Impact of Macromolecular Crowding and Compression on Protein

Article Cite This: Macromolecules XXXX, XXX, XXX−XXX

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Impact of Macromolecular Crowding and Compression on Protein− Protein Interactions and Liquid−Liquid Phase Separation Phenomena Karin Julius,† Jonathan Weine,† Mimi Gao,‡ Jan Latarius,† Mirko Elbers,† Michael Paulus,† Metin Tolan,† and Roland Winter*,‡

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†

Experimental Physics EIA/DELTA−Department of Physics, TU Dortmund University, Otto-Hahn-Str. 4, 44227 Dortmund, Germany ‡ Physical Chemistry I−Biophysical Chemistry, Faculty of Chemistry and Chemical Biology, TU Dortmund University, Otto-Hahn-Str. 4a, 44227 Dortmund, Germany S Supporting Information *

ABSTRACT: We determined the intermolecular interaction potential, V(r), of dense lysozyme solutions, which governs the spatial distribution of the protein molecules and the location of its liquid−liquid phase separation (LLPS) region, in various crowding environments applying small-angle X-ray scattering in combination with liquid-state theory. We explored the effect of polyethylene glycol (PEG) on V(r) and the protein’s phase behavior over a wide range of temperatures and pressures, crossing from the dilute to the semidilute polymer regime, thereby mimicking all crowding scenarios encountered in the heterogeneous biological cell. V(r) and hence the protein−protein distances and the phase boundary of the LLPS region strongly depend on the polymerto-protein size ratio and the polymer concentration. The strongest effect is observed for small-sized PEG molecules, leading to a marked decrease of the mean intermolecular spacing of the protein molecules with increasing crowder concentration. The effect levels off at intermolecular distances where the proteins’ second hydration shells start to penetrate each other. Strong repulsive forces like hydration-shell repulsion and/or soft enthalpic protein-PEG interactions must be operative at short distances which stabilize the protein against depletion-induced aggregation, also at pressures as high as encountered in the deep sea, where pressures up to the kbar-level are encountered. well as in the presence of polymers.7−10 The propagation by division and subsequent growth of such active self-organized liquid droplets may also have served as prebiotic protocells.11 Understanding of the physics of LLPS phenomena provides insight into the assembly and disassembly of such biomolecular condensates found in cellulo12,13 and into their role for cellular function in the presence of internal and external stress factors, such as high osmotic pressure induced by high osmolyte and crowder concentrations, extreme temperatures, or high hydrostatic pressure (HHP). In particular, the adaptational response of biomolecular systems toward the environmental stress factor pressure is still far from being understood. The deep sea, where organisms face unfavorable conditions like pressures up to 1.1 kbar,14 accounts for a significant part of the global biosphere (>60%) and is also presumed to be the cradle of life on Earth.15 Therefore, HHP studies on biomolecular systems also

1. INTRODUCTION In living cells, equilibria and rates of biochemical reactions as well as the conformational stability of biomolecules are strongly influenced by the high fractional occupancy (>30%) of “background” species like osmolytes, proteins, nucleic acids, and other biopolymers.1,2 Moreover, the shape, size, and concentration of such crowding agents modulate intermolecular interactions between biomolecules such as proteins and hence affect their dynamics, phase behavior, and spatiotemporal organization. Recently, next to lipid vesicles also membrane-less organelles were found to play a major role in compartmentalizing the cell, thereby achieving the necessary physical separation of the cellular compounds and processes. They consist of multicomponent viscous liquid droplets (coacervates), which form via segregation of molecules from protein or protein−nucleic acid mixtures by spontaneous liquid−liquid phase separation (LLPS).3 At high protein concentrations, metastable LLPS into coexisting dilute and dense protein-rich liquid phases has been observed at low temperatures and in the presence of additives such as salt4−6 as © XXXX American Chemical Society

Received: November 19, 2018 Revised: January 19, 2019

A

DOI: 10.1021/acs.macromol.8b02476 Macromolecules XXXX, XXX, XXX−XXX

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lysozyme molecule averaged over its spatial orientation. From the SAXS intensity of a dilute solution of noninteracting lysozyme molecules (clys = 1% (w/v)), the form factor can be modeled theoretically by the radially averaged scattering function of a prolate ellipsoid of revolution. The effective structure factor, Seff(q), an additional scattering contribution arising for solutions of higher protein concentration, is sensitive to the spatial arrangement and thus the intermolecular interactions of the scattering particles. Within the mean-spherical approximation (MSA), the structure factor is linked to the proteins effective intermolecular interaction potential, V(r) (see the SI for experimental and theoretical details).31,32 Unlike for neutron scattering experiments,33 the X-ray scattering contrast for PEG is lower than for lysozyme. Thus, in the analysis of the total scattering intensity of a binary mixture consisting of lysozyme and PEG, the polymer solution can be treated as a background solvent and can be subtracted from the scattering contribution of the protein solution to yield eq 1 (see the SI). For lysozyme molecules in solution, with centers separated by the distance r, the effective protein pair interaction potential, V(r), is modeled in the framework of the Derjaguin−Landau−Verwey−Overbeek (DLVO) theory as the sum of a long-ranged screened Coulomb potential, VSC(r), a repulsive hard-sphere potential, VHS(r), and a short-ranged attractive Yukawian-like potential, VY(r):18,20

