Specific monovalent cation effect on protein-protein interactions revealed by protein rotational diffusion analysis

Chemical Physics Letters 730 (2019) 89–94

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Research paper

Specific monovalent cation effect on protein-protein interactions revealed by protein rotational diffusion analysis☆ Akane Kato, Yudai Katsuki, Etsuko Nishimoto

T

⁎

Institute of Biophysical Chemistry, Faculty of Agriculture, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

H I GH L IG H T S

rotational diffusion reflects hydrodynamic interactions between proteins. • Protein lysozyme, hydrodynamic interactions are enhanced by adding lysozyme and cation. • For two- and repulsive three-body interactions are induced in lysozymes. • Attractive • Increase in the induced hydrodynamic interactions follows inverse Hofmeister series.

A R T I C LE I N FO

A B S T R A C T

Keywords: Protein-protein interactions Protein rotational diffusion Specific effect of cations Fluorescence anisotropy

The protein-protein interactions induced by cation specific effects were characterized by the rotational diffusion analysis. The rotational diffusion coefficient, Drot, estimated by time-resolved fluorescence anisotropy of fluorescent-labeled lysozyme was reduced responding to monovalent cation chlorides and was able to be approximated by quadratic functions of lysozyme concentration. The resultant first and second terms of lysozyme concentration were observed to be negative and positive according to the species and concentrations of monovalent cations, respectively. These two hydrodynamic interaction parameters demonstrated that the attractive and also repulsive interactions were induced between lysozymes in the order of inverse Hofmeister effect.

1. Introduction In aqueous solution, protein molecules diffuse, encounter with other molecules, and recognize biological target molecules to complete their specific biological roles. This sequence of protein dynamic behavior exhibited in the biological process is governed by the collective interactions between protein molecules. Therefore, the precise depiction of protein-protein interactions is essential to understand many biological and biophysical processes such as the complex formations and self-organization of proteins [1–4]. Nevertheless, the coherent theory on the protein-protein interactions explaining dynamic behavior of proteins in solution hasn’t been established yet. It is generally accepted that protein-protein interactions are derived from the integration of several weak non-covalent forces such as excluded volume effect, Coulombic electrostatic, van der Waals, hydration and hydrophobic force [5]. The intrinsic nature of protein-protein interactions is reflected in the translational or rotational diffusion of

proteins mediated by the radial distribution of protein in solution. The translational diffusion of proteins is exclusively used for characterizing protein-protein interactions, because it can be measured by the established techniques such as static and dynamic light scattering and is theoretically linked to the interaction of proteins via a spatial gradient of chemical potential [6]. On the other hand, the rotational diffusion analysis is rarely applied to the description of protein-protein interactions due to the limitation of measurement methods and the insufficiency of theory. However, it is not hard to expect that the rotational motion is more susceptible to the interactions with the neighboring, since the diffusion of macromolecule in solution is driven by the collective effect of small collisions of solvent molecules unlike one of gas molecule spreading through a vacuum [7]. Moreover, the rotational motion would significantly contribute to the relaxation processes in complex formation, polymerization and crystallization [8]. Therefore, the establishment of observation and analysis methods for the rotational diffusion is also essential for the precise description of

☆ ⁎

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Corresponding author. E-mail address: [email protected] (E. Nishimoto).

https://doi.org/10.1016/j.cplett.2019.05.019 Received 7 March 2019; Received in revised form 4 May 2019; Accepted 12 May 2019 Available online 16 May 2019 0009-2614/ © 2019 Elsevier B.V. All rights reserved.

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2.1. Labeling of N-terminal amino group of lysozyme with Alexa430

