On the Aggregation and Nucleation Mechanism of the Monoclonal Antibody Anti-CD20 Near Liquid-Liquid Phase Separation (LLPS)

The crystallization of Anti-CD20, a full-length monoclonal antibody, has been studied in the PEG400/Na2SO4/Water system near Liquid-Liquid Phase Separation (LLPS) conditions by both sitting-drop vapour diffusion and batch methods. In order to understand the Anti-CD20 crystallization propensity in the solvent system of different compositions, we investigated some measurable parameters, normally used to assess protein conformational and colloidal stability in solution, with the aim to understand the aggregation mechanism of this complex biomacromolecule. We propose that under crystallization conditions a minor population of specifically aggregated protein molecules are present. While this minor species hardly contributes to the measured average solution behaviour, it induces and promotes crystal formation. The existence of this minor species is the result of the LLPS occurring concomitantly under crystallization conditions.

The Z-potential is another indicator of colloidal stability, which measures the magnitude of the electrostatic or charge repulsion/attraction between particles 17 .It is related to the surface charge of the molecules, the adsorbed layer at the interface and the nature and composition of the surrounding environment.A large Z-potential value (|Z-potential| >30 mV) can be considered an indicator of colloidal stability.Recently, the use of the interaction parameter k d has been also suggested as a more high-throughput means to quantify protein-protein interactions 18,19 .
In this work, we focus on the relationships between the crystallization propensity of Anti-CD20 in the Na 2 SO 4 /PEG400 solvent system of different compositions and its relation with some measurable parameters normally used to assess protein conformational and colloidal stability in solution, with the aim to understand the aggregation mechanism of this complex biomacromolecule.Anti-CD20 is a full-length monoclonal antibody (mAb) and it is a therapeutic protein extensively used for treatment of chronic lymphocytic leukaemia and non-Hodgkin's lymphoma, which is commercialized with the brand name of Rituxan or Mabthera.Here, the crystallization of this biomolecule has been observed in a PEG400/Na 2 SO 4 /Water system near Liquid-Liquid Phase Separation (LLPS) conditions by both vapour diffusion and batch methods.LLPS is a very common phenomena for monoclonal antibodies 20 and is of great interest because the factors which induce the separation of protein solutions into coexisting protein-poor and protein-rich phases are observed to play a central role in protein interaction and crystallization 21 .For several protein/PEG or protein/salt systems both the LLPS and the aggregation propensity of proteins in solution have been shown to coincide with net attractive interactions between molecules [22][23][24] .Monte Carlo simulations performed on systems that undergo phase separation demonstrated that the interactions between the proteins fall into the short-range regime and are strongly anisotropic 25 .Over time, the anisotropic interactions may be responsible for the evolution of the system from the phase separation to reversible aggregation conditions.In this situation, the LLPS has been speculated to behave as a metastable state towards nucleation [26][27][28] .In fact, the pathway for the formation of crystal nuclei drastically changes near the metastable low density-high density liquid region coexistence, with the free-energy barrier for crystal nucleation being strongly reduced.In this scenario, the crystal nucleation rate increases by many orders of magnitude over that predicted from classical nucleation theory 28 , thus generating a fast and diffuse crystallization that often results in poor-quality crystals.
The results of this investigation allowed us to gain further insights into the mechanism governing the nucleation-crystallization of a complex system such as the Anti-CD20 mAb.
Protocols suitable for crystallizing Anti-CD20 reproducibly by vapour diffusion and batch methods were developed in previous works 29,30 .Precipitant solutions were made by dissolving sodium sulphate in the HEPES buffer solution containing PEG400 at the proper concentration.All solutions were filtered through a 0.22 µm Anotop 10 Filter Unit (Whatman).In sitting-drop vapour diffusion crystallization experiments, drops made of 10 μL of precipitant solution and 10 μL of protein solutions were equilibrated in a sealed well against 1 mL of a hypertonic solution of MgCl 2 •6H 2 O 30 wt.% used as reservoir.For the batch crystallization experiments, a volume of protein solutions having a certain initial concentration was mixed with the required volume of precipitant solution to obtain a supersaturated solution of known composition (final volume 1 mL).All crystallization experiments were performed in a vibration-free refrigerator at 20 °C.
Analysis of Anti-CD20 crystals.Crystals obtained from crystallization experiments were observed using an optical microscope (Eclipse LV 100ND, Nikon Instruments, Italy) equipped with a video camera, separated from the mother liquor by using a centrifuge (MiniSpin Plus Eppendorf model IVD) and centrifuge tubes (0.22 µm pore size) and extensively washed.Washing solution was made by 0.1 M HEPES, Na 2 SO 4 and PEG400 whose concentration was optimized to avoid crystal solubilisation according to standard procedures.Washed crystals were dissolved by using 0.01 M TRIS-HCl, NaCl 0.15 M, pH 8.0 and analysed by UV spectrophotometry (Lambda EZ201, Perkin Elmer) to estimate protein concentration.