help resolve the biochemical mechanisms underlying HHP adaption.16,17 Further, pressure perturbation has become a powerful tool for fine-tuning interparticle interactions in nanoparticle systems and in dense protein solutions18−20 and hence also for modulating LLPS phenomena.5,6,21 In general, pressure shifts chemical equilibria and redistributes the population of conformers by favoring the state of smallest partial molar volume. Hence, pressure is also a key variable for scrutinizing the roles of packing and hydration, both affecting the volumetric properties of biomolecules in solution markedly.22−24 The molecular interactions and the microscopic structure of ternary protein-cosolute-water systems as well as their implications for the temperature and pressure dependent phase behavior of protein systems are still largely terra incognita. Besides direct intermolecular interactions resulting from electrostatic, van der Waals, or hydrophobic forces, attractive forces between the proteins can be induced in the presence of crowders by the entropically driven excluded volume effect. Herein, we studied the intermolecular interactions governing the spatial distribution of proteins in solution and their impact on the temperature and pressure dependent LLPS region and reveal how they are modulated by various crowding environments employing lysozyme as a model protein. The effect of the crowded cellular environment is mimicked using the synthetic, biocompatible polymer polyethylene glycol (PEG) as well as the nanocrowder sucrose as crowding agents. PEG (−(CH2−CH2−O)n−) is a nonionic straight chain polymer, which exists in a random coil state in aqueous solution25 and is often used in biochemical and pharmaceutical applications.26 PEG has the capacity to exclude volume and dehydrates biopolymers at high concentrations through competition for hydration water. In combination with a liquid-state theoretical approach, small-angle X-ray scattering (SAXS) yields the intermolecular protein−protein interaction potential, V(r), and the second osmotic virial coefficient, B22, as a function of crowder concentration, and in concert with complementary light transmission (turbidity) measurements, the phase boundaries of the LLPS region. Employing more than 3 orders of magnitude of the polymer’s molecular weight (Mw ≈ 200−35000 g mol−1), we explore their effect on V(r) and the protein’s phase behavior by the impact of the size and shape of the crowding agent at concentrations crossing from the dilute to the semidilute polymer regime, thereby mimicking all crowding scenarios encountered in the heterogeneous biological cell. In addition to its biological relevance, these studies allow also to gain a deeper understanding of the forces controlling the B 22 region prone to lead to protein crystallization.27−29

l o o∞ ,r ≤ σlys VHS(r ) = m o o 0 ,r > σlys o n

l 0 ,r ≤ σlys o o o o o VSC(r ) = o m e−(r − σlys)/ λD Z2e 2 o o ,r > σlys o o 2 o r o 4πε0εr (1 + 0.5σlys/λD) n l 0 ,r ≤ σlys o o o o o VY(r ) = m o e−(r − σlys) / d o o ,r > σlys −Jσlys o o o r n (2)

Here, σlys describes the effective hard-sphere diameter of the protein, ε0 the dielectric permittivity of the vacuum, and e the elementary charge. The Debye−Hückel screening length of the solution, λD =

2NAe 2I

, depends on the solution’s ionic

strength, I, the Avogadro constant, NA, and the pressure dependent solvent’s static dielectric permittivity, εr. The change of εr upon pressurization is reasonably approximated by the pressure dependence of εr of water34 and the crowder’s dielectric increments determined by own dielectric spectroscopy experiments (see Figure SI 2). The protein’s effective net charge is set to a constant value of Z = +8e at pH 7, which is valid for all solution conditions studied here.35 Moreover, for the width of the attractive part of the potential, the value d = 0.3 nm is chosen, in accordance with previous works.18,20 It amounts to one hydration layer, only, independent of the presence of crowders. A further parameter in the refinement of the SAXS data is the volume fraction, Φlys, occupied by the protein in the sample volume, which increases upon compression. For a given protein concentration, the isothermal compressibility of the solution at high pressures depends

2. METHOLOGY AND EXPERIMENT The SAXS profile, I(q), of a solution of interacting monodisperse globular particles like lysozyme molecules can be modeled by I(q) ∝ n pΔρ2 Vp2⟨P(q)⟩Seff (q)

ϵ0ϵrkBT

(1)

within the so-called decoupling approximation.30,31 Here, np denotes the number density of particles in solution, Δρ the electron density contrast and Vp the volume of the particle. The momentum transfer q = (4π/λ) sin(θ/2) is defined by the wavelength λ and the scattering angle θ. The protein’s form factor, ⟨P(q)⟩, is determined by the shape and size of a single B


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We then explored the effects of different levels of nano- and macromolecular crowding on the pressure-dependent protein pair-interaction potential of dense aqueous lysozyme-crowder mixtures at 25 °C using high-pressure SAXS. As crowding agents, the nonadsorbing polymer polyethylene glycol of various molecular weights (200 g mol−1 < Mw < 35 000 g mol−1) and the disaccharide sucrose (Mw = 342.30 g mol−1) were employed at concentrations ranging from 1 to 50% (w/ v), the solubility limit of PEG.42 The pH value is neither affected by the presence of PEG nor sucrose.43 3.1. Influence of Sucrose on the Protein−Protein Interaction. The analysis of the SAXS data for dense proteincrowder mixtures is shown exemplarily in Figure 1 for 10% (w/ v) lysozyme in 25 mM Bis-Tris (pH 7, 25 °C) in the presence of the nanocrowder sucrose at concentrations, c, ranging from 5 to 40% (w/v). The DLVO potential is determined by the

strongly on the crowding level. Our own high-pressure X-ray transmission measurements on highly crowded 10% (w/v) lysozyme solutions allowed us to calculate Φlys for all crowding and pressure conditions (see SI 4). Of note, other potential factors contributing to the protein−protein interaction, such as steric/depletion forces, hydrogen bonding, soft crowderprotein interactions or liquid-like ordering of the solute, and hydration repulsion at short distances, are not included in the DLVO potential’s parametrization. The DLVO potential is determined by fitting the effective structure factor to the experimental scattering intensity. The sole free parameter in the refinement of the data is the strength of the attractive Yukawian-like part of the interaction potential, J. The overall protein pair-interaction with the effective DLVO potential, V(r), is related to the protein−protein osmotic second virial coefficient B22 = 2π

NA M w ,lys

2

∫0

i ∞j

y jj1 − expijjj− V (r ) yzzzzzzr 2 dr jj jj k T zzzz B {{ k k

(3)

of the virial expansion of the osmotic pressure Π(c)/cRT = 1/ Mw,lys + B22c + ..., where R is the ideal gas constant.36 The normalized dimensionless value b2 =

B22 M w,lys 2 NAB2HS

=1+

(σlys

3 + δσ )3

∫σ

∞ lys + δσ

(1 − e−V * (r)/kBT )r 2 dr (4)

obtained by factoring out the hard-sphere part, B2HS = 2π(σlys+δσ)3/3, of the integral in eq 3, depends neither on the protein-type nor its size or molecular weight, and reveals a predominantly attractive (−) or repulsive (+) nature of the two-body interaction simply by its sign. In accordance with literature data, we used δσ = 0.1437 nm to prevent divergence of the integral at r = σlys.18,37

