Interaction among bovine serum albumin (BSA) molecules in the presence of anions: a small-angle neutron scattering study

Abstract

Protein–protein interaction in solution strongly depends on dissolved ions and solution pH. Interaction among globular protein (bovine serum albumin, BSA), above and below of its isoelectric point (pI ≈ 4.8), is studied in the presence of anions (Cl^–, Br^–, I^–, F^–, SO₄^2–) using small-angle neutron scattering (SANS) technique. The SANS study reveals that the short-range attraction among BSA molecules remains nearly unchanged in the presence of anions, whereas the intermediate-range repulsive interaction increases following the Hofmeister series of anions. Although the interaction strength modifies below and above the pI of BSA, it nearly follows the series.

Introduction

Protein stability in solution and the related protein–protein interactions are the fundamental aspects of different biological applications [1, 2]. Globular proteins, e.g., bovine serum albumin (BSA), human serum albumin (HSA), lysozyme, etc. are charged colloidal particles [3, 4]. Depending upon the solution pH and isoelectric point (pI) of a particular protein, the net surface potential of protein changes, which influences the related interactions [5, 6]. The protein–protein interactions highly depend on protein concentration, pH, temperature, dissolved ions, and ionic strength [7–10]. Depending upon these parameters, various protein interactions such as protein crystallization, liquid–liquid phase separation, aggregation, and re-entrant condensation can be observed [11–14]. Among these different influencing factors, the nature of ions and their concentration highly influence the protein–protein interactions. A significant instability and stress can be observed in the living systems due to imbalance of salts [15]. The effect of ions on protein–protein interactions can be predicted from the Hofmeister series, which are categorized as direct and reverse [16–19]. Depending on salt concentration as well as solution pH, proteins may follow different Hofmeister series [20]. It is evident that the Coulombic and van der Waals interactions between protein lead to the different phase behaviours of the protein in solution [21, 22]. Some non-specific interactions, namely hydrophobic interactions, entropic contribution, and hydration forces, may also play a significant role in the interactions [23, 24].

The interaction among proteins in solution and related equilibrium phase behaviour can be explained using the well-known Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [25, 26]. Traditionally, the DLVO theory works well in low ionic concentrations; however, at higher salt concentration, the theory is validated by using effective interaction parameters [26, 27]. This theory cannot describe the rich and complex phase behaviour of proteins completely, due to its surface charge distribution as well as complex structure [3, 28]. Therefore, along with this theoretical model, few experimental methods, e.g. small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS), and dynamic light scattering (DLS), are also utilized to explain the interactions among proteins in solution [29, 30]. In the scattering study, the structure of protein can be predicted from the form factor, whereas interaction nature can be explained by studying the structure factor obtained from scattering intensity [29, 31]. In the SANS study, Yukawa potentials were also utilized in many cases to explain the interaction nature, which include the short-range attractive interactions, intermediate-range electrostatic repulsive interactions, and weak long-range attractive interactions [30, 32–34]. The protein–protein interactions can largely be affected by the charge of ions and can show phase separation behaviour in the presence of few ions [34, 35]. Effective interactions among BSA molecules enhance by replacing Cl^– ions with NO^3– ions [36]. The intermolecular interaction potential, specifically the attractive potential of lysozyme, shows pressure-dependent variation in the presence of anions [37]. Microstructural properties of protein gels also have an anion effect and follow the Hofmeister series partially [38]. Although a substantial study has been done using several experimental techniques and theoretical models to understand the protein–protein interactions in solution, further study is still essential for proper understanding of such complex systems.

Here, structure and interaction behaviour among BSA molecules are investigated in the presence of different anionic environment using SANS techniques. Interaction behaviours are studied in the presence of anions, namely, Cl^–, F^–, I^–, Br^–, and SO₄^2– ions, both above and below of the pI of BSA protein (pI ≈ 4.8). Using the two-Yukawa potential, the attractive and repulsive interactions among the BSA molecules were extracted. The relative strengths of the interactions with the concentration of salt are also explored. It is observed that, though the short-range attractive interactions remain nearly unchanged, the intermediate-range repulsive interactions vary in the presence of different anions. The variation of interactions is slightly modified depending on the solution pH above and below of the BSA pI but roughly follows the Hofmeister series of anions.

