Tuning phase transitions of aqueous protein solutions by multivalent cations

Abstract

In the presence of trivalent cations, negatively charged globular proteins show a rich phase behaviour including reentrant condensation, crystallisation, clustering and lower critical solution temperature metastable liquid–liquid phase separation (LCST–LLPS). Here, we present a systematic study on how different multivalent cations can be employed to tune the interactions and the associated phase behaviour of proteins. We focus our investigations on the protein bovine serum albumin (BSA) in the presence of HoCl₃, LaCl₃ and YCl₃. Using UV-Vis spectroscopy and small-angle X-ray scattering (SAXS), we find that the interprotein attraction induced by Ho³⁺ is very strong, while the one induced by La³⁺ is comparatively weak when comparing the data to BSA–Y³⁺ systems based on our previous work. Using zeta potential and isothermal titration calorimetry (ITC) measurements, we establish different binding affinities of cations to BSA with Ho³⁺ having the highest one. We propose that a combination of different cation features such as radius, polarisability and in particular hydration effects determine the protein–protein interaction induced by these cations. Our findings imply that subtle differences in cation properties can be a sensitive tool to fine-tune protein–protein interactions and phase behaviour in solution.

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1 Introduction

A thorough understanding of phase transitions in protein solutions is of utmost importance for the design and stabilisation of protein-based therapeutics,^1,2 disentangling cell-signalling processes,³ finding treatment options for protein condensation diseases⁴ as well as rationally manipulating pathways of protein crystallisation.⁵ The heterogeneous charge distribution and intricate interactions with their environment – the latter can additionally be influenced by various parameters including temperature, pH and pressure – make proteins highly complex molecules. In an attempt to better understand and investigate proteins and their interactions with their surroundings, it is thus helpful to make use of simplified physical models.

In this context, the framework of colloid theory with corresponding model interaction potentials provides a successful approach. An important insight from colloid science describes the influence of the interaction range between particles on their phase behaviour. Specifically, interparticle attraction on a range smaller than the particle diameter is reflected in a metastable liquid–liquid coexistence region which shifts below the gas-crystal line.^6–9 This liquid–liquid coexistence, also referred to as liquid–liquid phase separation (LLPS), can be considered analogous to the liquid–gas transition in the van der Waals gas.¹⁰ The experimental evidence for this phenomenon in colloidal systems, which also laid the foundation for its subsequent theoretical rationalisation by Gast et al.,¹¹ was provided by Sperry and co-workers¹² in a latex–polymer system with depletion attraction.

Importantly, such phenomena can also be observed in protein solutions. One of the earliest observations of LLPS in a protein system was documented by Tanaka et al. for an aqueous lysozyme–NaCl mixture.¹³ Since then, many more examples of LLPS in different protein solutions have been described. Examples include crystallins,^14–17 different types of hemoglobin,^18–20 lysozyme,^8,21 polypeptides derived from elastin²² as well as cellular structures.²³

Under physiological conditions, proteins and their interactions are influenced by cations such as Na⁺, K⁺, Ca²⁺, Mg²⁺ or Zn²⁺.²⁴ Moreover, many proteins, notably serum albumins, can directly bind and transport cations.²⁵ In addition to these physiologically occuring cation species, the interactions of proteins with less common cations such as lanthanides (Ln) are of fundamental interest in toxicology,^26,27 the onset and development of neurodegenereative diseases,^28,29 bacterial metabolism,³⁰ tumour treatment^31,32 as well as spectroscopic³³ and diagnostic methods.^34–36 Cation-specific effects are not limited to proteins, but similarly occur in soft matter systems. For example, a recent study by Yu et al.³⁷ showed a strong decrease in polyelectrolyte brush lubricity upon the addition of multivalent cations such as Y³⁺.

Throughout the past years, our group has successfully established a rich phase behaviour induced in negatively charged globular proteins by trivalent salts such as YCl₃. It has been found that Y³⁺ cations introduce a short-range attraction between the protein molecules by forming cation bridges between negatively charged residues of protein molecules,⁵ leading to a variety of phenomena including crystallisation,^5,38,39 cluster formation,³⁹ reentrant condensation,^38,40,41 and metastable LLPS³⁹ with a lower critical solution temperature (LCST–LLPS).^42–44

A representative salt–protein concentration (c_s–c_p) phase diagram of a negatively charged globular protein in the presence of a trivalent salt describing our experimental systems is shown in Fig. 1. The dashed arrow in the right part shows the phase transitions at constant c_p upon increasing c_s. In regime I, at low c_s, few cations bind to protein molecules. The overall protein surface charge is negative (left part of Fig. 1) and the net interactions are thus repulsive. An increasing c_s leads to a weakened protein surface charge and a subsequent condensation of the protein solution. This area of the phase diagram is referred to as regime II and is separated from regime I by a critical salt concentration c*. Under appropriate conditions, a sample located in a certain region of the phase diagram (orange sphere on yellow ellipsoid) can undergo liquid–liquid phase separation into a protein-rich and a protein-poor phase (brown and yellow spheres on the high- and low-c_p edges of the yellow ellipsoid, respectively), which is due to a short-range interprotein attraction induced by cation bridging.³⁸ An even further increase of c_s leads to a charge inversion of the protein surface due to an extensive binding of cations upon crossing a second critical salt concentration c**. These experimental findings can be rationalised from a theoretical point of view in the framework of an ion-activated patchy particle model⁴⁵ which combines a hard-sphere repulsion of the proteins and a square-well attraction induced by cations binding to patches (negatively charged amino acid residues) on the protein surface. This mechanism features similarities to cation-mediated condensation of DNA.^46,47 Interestingly, molecular dynamics and Monte Carlo studies by Pasquier et al.⁴⁸ show an anomalous development of the protein–protein potential of mean force with increasing salt concentration in a system of human serum albumin (HSA) and YCl₃. The results obtained by Pasquier et al.⁴⁸ are in excellent agreement with the different regions of the experimental phase diagram shown in Fig. 1.

