difference spectra, and thus these difference spectra can be regarded as the spectra arising from the proteins. It should be noted that increase in intensity observed in the region Q ≤ 0.4 Å-1 arises from coherent scattering of the protein27,29. Analysis was thus done on the spectra in the region Q > 0.4 Å-1.

Dynamic light scattering measurements The dynamic light scattering (DLS) measurements were carried out on the D2O-solutions of deoxyHb and COHb. The measurements were carried out using a system consisting of a 22 mW He-Ne laser (wavelength, λ = 632.8 nm), an avalanche photodiode mounted on a static/dynamic compact goniometer, ALV/LSE-5003 electronics and an ALV-5000 correlator (ALV, Langen, Germany). The measurements were made at scattering angles from 30° to 120° in 15° steps, at temperatures at 10°C, 17°C, 27°C, and 37°C. The CONTIN analysis30 was employed for data analysis, and the translational diffusion coefficients, DT, were evaluated.



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Results Figure 1 shows examples of the QENS spectra of deoxyHb and COHb at Q = 1.05 Å-1. These spectra can be fit with the equation31: SQ,ω A Qδω 1 A QL Q, ω⊗L Q, ω⊗RQ, ω BQ, 1

where A0(Q)δ(ω) is the elastic component with A0(Q) being the elastic incoherent structure factor (EISF) and δ(ω) being the Dirac delta-function, Llocal(Q,ω) and Lglobal(Q,ω) are the Lorentzian functions describing the local atomic motions within the proteins (Llocal(Q,ω) = (1/π) × (Γlocal(Q) /(Γlocal(Q)2 + ω2))) and the global diffusive motions of the proteins (Lglobal(Q,ω) = (1/π) × (Γglobal(Q) /(Γglobal(Q)2 + ω2))), respectively, where Γlocal(Q) and Γglobal(Q) denote the half-width at half-maximum (HWHM) of the corresponding Lorentzian functions, R(Q,ω) is the instrumental resolution function, which is obtained from the spectra of vanadium, B(Q) is the background, and ⊗ denotes the convolution operation. As shown in Fig. 1, the spectra are well fit with this equation. Using this phenomenological equation based on the assumption that the global motions and local motions are uncorrelated, the contributions of the global motions and the local motions of Hb can be separated.

Figure 1. Examples of the measured QENS spectra, Sexp(Q,ω), of (a) deoxyHb and (b) COHb at Q = 1.05 Å-1 at 280 K. The results of the fits, Sfit(Q,ω), with Eq. 1 are also shown. Upper


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panels show the spectra and the results of the fits, and lower panels show the difference between Sexp(Q,ω) and Sfit(Q,ω). The errors bars for the data points are within symbols.

Analysis of global motions The global motions of Hb can be characterized from analysis of Lglobal(Q,ω). In particular, Γglobal(Q) provides information on diffusive motions of the protein. Figure 2 shows Q2-dependence of Γglobal(Q). Γglobal(Q) increases linearly with increasing Q2 for both deoxyHb and COHb, indicating that the motions observed are free diffusion. According to the relationship, Γglobal(Q) = DappQ2, the values of the apparent diffusion coefficients, Dapp, can be evaluated. The values obtained are summarized in Fig. 3. Differences in Dapp are observed between deoxyHb and COHb.

Figure 2. Q2-dependence of Γglobal of (a) deoxyHb and (b) COHb. The results of the linear fits are also shown. Errors bars within symbols are not shown.



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Figure 3. Summary of Dapp obtained from the QENS spectra and the simulated values. Errors bars within symbols are not shown.

To investigate the origin of this discrepancy, we independently determined using DLS the pure translational diffusion coefficients of deoxyHb and COHb under similar conditions as used for the QENS measurements. Because deoxyHb has a much higher extinction coefficient at an incident laser wavelength of 632.8 nm compared to COHb, meaningful data could be obtained for deoxyHb at a concentration of 10 mg/ml or less while those obtained for COHb at concentrations of 10 mg/ml and 100 mg/ml (Fig. S2 in the supporting information). Furthermore, we calculated the DT values based on the crystal structures of deoxyHb and COHb (PDB codes 2DN2 and 2DN3, respectively) using HYDROPRO32, in which the protein molecules are assumed to be rigid (Fig. S2). The data in Fig. S2 demonstrate that the DT values obtained from a 10 mg/ml deoxyHb solution agree well with those from 10 mg/ml and 100 mg/ml COHb solutions, and also with the calculation for both ligation forms, indicating that the pure translational diffusion coefficients depend neither on the ligation state of Hb nor the concentration of Hb in the range from 10 to 100 mg/ml. It is important to note that the protein concentrations used in this study (> 10 mg/ml) are high enough to suppress the dimer formation33. In addition, note that the DT value calculated based on the crystal structure of the R2 state (PDB code 1BBB) is also similar to those of other structures (Fig. S2). Overall, the