Materials and methods

BSA (catalogue No. 05480) was procured from Fluka and was used as received. For the SANS experiments, BSA samples were prepared using the buffer solution of D₂O. The final solution of BSA for all the measurements was fixed at 10 wt%. The pD of the sample was adjusted for two conditions at around 7.0 and 4.0, respectively, in 20 mM acetate buffer in D₂O. The protein interactions in the presence of anions were studied by dissolving sodium chloride (NaCl), sodium fluoride (NaF), sodium bromide (NaBr), sodium iodide (NaI), and sodium sulphate (Na₂SO₄) salts in the protein solution. Two different salt concentrations were considered, i.e. 120 and 250 mM. SANS experiments were performed at Dhruva Reactor of Bhabha Atomic Research Centre (BARC), Mumbai [39]. The wavelength of the incident neutron beam (λ) was of 5.2 Å with a resolution (Δλ/λ) of ≈ 15%. All the data were collected in the scattering vector (Q) range of 0.017–0.35 Å^–1. The scattered neutrons were detected using a 100 cm long, 3.8 cm diameter position-sensitive gas detector. Standard procedures are used to correct and normalize the collected SANS data to a cross-sectional unit. Experimental temperature was 25 °C. At the end of final data fitting, the individual error for each parameter was evaluated.

SANS analysis

The SANS analysis was done using our earlier study [30, 33]. The intensity of the scattered neutron beam, $I(Q)$, is obtained from the SANS experiment. The scattering vector $Q$ can be defined as $\frac{4\pi }{\lambda }\sin \theta$, where the scattering angle is 2 θ. The absolute scattering intensity for a system of monodisperse particles can be written as [40]:

$$I\left(Q\right)=n_p{V}_p^2{\left({\rho }_p,-,{\rho }_s\right)}^{2}P\left(Q\right)S\left(Q\right)+B$$ 1

where the protein molecule’s number density in solution is denoted by $n_p$ and $V_p$ is the protein molecular volume. The scattering length density of the protein molecules is denoted by ${\rho }_p$ and that of solvent is denoted by ${\rho }_s$. After orientation averaging, the scattering from a single protein molecule, i.e. the normalized form factor, is indicated by $P(Q)$. In our analysis, a form factor of oblate ellipsoid was considered to model the BSA molecule [9, 30]. The structure factor and the incoherent background, which is a constant, are represented by $S(Q)$ and B, respectively. The two-Yukawa potential (U_TY) with the mean spherical approximation (MSA) was used to calculate $S(Q)$. The ellipsoidal protein molecules are considered a rigid sphere of diameter, $\sigma =2{({\mathit{ab}}^2)}^{1/3}$ where the semi-major and semi-minor axes of the ellipsoidal protein molecules are respectively denoted by a and b. Furthermore, using the U_TY model [32, 41], the short-range attractive force and repulsive long-range force between the protein molecules are described. The potential model can be described as:

$$U_{\mathit{TY}}\left(r\right)=\left\{\begin{array}{c}\infty forr<1\\ -K_1\frac{\exp \left[-,Z_1,\left(r,-,1\right)\right]}{r}-K_2\frac{\exp \left[-,Z_2,\left(r,-,1\right)\right]}{r}forr\ge 1\end{array}\right)$$ 2