protein-protein interactions. While depolarized dynamic light scattering and nuclear magnetic resonance relaxation have been used until now [9,10], fluorescence anisotropy is particularly relevant for the measurements of the rotation of protein because of the superior sensitivity [11]. However, all proteins do not contain fluorescent amino acids like Trp or Tyr and the excessive concentration of protein may be the sources of some distortion such as multiple light scattering, resonance energy transfer, and reabsorption process to make the result incorrect. These demerits of fluorescence anisotropy can be overcome by tracing a small number of fluorescent-labeled proteins which behave similarly to non-labeled protein in solution. The usage of fluorescencelabeled protein enables the correct measurement of protein diffusional rotations under much higher concentration region without any undesirable influences than the traditional methods like light scattering. In the present study, using Alexa430 for fluorescent-labeled proteins, we examined to describe protein-protein interactions in the salting-out model system from the standpoint of rotational diffusion analysis. The fluorescence spectrum and quantum yield of Alexa430 are not affected by the presence of cation chlorides. Besides, Alexa430 is stable against the photo-bleaching effect by the strong laser excitation. A typical globular protein, hen egg-white lysozyme, was employed as a model protein. Lysozyme was stable and the intact structure and enzymatic activity was preserved even on the solution including monovalent cation chloride higher that 1.2 M. The rotational diffusion coefficient, Drot, of fluorescent-labeled lysozyme molecules in solutions including various concentrations of lysozyme and monovalent cation chlorides was estimated by time-resolved fluorescence anisotropy measurements at a time resolution of a pico-second order. The lysozyme-lysozyme interactions reflected in the rotational diffusion is described by hydrodynamic interaction parameters extracted from the dependence of Drot on lysozyme concentration [12]. Furthermore, we show the steady-state fluorescence anisotropy method is also effective for the investigation of lysozyme-lysozyme interactions in our experiment conditions by comparing the time-resolved and steady-state fluorescence anisotropy results. We characterize the effects of monovalent cation chlorides (NaCl, KCl, LiCl, NH4Cl, and CsCl) on the interactions between lysozymes based on the hydrodynamic interaction parameters. The specific ion effect on protein, so-called Hofmeister effect, is ubiquitous and the detailed mechanism is still unclear in spite of the extensive investigations [13,14]. The potentials acting on the interacting proteins drastically change depending on ion species and their concentrations in solution because they are definitely limited by the charge density of protein surfaces. Presumably, the precise description of protein-protein interactions through the rotational diffusion analysis would provide valuable basis leading to the elucidation of the Hofmeister effect on molecular level. Moreover, it provides valuable information to overcome the protein condensation diseases such as Altzheimer’s disease and amyloidosis and to fabricate the nano-scale devise using self-assembling nature of protein.

The conjugating of Alexa430 with the N-terminal amino group of lysozyme and the determination of coupling ratio were conducted following the guideline of Brinkey [16]. For details, refer to supplementary material. 2.2. Measurement of time-resolved fluorescence anisotropy Time-resolved fluorescence anisotropy was measured by the timecorrelated single photon counting technique with sub-picosecond pulse laser. The details of the measuring method are shown in ref. [17]. The channel width was set to 9.9 ps/ch. The instrument response function (IRF) was determined measuring the scattering light from polystyrene latex suspension (1 µm diameter). In every measurement, the samples were excited at 440 nm and fluorescence emission was detected at 550 nm. For measurements of IVV(t) and IVH(t), Glan-Taylor polarizers was placed just behind the sample cell and set at 0° or 90°. The G-factor was decided to be 1.55 at 550 nm by measuring the vertically and horizontally polarized emission intensities against the horizontal excitation to compensate the sensibility difference of our emission detection system against the polarized emissions. The measurements were performed at 20 °C using a thermostat cell. The sample solutions contained small amount of F-lysozyme (3 µg/ml) as tracers. The concentrations of samples were adjusted to 0.1–40.0 mg/ml lysozyme and 0–1.2 M monovalent cation chloride by adding 100 mg/ml lysozyme stock solution and 3.0 M monovalent cation chloride stock solution filtered through 0.22 µm filter (MillexRGV; Millipore). Non-appearance of crystal or amorphous phase was confirmed within 1 day in every sample solution. 2.3. Analysis of time-resolved fluorescence anisotropy Fluorescence anisotropy decay data were analyzed by means of the nonlinear least-squares iterative convolution method based on the Marquart algorithm [18,19]. The fitting adequacy was assessed by the statistical parameters such as the sigma value, serial variance ratio, and plots of weighted residuals. Fluorescence intensity decay, I(t), was described as a sum of exponential functions [11].

I (t ) =

∑ αiexp(-t /τi)

(1)

αi and τi are i-th components of amplitude and corresponding fluorescence decay time, respectively. The decays of vertical and horizontal components, IVV(t) and IVH(t), are related to I(t) as follows [11]:

2. Materials and methods

IVV =

1 I (t )[1-r (t )], 3

(2)

IVH =

2 I (t )[1-2r (t )] 3

(3)

where r(t) is the decay of fluorescence anisotropy. r(t) was optimally fitted as a sum of double exponentials under every condition in this work. When the configuration of F-lysozyme molecule is considered, two decay components correspond to the entire rotation of F-lysozyme and the segmental motion of the N-terminal labeled by Alexa430, respectively.