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discrepancy observed in the values from the QENS measurements is not due to the differences in the translational diffusion.

The Dapp values from the QENS spectra contain, in addition to the contribution of translational diffusion, that of rotational diffusion34,35. The rotational diffusion coefficients, DR, can also be calculated by HYDROPRO. The Dapp values can then be evaluated by simulating the spectra based on a dense hard sphere approximation34 with the equation, *

(

S & Q, ω !2l 1 $ j& ' Qr4πr ' dr D0 Q' ll 1D( ⁄ω' D0 Q' ll 1D( ' , 2 )

)

where jl(·) is the spherical Bessel function of order l, and R is the hydrodynamic radius of the protein, which is obtained by the Einstein relationship R = kBT/(6πηDT), where kB denotes the Boltzmann constant, T is the temperature, and η is the solvent viscosity, calculated from the literature values36. Note, however, that the DT and DR values calculated by HYDROPRO are those of the long-time self-diffusion while those obtained from the QENS measurements are the short-time diffusion17,35. The calculated DT and DR values should thus be converted to the values describing the short-time diffusion. This was done by the scaling factors calculated for hard spheres37. The short-time DT values provide the values of R of 32.2 Å for both deoxyHb and COHb. For this R value, calculation of Strans & rot(Q, ω) in the range Q ≤ 1.85 Å-1 requires 65 terms (0 ≤ l ≤ 64). These calculated Strans & rot(Q, ω) can be fit with the single Lorentzian function. From the slope of the Q2-dependence of the HWHM of the Lorentzian function fit to the simulated Strans & rot(Q, ω), the Dapp values based on the calculated DT and DR values were evaluated. The solid and dashed lines in Fig. 3 are the results of this simulation.

The simulation values are very similar between deoxyHb and COHb. Note that the simulated Dapp values for the R2 state are also similar to those of deoxyHb and COHb (see Fig. S3 in the



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supporting information). The simulation values for deoxyHb show good agreement with the values obtained from the QENS measurements. This implies that deoxyHb can be regarded as a rigid body. On the other hand, the simulated values for COHb are different from those from the QENS measurements. This indicates that additional motions contribute to Dapp other than the translational and rotational diffusion of the entire molecules. It has been reported that Dapp contains the contributions of internal motions in addition to the translational and rotational diffusion of the entire molecule20,26,38. The difference in Dapp between deoxyHb and COHb should therefore arise from the differences in the internal motions.

Analysis of local motions Information on the frequency of the local motions of Hb can be obtained from analysis of Γlocal(Q). Figure 4 shows Q2-dependence of Γlocal(Q). Γlocal(Q) approaches asymptotically to a plateau at high Q2 though it does not reach the plateau within the observed Q-range. Such behavior of Γlocal(Q) can be described by an equation based on a jump-diffusion model, Γlocal(Q) = DQ2/(1+DQ2τ), where D is the jump-diffusion coefficient and τ is the residence time31. It, however, appears that Γlocal(Q) deviates from this equation in the low Q2 region. This behavior of Γlocal(Q) implies that the motions observed are diffusion in a confined space31. The fits with this equation were thus carried out for the data in the region Q2 > 0.5. The results of the fits are also shown in Fig. 4.

Since the residence time is a measure of the frequency of the local jumping motions, we compare the residence time between deoxyHb and COHb here. Figure 5 is the Arrhenius plot of the residence time. The residence times of deoxyHb are larger than those of COHb though the differences are small. This suggests that the frequency of the jumping motions is a little less in deoxyHb than in COHb. Slopes of the Arrhenius plot provide the activation energy for


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the jumping motions according to the Arrhenius law, τ = τ0exp(-Ea/kBT), where Ea is the activation energy, and kB is the Boltzmann constant, and T is the temperature. The evaluated activation energy is 5.20 ± 0.3 kcal/mol for both deoxyHb and COHb, indicating that the jumping process is similar between deoxyHb and COHb.