where r is the interparticle distance normalized by σ, the diameter of the particle. K₁ and K₂ are k_BT normalized interactions, where k_B and T are the Boltzmann constant, and absolute temperature, respectively. For attractive interactions, K₁, K₂ become positive, whereas for repulsive interactions, the values become negative. In our analysis, obtained K₁ and K₂ values are positive and negative, respectively. The specific interaction range is inversely proportional to Z. The short-range attractive interaction is basically a van der Waals interaction among two neighbouring molecules, which is effective in a very short distance (few Angstroms, typically 0–6 Å), and the energy varies as 1/r  (where r is the inter molecular distance); however, the magnitude of interaction or Hamaker constant associated with it is relatively small, and therefore at large distance, it has no effect. The long-range interaction between the same charged molecules is the electrostatic repulsion. The repulsive energy varies as $\frac{e^{-\kappa r}}{r}$ (where 1/κ is the Debye length) with an interaction constant. However, the magnitude of this interaction constant is relatively higher than the short-range attractive interaction. Typically, the effect of long-range repulsion can be observed from a few Å to up to some nanometre [4, 21, 42]. The charge of protein ($z_p$) and ionic strength (I) can be linked with the parameters K₂ and Z₂ using the DLVO theory [43]. The repulsive part of the Yukawa potential can be related with the screened Coulomb repulsion as

$$\frac{z_p^2{e}^2}{4\pi \epsilon {\epsilon }_0\sigma {(1+\frac{\kappa \sigma }{2})}^2}=K_2{k}_{B}T$$ 3

where e is the charge of the electron, ε is the dielectric constant of water, and $z_p$ is the effective charge of protein (in e units) due to electrostatic screening. K₂ is the repulsive strength in U_TY, and T is the absolute temperature. The ionic strength (I) is related to Z₂, the inverse of the repulsive range, by

$$\frac{3}{\sqrt{I}}={\kappa }^{-1}=\frac{\sigma }{Z_2};i.e.,I=\frac{9Z_2^2}{{\sigma }^2}$$ 4

The experimental data was analysed using IGOR Pro software selecting the specific model of scattering, where the macros were developed by the NIST Center for Neutron Research [44]. The nonlinear least-squares method was used for the optimization of the parameters [45]. The volume fraction, form factor, short- and long-range attractive and repulsive potential ranges, and background for pure BSA were initially constant to obtain the physically reasonable values of other fitting parameters. After that, all parameters were free during fitting excluding the form factor, volume fraction, short-range potential, and the background. The same procedure was followed for the case of protein in the presence of the salts. The effective structure factor was calculated using the effective sphere diameter ($\sigma$). The parameters except for which error will be calculated were fixed after the final data fitting, during error calculation. The individual error is calculated from the standard deviation of the data fitting.

Results

SANS data (open circle) and the corresponding fitted curves (solid line) for BSA solution at pD ≈ 7.0 are shown in Fig. 1a. The structure factor $S(Q)$, as obtained from the fitting of all the samples, is shown in Fig. 1b. The inset of the figure shows the form factor, $P(Q)$ of pure BSA. An oblate form factor of dimensions (a × b × b) ≈ 10.2 × 40.0 × 40.0 Å is used for pure BSA during fitting. Moreover, U_TY model was also used during data fitting. The SANS data (open circles) of BSA at the same pD and in the presence of different salts (NaI, NaBr, NaCl, NaF, and Na₂SO₄) at 120 mM concentration are shown in Fig. 1a, whereas corresponding fitted curves (solid lines) are also shown in the same figure. Almost the same form factor (≈ 9.8 × 40.0 × 40.0 Å) and the two-Yukawa potentials were used to study the variation of attractive and repulsive strength in the presence of different salts. The corresponding structure factor, $S(Q)$, of the samples as obtained from the data fitting is shown in Fig. 1b. In Table 1, the parameters corresponding to the data fitting are tabulated.

Fig. 1.

a SANS data (open circle) for 10 wt% BSA and related fitted curves (solid line) in presence and absence of NaI, NaBr, NaCl, NaF, and Na₂SO₄, at 120 mM concentration in the aqueous solution at pD ≈ 7.0. Curves are shifted vertically for better visualization. b Structure factor, $S(Q)$, of the respective data, extracted from the data fitting using the U_TY model. Inset: Pure BSA form factor $[P\left(Q\right)]$. c Variation of U_TY as a function of the normalized intermolecular distance ($r/\sigma$)

Table 1.