Circular dichroism (CD) measurements.
The far-UV CD spectra of Anti-CD20 under initial conditions, after buffer exchange with HEPES 0.1 M, and after mixing with the precipitant solution, were recorded between 200 and 300 nm on a Chirascan CD spectrometer (Applied Photophysics, UK) at 20 °C with a 1 nm bandwidth resolution and current time-per-point of 3 s. 100 μL of mAbs solution were added in a 0.1 mm path-length quartz cuvette that was placed in the spectrophotometer.Typically, three scans were recorded and baseline spectra were subtracted from each spectrum.Data were processed using Applied Photophysics Chirascan Viewer.
Melting point and Z-potential assessment by DLS.Thermal stability (melting temperature, T m ) of protein solutions was assessed by a Zetasizer Nano ZS instrument (Malvern) equipped with a 4 mW He-Ne laser at 632.8 nm and a detector placed at 173° in agreement to the proprietary NIBS (Non Invasive Back Scatter) technology.Samples were placed in quartz cuvettes (1 cm path-length), heated by a Peltier module and the average hydrodynamic diameter was measured as a function of temperature from 20 °C to 90 °C (temperature increment 0.5 °C).DLS can monitor the thermal denaturation of proteins, which leads to irreversible loss of their structure and function as the protein unfolds.When the average protein size is observed by DLS versus temperature, one will observe a significant increase in the average protein size for temperatures larger than the aggregation point, which is generally assumed as the onset of protein melting point.
For the Z-potential evaluations, the appropriate ratios of protein and buffer solutions were placed in disposable folded capillary cells (DTS 1070, Malvern), and then inserted into the Zetasizer instrument.The Z-potential was measured by laser Doppler micro-electrophoresis.Briefly, an electric field was applied to the protein solution and consequently each molecule moved with a velocity related to its Z-potential.The velocity was measured using a laser interferometric technique (M3-Phase analysis light scattering), which allowed the calculation of the electrophoretic mobility, and from this, the average Z-potential and Z-potential distribution.
Light scattering measurements.Static and dynamic light scattering measurements were performed on protein solution samples with a concentration between 0.1 and 5.0 mg mL −1 in different crystallization cocktails.The Anti-CD20 concentration in these solutions was checked by measurement of the absorbance at 280 nm.All the solutions were filtered on a 0.22 µm filter (Anotop 10, Whatman) before measurement.The samples were placed in quartz ultra-low volume cuvettes (ZEN 2112, optical path 3 mm, Malvern) to measure with the Zetasizer Nano ZS instrument (Malvern) in static mode for the second virial coefficient B 22 or dynamic mode for the protein diffusion coefficient D m .The light intensity and its time autocorrelation function were measured at 173° scattering angle.All measurements were performed at 20 °C after 2 min of equilibration using automatic time settings.
The Debye plots were generated by using Debye's light scattering equation: where R θ is the excess Rayleigh ratio of the protein in a solution with a protein concentration C and M W is the average molecular weight of the protein.K is the optical constant and is defined as: where n is the solvent refractive index, dn/dc is the refractive index increment, λ is the wavelength of the incident light, and N A is Avogadro's number.The second virial coefficient B 22 [mL mol g −2 ] was obtained from the slope of the linear Debye plot of KC/R θ versus protein concentration C. The static light scattering results for B 22 were accepted if the following criteria were satisfied: 1. Signal to noise ratio >130%, where noise is solvent kcounts; 2. Increasing trend for signal kcounts vs. protein concentration.
The interaction parameter k d [mL mg −1 ] and the self-diffusion coefficient D s [m 2 s −1 ] were determined by using linear fitting of the protein diffusion coefficient D m , determined from the dynamic light scattering measurements, plotted against the protein concentration C [mg mL −1 ], using the following Eq. 3 31 : The determined interaction parameter k d can be interpreted as the difference between a thermodynamic term related to the product 2B 22 •M W and a hydrodynamic term (ξ 1 + ν): where ξ 1 is obtained from the virial expansion of the concentration-dependent frictional coefficient and ν is the solvent viscosity.Solutions that showed turbidity, indicating phase separation and crystallization/precipitation, were not used for measurements.

Protein partitioning measurements.
Anti-CD20 repartition between aqueous and PEG phases has been estimated by the method described by Kress et al. 32 .A solution (5 mL) containing Na 2 SO 4 1.1 M (13.54 wt.%) and PEG400 10.46% V/V (10.22 wt.%) in HEPES 0.1 M at pH 7.4, was added with 200 μL Anti-CD20 solution 10.3 mg mL −1 in the same buffer.After vigorous stirring for 5 minutes by vortex, the mixture has been left to rest overnight.The concentration of the protein in the two separated phases visually detected and in presence of excess of precipitated protein, was then assessed by UV spectrophotometry at 280 nm.