Fig. 1 Phase diagram showing regimes I, II and III, reentrant condensation and LLPS. See text for details.

Previous studies showed that this phase behaviour also depends on the choice of the salt. We have found that trivalent salts other than YCl₃ (such as FeCl₃ and AlCl₃) also induce reentrant condensation. However, we established that as opposed to YCl₃, pH effects on the reentrant phase behaviour due to salt hydrolysis are significant in the case of FeCl₃ and AlCl₃.⁴¹ Furthermore, we found that for a protein solution with fixed YCl₃ concentration, the addition of a monovalent salt could be used to shift the phase boundaries to higher critical concentrations, suggesting a subtle balance of charge repulsion and salt-induced attraction to be essential for the phase behaviour.⁴⁹ The effect of different counterions of lanthanide cations on the phase behaviour of BSA is subject of a recent investigation.⁵⁰

Given that details of the interaction potential have a strong influence on the phase behaviour of colloidal systems, we aim at investigating the influence of cations with different radii and chemical properties (Ho³⁺, La³⁺ and Y³⁺). Note that none of these cations cause strong pH effects by hydrolysis, and therefore the changes observed are due to different effective interactions due to subtle differences in the cation properties. Our main interest consists in fine-tuning and controlling the phase behaviour of protein solutions using different cations.

In the present work, we first describe macroscopic observations which evidence that different trivalent cations lead to remarkably strong differences in the phase behaviour of bovine serum albumin (BSA). Determining transition temperatures of different protein–cation mixtures by UV-Vis spectroscopy, we observe a strong interprotein attraction induced by Ho³⁺ in BSA solutions, whereas these attractions are weaker in the presence of La³⁺. Systems consisting of BSA and Y³⁺ are used as a reference. Reduced second virial coefficient values (B₂/B^HS₂) obtained from small-angle X-ray scattering (SAXS) confirm this conclusion. In addition to cation-induced protein interactions, we study cation binding to BSA by zeta potential measurements and isothermal titration calorimetry (ITC) to obtain a comprehensive thermodynamic characterisation of cation–protein interactions.

2 Materials

Bovine serum albumin (BSA, product no. A7906), YCl₃, HoCl₃ and LaCl₃ were purchased from Sigma Aldrich (Taufkirchen, Germany, now Merck, Darmstadt, Germany) and used without further purification. Protein and salt powders were dissolved in ultrapure degassed water (18.2 MΩ, Merck Millipore, Darmstadt, Germany). The exact protein concentration was determined using UV-Vis spectroscopy (Cary 50 UV-Vis spectrometer, Varian Inc., now Agilent Technologies, California, USA; absorbance at 280 nm). Samples were subsequently prepared by mixing appropriate volumes of aqueous protein and salt stock solutions.

3 Experimental methods

3.1 Isothermal coexistence phase diagrams

c _s–c_p phase diagrams were determined at room temperature for 80 mg ml⁻¹ (1.2 mM) BSA and increasing concentrations of HoCl₃, LaCl₃ and YCl₃. The dilute phases were studied by visual inspection and light microscopy. Samples with dilute phases that were homogeneous under the microscope but appeared turbid upon visual inspection were classified as “turbid”. Where liquid–liquid phase separation was visible under the microscope, the samples were labelled as “LLPS”. In the absence of any inhomogeneity, samples were classified as “clear”.

3.2 T-Dependent UV-Vis spectroscopy

All of the BSA–trivalent cation systems studied here show a LCST–LLPS-type behaviour. To elucidate the differences in protein–protein interactions induced by the different cations, cation mixtures were used. In order to determine the respective transition temperatures T_trans from homogeneous to phase-separated states of the BSA–cation mixtures, temperature-dependent UV scans were performed using a Cary 50 UV-Vis spectrometer (Varian Inc., now Agilent Technologies, California, USA) connected to a water bath (Haake A 10B, Thermo Fisher Scientific, Schwerte, Germany). Samples were then subjected to temperature scans at a rate of 0.1 K min⁻¹ while their absorbance was monitored over a wavelength range from 400 to 800 nm. The intensity values of the spectra obtained were summed and divided by the respective number of data points. T_trans was determined from the maximum of the first derivatives with respect to temperature of the respective curves.