Fitted parameters obtained from BSA solutions (10 wt%), in different solution pD, in the absence and presence of 120 mM salt concentrations, by using two-Yukawa potential model with a fixed volume fraction of 0.09. The charge is in electron (e) units, and diameter of BSA is in Å. The values shown inside the brackets indicate maximum errors of the fitted parameters

pD	Salt	K1 (± 0.06)	Z1 (± 0.1)	K2 (± 0.01)	Z2 (± 0.02)	a (in Å)	b (in Å)	2R (σ, in Å unit) (± 0.2)	I (cal.)	I (expt.)	Charge (in e units) (± 0.05)	B
7.0	No salt	0.7	11.5	− 2.28	3.68	10.2	40	50.8	0.047	0.02	11.40	0.108
	NaI	0.7	11.5	− 2.20	5.13	9.8	40	50.1	0.090	0.14	13.96	0.099
	NaBr	0.7	11.5	− 2.06	5.31	9.8	40	50.1	0.101	0.14	13.85	0.095
	NaCl	0.7	11.5	− 1.75	5.77	9.8	40	50.1	0.119	0.14	13.57	0.095
	NaF	0.7	11.8	− 1.32	6.49	9.8	40	50.1	0.151	0.14	12.88	0.093
	Na2SO4	0.7	11.8	− 1.16	6.82	9.8	40	50.1	0.168	0.38	12.54	0.090
4.0	No salt	0.7	11.5	− 1.56	3.58	11.8	41.5	54.6	0.039	0.02	9.60	0.100
	NaI	0.7	11.5	− 1.54	4.06	10	40	50.4	0.058	0.14	9.96	0.082
	NaBr	0.7	11.5	− 1.30	4.47	10	40	50.4	0.071	0.14	9.77	0.078
	NaCl	0.7	11.5	− 1.14	4.77	10	40	50.4	0.081	0.14	9.57	0.083
	NaF	0.7	11.8	− 0.80	5.16	10	40	50.4	0.094	0.14	8.48	0.070
	Na2SO4	0.7	11.5	− 0.75	5.64	10	40	50.4	0.113	0.38	8.76	0.095

Figure 1a shows that the scattering intensity varies in the low-$Q$ region in the presence of different salts. The value of $I(Q)$ increases gradually, in the presence of NaI, NaBr, NaCl, NaF, and Na₂SO₄, respectively. It has a similarity with the Hofmeister series for anions [19]. The same nature is also reflected in the $S(Q)$ plots of Fig. 1b. From the $S(Q)$-$Q$ plots as extracted from the data fitting, monomer–monomer correlation peak is observed. Figure 1c corresponds to the variation of U_TY as a function of $r/\sigma$ (i.e. intermolecular distance normalized by the diameter σ of BSA) in the presence and absence of salt at 120 mM concentration. It is observed that in the presence of salts, the attractive interactions among protein remain almost the same, but the repulsive interaction strength increases. The order of strength enhancement depending upon the used anions is as follows: I^– > Br^– > Cl^– > F^– > SO₄^2–.

The SANS data of pure BSA and in the presence of above-mentioned salts at 250 mM salt concentration (open circles) are shown in Fig. 2a. The corresponding fitted curves are indicated in the same figure using solid lines. It is clear from the figure that, at low-$Q$ region, the SANS intensity increases in the presence of salt as before. Nearly the same form factor for pure BSA (i.e. ≈ 9.8 × 40.0 × 40.0 Å) and same potential model, U_TY, was used during data fitting. The extracted values of repulsive and attractive strengths and the related parameters as obtained from the fitted data are showed in Table 2. The structure factor $S(Q)$ and the variation of U_TY as a function of $r/\sigma$ are plotted in Fig. 2b and c, respectively. In the presence of salt, the attractive interactions among protein molecules remain almost the same, whereas the repulsive interactions decrease gradually for I^–, Br^–, Cl^–, F^–, and SO₄^2–. From Table 2, it is also observed that the repulsive interaction strength decreases with the increment of salt concentration. This may be due to the electrostatic screening which leads to such enhancement of attractive interaction strength [34].