Results and discussion
Anti-CD20 crystallization and crystals analysis.Anti-CD20 needle-like crystals (Fig. 1a) appear by sitting-drop vapour diffusion crystallization experiments using a 1:1 volume ratio mixture of a 20 mg mL −1 protein solution in HEPES buffer 0.1 M at pH 7.4 and a precipitant solution containing PEG400 9.6% V/V (9.4 wt.%) and Na 2 SO 4 0.86 M (10.6 wt.%) in the same buffer.Therefore, the initial composition of the drop in the vapour diffusion tests corresponds to 10 mg mL −1 Anti-CD20, 4.8% V/V PEG400, 0.43 M Na 2 SO 4 in 0.1 M HEPES at a pH of 7.4 and is shown by the diamond symbol in Fig. 2. The crystals appear when the volume of the drop is nearly halved with respect to its initial volume.Accordingly, the final concentration of the components in the crystallizing drops is almost doubled that compared to the initial compositions and it is indicated by the pentagon symbol of Fig. 2.
Batch experiments in similar solution composition as that for crystallizing drops in the vapour diffusion tests (the term "similar" is used since the exact composition of the droplet at the crystallization point under equilibration with the reservoir solution it is not known), give also rise to crystals.Therefore, the batch working point coincides with the final conditions of the vapour diffusion tests.Since the batch composition does not vary with time, due to the absence of solvent evaporation, it is evident that the solution is supersaturated immediately upon mixing the protein and precipitant solutions, which results in a shorter crystallization time (12-18 h) than that observed with the sitting drop set up (36-48 h).
The UV-Vis and DLS measurements of washed and dissolved crystals confirmed their protein nature.All the analysed samples showed an intense band centred at 280 nm, typical of proteins absorption.The size distribution analysis by intensities show a single peak near 12 nm, size expected for Anti-CD20 protein molecules 33 , and a polidispersity <20%, indicating a high monodispersity.
Liquid-Liquid Phase Separation (LLPS) is observed nearly simultaneously with, or just prior to, crystals appearance (Fig. 1b) both in the vapour diffusion and batch crystallization trials.In accordance with other mAbs crystallization studies reported in literature 20,34,35 , also here it appears that the LLPS is a key step in Anti-CD20 crystallization.
Crystallization trials, aiming to investigate the effect of precipitant solution composition on crystal quality have been also performed by changing the starting amount of PEG400 and/or Na 2 SO 4 .As expected, the shape, size and density of crystals (number of crystals per unity of volume) are found to depend on buffer composition, initial protein concentration and crystallization method (sitting drop or batch).All these parameters have also shown to impact on the time required to observe crystallization.Table 1 shows the effect of the salt concentration on the crystal appearance for the batch experiments.Needles with a size of nearly 20 µm are the largest crystals obtained for starting solutions with 9.6% V/V PEG400 and 0.70-0.80M Na 2 SO 4 .A further increase in Na 2 SO 4 concentration produces a faster and massive protein nucleation in less than 24 hours and crystals of smaller size (<10 µm) with a spherulite-like morphology appear.For a Na 2 SO 4 concentration of 0.9 M or larger, upon mixing the solution immediately turns opalescent due to a macroscopic LLPS in the solution, followed by a rapid protein precipitation as gel beads.On the opposite side, for the lowest amount of salt (Na 2 SO 4 ≤ 0.65 M), the solutions remain clear for months.
Figure 2 shows the experimental state diagram for the system PEG400/Na 2 SO 4 /H 2 O at 20 °C indicating the loci of the points related to solution compositions used for batch crystallization tests (circles) of Table 1, together with the starting (diamond) and ending (pentagon) solution compositions in vapour diffusion tests.; solid line: asymptotic fitting to tie-lines data from ref. 36 ; circles: batch crystallization conditions reported in Table 1; diamond: starting solution composition in vapour diffusion tests; pentagon: ending solution composition in vapour diffusion tests; triangles: measurements points for B 22 ; dotted line: shifted binodal curve in the presence of Anti-CD20 protein.Solution composition is expressed as weight fraction (wt.).  1. Mixed solution compositions, crystallization behaviour and crystal appearance in the batch crystallization experiments using an Anti-CD20 concentration 20 mg mL −1 , 9.6% V/V PEG400 and 100 mM HEPES buffer at a pH of 7.4.
SLS/DLS analysis.The protein stability in several formulation buffers but without precipitating agents (PEG and/or Na 2 SO 4 ), was assessed by DLS, resulting in values for the melting point and Z-potential.As reported in Table 2, all samples are characterized by similar values of melting point, Z-potential, intensity weighted mean hydrodynamic size Z avg and polydispersion index (PDI).All protein samples show low positive values of the Z-potential, indicating a reduced colloidal stability in the various buffer solutions.Nevertheless, due to a PDI close to 0.1, all samples can be considered monodisperse.No significant variations were observed in the sample aggregation state over time in the range 12-24 h.Accordingly, further SLS/DLS studies were performed by using HEPES as formulation buffer since it was used in previously published crystallization protocols 30 .
To study the aggregation propensity on Anti-CD20 in HEPES buffer and in various PEG400/Na 2 SO 4 solution compositions, SLS and DLS measurements were performed on freshly prepared samples allowing to determine the second virial coefficient B 22 and the interaction parameter k d , respectively.The value of KC/R θ was determined as a function of protein concentration, ranging from 0.1 to 5.0 mg mL −1 , by SLS.Results were used to evidence the combined effect of PEG400 and Na 2 SO 4 on Anti-CD20 colloidal stability and to compare these results with effective crystallization outcomes.