Figure 4. Q2-dependence of Γlocal(Q) of (a) deoxyHb and (b) COHb. Solid lines are the fits with the equation based on a jump-diffusion model. Error bars within symbols are not shown.

Figure 5. The Arrhenius plot of the residence time of the jump diffusion model, estimated from the fits shown in Fig. 4.

Information on the amplitudes of the local motions can be obtained by analysis of the EISF curve (A0(Q) in Eq. 1), which is calculated as the ratio of the intensity of the elastic peak to the sum of the intensity of the elastic peak and that of the quasielastic scattering. Figure 6 is a summary of the EISF curves. The differences in the EISF curves between deoxyHb and COHb are, if any, very small. 13 Environment ACS Paragon Plus


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We attempted to analyze the EISF curves by fitting with the equation based on the diffusion-inside-a-sphere model39, in which each atom is assumed to undergo diffusive motion in a sphere of a certain radius. The fits to the experimental curves were not very good (results not

shown).

We

thus

employed

two

extensions

of

this

model.

One

is

the

diffusion-inside-a-sphere model containing two kinds of atoms moving in spheres with different radii (model 1). For this model, the EISF curve is described as,

EISFQp0 p1 ×3j1 Qa1 ⁄Qa1 2 p2 ×3j1 Qa2 ⁄Qa2 2 ,

(3)

where p0 denotes the “immobile” fraction of atoms, motions of which are outside the current instrumental energy window, and p1 and p2 denote the fractions of atoms undergoing diffusive motions within spheres of radii a1 and a2, respectively (p0 + p1 + p2 = 1). The second and third terms in the right-hand side represent the diffusive motions of the atoms in the confined spheres of the radii a1 and a2, respectively.

The other is a model in which the radius of the confined sphere has a Gaussian distribution (model 2)34. Note, however, that the models with other kinds of distribution such as a lognormal distribution40 are possible. We employed the model with a Gaussian distribution for comparison with the previous studies using this model for analysis of the EISF curves of Hb17,18. According to this model, the EISF curve is described as, *

EISFQ=p+1-p $ fa:3j1 Qa⁄Qa; da, 4 2

where p denotes the immobile fraction, f(a) is a Gaussian distribution of the radius of the sphere, a, defined as fa :2⁄√2=σ' ;?@Aa2⁄2σ' , with a standard deviation σ, which is a fitting parameter. For this model, the mean value of the radius a is given by 〈a〉

ST2⁄=.


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Figure 6. The EISF curves of deoxyHb and COHb at (a) 280 K, (b) 290 K, (c) 300 K, and (d) at 310 K. Solid lines denote the results of the fit with Eq.3, and dashed lines denote the results of the fits with Eq. 4. Errors bars within symbols are not shown.

The results of the fits with the equations for the model 1 and 2 are also shown in Fig. 6. The major differences in the calculated EISF curves between these models are observed in the region Q < 0.4 Å-1, where the data points are omitted from the analysis because of the contribution of coherent scattering. It is therefore not possible to judge which model is better. Figure 7 summarizes the parameters obtained. For the model 1, the values of p0, p1, p2 (= 1 p0 - p1), a1, a2 are shown. In addition, the average radius over a1 and a2 is shown for comparison with of the model 2. For the model 2, the values of p and are shown. The parameters for both models show similar behavior: The fractions of the immobile atoms are similar between deoxyHb and COHb, and the radii of the confined spheres are similar, too. It is, however, noted that there may be differences in the radii of the confined sphere at the temperatures below 290 K, though it could be artefacts due to overfitting to the small differences in the EISF curves between deoxyHb and COHb. The amplitudes of the atomic



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motions in deoxyHb could be larger than those in COHb in the lower temperatures.