Fig. 2.

a SANS data (open circle) for 10 wt% BSA and related fitted curves (solid line) in the presence of NaI, NaBr, NaCl, NaF, and Na₂SO₄, at 250-mM concentration in the aqueous solution at pD ≈ 7.0. Curves are shifted vertically for better visualization. b Structure factor, $S(Q)$, of the respective data as obtained from the data fitting using the U_TY model. c Variation of U_TY of every sample as a function of the normalized distance ($r/\sigma$)

Table 2.

Fitted parameters obtained from BSA solutions (10 wt%), in different solution pD, in the absence and presence of 250 mM salt concentrations, by using two-Yukawa potential model with fixed volume fraction of 0.09. The charge is in electron (e) units, and diameter of BSA is in Å. The values shown inside the brackets indicate maximum errors of the fitted parameters

pD	Salt	K1 (± 0.06)	Z1 (± 0.1)	K2 (± 0.01)	Z2 (± 0.02)	a (in Å)	b (in Å)	2R (σ, in Å unit) (± 0.2)	I (cal.)	I (expt.)	Charge (in e unit) (± 0.05)	B
7.0	No salt	0.7	11.5	− 2.28	3.68	10.2	40	50.8	0.047	0.02	11.40	0.108
	NaI	0.7	11.5	− 2.07	5.56	9.8	40	50.1	0.111	0.27	14.36	0.120
	NaBr	0.7	11.5	− 1.84	5.80	9.8	40	50.1	0.121	0.27	13.97	0.120
	NaCl	0.7	11.5	− 1.56	6.32	9.8	40	50.1	0.143	0.27	13.72	0.110
	NaF	0.7	11.5	− 1.25	6.78	9.8	40	50.1	0.165	0.27	12.96	0.110
	Na2SO4	0.7	11.5	− 1.10	6.96	9.8	40	50.1	0.174	0.77	12.41	0.095
4.0	No salt	0.7	11.5	− 1.56	3.58	11.8	41.5	54.6	0.039	0.02	9.60	0.100
	NaI	0.7	11.5	− 1.48	4.53	10	40	50.4	0.073	0.27	10.52	0.095
	NaBr	0.7	11.5	− 1.29	4.73	10	40	50.4	0.079	0.27	10.12	0.090
	NaCl	0.7	11.5	− 1.01	5.45	10	40	50.4	0.105	0.27	9.91	0.085
	NaF	0.7	11.5	− 0.78	5.79	10	40	50.4	0.119	0.27	9.11	0.093
	Na2SO4	0.7	11.5	− 0.68	5.83	10	40	50.4	0.120	0.77	8.55	0.090

The pH effect on the interaction nature among proteins in the presence of anions is also investigated. Below the isoelectric point (pI ≈ 4.8), BSA possess net positive charge, and therefore, the interaction behaviour is studied at pD ≈ 4.0. The SANS profile of BSA (open circle) at pD ≈ 4.0 is shown in Fig. 3a, whereas the solid lines correspond to fitted curve. The $S(Q)$, obtained from the corresponding fitting, is shown in Fig. 3b. BSA form factor $P(Q)$ at that pD is shown in the inset of the figure. To fit the data, a form factor of oblate ellipsoid of dimensions (a × b × b) ≈ 11.8 × 41.5 × 41.5 Å and the same potential model (U_TY) was utilized. The SANS profiles (open circles) of BSA at the same pD in the presence of previously mentioned salts with 120 mM concentration are plotted in Fig. 3a. Solid lines of the figure correspond to the fitted curves for the respective samples. To study the variation of attractive and repulsive strength in the presence of different salts, form factor of dimension ≈ 10 × 40.0 × 40.0 Å and U_TY potential model were used. The obtained parameters after fitting are tabulated in Table 1. The structure factor, $S(Q)$, corresponding to the samples is also shown in Fig. 3b, whereas Fig. 3c corresponds to the variation of U_TY as a function of $r/\sigma$. From the figure, it is cleared that, at low-$Q$ value, the SANS profile increases gradually, almost the similar tend as followed at pD ≈ 7.0. Though, the profile for BSA in the presence of NaI salt is almost similar with pure BSA. Moreover, in the presence of NaF and Na₂SO₄, the SANS profiles of BSA are almost similar. The order intensity profiles of BSA in the presence of salts are as follows: No salt ≈ I^– < Br^– < Cl^– < F^– ≈ SO4^2–. In this experimental condition also, the relative strength of attraction almost remains constant, but the strength of repulsion decreases gradually as follows: I^–, Br^–, Cl^–, F^–, and SO₄^2–.