3.3 Zeta potential measurements

Zeta potentials were measured by electrophoretic light scattering (ELS) using a Nano Zetasizer (Malvern Instruments, Malvern, United Kingdom). Samples containing 1 mg ml⁻¹ (15 μM) BSA and increasing salt concentrations (0.1, 0.3, 0.5, 0.7 and 1 mM of HoCl₃, YCl₃ or LaCl₃) were prepared shortly before the measurements. The low BSA concentration was chosen to avoid phase separation of the samples. Every sample was measured at 5 different temperatures, with 10 min of equilibration time before each measurement. The ζ potential values were subsequently converted into effective surface charge values Q in units of elementary charge e as explained in the ESI.†

3.4 Isothermal titration calorimetry (ITC)

ITC measurements were performed using a MicroCal iTC200 (Malvern Instruments, formerly GE Healthcare). Salt solutions with concentrations of 800 μM or 3 mM were titrated into 1 mg ml⁻¹ (15 μM) BSA solutions in 0.5 μl steps with a duration of 1 s each. A preliminary titration step of 0.2 μl with a duration of 0.5 s was used for equilibration. In the case of the titrations performed with 3 mM salt solution, the durations of these steps were 0.4 and 1 s, respectively. In order to correct for the heat of dilution of the salt, a background measurement was performed by titrating the 800 μM or 3 mM salt solutions into water. The background measurements were subtracted from the salt–protein measurements. For each measurement, 60 injections were performed in total. The time interval between each injection was 90 s with a filter period of 5 s. For titrations with 3 mM salt solutions, these time intervals were 180 and 2.5 s, respectively. The stirring speed of the syringe was 750 rpm and the reference power was set to 1.3 μcal s⁻¹. All data sets were taken at 24 °C.

3.5 Small-angle X-ray scattering (SAXS)

SAXS measurements were performed at beamline ID02 (ESRF, Grenoble, France) at a sample–detector distance of 2 m and an energy of 12.46 or 16 keV (λ = 0.8–0.9 Å). The scattered intensity was recorded using a Rayonix MX160 or a FReLoN Kodak CCD detector, covering a q range within 0.01 to 5 nm⁻¹.

Samples containing 80 or 85 mg ml⁻¹ (=1.2 or 1.3 mM) BSA and increasing (0–50 mM) concentrations of HoCl₃, LaCl₃ or YCl₃ were prepared at room temperature (ca. 21 °C) and centrifuged for 5 min at 9500 rcf to facilitate phase separation for those samples located in the LLPS region of their respective phase diagrams. Samples were loaded into a flow-through capillary and measured at a constant temperature of 20 °C controlled by a Peltier element connected to the flow cell. In the case of phase-separated samples, the dilute phases were measured. Per sample, 5–10 acquisitions were performed with an exposure time of 0.05–0.1 s. The data were calibrated to absolute intensity using water as a reference.⁵¹ Data were averaged and background-corrected using either water or pure salt solutions with appropriate concentrations.

In a SAXS experiment, the scattering intensity I(q) is measured as a function of momentum transfer with a scattering angle 2θ.⁵² It can be expressed as

I(q) = ΦV_particle(Δρ)²P(q)S(q) (1)

where V_particle represents the volume of a particle (i.e. protein) in question, Φ the volume fraction of particles in the sample and Δρ the scattering contrast between solvent and particles. P(q), the form factor of the particles, represents the Fourier transform of their respective electron densities.

In systems with sufficiently high particle concentrations where intermolecular interactions cannot be neglected, the latter are accounted for by the structure factor

where ρ = N/V and h(r) = g(r) − 1 is the total correlation function.⁵³

Importantly, the structure factor at q → 0 is proportional to the osmotic compressibility (∂Π/∂c)⁻¹ of the system in question^54,55 which can be expanded into a series of virial coefficients A_n:^54,56

where R = 8.314 J K⁻¹ mol⁻¹ is the ideal gas constant, T is the temperature and M is the molecular weight of the particles investigated. The second virial coefficient B₂ is related to A₂via⁵⁷where N_A is Avogadro's constant (6.022 × 10²³ mol⁻¹). In this study, the normalised second virial coefficient B₂/B^HS₂ (with B^HS₂= 2πσ³/3 being the second virial coefficient of a system consisting of hard spheres with diameter σ⁵⁸) is calculated from the SAXS profiles in order to characterise the overall nature of their interactions.

For c_s = 0–3 mM, the form factor was combined with a screened Coulomb (SC) structure factor.^59,60 The screened Coulomb potential is expressed as

where x = r/σ (interparticle distance normalised by particle diameter) and k = κσ with κ being the Debye screening length. β = (k_BT)⁻¹ and γe^−k = βπε₀εσψ₀² (ε₀ is the vacuum permittivity, ε the permittivity of the solvent, σ the particle diameter and ψ₀ the surface potential) represents the potential upon contact of two particles (in this case, proteins).

For c_s ≥ 4 mM, a sticky hard sphere structure (SHS) factor was used.^61–63 The SHS potential is expressed as⁶³

where the range of the attractive part of the potential, R, is equal to λ − 1. The stickiness parameter τ is defined via^62,63

τ⁻¹ = 4[exp(−ε/k_BT) − 1][(a − σ)³ − 1] (7)

where a = σ + Δ and Δ is the attractive well width.⁶²

From τ, the reduced second virial coefficient is obtained via B₂/B^HS₂= 1 − 1/(4τ).⁵⁸ The fitting routine using the software Igor PRO⁶⁴ employed here has been described in detail elsewhere (see ref. 38, 43 and 65).