Hen egg-white lysozyme (lysozyme; 14 kDa, 3 times recrystallized, salt-free, albumin-free) was purchased from Wako (Osaka, Japan). Alexa Fluor430 NHS ester (Alexa430) was obtained from Thermo Fisher Scientific (Waltham, MA). Dimethyl sulfoxide, purchased from Katayama Chemical Industries (Osaka, Japan), was used as a solvent of Alexa430. Monovalent cation chlorides (NaCl, KCl, LiCl, NH4Cl, and CsCl) and other chemicals were guaranteed reagents purchased from Sigma-Aldrich (St. Louis, MO). In every measurement, lysozyme and monovalent cation chloride were dissolved into 20 mM sodium acetate buffer (pH 4.5) and then filtered through a 0.22 µm sterile filter (Millipore, Billerica, MO). Lysozyme and Alexa430 concentrations were determined by measuring their absorbance. The extinction coefficient of lysozyme at 280 nm is 2.64 mL mg−1 cm−1 [15], and that of Alexa430 at 430 nm is 15,000 M−1 cm−1.

r (t ) = βL exp(-t /φL ) + βSexp(-t /φS)

(4)

where φL is the longer correlation time relating to the entire rotation of F-lysozyme, and φS is approximately coincident with the rotational correlation time of the faster segmental motion of the fluorescent-labeled N-terminal. The corresponding amplitude to each rotational component was given by βL and βS, respectively. Here, assuming that Flysozyme is a hard sphere, the apparent rotational diffusion coefficient (Drot) can be estimated from φL by applying Stokes-Einstein-Debye 90

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7000

Drot =

1 k T = B 6φL 6ηV

Photon conunts

relation: (5)

where kB is Boltzmann’s constant, and V is the hydrodynamic volume of F-lysozyme molecule. T and η is the temperature and viscosity of the solution, respectively.

5000 4000 3000 2000

VH

1000

Residuals

2.4. Hydrodynamic interactions (HI) on the rotational diffusion coefficient The rotational diffusion is influenced by indirect hydrodynamic interactions (HI) mediated by solvent. The normalized rotational diffusion coefficient, written as hydrodynamic function (Hsr ), can be expressed as a power series by using a cluster expansion [7].

Drot = Hsr = 1 + Hs1r c + Hs2r c 2 + ··· 0 Drot

A

VV

6000

0 3 0 -3 3 0 -3

VV VH 0

200

400

600

800 1000 1200 1400 1600 1800 2000

Channel (9.9 ps/ch )

(6)

Fluorescence anisotropy, r (t)

0 denote the rotational diffusion coefficients in interDrot and Drot acting and non-interacting systems, respectively. c is particle concentration. The coefficient Hs1r of the second term represents the effects of two-body HI on rotational dynamics, explained by an integral of the product of two-body mobility function and pair distribution function [7]. The coefficient Hs2r of the third term involves three-body hydrodynamic contribution [7]. We characterize the HI between F-lysozyme and lysozyme by applying Eq. (6) to the fluorescent-labeled protein system.

2.5. Measurement and analysis of steady-state fluorescence anisotropy The details of measurement and analysis of steady-state fluorescence anisotropy are shown in supplementary material.

0.4

B 0.3

0.2

0.1

0.0

3. Results and discussions

0

2

4

6

8

10

12

14

Time (ns)