3. RESULTS AND DISCUSSION First, to exclude potential pressure-dependent changes in the protein’s native folded state, high-pressure SAXS measurements were carried out on diluted 1% (w/v) lysozyme in 25 mM Bis-Tris buffer (pH 7, 25 °C) at pressures ranging from 1 bar to 3.5 kbar, yielding the shape and size of the protein (details of the experimental setup are described in the SI). Moreover, the system was checked for crowder-induced conformational changes at ambient as well as elevated pressures upon addition of 15% (w/v) of small (PEG 200 and PEG 600), midlevel (PEG 2000), and high molecular weight (PEG 35000) polymer to the buffer solution (see SI 5). The protein’s radius of gyration, RG,lys, is determined from the low-q Guinier region of the scattering data,38 where I(q) = I(0) exp(−(qRG,lys)2/3) for qRG,lys < 1.3, employing the program PRIMUS,39 and by the inverse Fourier-transformation program GNOM from the pair-distance distribution function P(r).40,41 In good agreement with literature data,20 lysozyme is conformational stable with a constant radius of gyration of RG,lys = 1.45 ± 0.05 nm in the whole pressure range covered, regardless of the respective crowding agent added. It is adequately described by the form factor of a prolate ellipsoid of revolution of the semiaxes ap = 1.57 nm and bp = 2.42 nm and an effective hard sphere diameter of σlys = 2(ap2bp)1/3.

Figure 1. (a) SAXS data of 10% (w/v) lysozyme dissolved in 25 mM Bis-Tris (pH 7) at various sucrose concentrations, c, at ambient pressure and 25 °C, shown together with the corresponding refinements (solid black lines). (b) Refinements for the effective structure factor, Seff(q), as a function of sucrose concentration (curves are shifted for clarity, see SI 6 for the nonshifted representation). (c) Total effective pair-interaction potential with its contributing parts for various amounts of sucrose at ambient pressure. (d) Strength of the attractive part of the pair-interaction potential, J, as a function of pressure, p, and sucrose concentration, c. (e) Pressure dependence of the normalized osmotic second virial coefficient, b2, for various sucrose concentrations. C


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entropically favored and results in an effective attraction between the protein molecules.53,54 Hence, for a sufficient amount of sufficiently large polymer, attractive protein− protein depletion interactions may be induced in a naturally repulsive polymer−protein mixture. Due to fluctuations of the coil shape in polymer solutions, the short-ranged depletion attraction is not cut off abruptly but falls off slowly. To describe the interaction between the proteins, the length scales of the various polymer solutions need to be characterized. For the polymer’s radius of gyration in dependence of the relative molecular weight, a power-law behavior, RG,PEG,0 = 0.0215 Mw(0.583±0.031)/nm is reported,55 which corresponds to the conformation of a swollen globule (see SI Table 1). Beyond the polymer’s overlap concentration, c*, which depends on the degree of polymerization (and hence Mw), the volume excluded per polymer molecule diminishes due to shrinking and/or increasing compactness, according to RG,PEG = RG,PEG,0(cPEG/c*)−1/8.56 For example, the radius of gyration of a single PEG 3400 chain decreases with increasing polymer concentration from 1 to 30 wt % by about 6%.57 At the crossover from the dilute to the semidilute polymer regime, marked by c* = Mw/(4/3πR3G,PEG,0NA)/mg mL−1,58 an extensive entanglement of PEG molecules takes place and the entire volume is occupied by nonoverlapping polymer coils (see SI Table 1). While for dilute solutions (cPEG ≪ c*) the identity of the individual polymer chain is preserved and determinant for the solution properties, for cPEG ≥ c* the system transitions from individually dispersed random coils to an entangled mesh of polymers,59 whose thermodynamic properties are being solely a function of the polymer’s volume fraction.50,60 As characteristic length scale, the polymer’s radius of gyration is not suitable anymore and has to be replaced by the correlation length (mesh size51,55 ξb ≈ RG,PEG,0(cPEG/ c*)−3/4.56 It decreases with increasing polymer concentration (volume fraction). To explore the effect of the macromolecular crowder PEG of various molecular weights, crossing over from the dilute to the semidilute concentration regime, on the pressure-dependent protein−protein interaction, SAXS curves were recorded of dense lysozyme-PEG mixtures at 25 °C in a pressure range from 1 up to 3500 bar. Figure 2a depicts the SAXS data for 10% (w/v) lysozyme in 50 mM Bis-Tris (pH 7) solutions containing 20% (w/v) PEG 20k, 2k, 600, and 200 together with the associated refinements of the effective structure factor, Seff(q), and the lysozyme’s form factor, ⟨P(q)⟩ (see also Figure SI 7). Clearly, marked changes in the position and magnitude of the structure factor’s first maximum, qmax, as well as changes in potential parameters are visible with varying polymer size (Figure 2b). Still, the repulsive energy barrier in V(r) is persistent and effectively does not get below the pure buffer value regardless of the additive’s identity. The repulsive nature of V(r) is reflected in positive values for the osmotic virial coefficient B22 (Figure 2c). Here, the transition to the semidilute regime (cPEG ≥ c*(Mw)) is visualized by empty symbols for each molecular weight of the polymer. At ambient pressure and 25 °C, B22 for pure aqueous 10% (w/v) lysozyme in the neat buffer solution amounts to 5.32 × 10−4 mL mol g−2, in accordance with reported literature data under similar buffer conditions.61 Scaling to the excluded volume contribution, B2HS, leads to the corresponding reduced osmotic second virial coefficient b2 = 1.61. Upon addition of 20% (w/v) PEG of molecular weights between 200 and 6000 g mol−1, B22 decreases from 7.15 × 10−4