4 Results

4.1 Macroscopic properties of phase-separated samples

Fig. 2 shows a series of samples consisting of aqueous solutions of 80 mg ml⁻¹ (=1.2 mM) BSA and the same concentration (14 mM) of different trivalent salts prepared at 21 °C. In the sample containing YCl₃, a moderate amount of a clear, yellowish, dense liquid phase is observed, consistent with earlier observations.^5,40,42 The samples made with HoCl₃ and GdCl₃ form a substantial amount of dense phase; the dense phases are opaque, but still flow slowly. Using CeCl₃ leads to a strong decrease of the amount of dense phase, which in this case is transparent. When LaCl₃ is used, no dense phase is formed at 21 °C (see also ref. 43). The diffuse turbid region at the bottom of this sample and in the dilute phases of the samples prepared with YCl₃ and CeCl₃ is presumably due to cluster formation in regime II. This macroscopic observation thus indicates differences in protein–protein and protein–salt interactions induced by the different lanthanide salts used. Based on Fig. 2, the strongest protein–protein interactions are expected for HoCl₃ and the weakest ones for LaCl₃. We therefore focused our studies on HoCl₃ and LaCl₃, using YCl₃ as a reference system based on extensive previous work.^5,38–40,68

Fig. 2 Comparison of dense phases of liquid–liquid phase separated samples containing 80 mg ml⁻¹ BSA and different trivalent salts. The protein concentration (c_p) is 80 mg ml⁻¹, the salt concentration (c_s) is 14 mM in every sample. All samples are located in the LLPS region of regime II of their respective c_s–c_p phase diagrams. Note that the dense phases obtained in the presence of Ho³⁺ and Gd³⁺ may correspond to an arrested state (see text for details). The cationic radii of the lanthanides are obtained from ref. 66 and that of Y³⁺ from ref. 67. The dashed vertical line between YCl₃ and HoCl₃ indicates that YCl₃ is used as a reference system.

4.2 Isothermal coexistence c_s–c_p phase diagram

As a first step towards a more quantitative description of the phase behaviours of our systems, phase diagrams were established for BSA in the presence of YCl₃, LaCl₃ and HoCl₃. Homogeneous samples with salt concentrations below c* and beyond c** as well as liquid–liquid coexistence diagrams of phase-separated samples in regime II are shown in Fig. 3.

Fig. 3 Isothermal phase diagrams of BSA in the presence of LaCl₃, HoCl₃ and YCl₃. Data in (a) are replotted based on ref. 43. In the presence of HoCl₃, the dense phases formed feature network-like structures which may indicate aggregation. Nevertheless, these samples still show LCST behaviour and are therefore classified as showing both aggregation and LLPS.

Fig. 3 illustrates the differences in the isothermal phase behaviour of BSA induced by the three different salts studied here. The most striking feature is the complete lack of LLPS at room temperature when LaCl₃ is used.⁴³ Using HoCl₃, however, leads to a rather broad region of LLPS, larger still than the one induced by YCl₃. The BSA–HoCl₃ one shows more aggregation than the BSA–YCl₃ one. A detailed characterisation of the properties of these dense phases is beyond the scope of the present publication. Nevertheless, the presence of aggregates suggests that the dense phases of the BSA–Ho³⁺ system may be in an arrested state caused by a stronger intermolecular attraction, as observed for other protein systems.²¹ This interpretation is further supported by the observation that dense BSA–Ho³⁺ (and BSA–Gd³⁺) phases appear turbid after preparation, but can mature into clear dense phases after several weeks.

4.3 Temperature-dependent UV spectroscopy

As an alternative route to investigate the effect of different cations on the macroscopic phase behaviour of our experimental systems, we systematically determined the cloud temperature T_trans for BSA in the presence of cation mixtures. Fig. 4 shows a typical data set obtained for a constant BSA concentration of 80 mg ml⁻¹ (1.2 mM). The total salt concentration was also kept constant at 10 mM while increasing the HoCl₃ fraction and simultaneously decreasing that of LaCl₃. Similar scans were also performed using different YCl₃/LaCl₃ and YCl₃/HoCl₃ ratio combinations. The transition temperature T_trans of each system was determined as the maximum of the first derivatives with respect to temperature of the respective integrated absorbance curves.

Fig. 4 Typical series of T-dependent absorbance measurements (raw data) of samples containing a constant c_p of 80 mg ml⁻¹ (1.2 mM) BSA and a constant total ionic strength of 10 mM consisting of different salt ratios (here: HoCl₃ & LaCl₃). Similar series were also recorded for mixtures of HoCl₃ & YCl₃ as well as YCl₃ and LaCl₃. T_trans values of all samples were compared to a sample with 10 mM pure YCl₃ (Fig. 5).

In order to quantify the influence of different cations on T_trans of the different cation mixtures, the differences in T_trans values (ΔT_trans) between different mixtures and samples containing 100% YCl₃ (the T_trans of which is 30.6 °C) were calculated (Fig. 5). As can be seen from the rightmost part (HoCl₃/LaCl₃ mixtures), the strongest ΔT_trans (−15 °C) is obtained in a mixture of 20% LaCl₃ and 80% HoCl₃. In other words, with higher fractions of HoCl₃, the samples phase-separate already at lower T. This is also the lowest overall ΔT_trans observed amongst all mixtures investigated and supports the hypothesis that Ho³⁺ cations induce the strongest interprotein attraction of all cations studied here. This conclusion is also reflected in the fact that samples containing HoCl₃ percentages higher than 80% already phase-separate at 12 °C, the initial equilibration temperature for the measurements presented here. Due to this behaviour, no measurements of BSA–HoCl₃/LaCl₃ samples containing more than 80% HoCl₃ could be performed. When mixtures of YCl₃ and HoCl₃ (leftmost part of Fig. 5) are considered, any sample with a HoCl₃/YCl₃ ratio higher than 50/50 also phase-separates already at 12 °C. The higher the fraction of HoCl₃, the higher the T_trans difference to a sample containing only YCl₃. Again, this indicates a strong interprotein attraction induced by Ho³⁺.

