Dynamics of proteins with different molecular structures under solution condition

Incoherent quasielastic neutron scattering (iQENS) is a fascinating technique for investigating the internal dynamics of protein. However, low flux of neutron beam, low signal to noise ratio of QENS spectrometers and unavailability of well-established analyzing method have been obstacles for studying internal dynamics under physiological condition (in solution). The recent progress of neutron source and spectrometer provide the fine iQENS profile with high statistics and as well the progress of computational technique enable us to quantitatively reveal the internal dynamic from the obtained iQENS profile. The internal dynamics of two proteins, globular domain protein (GDP) and intrinsically disordered protein (IDP) in solution, were measured with the state-of-the art QENS spectrometer and then revealed with the newly developed analyzing method. It was clarified that the average relaxation rate of IDP was larger than that of GDP and the fraction of mobile H atoms of IDP was also much higher than that of GDP. Combined with the structural analysis and the calculation of solvent accessible surface area of amino acid residue, it was concluded that the internal dynamics were related to the highly solvent exposed amino acid residues depending upon protein’s structure.


Scientific Reports
| (2020) 10:21678 | https://doi.org/10.1038/s41598-020-78311-4 www.nature.com/scientificreports/ profile hinders quantitative characterization of the remaining motion, internal dynamics. To overcome such a problematic situation, double Lorentzian function, which takes into account for the contribution of both rigid body motion and internal dynamics, was developed by Perez et al. 12 Through the optimum selection of energy resolution and energy window of QENS spectrometer, the internal dynamics were successfully decoupled from the observed iQENS profile with this function [12][13][14] . In order to extend the further usability of this function, we developed a new analyzing method that provides the precise contributions of translational and rotational diffusions to the observed iQENS profile explicitly with the aid of computational technique. We then apply this newly developed method for studying the internal dynamics of two proteins, GDP and IDP. We investigated MurD 15 as a typical GDP, and the intrinsically disordered region (IDR) of Hef (helicaseassociated endonuclease for fork-structured DNA) (Hef-IDR) as a typical IDP 16 . These proteins have similar translation and rotational diffusion constants, thus, offering an advantage for studying the effects of different molecular structures on internal dynamics. Here, we characterized and elucidated origin of internal dynamics.

Solution structures of MurD and Hef-IDR.
With the usage of recent state-of-the art software 17,18 , it is possible to reconstruct low-resolution three-dimensional structure from one-dimensional SAXS profile. Our aim for reconstruction of low-resolution three-dimensional structure from SAXS measurements is to compute the translational and rotational diffusion constants, which are used to calculate the contribution of rigid body motion to iQENS profile. We then performed SAXS measurements prior to iQENS measurements.
The crystal structure of MurD (PDB code: 1e0d.pdb) deviated from that calculated from the SAXS profile (χ 2 = 90.9) 19 . We then conducted normal mode analysis (NMA) of the crystal structure to determine the structure of MurD in solution 19 . The SAXS profile of the NMA-deformed structure reproduced the experimental SAXS profile of MurD (χ 2 = 5.4) as shown in, Fig. 1a. Contrary to GDP, IDP has largely different configurations 20 . Following this notion, we searched the configurations of Hef-IDR with MultiFoXS 18 , which enables structural modeling and generated the representative structures 1-5. Considering that the populations of structures 1-5 ). By averaging the two-dimensional S(Q, ω) over each region, one dimensional S(Q, ω) at six values were gained for MurD and Hef-IDR (Fig. S2). We then analyzed their S(Q, ω) and Fig. 2 shows S(Q, ω) at = 0.80 Å −1 , as a representative. Compared with the resolution function (orange broken lines), the spectra broadened in both samples, indicating that the motion of the proteins was anharmonic.
Since the observed S(Q, ω) consists of three dynamics, translational diffusion, rotational diffusion and internal dynamics 22 , we had to decompose the observed S(Q, ω) into them. The sum of translational and rotational diffusions 12 named as a rigid body motion and then its contribution to S(Q, ω), S(Q, ω) rb is given by following functions: www.nature.com/scientificreports/ S(Q, ω) rb is the S(Q, ω)of rigid body motion, S(Q, ω) trans is the S(Q, ω)of translational diffusion, S(Q, ω) rot is the S(Q, ω)of rotational diffusion, Res(Q, ω) is the resolution function, S(Q, ω) rb,ex is the S(Q, ω) rb convoluted with a resolution function,D t is the translational diffusion constant, H t is the hydordynamic function to translational diffusion constant, R h is the hydrodynamic radius, r is the the distance from the center of hard sphere where an isotropic diffusion was assumed, j l is the lth order sperical Bessel function, ⊗ is the convolution operator.