Fig. 3.

a SANS data (open circle) for 10 wt% BSA in absence and presence of NaI, NaBr, NaCl, NaF, and Na₂SO₄, at 120 mM concentration in the aqueous solution at pD ≈ 4.0 and related fitted curves (solid line). Curves are shifted vertically for better visualization. b Structure factor, $S(Q)$, of the respective data, obtained from the fitting using the U_TY model. Form factor $P(Q)$ for pure BSA at pD ≈ 4.0 is at inset. c Variation of U_TY of every sample as a function of the normalized distance ($r/\sigma$)

The SANS data of BSA in the absence and presence of the above-mentioned salts at pD ≈ 4.0, for 250 mM concentrations (open circles), are shown in Fig. 4a, whereas the solid lines of the same figure correspond to the fitted curves. A similar form factor of ≈ 10 × 40.0 × 40.0 Å is used for pure BSA during fitting, whereas the U_TY model is utilized to fit the scattering data. It is observed that, at low-$Q$ region, the SANS intensity increases depending up on the salts as found in the presence of 120 mM salt at pD ≈ 4.0. The extracted values of attractive and repulsive strengths and related parameters from the fitting are shown in Table 2. The structure factor $S(Q)$ and the variation of U_TY with respect to $r/\sigma$ are shown in Fig. 4b and c, respectively. In this condition also, the strength of short-range attraction remains nearly constant, whereas the strength of long-range repulsion decreases following the order as mentioned previously, i.e. strength is maximum and minimum for NaI and Na₂SO₄, respectively. It is also found that the strength of the repulsive interactions is lowered at higher salt concentration for a particular solution pD. The repulsive strength of BSA for a particular salt is also decreased at pD ≈ 4.0 than pD ≈ 7.0.

Fig. 4.

a SANS data (open circle) for 10 wt% BSA at pD ≈ 7.0 in the absence and presence of NaI, NaBr, NaCl, NaF, and Na₂SO₄, at 250 mM concentration in the aqueous solution and related fitted curves (solid line). Curves are shifted vertically for better visualization. b Structure factor, $S(Q)$, extracted from the data fitting using the (U_TY) model. c Variation of the U_TY of the samples as a function of the normalized distance ($r/\sigma$)