refinement of the experimental effective structure factor, Seff(q), which is extracted from the scattering intensities I(q) by dividing them by the analytical protein form factor (Figures 1a,b and SI 6). The pronounced correlation peak in the SAXS intensity curves, I(qcorr), indicates a repulsive short-range ordering of the lysozyme molecules in solution. Accordingly, the position of the first maximum, qmax, of Seff(q) corresponds to the mean intermolecular spacing, dlys = 2π/qmax, between neighboring protein molecules. The rise of Seff(qmax) and qmax with increasing sucrose concentration implies that the mean distance between the proteins is gradually reduced upon addition of sucrose to the buffer solution, which is due to the growing excluded volume imposed by the nanocrowder (see Figure SI 6). Figure 1c depicts the resulting effective protein− protein interaction potential, V(r), together with its contributing parts. For all sucrose concentrations, c, the V(r) shows a maximal value (energy barrier) followed by a rapid decrease at higher distances, yet remaining overall repulsive. The solvent’s dielectric permittivity decreases with rising sucrose concentration (see Figure SI 2). For sucrose, the decrement44 dεr/dc = −1.19 (10% w/v)−1 results in a reduced range of the repulsive Coulomb potential, VSC(r), due to a decreasing Debye−Hückel screening length, λD, but also in an increased strength with increasing sucrose concentration. The strength of attraction, J(c,p), decreases monotonously with increasing sucrose concentration, whereas it essentially retains its nonmonotonous behavior upon pressurization, as reported in previous studies on dense lysozyme solutions in neat buffer20 as well as in the presence of salts18,45 and various organic osmolytes46,47 (Figure 1d). A pressure increase up to ∼1.6 kbar results in a decrease of the mean intermolecular distance of the proteins in the compressed solution, dlys, and of the strength of the attractive part of the protein−protein interaction potential, J, which is followed by a trend reversal upon further pressurization. The origin of this increase in attraction and growing intermolecular spacings upon further compression was suggested to be due to structural changes in the bulk water and increased hydration repulsion.48,49 As also seen by the increase of the normalized second osmotic virial coefficient b2 (Figure 1 e), the nanocrowder sucrose renders the system overall slightly more repulsive. 3.2. Influence of PEG on the Protein−Protein Interaction. High molecular weight PEGs exhibit properties of a quasi-random coil with some solvent-induced short-range ordering near the polymer backbone.50 The number of possible chain conformations of the PEG polymer in solution increases with the degree of polymerization, i.e., Mw. The neighborhood of an impenetrable surface like a protein causes constraints on the conformational freedom of the polymer, i.e., is entropically unfavorable. Hence, the polymers are excluded from a sphere of radius σlys/2 + δdepl around the globular protein, where the depletion thickness, δdepl, is of the order of the characteristic length scale describing the polymer in solution. If δdepl exceeds half of the protein’s surface-to-surface distance, the depletion zones surrounding the proteins overlap and the polymer is effectively excluded from the intermediate space of the protein.51,52 Because of the unbalanced osmotic pressure, Π, an attractive depletion potential of a range dependent on the effective polymer size and a strength dependent on polymer concentration, acts on the noninterpenetrating proteins. Since extra volume is recovered for the polymer when the depletion zones of the proteins overlap, the downsizing of the inaccessible space for the polymer is D


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of 30% (w/v) of the polymer and from ∼2.67 to ∼0.95 nm for 30% (w/v) sucrose in 25 mM Bis-Tris buffer. A study of the characteristics of hydration water around hen egg lysozyme, employing FTIR spectroscopy and molecular dynamics simulations,62 reports three distinct hydration shells for lysozyme in aqueous solution. Starting from the protein’s surface, the hydration shells I and II are located at RI = 0.0−0.3 nm and RII = 0.3−0.58 nm, respectively. The third hydration shell at RIII = 0.58−1.26 nm may almost be treated as bulk water-like. In this respect, the crowder’s effect on the mean intermolecular spacing of the proteins levels off at intermolecular distances where the proteins’ second hydration shells penetrate each other. This effect can be further tested by means of elevating the solutions ionic strength. Increasing the ionic strength in aqueous 10% (w/v) lysozyme solutions at pH 7 by adding NaCl leads to a significant reduction of Coulomb repulsion (e.g., B22 = 3.07 × 10−4 mL mol g−2 in 25 mM BisTris +75 mM NaCl, T = 25 °C), since the protein’s net surface charge is effectively screened at ∼100 mM NaCl.61 Thereby, the mean protein−protein spacing is reduced beforehand (dlys − σlys ≈ 2.21 nm in 25 mM Bis-Tris +75 mM NaCl, T = 25 °C) up to a value where the proteins’ hydration shells start touching each other. However, as shown in Figures 3 and SI 8, the comparison of the protein−protein surface separations as a function of the crowder concentration for 50 mM Bis-Tris buffer, 25 mM Bis-Tris +75 mM NaCl buffer solutions (tagged dark gray) and 25 mM Bis-Tris buffer solutions (tagged light gray), reveals that the crowder-effect is consistent in the investigated concentration regime for all buffer compositions. Here, the net effective protein−protein interaction becoming more attractive due to the added salt seems to cause an offset, only. Figure 3 depicts the impact of the polymer’s molecular weight specific crossover from the dilute to the semidilute region at cPEG = c*(Mw) on the intermolecular surface-tosurface distances, dlys − σlys, as well as on the length scale, ξb. Below the overlap concentration, at cPEG/c* < 1, the system can be described by a dilute solution of single dispersed crowders of a size determined by their radius of gyration, i.e., ξb ≈ RG,PEG,0. At these conditions, addition of the polymer crowder leads to a decrease of the surface-to-surface distances of the proteins with increasing crowder concentration, most pronounced for small crowder sizes. For PEG 200, the transition from single dispersed chains to a network occurs at a significantly higher weight fraction, and its overlap concentration is not reached in the concentration range studied here. The concentration dependence of dlys − σlys shows a nonmonotonous behavior with a crossover around cPEG/c *= 1, where the polymer chains build up an extensive entanglement. The mean intermolecular spacing of the proteins in the polymer solution starts to rise again, until, deep in the semidilute regime, where cPEG/c* ≫ 1, dlys − σlys reaches a plateau value that is comparable to the polymer-free buffer system. 3.2.2. Depletion Interaction. In terms of pure depletion theory, the depletion attraction between two proteins in the protein−polymer mixtures depends on the concentrationdependent protein-to-blob size ratio in a nonmonotonous manner. In the case ξb < RG,lys, the polymer chains are depleted from the protein surface due to repulsive excluded volume interactions. The thickness of the depletion zone, δdepl, scales with ξb and shrinks with increasing polymer volume fraction.63,64 Strong attractive depletion forces between the