It is well known that the addition of salts can cause an electrostatic double layer around the protein surface charges, which involves a shielding and the reduction of repulsive interactions among macromolecules.Furthermore, the salts ions compete with the protein for water molecules and dehydrate the protein (salting out effect 37 ), thus inducing aggregation by mainly electrostatic and hydrophobic interactions.On the other side, polymers such as PEG bring the protein molecules together due to preferential interactions and osmotic potential 38 .Accordingly, the addition of PEG400 or Na 2 SO 4 to Anti-CD20 solutions is expected to increase the aggregation aptitude of the protein and facilitate crystallization, as experimentally observed, e.g., in batch crystallization tests of Table 1.However, as displayed in Figs. 3 and 4, for increasing amounts of PEG or Na 2 SO 4 when both components are present in solution, the B 22 moves towards larger positive values, theoretically indicative of an increase in repulsive interactions.Furthermore, effective Anti-CD20 crystallization conditions seems to lay outside the crystallization slot defined by George and Wilson 15 .
Both Figs. 3 and 4 show that the combined effect of PEG400 and Na 2 SO 4 has a noteworthy consequence on the B 22 value.For instance, for the solution containing 0.48 M Na 2 SO 4 in absence of PEG, a B 22 value of −8.9 × 10 −4 mL mol g −2 is obtained (Fig. 3) that is slightly below the crystallization slot.However, when adding PEG400 to the solution while keeping salt concentration constant, B 22 steeply increases through the crystallization window towards positive values already at 3% V/V of PEG.The B 22 value for the solution containing 4.8% V/V PEG400 in absence of Na 2 SO 4 is found to be slightly positive (B 22 = 1.8 × 10 −4 mL mol g −2 ), becoming negative (B 22 = −2.26× 10 −4 mL mol g −2 ) when increasing PEG400 up to x PEG = 9.6% V/V without Na 2 SO 4 (Fig. 4).This is in agreement with results from Ahamed et al. 39 , who observed the reduction in solubility for a mAb for increasing amounts of PEG400.Nevertheless, when salt is added to the solution ( ), the virial coefficient rises steeply with the salt concentration.These observations clearly indicate that a different effect on the measured value of B 22 takes place when PEG400 and Na 2 SO 4 are combined together, compared to the cases when they are used separately.
It is expected that protein-protein interactions at a pH substantially below or above the pI are repulsive, while at a pH near the pI they become increasingly attractive due to the overall neutral charge of the protein.However, the actual pI of biomolecules might change with ionic environment, and generally decreases at different extents with increasing ionic strength, depending on the nature of the counter-ion 41,42 .It is speculated that in the presence of 0.43 M Na 2 SO 4 , PEG400 4.8% V/V and 0.1 M HEPES, the effective pI of Anti-CD20 is around 8.0.Therefore, for pH < 8.0, the slightly positive B 22 values are most likely due to partially screening of the net positive electrostatic charges of protein molecules, while at pH = 8.0, where the net charge becomes null, the net resultant  Since solution composition strongly affects protein stability and aggregate formation, the Na 2 SO 4 concentration dependence of B 22 was also investigated at higher PEG and salt concentrations, thus reaching compositions close to that used for crystallization experiments of Table 1.Correlation between B 22 and Na 2 SO 4 concentration is shown in Fig. 6, confirming an increasing trend similar to that observed for lower concentrations of Fig. 4 also in this case.
In Fig. 6 it can be seen that the B 22 values are negative (attractive interactions) for Na 2 SO 4 concentration ranging from 0.55 to 0.6 M, corresponding to conditions in Table 1 that give clear solutions, while they become positive (repulsive interactions) when the salt concentration is further increased up to 0.9 M. Within the crystallization window, i.e.Na 2 SO 4 ranging from 0.7 to 0.86 M, the B 22 values range from 3.2 × 10 −4 to 5.7 × 10 −4 mL mol g −2 .This would be theoretically indicative of the absence of attractive colloidal interactions, in opposition to the results of the crystallization tests.
DLS measurements were then used to determine the interaction parameter k d .Generally, k d and B 22 display a qualitatively similar trend 43 .However, looking at the behaviour of the interaction parameter k d in the crystallization range of Fig. 6, negative values are found for x PEG = 9.6% V/V and sodium sulfate 0.55-0.80M, with slight variations within this range.Generally, a negative value of k d implies the existence of attractive interactions between protein molecules which slow down their diffusion in solution 44 .Since under the same conditions B 22 is negative only for Na 2 SO 4 < 0.6 M and then increases up to 1.23-4.94× 10 −4 mL mol g −2 in the salt concentration range 0.6-0.8M, this indicates that underlying attractive interactions do not have a thermodynamic origin of colloidal nature.We can instead conclude that these interactions result from the hydrodynamic effects included in the second term of Eq. 4 45 , most likely due to the increase of solution viscosity (from 1.949 cP in the PEG400 9.6% V/V solution without salt to 2.546 cP for PEG400 9.6% V/V and Na 2 SO 4 0.9 M).Nevertheless, as for B 22 , the increasing trend of k d with the concentration of Na 2 SO 4 does not comply with the outcome of crystallization tests.In fact, the increase of Na 2 SO 4 concentration at values larger than 0.8 M gives rise to a theoretically significant increase of the strength in protein-protein repulsions, according to measured B 22 , values that are exacerbated near the LLPS region, while crystals are obtained in such conditions.
From the observed trends of B 22 and k d , we can conclude that neither PEG400 nor Na 2 SO 4 act as conventional precipitants for Anti-CD20 when used together since, on average, Anti-CD20 monomers apparently repel one another.Nevertheless, this evidently contradicts the experimental outcomes of crystallization tests.The B 22 values are negative (attractive interactions) in formulations that remain clears for months, whereas positive values, corresponding theoretically to net repulsive interactions, have been found for the best-performing crystallizing or either in precipitating conditions.