The time-resolved fluorescence anisotropy of F-lysozyme was measured under the conditions including 0.1–40 mg/ml lysozyme and 0–1.2 M monovalent cation chloride salts (NaCl, KCl, LICl, NH4Cl, and CsCl). Fig. 1 represents the time evolution of fluorescence anisotropy of F-lysozyme in 20 mM sodium acetate buffer (pH4.5) containing 0.1 mg/ ml lysozyme. This fluorescence anisotropy decay gave the best fit against double exponential kinetics expressed in Eq. (4). Two rotational correlation times were determined to be φL = 8.18 ns (βL = 0.26) and φS = 1.10 ns (βS = 0.10) by the global analysis. The acquired sigma value was 1.023 and the serial variance ratios of IVV and IVH were 1.910 and 1.967, respectively. The hydrodynamic radius calculated from φL (8.18 ns) based on SED relation (Eq. (5)) was 19.9 Å, which roughly matched with the equivalent spherical radius of a lysozyme monomer (17.2 Å) estimated from the crystallographic structure. Therefore, φL corresponds to the correlation time of entire rotation of F-lysozyme. On the other hand, φS marked approximately one-tenth time scale of φL, relating to the faster fluorescence depolarization process ascribed to the segmental motion of the N-terminal. The time-resolved fluorescence anisotropy decay observed here was precisely described with double exponential kinetics in the present experimental conditions. Fig. 2 shows the lysozyme concentration dependences of φL and φS in the solution including 0.2 M NaCl. φL was prolonged as increasing in the lysozyme concentration while φS remained almost constant. Similar results were also obtained under the conditions including other monovalent cation salts. These results demonstrate that HI would not be reflected in the segmental motion of the N-terminal but in the entire rotation of F-lysozyme. Moreover, we confirmed the validity of the φL value (3.76 ns to 27.10 ns) estimated in every sample condition by comparing with the time range for observing correctly the rotational correlation time (0.1τav < φ < 10τav). The average fluorescence lifetime (τav) was calculated to be around 3.56 ns using the fluorescence intensity decay kinetics simultaneously decided in the global analysis of

Fig. 1. Time evolution of fluorescence anisotropy of F-lysozyme under the condition including 0.1 mg/ml lysozyme in 20 mM sodium acetate buffer (pH 4.5). (A) Upper panel, the decay curves of vertically (IVV) and horizontally (IVH) polarized emissions of F-lysozyme; lower panel, the plots of weighted residuals of IVV and IVH. (B) Fluorescence anisotropy decay profile of F-lysozyme obtained from the experimentally measured IVV and IVH.

correlation time (ns)

22 20 18 16 14 12 10 8 6 4 2 0

0

5

10

15

20

25

30

35

40

45

lysozyme (mg/ml) Fig. 2. Lysozyme concentration dependence of the rotational correlation times of F-lysozyme in the buffer solutions including 0.2 M NaCl. Red circle ( ) and blue square ( ) are the longer (φ L) and the shorter (φ S) rotational correlation times, respectively. The uncertainties of 20 ps were included in data points. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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1.4

A

0

0.8 0.6 1.2 M

0.4

0.2 M

0

5

10

15

20

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30

1.0

0M

0.8 0.6 1.2 M

0.4 0.2

35

40

0.0

45

0.5 M 0

5

1.4

1.2 M

25

30

35

40

45

0.85 M 0

5

10

15

20

25

30

35

rot

0M

0.6 0.85 M

0.2

0.5 M 40

45

Fig. 3. Dependence of the normalized rotational diffusion coefficient (Drot/D0rot) on the lysozyme concentration in lysozyme-NaCl system (A), lysozyme-KCl system (B), lysozyme-LiCl system (C), lysozyme-NH4Cl system (D) and lysozyme-CsCl system (E). Black square (■), red circle ( ), green triangle ( ), blue inverted triangle ( ), and sky blue rhombus ( ) represent absence of monovalent cation salts, 0.2, 0.5, 0.85, and 1.2 M monovalent cation chloride salts, respectively. The solid curves are described by the quadratic approximation based on Eq. (6). The error range is limited within about 0.2 per cent. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

D

0.4

0.0

0.5 M 0.2 M

1.2 M 0

5

10

15

20

25

30

35

40

45

lysozyme, cp (mg / ml)

lysozyme, cp (mg / ml) 1.4

E

1.2 rot

0.8

0

0.2 M

0.2

0

1.0

Drot / D

rot

0

Drot / D

0.4

Drot / D

20

1.2

0M

0.6

0.0

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C

1.2

0.8

10

lysozyme, cp (mg / ml)

lysozyme, cp (mg / ml)