The behavior of the parameters for the model 2 is consistent with the results of the similar analysis in the previous studies on metHb17,18: The values increases with increasing temperature, and the p values also increases slightly. However, the immobile fraction (p0) for the model 1 does not increase with increasing temperature. Considering the differences in the calculated EISF curves between the models 1 and 2 are in the region Q < 0.4 Å-1, the difference in the behavior of the immobile fraction (p or p0) may be due to the lack of the data in the small-Q region. The differences in the values of between this study and the previous studies (4 – 6 Å in this study and around 2.5 Å in the previous studies17,18) are likely to be due to the differences in the energy resolution employed in the QENS measurements (12 µeV in this study and 41 – 100 µeV in the previous studies).

Figure 7. Summary of the parameters of the models describing the EISF curves.

Discussion In this study, the picosecond dynamics of deoxyHb and COHb was investigated by QENS. By


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fitting the QENS spectra with Eq. 1, two pieces of information on the global motions and the local motions were obtained. The most significant difference between deoxyHb and COHb is observed in the apparent diffusion coefficients, Dapp, evaluated from the analysis of the global motions. Whereas the Dapp values of deoxyHb can be described by assuming a rigid body, those of COHb contain a significant contribution of internal motions. Considering the fact that the contribution of the additional internal motions to Dapp is observed for the intrinsically disordered proteins such as myelin basic protein38 and α−synuclein26, which show significant segmental motions such as bending and stretching of the flexible segments, the motions that contribute to Dapp should be those on similar and/or larger scales than the segmental motions. Neutron spin-echo spectroscopy detected the relative motions of the two αβ dimers within metHb20. Furthermore, the major difference in the structures of Hb between the T states, R states, and various intermediate states is in the relative orientation of the α2β2 dimer to the α1β1 dimer2,3,41-43. It is thus likely that the internal motions contributing to Dapp are the relative motions of two αβ dimers within the Hb molecule. The results in this study thus imply that whereas the significant relative motions of the αβ dimers occur in COHb, these motions are suppressed in deoxyHb.

Surveys of more than a hundred of crystallographic structures of Hb in various states showed that the conformational space in the R state is significantly larger than that in the T state44,45. As each crystallographic structure is a snapshot of a conformation in the structural ensemble, this implies that the structural ensemble in the R state has significantly broader distribution than that in the T state. The NMR measurements on COHb showed that Hb in the R state in solution is in equilibrium between the distinct structural states9, whereas those on deoxyHb showed that Hb in the T state appears to adopt a conformational state close to one of the crystallographic structures46. These results imply that in solution, conformational fluctuations



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of Hb occur between various conformations in the structural ensemble, and the apparent difference in the NMR measurements arises from the difference in the distribution of the structural ensemble between the T and R states. This implication is consistent with the observation in this study.

Unfortunately, no theory has been developed to deconvolute the contributions of the internal motions and the translational and rotational diffusion of the entire molecule in the QENS spectra. Quantitative evaluation of the internal motions is thus not possible. However, we carried out a test simulation for a hypothetical system having DT of the COHb tetramer and DR of the αβ dimer in COHb. Although this system is obviously a too-simplified system, the simulation could provide an idea how the rotational motion of the αβ dimer affects Dapp. DR of the αβ dimer was calculated using HYDROPRO for the crystal structure of COHb (pdb code: 2DN3). The simulation was carried out using Eq. 2, similarly to those for the data shown in Fig. 3, except for using the DR value (and the value of the hydrodynamics radius, R, which was also calculated using HYDROPRO, for defining the range of integration in Eq. 2) of the αβ dimer. The results of the simulation is shown in Fig. S4 in the supporting information. The Dapp values of this system are found to be similar to the experimental values. Including the contribution of the rotational motions of the αβ dimer could thus interpret the Dapp values of COHb. This provides additional evidence suggesting the significant relative motions of the αβ dimers in COHb. It is therefore likely that the significant motions of the dimers occur in COHb but the amplitudes of such motions are small in deoxyHb. The observation in this study is also consistent with the results of the EINS measurements on the Hb solutions in 65% glycerolD8/D2O, showing that Hb in the T state is more rigid than in the R state22. QENS is thus sensitive to detect such differences in the dynamics of the quaternary structures of proteins.