Considering the possible variations in their structure, morphology, size, surface charge and chemistry, proteins definitely represent one of the most complex colloidal systems.Several mechanisms could lead to molecular aggregation in solution and it is not excluded that more than one is active in certain conditions.Therefore, it is not surprising that B 22 does not always reflect the aggregation propensities of proteins in a given formulation.Several papers can be found in literature reporting discrepancies between B 22 and the susceptibility to aggregation of structurally complex macromolecules, like monoclonal antibodies 43,46 .Crystallizing conditions with positive B 22 values were found for a mAb molecule with PEG400 by Rakel et al. 35 .This behaviour has been ascribed to the ambivalent character of PEG400 as precipitant and stabilizer 35,47 .Kress et al. 48observed the decrease in B 22 of an immunoglobulin G (IgG) when increasing PEG2000, sodium citrate and NaCl solute concentration, if used separately.However, the mutual effect of PEG and salts resulted in a shift of B 22 from negative to almost neutral values when increasing the NaCl amount if used together 32 .This behaviour has been explained by a solubilizing effect of IgG in PEG2000 induced by NaCl until a maximum salt concentration.Exceeding this NaCl value, a solid-liquid equilibrium, due to protein precipitation, was observed.Herhut et al. 49 1) are highlighted by the dotted vertical lines.The solid lines are guides for the eyes.D-xylose ketol-isomerase (172.3 kDa) with ammonium sulphate and PEG12000 and PEG2000, respectively.They observed the initial decrease in B 22 at low PEG concentration, passing through a minimum and then increasing for higher PEG concentrations.This behaviour has been explained by considering that polymer-induced interactions are not solely attractive over the whole polymer concentration range.Normally, polymer chains behave as coil-inducing attractive interactions between protein molecules at low-polymer concentration.However, at high polymer concentration, flexible coils elongate and enter space between the proteins, so that repulsive interaction are induced 50,51 .This explanation has been also confirmed by molecular dynamic simulations at different polymer concentration by Cao et al. 52 .
It has also been reported that conformational stability plays an important role in aggregation propensity, with partially unfolded conformational intermediates being responsible of aggregate formation 9 .In this case, the B 22 value is unlikely to correlate with long-term aggregation because the structurally perturbed state susceptible to aggregation could be present in a small fraction of molecules compared to the native species 46 .Aiming to shed light on this aspect, protein structure in solution has been investigated in the present work.
protein structure in the solution.On the bases of the results above, measurements of melting temperature (T m ) for several solution compositions, including x PEG = 9.6% V/V and Na 2 SO 4 at various concentrations, and Circular Dichroism (CD) in selected formulations, were performed aiming to investigate conformational stability of Anti-CD20.Results show slight variations of the melting points: T m = 67.0,67.5, 68.0, and 67.5 ± 0.5 °C for 0.55, 0.65, 0.75, and 0.85 M Na 2 SO 4 , respectively, confirming that samples, on average, share similar water activity according to the Wyman-Tanford equation 53 .
Circular Dichroism spectra of protein solutions give information on the secondary structure, folding properties and conformational variation of the proteins 54 .The general shape of the spectrum of the provided Anti-CD20 solution (Fig. 7, initial conditions) corresponds to the expected spectra for Anti-CD20, as it shows the typical shape of a monoclonal antibody with a minimum around 220 nm and a maximum around 200 nm, suggesting a secondary structure dominated by β-sheet motif 54 .Moreover, these spectra correspond to the CD-spectra of Anti-CD20 from literature 55 .
These spectra show that the protein is well folded in every buffer, i.e. the 3D-structure of Anti-CD20 is preserved under all conditions tested.However, the maximum ellipticity (around 200 nm) is much higher after the buffer exchange (red and green spectra in Fig. 7) than in the initial buffer (blue spectrum), while ellipticity at other wavelengths is similar in every buffer.This suggest that the β-sheet motifs of the mAbs are favoured and stabilized in the new HEPES buffer, in comparison to the initial buffer (0.025 M sodium citrate at pH 6.5 and 0.154 M sodium chloride).
There is no significant difference in the far-UV CD spectra of Anti-CD20 before (Fig. 7, red spectrum) and after the addition of Na 2 SO 4 and PEG400 as precipitating agents (Fig. 7, green spectrum), although a small shift can be observed, showing slight changes in the 3D-structure.The main difference between these spectra is around 230 nm, but the peak is quite narrow and this wavelength does not correspond to any typical feature of protein structure.Therefore, the difference could be due to Na 2 SO 4 or PEG400 absorbance or might be due to some noise.It should be noted, though, that the crystallization solution had to be diluted in order to enable CD measurement.Since the spectra before and after the concentrated crystallization conditions are the same, it can be concluded that the concentrated crystallization conditions do not alter the secondary structure of the protein.
The Anti-CD20 secondary structure is preserved after centrifugation and addition of the precipitating agents, as the typical β-sheet motif appears clearly in the spectrum (Fig. 7, green spectrum).Moreover, this secondary structure seems to be favoured in the crystallization buffer, meaning that the 0.1 M HEPES at pH 7.4 buffer promotes Anti-CD20 crystallization by making the secondary structure less flexible.However, no clear effect of Na 2 SO 4 or PEG400 on the Anti-CD20 secondary structure is visible.