1.0

0.2 M

0.85 M

0.5 M

0.85 M

0.2 0.0

rot

1.2

0M

1.0

Drot / D

rot

Drot / D

0

1.2

B

0M

1.0 0.8 0.6

0.2 M

0.4

0.85 M

0.2 0.0

1.2 M 0

5

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0.5 M 30

35

40

45

lysozyme, cp (mg / ml) the time-resolved fluorescence anisotropy. According to Eq. (5), the acquired φL values were converted to the apparent rotational diffusion coefficients (Drot) of F-lysozyme molecule. The normalized rotational diffusion coefficients (Drot/D0rot) of F-lysozyme were plotted as functions of lysozyme concentration (cp) in Fig. 3. In the presence of monovalent cation chlorides, Drot/D0rot decreased with increasing cp, suggesting that the entire rotational diffusion of Flysozyme was delayed. The extent of the decrease was intensified with increasing salt concentrations. The retardation of the entire rotational diffusion of F-lysozyme would be caused by HI between F-lysozyme and the adjacent lysozyme molecules, which become more intense by adding monovalent cation chlorides. This tendency was shown clearly in NaCl, KCl and LiCl but not so evident in CsCl and NH4Cl. In the presence of cation chlorides, Drot/D0rot value almost linearly decreased with cp in the low cp region. However, the value of Drot/D0rot deviated from the linear line at cp region higher than 5–15 mg/ml. Considering the nonlinearity of Drot/D0rot-cp plot, we examined non-linear curve fitting against Drot/D0rot-cp plot using truncated form of Eq. (6) after the third term. As shown in Fig. 3, the resultant fitting curves with higher precisions were obtained through cp range of 0.1–45 mg. The obtained Hs1r and Hs2r were plotted as functions of monovalent cation chloride concentration in Fig. 4. Two-body HI parameter, Hs1r, showed slightly positive value in the absence of cation chlorides and decreased to negative value with increasing the concentration of cation chloride to suggest that monovalent cations and chloride ion induce the attractive

interactions between F-lysozyme and the adjacent lysozyme. The significant difference in Hs1r value among five cations was recognized in the solution including 1.2 M, while Hs1r value due to each cation is similar at 0.2–0.5 M apart from NH4Cl. In the cases of NaCl, KCl, or LiCl, Hs1r monotonically decreased with increase in cation chloride concentration from 0 M to 1.2 M. Under the conditions including CsCl or NH4Cl, Hs1r substantially reached to the constants, while NH4Cl gave more negative Hs1r value than CsCl. Compared at 1.2 M of salt conHs1r centrations, decreased in the ranking of + + Na > K > Li+ > NH4+ > Cs+, which agrees with inverse Hofmeister series (Li+ > Na+ > K+ > NH4+ > Cs+) except for Li+ [20]. The three-body HI parameter, Hs2r , was slightly negative in the absence of cation chlorides and increased to the positive value by increasing cation chlorides. The value of Hs2r depended on monovalent cation species and their concentrations as well as Hs1r and indicated larger value in the order of Na+ > K+ > Li+ > NH4+ > Cs+ at 1.2 M of cation chloride. The positive Hs2r value estimated in the present work would suggest that some three-body repulsive interactions would be induced among one F-lysozyme and two neighbor lysozyme molecules. It is well known in the static thermodynamics that simple gas molecules are polarized on the simultaneous contact to create the repulsive three-body interaction at low temperature. Such type of polarization interaction is also predicted for protein molecules and may be related to Hs2r presented here [21]. As shown in Fig. 2, the rotational diffusion coefficient 92

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Fig. 4. Monovalent cation chloride salt concentration dependence of HI parameters, Hs1r and Hs2r , estimated by approximating Drot/D0rot-cp plot by a power-series truncated after the third term in Eq. (6). (A) Two-body HI parameter, Hs1r . (B) Three-body HI parameter, Hs2r . Black square ( ), red circle ( ), green triangle ( ), blue inverted triangle ( ), and sky blue rhombus ( ) represent NaCl, KCl, LiCl, NH4Cl, and CsCl, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