The D t and D r values of MurD and Hef-IDR were computed using "HYDROPRO" 23 . The D t and D r values of MurD determined using the single structure resolved by the SAXS measurements were 6.42 × 10 -7 cm 2 /s and 5.34 × 10 6 s −1 , respectively. As described above, the SAXS profile of Hef-IDR reproduced the ensemble-averaged profile over five structures. For Hef-IDR, the D t values of structures 1-5 of Hef-IDR were calculated to 6.98 × 10 -7 cm 2 /s, 6.47 × 10 -7 cm 2 /s, 6.68 × 10 -7 cm 2 /s, 7.05 × 10 -7 cm 2 /s and 7.23 × 10 -7 cm 2 /s, respectively. The D r values of structures 1-5 of Hef-IDR were calculated to 5.73 × 10 6 s −1 , 5.42 × 10 6 s −1 , 5.03 × 10 6 s −1 , 5.85 × 10 6 s −1 and 6.54 × 10 6 s −1 , respectively. Five sets of separately calculated D t and D r values were averaged depending on their populations in the ensemble-averaged profile, and the averaged D t and D r values were 6.71 × 10 -7 cm 2 /s and 5.51 × 10 6 s −1 , respectively, for Hef-IDR. It was confirmed that the diffusion constants of MurD and Hef-IDR were almost the same. Considering the concentration of MurD and Hef-IDR used for iQENS measurements, we also calculated H t for both samples. A modified function was then considered to reproduce the observed S(Q, ω). Sarter et al. 14 reported that observed S(Q, ω) could be expressed as a convolution of two dynamic scattering functions S(Q, ω) rb and S(Q, ω) int , which describes the internal dynamics given by Eq. (2): where δ(ω) and A(Q) correspond to the delta function and elastic incoherent structure factor, respectively. For the simplification of calculation, it is assumed that the S(Q, ω) int is described by a single Lorentz function as follows.
where Γ indicates the relaxation rate of internal dynamics. By substituting S(Q, ω) rb into Eqs. (2) and (4) is obtained as follows: Taking into consideration of fast dynamics such as the rotation of methyl groups 24 in the modified fit function, we also introduced the contribution of a flat background (B(Q)). Finally, the following modified fit function was obtained: where S(Q, ω) mod,ex corresponds to S(Q, ω) mod convoluted with a resolution function. The pink and blue lines in Fig. 2 show the results of fits with Eq. (5) for MurD and Hef-IDR, respectively, and both S(Q, ω)s were appropriately described by this modified function. Figure 3a shows the Q 2 dependence of Γ values from both samples. The Γ values were larger for Hef-IDR than MurD, meaning that the averaged internal dynamics were faster for Hef-IDR than MurD. Namely, we succeeded to exhibit the difference of internal dynamics between GDP and IDP quantitatively through the application of newly developed analyzing method to the observed S(Q, ω) profiles. Prior to the further detailed analysis of internal dynamics, we briefly explain the observable H atoms of proteins in iQENS measurements. Both MurD To consider the origin of the difference in the internal dynamics between GDP and IDP, we focused on the mobility of H atoms embedded on the peptide chains. We then analyzed the Q dependence of the elastic incoherent structure factor (A(Q)) ( Fig. 3b) because the mean square displacement (< u 2 >) of mobile H atoms within a protein can be determined using the following equation 14,25 : where the value of p corresponds to the fraction of mobile H atoms. The calculated values for < u 2 > and p were 2.1 ± 0.4 Å 2 and 0.33 ± 0.07, respectively, for MurD, and 2.1 ± 0.2 Å 2 and 0.85 ± 0.05 respectively, for Hef-IDR. Although < u 2 > was not affected by the different molecular structures, the fraction of mobile H atoms was higher in Hef-IDR than that in MurD. It should be an origin of difference of internal dynamics between them.