The role of LLPS in Anti-CD20 crystallization.
A complementary scenario can be envisioned when considering LLPS phenomena observed concurrently or just prior of Anti-CD20 crystallization.
For simple protein/salts or protein/PEG systems, it has been often reported that the B 22 value can be used as a predictor of LLPS formation, since weak protein-protein interactions, in general hydrophobic in nature or even limited to specific protein chain sequences, are at the origin of the phase separation 22 .However, our results seem to suggest that the LLPS (observed just prior or at the point of protein crystallization) proceeds without attractive interactions, since B 22 is negative when a mono-phase system is observed while it turns positive as approaching the liquid phase separation and crystals formation.
It could be argued that, in our complex mixture that includes several components, the B 22 values fail to predict the experimentally observed crystallization since it may be rather related to the polymer-salt phase separation that can occur without protein.The liquid-liquid separation of PEG/salt aqueous solutions is a fundamentally different phenomenon from PEG/protein or salt/protein LLPS, which originate by a combination of hydrophobic and salting-out effects, whose origin has been attributed to the different conformations of the PEG polymer chain in aqueous solution and their respective hydration 24 .Actually, the PEG400/Na 2 SO 4 /H 2 O system is known to generate aqueous two-phase systems 36,56,57 .Figure 2 displays the experimental binodal curve together with liquid-liquid equilibrium tie-lines data for PEG400 + Na 2 SO 4 + H 2 O system at 293.15 K (the temperature used in this work for crystallization experiments and SLS/DLS measurements) 36 .
Concerning the specific system studied in this work, for a protein concentration of 20 mg mL −1 and a PEG400 content of 9.6% V/V (9.4 wt.%), phase separation is observed for salt concentrations ≥0.7 M (≥8.6 wt.%) (crystallization points of Table 1 and dark circles in Fig. 2), that is quite far from both binodal curve.However, the presence of the protein can reduce the amount of salt needed for observing LLPS in the multicomponent PEG/ salt/protein/water systems 24 .Consequently, it cannot be excluded that the effective binodal curve for PEG/salt LLPS is shifted down to conditions corresponding to the observed crystallization points, in a region of poor solvent conditions, thus giving a decisive contribute to the aggregation/crystallization behaviour of Anti-CD20.
Figure 8 shows the change in turbidity (Residual Intensity) for a solution containing PEG400 9.6% V/V in 0.1 M HEPES at pH 7.4 and increasing amount of Na 2 SO 4 .It is observed that, in absence of the Anti-CD20, a sharp increase in solution turbidity is observed for salt concentration >1.1 M (>13.5 wt.%), that is very close to the binodal curve reported in Fig. 2 for the PEG400 + Na 2 SO 4 + H 2 O system.Since in the presence of the protein turbidity due to liquid-liquid phase separation is observed for salt concentration larger than 0.65 M for the same amount of PEG, this proves the shift of LLPS region towards lower values of PEG and/or salt components when Anti-CD20 is present in the solution.
It is worth noting that B 22 measurements reported in Figs. 3 and 4 have been made in a region of Fig. 2 where LLPS (and crystallization) are not observed (triangles in the left-bottom side of the figure).This means that PEG/ salt LLPS is not responsible for the contradiction between B 22 measurements and the outcome of crystallization trials, but rather the intrinsic complexity of the system makes ineffective the measurement of the osmotic coefficient as predictor parameter for crystallization conditions.
According to our results, it can be proposed that PEG/salt LLPS causes the preferential partitioning of proteins in a specific salt-or PEG-rich phase.In general, the affinity of the protein for the polymeric component, due to hydrophobic interactions, favours the protein concentration in the PEG-rich phase 39,58 .This is particularly true for PEG400, which is a low molecular weight polymer and, therefore, its size exclusion effects on proteins Figure 7. Far-UV CD spectra of Anti-CD20 under initial conditions (blue spectra, mAbs concentration 9.95 mg mL −1 in stock buffer), after buffer exchange with HEPES 0.1 M pH 7.4 (red spectra, mAb concentration 100 mg/mL in crystallization buffer) and after salt mixing (green spectra, mAb concentration 60 mg/mL in crystallization buffer and with 0.9 M Na 2 SO 4 and 9.6% V/V PEG400).are negligible while the dominant factor in the separation is the salting out effect, produced by the sulphate, which causes the protein to migrate to the PEG-rich phase.This effect has been confirmed by measurements on Anti-CD20 partitioning, showing that more than 90% of the solution protein migrates in the PEG-rich phase in the protein-saturated Anti-CD20/PEG400/Na 2 SO 4 /HEPES/H 2 O mixture displaying phase separation.
In such conditions, during LLPS, the Anti-CD20 concentrates in droplets that have a density higher than the average density of the whole system thus generating a much higher supersaturation.When the protein concentration exceeds a certain limit, precipitation at the interface is observed and the precipitated protein is in equilibrium with the protein solubilised in each phase 59 .For particularly high Anti-CD20 (>30 mg mL −1 or PEG/salt concentrations (i.e.PEG400 9.4 wt.% and Na 2 SO 4 ≥ 11.1 wt.%), these droplets look not to be as liquid, having instead the appearance of gel beads.Protein crystals initiate to nucleate and grow near the boundary of the most protein-concentrated droplets (Fig. 9), suggesting that the droplet interface participates in the nucleation mechanism 60 .Subsequently, crystals appear within the bulk of the droplets, which spread and coalesce.Many droplets disappear as crystal growth proceeds, suggesting that a continuous exchange exists between the droplets and the surrounding medium.
Experimental observations clearly indicate the important role of LLPS and of the established liquid-liquid interface in inducing Anti-CD20 nucleation, even in absence of underlying net attractive interaction between proteins.It is likely that only protein molecules distributed at the droplets interface experience local short-range attractive interactions, due to the specific environment and/or conformational changes, not influencing the mean B 22 value.
On the basis of our results, it could be hypothesized that the occurrence of LLPS in crystallizing/precipitating conditions results in a partially unfolded protein conformation or in a suitable variation of the secondary/tertiary protein structure, as already reported in other cases 27 , which can be the species prone to aggregation through a mechanism driven by conformational change rather than colloidal interactions, and which initiate the crystallization process.The conformationally perturbed protein can be a minor species, which does not alter significantly the predominant native protein population and only slightly contributes to the net protein-protein interaction value measured by B 22 .Indeed, SLS is an integrative technique, which provides only averaged information.If only specific short-range orientations or aggregation-prone structurally perturbed states can lead to attractive interactions, the remaining repulsive orientations or species dominate in the light scattering results.
It is important to note that the measurements of intermolecular interactions were performed under low protein concentration conditions (≤5 mg mL −1 ), while crystallization trials are generally conducted at higher concentrations (≥20 mg mL −1 ).Both B 22 and k d determined in dilute conditions are considered generally predictive of high-concentration behaviour.Nonetheless, high concentration behaviour can differ from that observed at dilute conditions, since "crowding" effects, i.e. the increased chance of molecular interactions, deviation from thermodynamic ideality and higher-order interactions (e.g., B 23 , B 222 ) can significantly alter the net inter-protein interactions 55,61 .The contribution of these effects to aggregation propensity of structurally complex molecules such as mAbs, cannot be ruled out.