corresponding to the entire rotation of F-lysozyme was sensitive to HI whereas the correlation times ascribed to the segmental motion of labeled N-terminal was short and independent on cp. It is reasonable to employ the longer rotational correlation times for the evaluation of HI. However, we have to examine the way by the steady-state fluorescence methods. The details of the results by steady-state measurements are described in supplementary material. The normalized reciprocal value, rss/ rapp , which is the ratio of the fluorescence anisotropy in the noninteracting and interacting conditions, decreased linearly with cp at low cp and deviated from the linear line in the cp range of 4–12 mg/ml. HI parameters, Hs1r and Hs2r , extracted from rss/ rapp -cp plot, mostly corresponded to those from Drot/D0rot-cp plot. Therefore, steady-state fluorescence anisotropy method can be applicable to the characterization of HI, although some cares must be paid for the rotational correlation time of the segmental motion of N-terminals. To assess the validity of two-body HI parameter, Hs1r, presented here and to deepen the understanding of protein interactions characterized by the protein rotational diffusion, we compared the approximated r value of B22 calculated from Hs1r with the osmotic virial coefficient, B22, reported for lysozyme-NaCl system. B22 is now considered as the most common indicator of two-body interactions. Based on the similarity in the concentration dependence between translational and rotational r diffusion, we estimated B22 values from Hs1r in a similar manner as in r = (Hs1r + vsp)/2Mw . Mw and νsp denote the translational diffusion by B22 molecular weight (14,307 g/mol) and the partial specific volume r (0.703 mL/g) of lysozyme, respectively [6]. In Fig. 5, B22 values calculated from Hs1r were plotted as a function of NaCl concentration together with B22 previously reported by using static light scattering r technique [22,23]. Although B22 and B22 decreased with similar disr placement with increasing NaCl, evident difference was recognized. B22 −4 2 4 decreased from 10.3 × 10 mL · mol/g to −30.6 × 10 mL · mol/g2 in the 0–1.2 M NaCl concentration range whereas B22 declined from 33.3 × 10 4 mL · mol/g2 to only −7.4 × 10−4 mL · mol/g2 at 1.2 M of NaCl [22,23]. Main possible cause of the difference would be the contribution of the mobility function, which is a peculiar property to HI parameters based on the rotational diffusion. The mobility function is

r Fig. 5. Comparison of B22 calculated from Hs1r values (red closed square; ) with the osmotic virial coefficient B22 measured by static light scattering. The symbols of open triangle ( ) and open circle ( ) indicate values from Velev et al. [22] and Guo et al. [23]. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the determinant factor of Hs1r and relates the angular velocity of a protein to the torque exerted on the neighboring proteins. The differr ence between B22 and B22 suggests that the determinant factor of r Hs1would be not just the radial distribution of protein but the stronger force affecting the neighboring proteins. As shown in Fig. 4, two-body attractive interactions reflected in Hs1r increased in the monovalent cation ranking of Na+ > K+ > Li+ > NH4+ > Cs+ in the conditions including 1.2 M monovalent cation chloride. This cation order corresponds to that of the effectiveness for lysozyme crystallization observed in our preliminary experiment and the lysozyme solubility experiment [24]. The saltingout ability of monovalent cation against lysozyme seems to be involved with the ranking of the affinity to negatively charged carboxyl groups: 93

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Na+ > K+ > Li+ > Cs+ [25]. Based on the coincidence between our results and the cation order in adsorption ability to carboxylic group, the neutralization of the negatively charged surface of lysozymes would allow the mutual approach of F-lysozyme and lysozyme molecules to change the rotational dynamics of F-lysozyme. The involvement of some repulsive interactions is indicated by the dependence of rotational motion of F-lysozyme on cp as shown in Fig. 3. Without the repulsive interactions, the reduced Drot could be decline more rapidly with increase in cp. In order to describe the effects of the repulsive interactions, three-body HI parameter, Hs2r , was estimated by a powerseries expansion truncated after the third term to Hsr . The repulsive HI reflected in Hs2r at 1.2 M monovalent cation chloride increased in the same cation ranking with that of the attractive HI shown in Hs1r: Na+ > K+ > Li+ > NH4+ > Cs+. Clearly, the repulsive HI increased concomitantly with attractive HI. The repulsive HI would be induced when F-lysozyme molecule come closer to lysozyme molecule. The cause of the repulsive HI would be the asymmetric shape and anisotropic surface charge distribution peculiar to protein since this repulsive HI has not shown in a simple charged colloid-electrolyte system [12]. Considering the protein crystallization and complex formation of protein, it would be a promising hypothesis that the molecular orientation process is enabled by the repulsive HI contributes to the relaxation for maintaining regular arrangements of lysozyme molecules. However, the more detailed study is required for specifying the physicochemical property inducing three-body repulsive force among lysozymes.