Fig. 5 Difference between T_trans values determined for each sample consisting of BSA and a cation mixture and T_trans of a sample containing 80 mg ml⁻¹ BSA and 10 mM pure YCl₃. Where not visible, error bars are smaller than the data symbols.

In the case of YCl₃/LaCl₃ mixtures (central part of Fig. 5), the highest ΔT_trans is obtained with the highest LaCl₃ concentration. This implies that addition of LaCl₃ shifts T_trans towards higher values, confirming that Y³⁺ cations induce a stronger interprotein attraction than La³⁺ cations. Based on these measurements, the cations can be ranked according to the order of increasing cation-induced protein–protein interaction strengths as La³⁺ < Y³⁺ < Ho³⁺.

4.4 Effective interactions characterised by small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) was performed in order to characterise the influence that the different cations investigated have on the protein–protein interactions of BSA. Background-corrected SAXS data obtained for BSA in the presence of an increasing HoCl₃ concentration are shown in Fig. 6.

Fig. 6 SAXS profiles of BSA with increasing HoCl₃ concentrations. Samples were prepared at a protein concentration of 85 mg ml⁻¹ (1.3 mM). In case of phase separation, the SAXS measurements were performed in the dilute phase. Data were normalised to the high q region of a BSA sample without salt (0 mM HoCl₃) and only every 5th data point was plotted for clarity. The dark grey line in the top left part represents an SHS model fit (as also done for the other curves, but omitted for clarity) to the curve obtained in the presence of 7 mM HoCl₃.

Fig. 6 shows that the intensity at low q, I(0), increases and decreases in an alternating fashion. The intensity I(0) at low q was used to qualitatively estimate the strength of the interactions in the systems investigated (Fig. 7).

Fig. 7 Inverse I(0) values (determined at q = 0.068 Å⁻¹) from the respective SAXS curves. Dashed lines represent guides to the eye. c_p is 80 mg ml⁻¹ (=1.2 mM) for the BSA–YCl₃ and BSA–LaCl₃ systems and 85 mg ml⁻¹ (=1.3 mM) for the BSA–HoCl₃ system. Where not visible, the error bars are smaller than the symbols.

Fig. 7 shows three c_s/c_p regimes with consistent results: first, for c_s/c_p < 7, 1/I(0) behaves comparably for all cations, with a slightly lower 1/I(0) for Ho³⁺. For c_s/c_p in the range from 7 to 22, the different phase behaviours induced by Ho³⁺, Y³⁺ and La³⁺ are reflected in the strengths of the respective humps. While no hump is observed for La³⁺, the humps for Ho³⁺ and Y³⁺ are related to the reduced protein concentration in the dilute coexisting phases. As in Fig. 3, the LLPS appears more prominent for HoCl₃ (i.e. the density difference between the corresponding dense and dilute phases is larger) than for YCl₃, and is absent for LaCl₃. Finally, at higher c_s/c_p (>22), 1/I(0) follows the order Ho³⁺ < Y³⁺ < La³⁺. Together with the trend towards lower T_trans values for samples containing HoCl₃ (Fig. 5), all these features indicate an interprotein attraction decreasing in the sequence HoCl₃ > YCl₃ > LaCl₃, consistent with the above UV-Vis absorbance data in Section 4.3.

In order to further quantify the cation-induced protein–protein interactions, the SAXS curves were treated as follows: for salt concentrations c_s < 6 mM, data were fitted using a screened Coulomb (SC) potential structure factor; at higher salt concentrations, a sticky hard sphere (SHS) potential structure factor was used (see model fit in Fig. 6). From the curves fitted with the SHS structure factor, stickiness parameters τ were extracted and used to calculate the reduced second virial coefficients (B₂/B^HS₂ = 1 − 1/(4τ)⁵⁸). Being related to the osmotic compressibility of the system investigated (see Methods section), these values can be used as a means to determine the overall strength of the interactions of the system in question. In particular, a positive B₂/B^HS₂ indicates overall repulsion whereas negative values indicate net attraction. A value around −1.5 moreover indicates proximity to the critical point of LLPS in colloidal theory.⁶⁹ The B₂/B^HS₂ values obtained for BSA in the presence of HoCl₃, LaCl₃ and YCl₃ are shown in Fig. 8 as functions of the c_s/c_p ratio.

Fig. 8 2nd virial coefficients determined from sticky hard sphere potential fits to background-corrected SAXS data. Dashed lines represent guides to the eye. c_p is 80 mg ml⁻¹ (1.2 mM) for the BSA–YCl₃ and BSA–LaCl₃ systems and 85 mg ml⁻¹ (1.3 mM) for the BSA–HoCl₃ system. The dark-red dotted line indicates the critical B₂/B^HS₂ value below which phase separation is expected to occur.⁶⁹ Where not visible, the error bars are smaller than the symbols.