conclusions
This work reports about the study of Anti-CD20 (a full-length monoclonal antibody) crystallization in a PEG400/ Na 2 SO 4 /H 2 O system occurring near LLPS conditions.The DLS/SLS studies performed to verify the correlation between the second virial coefficient and molecular diffusivity with the protein aggregation propensity in selected solution formulations indicates that B 22 remains strongly positive (a sign of repulsive protein-protein interactions) for all conditions that have been instead ascertained to be effective for protein crystallization or precipitation.For all the crystallizing or precipitating conditions, the occurrence of LLPS phenomena was observed concomitantly or near the nucleation stage.Even in this case, the second virial coefficient does not correlate with the LLPS, which mainly proceeds without attractive protein interactions, and that may be rather related to the polymer-salt phase separation that can occur without protein.The possible interplay between the salt/PEG and protein/PEG phase separation, which can affect the solvent quality, can have a role on the polymer mediated forces and finally on Anti-CD20 aggregation.On the basis of these measurements and the experimental observation of LLPS near the nucleation zone, it is proposed that a minor population of protein molecules can experience valuable protein-protein attractive interactions, induced by local environmental factor, slightly affecting the averaged B 22 parameter.

Figure 1 .
Figure 1.Optical microscope image of (a) crystalline Anti-CD20 monoclonal antibody obtained by sittingdrop vapour diffusion method and (b) Liquid-Liquid Phase Separation occurring just prior to crystallization.Solution composition near the crystallization point: 20 mg mL −1 Anti-CD20, 9.6% V/V PEG400, 0.86 M Na 2 SO 4 in 0.1 M HEPES buffer at pH 7.4.