information obtained by rotational diffusion analysis in combination with translational diffusion analysis is useful to elucidate the details of protein-protein interactions and finally the complex biological process. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Appendix A. Supplementary material Supplementary material shows the details of the fluorescent labeling method and the steady-state fluorescence anisotropy method and result. Supplementary data to this article can be found online at https://doi. org/10.1016/j.cplett.2019.05.019. References [1] S. Jones, J.M. Thornton, Proc. Natl. Acad. Sci. USA 93 (1996) 13–20. [2] J.J. McManus, P. Charbonneau, E. Zaccarelli, N. Asherie, Curr. Opin. Colloid Interface Sci. 22 (2016) 73–79. [3] R.A. Curtis, L. Lue, Chem. Eng. Sci. 61 (2006) 907–923. [4] A. George, Y. Ciang, B. Guo, A. Arabshahi, Z. Cai, W.W. Wilson, Methods Enzymol. 276 (1997) 100. [5] B.L. Neal, D. Asthagiri, A.M. Lenhoff, Biophys. J. 75 (1998) 2469. [6] J. Zhang, X.Y. Liu, J. Chem. Phys. 119 (2003) 10972–10976. [7] G.H. Koenderink, M.P. Lettinga, A.P. Philipse, J. Chem. Phys. 117 (2002) 7751–7764. [8] Y.Y. Kuttner, N. Kozer, E. Segal, G. Schreiber, G. Haran, J. Am. Chem. Soc. 127 (2005) 15138–15144. [9] S.B. Dubin, N.A. Clark, G.B. Benedek, J. Chem. Phys. 54 (1971) 5158–5164. [10] N. Tjandra, S.E. Feller, R.W. Pastor, A. Bax, J. Am. Chem. Soc. 117 (1995) 12562–12566. [11] J.R. Lakowicz, Principles of fluorescence spectroscopy, Springer, New York, U. S. A, 2006 Chap. 10. [12] M. Watzlawek, C. Nägele, Phys. A 235 (1997) 56–74. [13] Y. Zhang, P.S. Cremer, Curr. Opin. Chem. Biol. 10 (2006) 658–663. [14] A. Salis, F. Cugia, D.F. Parsons, B.W. Ninham, M. Monduzzi, Phys. Chem. Chem. Phys. 14 (2012) 4343–4346. [15] K.C. Aune, C. Tanford, Biochemistry 8 (1969) 4579–4585. [16] M.A. Brinkey, Bioconjug. Chem. 3 (1992) 2–13. [17] D. Takahashi, E. Nishimoto, T. Murase, S. Yamashita, Biophys. J. 94 (2008) 4484–4492. [18] K.J. Willis, A.G. Szabo, Biochemistry 28 (1989) 4902–4908. [19] M. Zuker, A.G. Szabo, L. Bramall, D.T. Krajcarski, B. Selinger, Rev. Sci. Instrum. 56 (1985) 14–22. [20] H.I. Okur, J. Hladílková, K.B. Rembert, Y. Cho, J. Heyda, J. Dzubiella, P.S. Cremer, P. Jungwirth, J. Phys. Chem. B 121 (2017) 1997–2014. [21] O.A. von Lilienfeld, A. Tkatchenko, J. Chem. Phys. 132 (2010) 234109. [22] O.D. Velev, E.W. Kaler, A.M. Lenhoff, BioPhys. J. 75 (1998) 2682–2697. [23] B. Guo, S. Kao, H. McDonald, A. Asanov, L.L. Comb, W.W. Wilson, J. Cryst. Growth 196 (1999) 424–433. [24] M.M. Rise-Kautt, A.F. Ducruix, J. Biol. Chem. 264 (1989) 745–748. [25] K.D. Collins, Methods 34 (2004) 300–311.

4. Conclusion Hydrodynamic interactions (HI) between lysozymes induced by monovalent cation chlorides (NaCl, KCl, LiCl, NH4Cl, and CsCl) were characterized by evaluating the dependence of the rotational diffusion coefficient (Drot) on the lysozyme concentration (cp). Clearly, Drot was reduced by increasing lysozyme to indicate that HI would be enhanced by cation chlorides. The quadratic curve fitting of Drot/D0rot against cp demonstrated that two HI parameters (Hs1r and Hs2r ), were negative and positive, respectively and showed the attractive and repulsive HI would be simultaneously induced by the specific effect of cation chlorides. The HI estimated here increased in the monovalent cation order of Na+ > K+ > Li+ > NH4+ > Cs+, which corresponds to inverse Hofmeister series apart from Li+. Since the osmotic second virial coefficient, B22, is established as a major criterion of the protein-protein r r interactions, B22 was estimated from Hs1r for comparison. B22 responded to the cation chloride concentration similarly to B22 although some difference was seen probably due to the mobility function peculiar to rotational diffusion. The three-body repulsive HI given by Hs2r increased concomitantly with attractive HI has not been mentioned so far. The

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