The B₂/B^HS₂ values obtained for the BSA–LaCl₃ system show that these samples nearly always show net attractive interactions, but, as confirmed by macroscopic experimental data, do not phase-separate under the given conditions. In the BSA–YCl₃ and BSA–HoCl₃ systems, however, the B₂/B^HS₂ values indicate phase separation, as is confirmed from macroscopic observations. The systems containing YCl₃ and HoCl₃ therefore feature overall stronger attractive interactions.

The B₂/B^HS₂ values of the BSA–HoCl₃ system are overall more negative than those of YCl₃ and differ in spite of the rather similar cationic radii of Y³⁺ and Ho³⁺. Note that the reason for the absence of humps as they are observed in the case of the 1/I(0) data in the B₂/B^HS₂ values is the fact that the density difference between the two phases only manifests itself in the 1/I(0) values. The B₂/B^HS₂ values, however, are equal in coexisting dense and dilute phases (see e.g.ref. 69), meaning that no density-dependent signature like the 1/I(0) hump is visible in the B₂/B^HS₂ plot (Fig. 8).

The macroscopic phase behaviours observed here are linked to a combination of cation-induced interprotein interactions and cation–protein binding. To explore the cation binding behaviours to BSA and to explain potential differences between them, a comprehensive thermodynamic analysis using ζ potentials and isothermal titration calorimetry was performed. The results are summarised in the next section.

4.5 Thermodynamics of cation–protein binding: zeta potential and ITC measurements

In order to characterise the binding behaviour of cations to BSA, we measured BSA–salt sample series with increasing salt concentrations at different temperatures.

In Fig. 9 an exemplary temperature-dependent raw zeta potential data set of BSA in the presence of HoCl₃ system is shown. Corresponding data sets were also obtained for BSA in the presence of YCl₃ and LaCl₃. For further analysis, the data were fitted using the following equation (see ESI† for derivation):

where Q₁ is the protein surface charge at the maximum salt concentration of c₁ = 1 mM, and c₀ is the salt concentration at the point of zero charge. The initial protein charge Q₀ without added salt was fixed to −9 e, consistent with ref. 42.

Fig. 9 Temperature-dependent ζ potential data of 1 mg ml⁻¹ BSA with increasing HoCl₃ concentrations. Each data point is an average of five measurements, error bars represent the standard deviation. The grey line indicates the point of zero charge (c₀, Q = 0). The zeta potential values obtained were converted to elementary charge values using the calculations described in the ESI.† The dashed lines represent fits to the data (eqn (8)).

A first quantitative parameter obtained from the fit is c₀ as a function of temperature and type of salt. c₀ can be regarded as a measure for the cation–protein affinity. As can be seen from Fig. 10, c₀ decreases with temperature in every experimental system. This behaviour underlines the entropy-driven character of cation binding.⁴² Moreover, a strong difference between the BSA–HoCl₃ system and the two other systems becomes obvious – overall, less Ho³⁺ cations are needed to neutralise the BSA charge, indicating a stronger binding affinity of Ho³⁺ to BSA.

Fig. 10 c ₀ values for the BSA–YCl₃, BSA–LaCl₃ and BSA–HoCl₃ systems (c_p = 1 mg ml⁻¹ = 15 μM). The c₀ values were determined from fits (eqn (8)) to the raw ζ potential data as shown exemplarily in Fig. 9. Dashed lines are guides to the eye.

The average number of cations binding to the protein surface, N, can be calculated via the relation N = (Q₁ − Q₀)/3 with Q₀ = −9 exploiting the fact that every cation has a charge of +3. The respective values are shown in Fig. 11. As can be seen in Fig. 11, the average number again shows the sequence Ho³⁺ > Y³⁺ > La³⁺, with overall roughly 0.5–0.7 more cations bound for Ho³⁺ compared to La³⁺. We remark that the exact choice for Q₀ is not essential for comparison between the cations, as the relative sequence in N is robust against variations of Q₀.

Fig. 11 Average number of cations, N, binding to BSA as calculated from ζ potential data as (Q₁ − Q₀)/3, Q₀ = −9. Dashes lines are guides to the eye.

In order to thermodynamically quantify cation–protein binding, isothermal titration calorimetry (ITC) measurements were performed, as shown in Fig. 12. While the profiles for HoCl₃ and YCl₃ appear to be very similar, the systems with LaCl₃ show a smaller enthalpic gain.

Fig. 12 ITC profiles of BSA titrated with YCl₃, HoCl₃ and LaCl₃. Magenta data points were considered outliers and therefore excluded from the analysis. The data sets were merged from measurements performed with 3 mM and 800 μM salt solutions.

ΔH_bind was calculated by determining the integral of the curve until the respective molar ratios of zero charge (=20.4 for HoCl₃, 29.1 for LaCl₃ and 30.9 for YCl₃) and divided by Q₀/−ν_s.⁴² The obtained values read 10.6 kcal mol⁻¹ for HoCl₃, 10.4 kcal mol⁻¹ for YCl₃ and 7.8 kcal mol⁻¹ for LaCl₃, reiterating the observation that LaCl₃ shows a smaller value, while HoCl₃ and YCl₃ appear similar. We note that due to batch-to-batch variations of BSA,⁷⁰ potentially due to different content of co-ions remaining after the purification process, the absolute values of ΔH_bind should not be overinterpreted. Nevertheless, we argue that the values obtained here can be used for a semi-quantitative characterisation of our systems, in particular when comparing the cation–BSA binding for different cations within the same BSA batch.