Figure 2 .
Figure 2. Experimental state diagram for the system PEG400/Na 2 SO 4 /H 2 O at 293.15 K. Squares: experimental liquid-liquid equilibrium data from ref.36 ; solid line: asymptotic fitting to tie-lines data from ref.36 ; circles: batch crystallization conditions reported in Table1; diamond: starting solution composition in vapour diffusion tests; pentagon: ending solution composition in vapour diffusion tests; triangles: measurements points for B 22 ; dotted line: shifted binodal curve in the presence of Anti-CD20 protein.Solution composition is expressed as weight fraction (wt.).

Figure 3 .
Figure 3.The second virial coefficient B 22 as a function of PEG400 volume concentration (X PEG ) at a constant amount of 0.48 M Na 2 SO 4 in HEPES 0.1 M buffer at pH 7.4.The crystallization slot according to ref. 15 is shown in light grey.The solid line is a guide for the eyes.

Figure 4 .
Figure 4.The second virial coefficient B 22 as a function of Na 2 SO 4 molar concentration (C Na SO 2 4 ) for constant PEG400 volume concentration x PEG = 4.8% V/V in HEPES 0.1 M, pH 7.4.The solid square symbol indicate B 22for a PEG400 concentration of 9.6% V/V without NaCl.The crystallization slot according to ref.15 is shown in light grey.The solid line is a guide for the eyes.

Figure 5 .
Figure 5. pH dependence of B 22 for Anti-CD20 solutions with 4.8% V/V PEG400, 0.43 M Na 2 SO 4 , and HEPES 0.1 M. The crystallization slot according to ref. 15 is shown in light grey.The solid line is a guide for the eyes.
measured B 22 for an IgG and

Figure 6 .
Figure 6.B 22 and k d as a function of Na 2 SO 4 concentration for x PEG = 9.6% V/V and pH 7.4.The experimental crystallization window boundaries (see Table1) are highlighted by the dotted vertical lines.The solid lines are guides for the eyes.

Figure 8 .
Figure 8. Residual Intensity measured by DLS at a fixed scattering angle of 173° for a solution containing PEG400 9.6% V/V in 0.1 M HEPES at pH 7.4 and increasing amount of Na 2 SO 4 , without protein.The solid line is a guide for the eyes.

Figure 9 .
Figure 9.Protein crystals nucleating near the boundary of the droplets (a) and crystals forming within the bulk of the droplets (b,c).