Discussion
We considered the difference in p values between MurD and Hef-IDR. It is considered that the H atoms with high mobility are considered to be located at the surface of protein based on theoretical shell model 26 . In consistent with this idea, Zanotti et al. 27 also reported that peripheral water-protein interaction affected the internal dynamics of protein through the combination of QNES and 13 C-NMR. To clarify H atoms in MurD and Hef-IDR that were exposed to solvent, we obtained their solution scattering data using SAXS. The mean solvent accessible surface areas of the amino acid residues of MurD and Hef-IDR with their solution structures determined by GETAREA 28 (probe particle radius of 1.4 Å), were 44.1 and 117.2 Å 2 , respectively. It implies that the mean value of SASA of Hef-IDR was higher than that of MurD. From the normal mode analysis for MurD, it was revealed that higher SASA possessed higher mobility from NMA (refer to Fig. S3). It is considered that there exist the www.nature.com/scientificreports/ relationship between internal dynamics and SASA. Then, we adopted the idea that amino acid residues exposed to a solvent could affect the internal dynamics. In the following, we explain our idea in more detail.
1. Under the assumption that a shape of amino acid residue is sphere, the entire surface area (S whole ) of each amino acid residue was calculated from its volume. 2. The number of H nex in the entire protein, N whole , was calculated 29 . 3. The solvent accessible surface area (S solvent ) of each amino residue was calculated for both MurD and Hef-IDR as shown in Fig. 4. 4. The fractions of solvent exposed surface area to the entire surface area (S solvent /S whole ) were defined as f. and f values were calculated for all the constituting amino acid residues for both MurD and Hef-IDR. 5. To judge whether a given amino acid residue is located at the solvent or not, we set the threshold f value (f* t ) as the quantitative criteria: Here, the amino acid residue with f values exceeding f* t (f > f* t ) is regarded to be exposed to the solvent and named as a exp . 6. For each setting f* t value (0.0 ~ 0.8), the entire amino acid resides were classified and then the number of non-exchangeable atoms (H nex ) in the a exp (N surface (f* t )) was calculated. 7. The number ratio r H (f* t ) (= N surface (f* t )/N whole ) was calculated. Pink and blue lines in Fig. 5 indicate the results for MurD and Hef-IDR, respectively. 8. Because exchangeable H atoms of protein in D 2 O were replaced with deuterium atoms, the iQENS of the protein was dominated by mobile non-exchangeable H atoms that are mainly located in amino acid residues exposed to solvent. This means that the p values should agree with the r H value. In this procedure, we should find the optimum f* t value that reproduce the r H (p) values from both MurD and Hef-IDR simultaneously. For this purpose, we firstly calculated the following χ 2 values against r H (p) for MurD (χ 2 m (f* t )) and Hef-IDR (χ 2 h (f* t )), respectively.   ) from Hef-IDR, r H (p) value from Hef-IDR, and error value of r H (p) value from Hef-IDR, respectively. As a next step, we named the sum of χ 2 m (f* t ) and χ 2 h (f* t ) as a total χ 2 (χ 2 tot (f* t )). It is considered that optimum f* t value could be determined by finding the condition where χ 2 tot (f* t ) exhibited the lowest value. We then plotted χ 2 tot (f* t ) in Figs. 1-3 and χ 2 tot (f* t ) exhibited the smallest value at f* t = 0.6. We then concluded that f* t value of 0.6 satisfied the value calculated with SAXS and that observed using iQENS.
All steps are schematically summarized in Fig. S5. Figure 6 shows a schema of amino acid residues in both MurD and Hef-IDR located in surface area that can access the solvent under conditions of f* t = 0.6. Such amino acid residues were notably segregated only on the surface of MurD, but these were distributed and chained within the entire structure of Hef-IDR. These findings indicated that the amino acid residues at a surface with access to a solvent is responsible for the internal dynamics of proteins depending on their molecular structures. Thanks to the application of the newly developed analyzing method, we could discuss the difference of internal dynamics of GDP and IDP quantitatively. Furthermore, we could reach the present conclusion that can interpret the internal dynamics of GDP and IDP without inconsistency.