Discussion

Proteins typically have a net surface charge. However, the interactions of proteins with specific ions and the ion cloud distribution over the protein are not easy to predict. In the presence of ions, a charge screening is observed among the charged protein molecules. The net effects of short-range and long-range interactions determine different phase behaviours of protein solutions. The dominating behaviour of short-range attraction is responsible for different phase separation behaviours such as liquid–liquid phase separation (LLPS), re-entrant condensation (RC), and protein crystallization. An effective short-range attraction over long or intermediate range repulsions is observed in the RC behaviour of globular proteins in the presence of tri- and tetra-valent ions [35, 46]. In case of metastable LLPS, the effective attraction among proteins is shorter than the size of the particles [47]. From the results as obtained from the SANS analysis, it is clear that the interactions among BSA molecules modifies in the presence of anions and also with ion concentrations. In addition to this, the effective interaction changes with the solution pD. As discussed before, it is observed that the strength of short-range attraction (K₁) remains almost constant, but the intermediate range repulsive strength (K₂) varies with the presence of different anions. The variations of K₂ in the presence of anions for both the salt concentrations and at two solution pD conditions, i.e. above (pD ≈ 7.0) and below (pD ≈ 4.0), the isoelectric point of BSA are shown in Fig. 5a and c, respectively. Depending on the isoelectric point, BSA possesses net negative surface potential at pD ≈ 7.0. Though the Na⁺ ions are present in the solution and are responsible for charge screening, the anions present in the solution interact with the positively charged side chains of BSA molecules. It is observed that the attractive short-range potential remains nearly unchanged, but the long-range repulsion potential decreases from I^– to SO₄^2–. Therefore, the effective strength of attraction becomes larger in the presence of SO₄^2–, and these ions interact more with the BSA molecules. Probably, due to the higher valency, the SO₄^2– ions show strong electrostatic interactions than the monovalent anions. For the monovalent anions, charge density follows as I^– < Br^– < Cl^– < F^–, and the effective strength of interactions among proteins also follows the same trend. Due to more interaction in the presence of F^– among all the monovalent anions, the effective charge of protein ($z_p$) is also reduced. The variations of $z_p$ in the presences of the salts are shown in Fig. 5b and d, respectively, for pD ≈ 7.0 and 4.0. Therefore, the interactions among protein molecules in the presence of anions effectively follows a series such as I^– < Br^– < Cl^– < F^– < SO₄^2–, which is nothing but the Hofmeister series of anions. Similarly, at pD ≈ 4.0, also the same series is followed. At this pD, i.e. below the isoelectric point, protein shows net positive surface potential. Therefore, the effective strength of attraction becomes larger than in the case of pD ≈ 7. Thus, the surface charge density, relative binding strength, and the valency of ions play an important role in modifying the protein–protein interactions. The kosmotropic and chaotropic effects of salts can also be related with these interactions. Kosmotropic ions stabilize the protein structure by promoting the degree of hydrogen bonding in solution, whereas chaotropic ions disrupt the hydrogen bonding network and destabilize the protein structure [48, 49]. Therefore, in the presence of kosmotropes, the interactions among proteins in solution will be stronger. SO₄^2– is a well-known kosmotropes from Hofmeister series and shows more effective attraction. In case of chaotropic anions such as I^– and Br^–, the interactions are relatively weaker. Therefore, the protein–protein interactions may follow a more general series such as (chaotropic) I^– < Br^– < Cl^– < F^– < SO₄^2– (kosmotropic).

Fig. 5.

Variation of K₂ (a and c) as extracted from the data fitting using the U_TY model and effective charge ($z_p$) (c and d) of BSA in the presence for different salts at around (a and b) pD 7.0 and (c and d) pD 4.0

In conclusion, BSA is a well-known and widely used model protein to study both protein–protein interactions and protein-salt interactions due to its abundance and similarity with human serum albumin. We have used five different anions, I^–, Br^–, Cl^–, F^–, and SO₄^2–, to study the interactions among BSA molecules both above and below the pI value of BSA. The short-range attraction among protein molecules remains nearly unchanged, whereas the intermediate range repulsive interactions decrease as I^– > Br^– > Cl^– > F^– > SO₄^2–. With the variation of solution pD, the interactions follow the same trend, but the decrement of repulsive strength is larger for BSA below the pI value of BSA, i.e., at pD ≈ 4.0. The interactions among the protein molecules, in the presence of anions, follow the Hofmeister series of anions, and the surface charge density and valency of anions play a crucial role in such interaction behaviour. This interaction study may be helpful to have a quantitative description and to understand the effect of anions on protein–protein interaction. However, actually it is a simplified model to explain such complex system only with the short-range or long-range interactions. There are some other factors, e.g., ion adoption, chaotropic effect, hydrophobic effect, hydration effect, and hydrogen bonding, which may also play some important roles in such protein-ion system and therefore need further investigation.

Author contribution

SP, SK, and VKA performed all the experiments, analysed the data, and wrote the manuscript. SK and VKA validated and supervised the work. All approved the manuscript.

Funding

SP obtained the financial support through INSPIRE Fellowship (Grant no. IF 160402) supported by the Department of Science and Technology, Govt. of India.

Data availability

Not applicable.

Code availability

Not applicable.

Declarations

Conflict of interest

The authors declare no competing interests.