5 Discussion

Based on the characterisation of cation–protein association and cation-induced protein interactions for different trivalent cations, we now discuss the implications for a general understanding which physicochemical parameters determine the interactions between proteins and multivalent cations.

Cation radii are obvious parameters that can be seen as influencing the overall protein–ion interactions. In the present study, this is most clearly reflected in the B₂/B^HS₂ values where stronger attractions go along with smaller cation radii. Similar findings were obtained by Schomäcker et al.⁷¹ in a study showing a clearly linear dependence of human serum albumin and human blood serum affinity to Ln cations on cation radius. A publication by Smolka et al.⁷² furthermore provides a detailed discussion of the role of the cation radius regarding the affinity of Ln cations to α-amylase, a system that is Ca²⁺-dependent under physiological conditions. According to the authors, the smallest cation is likely to experience the strongest attraction to the protein due to the fact that its charge is concentrated near its binding site on the protein. In the case of a strong cation binding site, this effect can compensate the high hydration free energy of the cation, which leads to an increased protein–cation affinity with decreasing cationic radius.⁷²

While the relationship between cation radius and protein attraction strength appears straightforward in the case of the B₂/B^HS₂ data, the c₀ calculations and ITC measurements indicate that the situation is more complex. This suggests that cation–protein binding energies (measured by ITC and zeta potentials) and cation-induced protein–protein bridging energies (measured by T_trans and B₂/B^HS₂) are not directly coupled. In particular, c₀, the salt concentration at the point of zero charge as a measure of cation–protein affinity, is rather similar for Y³⁺ and La³⁺, while the c₀ values of Ho³⁺ differ strongly. In contrast, the B₂/B^HS₂ values of Ho³⁺ and Y³⁺ resemble each other, whereas those of La³⁺ are clearly higher. In the case of ITC, the ΔH_bind values are comparable for Y³⁺ and Ho³⁺ whereas they are lower for La³⁺, which indicates that no strong trends of cation–protein binding are seen in ITC. This may be caused by uncertainties of the experimental procedure and product purities. Since c₀ and B₂/B^HS₂ measure cation–protein binding and cation-mediated protein–protein bridging, respectively, these findings appear to indicate that binding and bridging strengths can be different for the same cation.

A probable explanation for this difference is the different surface geometry in the case of a cation being bound to one protein as opposed to when it is bridging two proteins. As the binding appears to be driven by entropy of hydration water,⁴² the dehydration due to the first bond to one protein molecule might be very different from that of the second bond to another protein. This explanation also emphasises that cation radii are not the only parameters that need to be taken into account in order to rationalise the influence of different cations on protein phase behaviour. This assumption is corroborated by a study conducted by Gomez et al.⁷³ The authors investigated the abilities of lanthanide and Y³⁺ cations to restore the Ca²⁺-dependent biological activity of trypsinogen – another protein known to bind Ca²⁺ as well as lanthanide and Y³⁺ cations at aspartic acid residues – after depleting their trypsinogen system of Ca²⁺. At low lanthanide concentrations (around 10⁻⁴ M), the authors did not find a simple relationship between the cation radii and their efficiency in restoring the biological activity. Similarly, a non-monotonic relation between protein–lanthanide affinity and lanthanide radius has been found by Mulqueen et al.⁷⁴

Gomez et al.⁷³ attribute their findings to potentially incomplete dehydration of different cations upon trypsinogen binding and to different amounts of water molecules bound to the protein–lanthanide complex. This aspect is very important to consider since our experimental system is known to be driven and strongly influenced by hydration effects.^42,43 Gomez et al.⁷³ furthermore observe that Y³⁺ has a protein–cation affinity not fitting into the expected trend based on the cationic radii of the lanthanides. Along with findings indicating that the strengths of different Y³⁺–ligand complexes vary strongly depending on the ligand chosen and can thus interfere with a straightforward integration of yttrium into trends of the lanthanide series^75,76 this provides further evidence that parameters other than radius can play a role in the interactions between proteins and multivalent cations. These can e.g. include electron configuration^76,77 as well as cation polarisabilities and resulting dipoles.⁷⁸

Previous work on the thermodynamic properties of lanthanides⁷⁹ reports higher entropic contributions for the complexation of Ho³⁺ to ethylenediaminetetraacetic acid (EDTA). While a protein is certainly more complex than the rather simple EDTA molecule, coordination of lanthanide cations in the case of BSA nevertheless also proceeds via carboxylic groups, making EDTA–lanthanide complex formation a reasonable reference point. Our previous work⁴² was strongly supported by earlier results obtained for lanthanide and Y cations binding to amino acids in solution.^80,81 Together with the zeta potential results which indicate a higher number of cations bound for Ho³⁺, this can help explain the stronger overall interprotein attraction induced by these cations.

The trypsinogen system investigated by Smolka et al.⁷² which we mentioned earlier is known to have two cation binding sites, whereas our system features several (around four) sites with varying local geometry. In addition to this, the cations used in the present work do not simply bind to BSA, but also bridge protein molecules and lead to an overall more complex phase behaviour of our system.^42,45 The aspects mentioned by Gomez et al.,⁷³ especially cation and complex hydration, might thus have even more intricate effects on our systems. We suggest that these two aspects can thereby help explain the differences in BSA phase behaviour induced by different cations and the difference between Y³⁺ and Ho³⁺ in spite of the closeness of their cationic radii. This finding is consistent with the lower T_trans values in the presence of HoCl₃ as well as the larger LLPS areas obtained for BSA with HoCl₃.