Summary
The internal dynamics of two proteins, globular domain protein (GDP) and intrinsically disordered protein (IDP) in solution, were studied by measuring incoherent quasielastic neutron scattering (iQENS) with state-of-the art spectrometer QENS spectrometer and analyzing them with a newly developed method assisted by computational technique. It was clarified that the average relaxation rate of internal dynamics in IDP was larger than that of GDP quantitatively. From the further detailed analyzes, the fraction of mobile hydrogen (H) atoms of IDP was higher than that of GDP. Calculation of the solvent accessible surface areas per amino acid residues revealed that the fraction of highly solvent exposed H atoms was related to the fraction of mobile H atoms. Then, present iQENS studies clarified that non-exchangeable H atoms that are mainly located in amino acid residues exposed to solvent was relevant to the internal dynamics depending upon protein's structures. It is strongly expected  Small-angle X-ray scattering (SAXS) measurements. SAXS measurements of Hef-IDR (3.4 mg/mL) were performed with a BioSAXS 1000 system mounted on a MicroMax007HF X-ray generator (Rigaku, Tokyo, Japan) at 25 °C and a PILATUS100K detector (DECTRIS, Baden-Dättwil, Switzerland) located 485 mm from the sample. The X-ray wavelength was 1.542 Å. One-dimensional scattering data (I(Q)) were obtained by radial averaging. Scattered intensity was converted into absolute scatter intensity, and calibrated based on the scatter (b) (a) 90°F igure 6. Schematic view of solvent-exposed amino acid residues for MurD and Hef-IDR when f* t = 0.6. (a) In the case of f* t = 0.6, the amino acid residues, which are located in solvent accessible surface area, were depicted for MurD by purple spheres. The domain 1, 2, 3 were depicted by green, red and blue sticks, respectively. (b) In the case of f* t = 0.6, the amino acid residues, which are located in solvent accessible surface area, were depicted for Hef-IDR by blue spheres. This figure is prepared by the usage of Adobe Illustrator CC 2015. www.nature.com/scientificreports/ intensity of water (I(Q) water = 1.632 × 10 -2 cm −1 ). Data were processed using SAXSLab (Rigaku) and the ATSAS package 17,31 . SAXS measurements of MurD (3.0 mg/mL) at 25 °C were performed with a NANOPIX (Rigaku, Tokyo, Japan). X-rays emanating from a high-brilliance point-focused X-ray generator (MicroMAX-007HF, Rigaku, Tokyo, Japan) were focused using a confocal mirror (OptiSAXS) and collimated with a confocal multilayer mirror and a two-pinhole collimation system with lower parasitic scattering. The scattered X-rays were detected using a two-dimensional (2D) HyPix-6000 semiconductor detector (Rigaku, Tokyo, Japan). We covered the Q range (0.015-0.5 Å −1 ) by measuring SAXS profiles at sample-to-detector distances (SDD) of 1320 and 300 mm. One-dimensional I(Q) values were obtained by radial averaging the 2D scattering patterns. The scatter intensity from the protein was converted to an absolute scale by comparison with the scatter intensity of water. All data were reduced and processed using SAngler 32 .
iQENS measurement. We measured iQENS measurements using an inverted geometry time-of-flight spectrometer (BL02 DNA) installed 21 at the Materials and Life Science Experimental Facility (MLF) in J-PARC, Tokai, Japan. The magnitude of the scattering vector Q (Q = 4πsinθ/λ f , where 2θ and λ f = 6.26 Å are the scattering angle and the wavelength of the analyzed neutron, respectively) ranged from 0.12 to 1.78 Å −1 . Samples were loaded into double-cylindrical aluminum cells (outer diameter: 14 mm, inner diameter: 13 mm, height: 45 mm) under a helium atmosphere. The resolution function was determined from the measurement of vanadium at 298 K and the calculated energy resolution (δE) was 12 µeV. Solutions of Hef-IDR and MurD (8.0 and 52.0 mg/ mL, respectively) were measured at 25 °C. Dynamic scattering laws from D 2 O buffer were subtracted from those of protein solutions based on their volume fractions to obtain the protein dynamics.

Data availability
The datasets generated and analyzed during the current study are available from the corresponding authors on reasonable request. www.nature.com/scientificreports/