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On the other hand, the differences in the local motions between deoxyHb and COHb are small. The residence time of the local jumping motions is a little larger in deoxyHb than in COHb, indicating lower frequency of the local motions in deoxyHb. The amplitudes of such motions, evaluated from the analysis of the EISF curves, are, however, similar between deoxyHb and COHb. The lower frequency of the local motions in deoxyHb is in line with the results of the global motions. Small amplitudes of the dimer motions in deoxyHb could restrict the motions of the residues at the interface between the dimers and thereby slowing the motions of these residues. Similar restriction of the motions by association was observed for F-actin47: The residence time of F-actin, formed by helical association of the actin molecules, is larger than that of G-actin, representing the actin monomers.

Song et al.48 showed using NMR that backbone dynamics is similar between deoxyHb and COHb except for specific residues. These results by the NMR measurements are, however, not inconsistent with the results from our QENS measurements, because observation regions by the two methods are different. Whereas NMR could measure the backbone dynamics of all individual amide groups, QENS measures the average dynamics of hydrogen atoms particularly in the side chains of the entire molecule because labile amide hydrogens in the main chains have been replaced with deuteron in D2O-solutions. The QENS observation that the residence time of the local motions of the side chains in deoxyHb is a little longer than that in COHb implies that the side chains in deoxyHb face, on average, more energy barriers for the motions. The fact that the activation energy of these local motions is nevertheless similar between deoxyHb and COHb implies that a number of the side chains that face the energy barriers that are changed by ligation are rather few. This is consistent with the NMR measurements48 showing that the increase in mobility is observed only in several residues in



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each subunit including the residues involved with the salt bridges, which are broken by ligation, such as β146His.

Wide-angle X-ray scattering (WAXS) studies on Hb showed that structural fluctuations in Hb are more significant in deoxyHb than in COHb21,49. The observation by WAXS that these fluctuations are inhibited by the molecular crowding effect50 implies that the time scale of these fluctuations is comparable to that of the interactions between the proteins, and thus these fluctuations are related to the long-time collective motions. On the other hand, the motions observed by QENS are the short-time self-diffusion. Thus, the apparent discrepancy between the WAXS measurements and the QENS measurements may be attributed to the fact that these measurements observe different kinds of motions. MD simulations on Hb in various states also showed that Hb exhibits increased structural fluctuations by changing from the oxy-state to the deoxy-state51. This apparent discrepancy is similar to the situation with the WAXS studies: The MD simulations investigated the concerted motions of backbone atoms within each subunit, and thus the observed motions are different from those in this study. Other MD studies showed that spontaneous transitions from the T state to the R state occur, but those from the R to T states do not, suggesting the instability of the T state52,53. These transition, however, occur in the time scales slower than 10 nsec, which is three orders slower than the time scale of the motions observed by QENS. The motions observed by QENS are the elementary process that underlies the structural transitions such as the T-R transitions occurred at much slower time scales.

Conclusions The QENS measurements were carried out on deoxyHb and COHb in D2O solution, which correspond to the T state and the R state, respectively, and by analyzing the QENS spectra, the


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changes in the dynamics between these states are detected. Analysis of the global motions shows that whereas the apparent diffusion coefficient of deoxyHb corresponds to that of the rigid particle, that of COHb contains significant contributions from the internal motions of Hb, which are likely to arise from the relative motions of two αβ dimers, in addition to the translational and rotational diffusions of the entire particle. On the other hand, analysis of the local motions shows that the differences in the local motions are small between deoxyHb and COHb: the frequency of these motions is a little lower in deoxyHb than in COHb, but the amplitudes of the motions are similar.

The results obtained in this study are consistent with the earlier neutron scattering studies and the crystallographic studies identifying various structures related to the R state. The apparent discrepancy with the MD and WAXS studies suggests various modes of motions that occur in different time scales. Future studies thus require the dynamics measurements at various time scales, which can be carried out by the QENS measurements at various energy resolutions.

Acknowledgments We thank Dr. R. Inoue and Prof. M. Sugiyama for their help in the DLS measurements. We also thank Dr. Y. Fukushima for the approval of the trial use program for the experiments at J-PARC MLF (Proposal No. 2015A0143). This work was partly supported by JSPS KAKENHI Grant Number JP15H01646 (N.S.)

Supporting Information. Examples of the QENS spectra of deoxyHb and COHb (Figure S1): The translational diffusion coefficients obtained by the DLS experiments (Figure S2): The Simulated values of the apparent diffusion coefficients of the crystal structures (Figure S3): The simulated values of the apparent diffusion coefficients of COHb (Figure S4).



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