Figure 2. (a) Experimental SAXS intensities of 10% (w/v) lysozyme dissolved in 50 mM Bis-Tris (pH 7, 25 °C) and 20% (w/v) PEG of selected Mw at ambient pressure, shown together with the refinements for the scattering intensities (solid lines), I(q) and ⟨P(q)⟩, and the effective structure factors, Seff(q) (curves are shifted for clarity, see Figure SI 7 for the nonshifted representation of Seff(q)). (b) The corresponding effective pair-interaction potential with its contributing parts and (c) osmotic second virial coefficients, B22, as a function of the spatial correlation length ξb. Empty symbols visualize the B22 values for PEG concentrations exceeding c*.

to 4.92 × 10−4 mL mol g−2 at ambient pressure and 25 °C. For higher molecular weights, B22 levels off close to the pure buffer value, which is most likely due to changes in the PEG structure from single dispersed chains to a polymer network.50 Thus, even though the volume fraction of 20% (w/v) polymer in the system remains constant at Φ ≈ 0.17, the changing nature of the polymer’s solution structure, as described by the mesh (blob) size, ξb(cPEG, Mw), is able to modulate the protein− protein interaction. 3.2.1. Spatial Distribution of the Protein Molecules. As shown in Figures 3 and SI 6, the impact of crowder concentration, ccrowder, on the mean spacing between protein surfaces, dlys − σlys, in comparison to the corresponding crowder-free buffer system (see the SI for detailed sample compositions) depends markedly on the different crowder sizes. The strongest effect is observed for the similarly sized nanocrowders PEG 200 and sucrose. In the presence of PEG 200, the intermolecular distance decreases from dlys − σlys ≈ 2.48 nm in 50 mM Bis-Tris buffer to ∼0.78 nm upon addition E


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Figure 3. Experimentally derived protein surface separation for a 10% (w/v) lysozyme in 50 mM Bis-Tris and 25 mM Bis-Tris +75 mM NaCl (tagged dark gray) buffer solution (pH 7, 25 °C) as a function of the polymer concentration ratio cPEG/c*, depicted together with the particular length scales of the polymer solution in the dilute (RG,PEG,0) and semidilute (ξb) regime. The dimensions of the three hydration shells of lysozyme (RI−III) and the proteins radius of gyration (RG,lys) are depicted as well for reference. The dlys − σlys values for PEG concentrations exceeding c* are visualized by empty symbols (50 mM Bis-Tris buffer) and dark gray filled symbols (25 mM Bis-Tris +75 mM NaCl buffer), respectively.

z = NNAc PEGσ 3

proteins are only induced if the electrostatic repulsion due to the surface charge of the protein is small enough and the protein concentration high enough for the depletion zones of the proteins to overlap. Mesh sizes comparable to the protein’s radius of gyration (ξb ≈ RG,lys) lead to a minimal to no depletion attraction since the proteins fit perfectly into the polymer mesh spaces without distorting the network.50,64 If the size of the protein is significantly smaller than the blob size (RG,lys ≪ ξb), the protein is capable of diffusing through the mesh. Since there is no explicit parametrization in the DLVO potential for attractive forces between the proteins originating from the entropically driven excluded volume (depletion) effect in the presence of crowders, their contribution to the modeled effective proteins’ pair-interaction is comprised, among others, in the attractive Yukawian part. To quantitatively explore the impact of the polymer on the attractive depletion interaction between two protein molecules with centers separated by r, the depletion potential, Vdepl(r), can be calculated in the framework of the polymer reference interaction site model (PRISM),65−67 which is not covered by the DLVO potential. Within PRISM, Vdepl(r) predicts the polymer-mediated protein−protein interaction for all polymer coil dimensions at polymer concentrations below and beyond c* with no adjustable parameters, from

δdepl = σ

R G,PEG = σ N/6

(5b)

(5d)

PEG − buffer V *(r ) = (VHS(r ) + VYbuffer(r ) + VSC (r ))DLVO PEG − buffer + Vdepl (r )

(6)

For VY(r) and VHS(r), the potential parameters obtained for the system in the absence of the polymer are applied, whereas the electrostatic repulsion described by VSC(r) accounts for the changes of the dielectric constant εr(Mw, cPEG) (see Figure SI 2) and of the Debye−Hückel inverse screening length κ(εr(Mw, cPEG)) upon addition of polymer. The predictions for the modulated effective protein−protein interaction potential V*(r) in 10% (w/v) lysozyme +50 mM Bis-Tris (pH 7) solutions upon addition of PEG (200 g mol−1 < Mw < 35 000 g mol−1) at 0.05% < cPEG < 30% (w/v) are shown in Figure 4 (top half). Clearly, the polymer-induced depletion interaction is too weak and short-ranged to induce a significant attraction between the protein molecules when the

(5)

(5a)

1 12/N + πz /3

Here, σ is the effective statistical segment length of the polymer chain with a monomer segment length of σ0 = 0.4 nm68 and N ≈ Mw/44 g mol−1 defines the number of segments per chain. Fluctuations in polymer concentration are spatially correlated over a distance described by the depletion thickness δdepl.58 R describes the polymer segment-to-protein distance of closest approach, which equals the protein radius under the assumption of additivity of the hard core diameters.67,69 Here, we set R ≈ RG,lys = 1.45 nm. Following previous works on the intermolecular interactions in lysozyme-PEG solutions,70,71 we make the assumption that the standard DLVO and depletion interactions are additive.72 Combining eqs 2 and 5, the overall effective pair-interaction potential, V*(r), of lysozyme molecules in the polymer solution is given by

i πz ji R zyji R zy −(r − 2R)/ δdeplyz zz, r > 2R jj zzjj zze Vdepl(r ) = −kBT lnjjjj1 + z 3 k r {k σ { k { l σ0 c PEG < c* o o o o o σ=o m i c y−1/8 o j PEG zz o c PEG ≥ c* o σ0jj z o n k c* {

(5c)

F


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between the strength of attraction, J, and the molecular weight, Mw, can be described by a power-law function (see Figure 5),

Figure 5. (a) Double-logarithmic representation of the strength of the attractive part, J, of 10% (w/v) lysozyme in 50 mM Bis-Tris solution (pH 7) at ambient pressure and 25 °C as a function of the PEGs molecular weight, Mw, and (b) depletion thickness, δdepl, for 10 and 20% (w/v) of the polymer. The corresponding power-law trend-lines J(cPEG < c*) ∝ α (Mw)m and J(cPEG < c*) ∝ μ (δdepl)k are depicted as well. Empty symbols visualize the J values for PEG concentrations exceeding c*.