From a broader perspective on biological matter, it is interesting to compare the protein system to the well-studied example of DNA: analogously to the observations in our protein–cation systems, cation-⁸² and polymer-⁸³ induced attraction between DNA strands can similarly stabilise and shift the melting temperature of DNA to higher values. An additional factor influencing the melting transition of DNA is its degree of hydration,⁸⁴ which provides another conceptual link between phase transitions of DNA and proteins. The crucial aspect of hydration in our protein–cation systems will be discussed in more detail in the following.

Computational results on lanthanide cations in the absence of proteins confirm the importance of hydration effects and differences in cation hydration along the lanthanide series. Duvail et al.⁸⁵ performed an explicit polarisation molecular dynamics study on the exchange frequency (EF) of water molecules between the first hydration shell of lanthanide cations and bulk water. The EF shows a strongly non-monotonic behaviour along the lanthanide series with the maximum EF being observed for Tb³⁺, a lanthanide cation located close to Ho in the periodic system. Additionally, the authors provide evidence for a change in both hydration water structure and coordination number along the lanthanide series, a result corroborating earlier findings by Habenschuss and Spedding^86–88 and studied in even more detail by Zhang et al.⁸⁹ Persson et al.⁹⁰ furthermore identified Ho³⁺ as the cation with the strongest change in hydration structure.

As a general caveat, it should be kept in mind that simulations and calculations for lanthanides and their properties encounter difficulties due to non-negligible relativistic effects⁸⁹ caused by strong shielding of the nuclear charge,⁹¹ a generally large number of electrons and incomplete 4f electron orbital occupation.⁸⁹ Nevertheless, the above examples show that a large number of such studies exhibits good reproducibility and consistency. We assume that these findings can potentially help explain non-monotonous effects that we observe in our experimental systems and that cannot be explained only by cation radii.

When discussing the effects the cations studied here have on protein phase behaviour, the classification of Y with respect to the lanthanide series is an important aspect to be mentioned. As apparent from the study by Gomez et al.,⁷³ this is not always straightforward. On the one hand, the chemical properties of Y are sufficiently close to the lanthanide series for it to be treated like a lanthanide;⁹² on the other hand, extensive studies classifying lanthanide and Y complexes with various ligands show that depending on the ligand, Y can behave similarly either to the heavy or the light lanthanides.^75,76 This is consistent with our own observations that points of zero charge or enthalpies of Y–BSA binding do not always follow a trend that could be expected based on cation radii or position in the periodic system. Our results confirm that while BSA phase behaviour induced by Y³⁺ cations is sufficiently similar to that induced by lanthanides, it cannot always be expected to follow similar trends.

6 Conclusions

The experiments presented here offer an insight into the differences in protein phase behaviours – in particular liquid–liquid phase separation (LLPS) – induced by the trivalent cations Y³⁺, Ho³⁺ and La³⁺. Whereas in the case of La³⁺ no phase separation is observed, Ho³⁺ leads to the formation of a dense phase which is potentially arrested. When Y³⁺ is used, the dense phase is more liquid-like. This difference in protein–protein attractions induced by the different cations is reflected in the increase and decrease of the transition temperature T_trans upon LaCl₃ and HoCl₃ addition to the BSA samples, respectively. In addition, the stronger interprotein attraction manifests itself in lower reduced second virial coefficient B₂/B^HS₂ values as determined from SAXS experiments. The different cations used in this work can therefore tune thermal sensitivity of the samples. We emphasise that cation radius may not be the only parameter that should be considered when quantifying both cation–protein binding as well as cation-induced protein–protein interactions, and that hydration effects can be particularly important.

By carefully choosing multivalent cations, we are able to tune the phase transitions of aqueous BSA solutions. Our results thus provide a deeper understanding of thermodynamic fundamentals of colloidal and soft matter systems. Additionally, our findings are of relevance in the area of stimuli-responsive materials (e.g. for targeted drug delivery and release⁹³ or water pollutant clearance⁹⁴) where tuning the sensitivity to different environmental factors is of pivotal importance.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

The authors gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft (DFG) and thank the ESRF for beamtime on beamline ID02. O. M. acknowledges a PhD fellowship by the Studienstiftung des Deutschen Volkes (German Academic Scholarship Foundation) and thanks the PSCM (Grenoble), Thilo Stehle and Nina Jaspert (Tübingen) for sharing their laboratory resources as well as Pinelopi Christodoulou for help with the ITC measurements. F. R.-R. acknowledges funding from the Knut and Alice Wallenberg Foundation (project grant KAW 2014.0052). The authors are grateful to Theyencheri Narayanan (ESRF, Grenoble), Leonardo Chiappisi (ILL, Grenoble), Stefano Da Vela, Martin Oettel and Roland Roth (Tübingen) and Michael Dolg (Cologne) for valuable discussions.

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Footnote

† Electronic supplementary information (ESI) available: Calculation of effective protein surface charge from zeta potentials and derivation of zeta potential fitting equation. See DOI: 10.1039/c8cp05884a

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