J(cPEG < c*, Mw) ∝ α (Mw)m ∝ μ (δdepl(Mw, cPEG))k. Within experimental error, the increment dk/dcPEG (relation is not linear) was found to be essentially independent of the buffer composition (ionic strength), i.e., is not affected by the screening of the protein charge (see Figure SI 11). The reduced Coulomb repulsion is visible in an increase in magnitude, μ (shift of J to larger values). At elevated ionic strength, the addition of PEG to the buffer results in an even more repulsive protein−protein interaction. In contrast to the salt-free case, for both cPEG < c* and cPEG ≥ c*, the pure buffer value for J is never revisited in the protein−polymer mixtures. This increased effective repulsion may be rationalized by a modulation of the protein’s (preferential) hydration due to the additives (PEGs), which plays a prominent role when the mean spacing between the proteins is reduced and hydration repulsion becomes operative. At both buffer compositions, the depletion thickness, δ depl , levels off at high polymer concentrations before a large enough value is reached that could induce a significant attraction between the protein molecules (Figures 5b and SI 10f). The normalized second osmotic virial coefficient, b2*, calculated from eq 4 employing V*(r), is shown in Figure SI 9 and compared to the experimental data. For all polymer sizes and concentrations investigated in this work, the induced depletion interaction is predicted to be too weak and short ranged to induce an attractive (negative) value for the normalized second osmotic virial coefficient b2*. Its contribution to the protein−protein interaction is not strong enough to overcome the repulsive contributions significantly, which dominate the experimental b2 data. For higher molecular weights of the polymer, b2* shows a pronounced nonmonotonous behavior with increasing polymer concentration in form of an attractive minimum around the crossover concentration c*. Here, the competing effects of the decreasing mesh size ξb, reducing the range of the attractive depletion force, and the rising polymer osmotic pressure Π gradient lead to a trend reversal. 73 Moreover, around the overlap concentration, polymers tend to mutual avoidance to maintain coil conformational entropy.59 Consequently, the polymer-

Figure 4. (top half) Effective protein pair-interaction potential, V*(r), calculated from eq 6, as a function of polymer concentration for various PEG sizes, shown together with its contributing parts. VYbuffer and VHS are obtained by the refinement of the SAXS curves of polymer-free 10% (w/v) lysozyme +50 mM Bis-Tris aqueous solution (pH 7, T = 25 °C, p = 1 bar) carried out in the framework of the DLVO theory, just as VSCPEG‑buffer, which is solely modified for the polymer solution’s dielectrics. VdeplPEG‑buffer is calculated from eq 5 applying the PRISM model.67 (bottom half) Corresponding depletion thickness, δdepl(cPEG, Mw), calculated from eq 5d, as a function of polymer molecular weight for various polymer concentrations. Empty symbols visualize the δdepl values for PEG concentrations exceeding c*.

polymer’s blob size is much smaller than the lysozyme molecule (ξb ≪ RG,lys), and also the decrease of the depletion thickness, δdepl, with increasing polymer concentration is markedly emphasized for large PEGs (Figure 4, bottom half). For dilute polymer systems, δdepl scales with the polymer’s molecular weight (size) by a power law function. For higher polymer concentrations and thus increasing entanglement of the polymer chains, this dependency gradually breaks down at a particular molecular weight-specific concentration. For 5% (w/v) PEG, the predicted breakpoint in δdepl(c, Mw) is located at a molecular weight around 6000 g mol−1, for 10% (w/v) PEG around 2000 g mol−1, and for 20% (w/v) PEG around 600 g mol−1. At ambient pressure and 25 °C, for lysozyme−polymer mixtures below c* where ξb ≈ RG,PEG,0, the relationship G


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Macromolecules induced depletion attraction vanishes at high polymer concentrations, leading to the stabilization of the protein solution and the proteins maintain a separation distance large enough for the depletion forces to be damped out completely. The comparison of the theoretically predicted b2* with the experimentally derived values reveals that the protein−protein interactions in these polymer−protein mixtures might be modulated by the depletion mechanism, but the strong disagreement of the concentration dependence of the theoretical b2* and experimental b2 data for cPEG < c* suggests that additional (repulsive) forces must dominate the protein− protein interaction at short distances in the presence of polymer, thereby stabilizing the protein against strong depletion attraction. In the semidilute regime, the protein− protein interaction no longer depends on the polymers’ identity, only on the polymer concentration. The experimentally derived normalized second osmotic virial coefficient decreases rapidly beyond c* (Figure 7). 3.2.3. van der Waals Interactions. The van der Waals (vdW) attraction, contributing to the attractive Yukawian part of the DLVO potential is diminished by changes of the solution’s dielectric constant, εr(Mw, cPEG), and refractivity, ns(Mw, cPEG), in the presence of the polymers (see the SI for details). While for small PEG sizes the rise of ns (and decline of εr) with increasing polymer concentration increases significantly with increasing polymer molecular weight, the effect levels off for larger PEGs. In this case, the van der Waals interaction as represented by the Hamaker constant, A(εr, ns), scales with the polymer concentration, only.74 Since the magnitude of the repulsion brought about by the decrease of the Hamaker constant (e.g., Hsucrose = 2.15 kBT < HPEG10k = 2.18 kBT < HPEG200 = 2.25 kBT < Hbuffer = 2.84 kBT for ccrowder = 20% (w/v), see the SI) is much smaller than featured in the experimental data, and the trend observed with respect to the crowder identity at a given crowder concentration does not coincide with the experimental findings, we surmise that other mechanisms, such as enthalpic attractive polymer−protein interactions, volume exclusion due to strong preferential protein hydration or hydration repulsion, are responsible for the observed effect. 3.2.4. Protein−Polymer Interactions. Any attractive polymer−protein interaction is expected to translate into protein repulsion and steric stabilization at high polymer concentrations. Studies on the weak hydrophobic interactions between polyethylene glycol polymers and lysozyme molecules in aqueous solution revealed that the interactions increase with PEG concentration and molecular weight, which is mainly attributed to the change of hydrophilicity to amphiphilicity of PEG with increasing chain length.75 We find that smaller polymers render the effective pair-interaction more repulsive than the larger ones, which may be due to the effect that they can intercalate between neighboring protein molecules more easily. At a fixed polymer volume fraction, the decrease of the strength of the attractive interaction potential, J, is most pronounced for the small polymer molecular weights of 200 and 600 g mol−1 (Figures 6a and SI 10b). Hence, we presume that, next to the repulsive effect owing to hydration repulsion at very short protein distances, weak attractive protein− polymer interactions may be operative for small crowder molecules, rendering the net effect on the protein−protein interaction effectively more repulsive.76 3.2.5. Hydration Effects. Exclusion of compatible osmolytes such as sucrose from the vicinity of proteins are known to

Figure 6. (a) Strength of the attractive interaction, J, in 10% (w/v) lysozyme +50 mM (25 mM) Bis-Tris (pH 7) solution as a function of crowder (PEG, sucrose) concentration at ambient pressure and 25 °C. (b) Normalized second osmotic virial coefficient, b2, as a function of the polymer concentration, normalized to the overlap concentration, i.e., cPEG/c*. (c−e) Pressure dependence of J and b2 for 10% (w/v), 20% (w/v), and 30% (w/v) crowder of various sizes added to the buffer solution at 25 °C. Empty symbols visualize the J and b2 values for PEG concentrations exceeding c*.

result in an excess of water in the surface region of the protein and therefore in preferential hydration of the protein.77−79 The cosolute stabilizes the native state against unfolding, since the surface area of the native fold is smaller than of the denatured protein and therefore thermodynamically favorable. Polyethylene glycols have also been found to cause preferential hydration of proteins, which becomes more pronounced with increasing PEG molecular weight.76,80,81 Hence, a decrease of the intermolecular spacing of proteins can also be induced in the presence of polymer sizes not satisfying depletion conditions, where the dominating mechanism is not the depletion force but the excluded volume effect due to preferential hydration of the protein surface.82 Upon closest approach, where the hydration shells of the protein molecules start to overlap, strong hydration repulsion may be operative, however. 3.2.6. HHP Effects on the Protein−Protein Interaction. The results of the refinement of the high-pressure SAXS data for various PEG molecular weights and degrees of crowding in 10% (w/v) lysozyme solutions, buffered by 50 mM Bis-Tris H


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were determined in the presence of 1.25, 2.5 and 5% (w/v) PEG of various molecular weights for hydrostatic pressures up to 4.5 kbar (Figure 7). Within the limits of the polymer overlap

(pH 7), are displayed in Figure 6 (and Figure SI 10 for the case of elevated ionic strength (75 mM NaCl). As already reported for 10% (w/v) lysozyme dissolved in pure Bis-Tris buffer (pH 7),20,47 the application of pressures below ∼1.6 kbar results in a reduction of the mean intermolecular spacing, dlys, of the lysozyme molecules, accompanied by an increase of b2. Upon further pressurization, this trend is reversed and b2 drops well below the value found for ambient conditions as the mean intermolecular distance of the protein gradually increases. At ambient conditions, b2 reportedly changes sign from positive to negative values only at high solution ionic strengths, I, such as of 0.1 M NaCl,83 when the surface charges of the lysozyme molecule are effectively screened. Negative b2 values are also observed here for 75 mM NaCl at high pressure and in the presence of 10% (w/v) PEG 35k (Figure SI 10). In lower molecular weight PEGs ( 0.3.52 Even though all polymer sizes Mw > 600 g mol−1 meet this criterion for cPEG < c*, the magnitude of the attractive depletion interaction term seems to be too low to induce LLPS at room temperature at the employed concentration level of the polymer (1.25−5.0% (w/v) PEG). The phase transition temperature in the binary lysozyme-PEG mixtures is even shifted to lower values in comparison to the pure buffer system (Figure 7a,b). The effect can be quantified by a power-law trend line Tcloud(Mw, p = 1 bar, clys, cPEG < c*, I) ∝ η (Mw)s , describing the dependency of the LLPS temperature on the molecular weight at ambient pressure in the dilute polymer regime. In double-logarithmic representation, the slope, s, for 100 mg mL−1 lysozyme +1 M NaCl + 5% (w/v) PEG solution matches the one of the 200 mg mL−1 lysozyme +1 M NaCl + 2.5% (w/v) PEG system within experimental error. Clearly, the influence of lysozyme concentration on the polymer−polymer interaction and the polymer coil’s conformational properties cannot be neglected at this crowding level. When the proteins occupy less volume in the system, more polymer is needed to induce LLPS. Moreover, in pure lysozyme solutions of 25 mM Bis-Tris +0.5 M NaCl (pH 7), the phase transition temperature shifts to slightly lower values with a decrease of protein concentration from 20% to 10% (w/v), as found in previous works.5,6 Owing to the protein’s surface charge screening, an increase of the ionic strength results in a shift of the binodal to higher temperatures, by increasing of the magnitude η. For polymer concentrations cPEG < 5% (w/v), we are well below the threshold for polymer−polymer interpenetration, c*. Thus, the polymer can be regarded as single dispersed sphere of radius RG,PEG,0. In this diluted regime, the extrapolated power-law trend lines Tcloud ∝ γ (δdepl)b coincide, i.e. are independent of protein concentration and ionic strength, with the respective phase transition temperature found for the pure buffer value (Tcloud of 17.5 and 26 °C for 0.5 and 1 M NaCl, respectively) at ambient pressure for a screening length comparable to the hydrodynamic radius of the protein, Rlys = 1.72 nm (see Figure 7c,d).87 Figure 7e−g displays the cloud point temperatures of the ternary protein-PEG-water systems as a function of pressure in the p−T plane for three PEG concentrations and for various polymer molecular weights. The reentrant liquid−liquid phase transition at high pressures (HP-LLPS) found for dense polymer-free protein solutions at kbar pressures mirrors the increasing attractivity of the protein’s pair interaction upon pressurization, likely due to pressure-induced changes in the water network structure.5 The decrease of Tcloud in the presence of PEG observed at ambient pressure persists also at high hydrostatic pressures. Whereas the pressure dependence of the low-pressure (LP-LLPS) phase boundary, which may be largely due to a release of void-volume of the closed-packed protein system, changes little compared to the neat buffer system, the phase boundary of the HP-LLPS region is shifted markedly to higher pressures, most pronounced for small PEGs. Hence, the effect of the added polymer on the cloud point of the LLPS at ambient as well as elevated pressures is very similar to its effect on the strength, J, of the attractive part of the interaction potential. Enhanced by a decreasing effective size ratio of the single polymer chain to the protein and amplified by an increasing polymer concentration for cPEG < c*, the presence of the polymer renders the attractive part of the protein pair-interaction potential in protein−polymer mixtures

4. CONCLUSIONS In this work, the intermolecular interaction potential, V(r), governing the spatial distribution of lysozyme molecules in solution and the shape of its temperature and pressure dependent LLPS phase diagram have been analyzed. Employing more than 3 orders of magnitude of the polymer’s molecular weight, we explored the effect of macro- and nanomolecular crowding over a wide range of temperatures and pressures as well as crowder concentrations, crossing from the dilute to the semidilute polymer regime, thereby mimicking all scenarios encountered in the heterogeneous biological cell. In this sense, a synthetic linear polymer that forms networklike structures, such as PEG, mimics aspects of a eukaryotic cell, such as the dynamic cytoskeleton network. We find that the impact of crowder concentration on the mean spacing between protein molecules depends markedly on the crowder size. The strongest effect is observed for smallsized PEG molecules and sucrose, leading to a marked decrease of the mean intermolecular spacing of the protein molecules with increasing crowder concentration. Interestingly, the effect levels off at intermolecular distances where the proteins’ second hydration shells start to penetrate each other. Conversely, increasing the polymer concentration beyond the polymer-size specific threshold (cPEG/c* ≥ 1), where the polymer solution structure changes from single dispersed polymers to a strongly entangled polymer network, results in recovery of the system where the proteins eventually maintain a separation distance comparable to the polymer-free system. Further, the net effect of polymer size and concentration on the protein−protein interaction potential, quantified by the protein’s second osmotic virial coefficient, b2, is strongly correlated to the phase boundaries of the liquid−liquid phase region in protein−polymer mixtures in the dilute polymer regime (cPEG/c* < 1). Reinforced by a decreasing effective size ratio of the polymer chain to the protein and amplified by an increasing polymer concentration, the presence of the polymer renders the proteins’ pair-interaction more repulsive, leading to an increase of b2. Accordingly, the cloud point temperature, Tcloud, is lowered and the entry of the high-pressure-LLPS region shifted to higher pressures. At a given polymer concentration (for cPEG/c* < 1) and ambient pressure, the impact of the polymer molecular weight (size) on both the strength, J, of the attractive part of the intermolecular interaction potential and Tcloud exhibits a power law behavior, similar to the one reported for the polymer’s radius of gyration RG,PEG,0(Mw). This indicates that (steric) excluded volume and depletion forces, which scale with polymer size, are able to strongly modulate protein pair-interactions. Invoking a nonspecific depletion interaction term on top of the DLVO description for V(r), we find the depletion-induced attraction between the protein molecules being reinforced by an increased polymer concentration, which levels off due to a decreasing range of the depletion interaction as polymer network structures emerge at cPEG/c* ≥ 1. However, especially for cPEG/c* < 1, we report a strong disagreement between the predicted and experimental b2 values. This suggests that additional non-DLVO repulsive forces must be operative, controlling the intermolecular protein−protein interactions at short distances, which stabilizes the densely packed protein solution also against depletion-induced aggregation. Hydration J


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(bl8) for assistance during beam times. Furthermore, we thank M. A. Schroer for fruitful discussions and A. Ott, T. Arto and , M. Büyükasik for experimental support during the turbidity and density measurements. Financial support by the Cluster of Excellence RESOLV (EXC 1069) funded by the Deutsche Forschungsgemeinschaft is gratefully acknowledged (Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy, EXC-2033, Projektnummer 390677874).

repulsion upon closest approach of protein molecules, when their hydration spheres start to overlap, is very likely to become important here. However, attractive protein-PEG interactions owing, e.g. to hydrophobic interactions between lysozyme and crowders, may be important as well, and this effect would in particular operate when the small PEG molecules are able to reside between protein molecules. Pressure modulation is a convenient means to fine-tune intermolecular distances and explore interaction forces. In polymer-free solution, the approach of lysozyme molecules upon compression and the concomitant increase of b2 level off around ∼1.6 kbar, most likely due to structural changes of the water H-bond network, eventually resulting in a trend reversal upon further pressurization.20 This nonmonotonous pressure dependent behavior of the proteins’ mean spacing and pairinteraction is affected by PEG-induced depletion forces, which gradually decrease as the depletion thickness decreases owing to the decreasing polymer size upon compression, however. Hence, pressurization reduces the protein distance, but also the depletion thickness of the crowder, i.e., HHP counteracts the depletion interaction. In this sense, high hydrostatic pressures as encountered in the deep sea where organisms thrive at pressures even up to 1000 bar, may alleviate macromolecular crowder-induced attractive forces, and thereby help prevent a too close approach of protein molecules upon compression that could cause protein aggregation. Finally, owing to the strong correlation of the LLPS with the sold-liquid phase transition,86 i.e., with protein crystallization, we envisage that solution conditions and the kinetics for protein nucleation and crystal growth may be optimized by modulation of the solution properties using both variables, PEG and HHP. Hydrostatic pressure is a powerful but so far rather unexplored tool in controlling and fine-tuning protein− protein distances and hence crystal growth next to the excluded volume (osmotic pressure) effect imposed by PEGs.84,88

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S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.macromol.8b02476. Materials and methods and additional figures (PDF)

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REFERENCES

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Roland Winter: 0000-0002-3512-6928 Author Contributions

All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the European Synchrotron Radiation Facility (ESRF), the Diamond Light Source (DLS), Petra III (DESY), and the Dortmunder Elektronen Testspeicherringanlage (DELTA) for providing synchrotron radiation, and J. Möller (ID02), A. Smith (I22), W. Ohm (P03) and R. Wagner K


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