Enhanced Crystallization of Lysozyme Mediated by the Aggregation of

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Enhanced crystallization of lysozyme mediated by the aggregation of inorganic seed particles Ulrike Weichsel, Doris Segets, Thaseem Thajudeen, Eva-Maria Maier, and Wolfgang Peukert Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.6b01026 • Publication Date (Web): 04 Nov 2016 Downloaded from http://pubs.acs.org on November 12, 2016

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Crystal Growth & Design

Enhanced crystallization of lysozyme mediated by the aggregation of inorganic seed particles Ulrike Weichsel1, Doris Segets1,2, Thaseem Thajudeen1,2, Eva-Maria Maier1, Wolfgang Peukert1,2* 1

Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstraße 4, 91058 Erlangen, Germany 2

Interdisciplinary Center for Functional Particle Systems (FPS), Haberstraße 9a, 91058 Erlangen, Germany

KEYWORDS Heterogeneous nucleation, seeded protein crystallization, shear-induced aggregation, lysozyme, silica nanoparticles.

ACS Paragon Plus Environment

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ABSTRACT

We show that aggregation plays a major role in seeded growth of protein crystals. The seeded batch approach provides the opportunity to set the starting conditions for protein crystallization by adding a defined amount of well-characterized seed particles. The experimental observations for tetragonal hen egg-white lysozyme (LSZ) confirm the concept of the oriented aggregation of larger building blocks to form a protein crystal. It was shown that the aggregation of the seed particles/bioconjugates is advantageous for the product quality in terms of larger and more defined LSZ crystals and in terms of accelerated reaction kinetics. We present a population balance (PB) model for the seeded batch crystallization of LSZ considering the aggregation of growth units to form protein crystals. For the modeling of crystal growth, evolving particle size distributions (PSDs) of agglomerating LSZ molecules were measured by dynamic light scattering (DLS). Moreover, the aggregation of seed particles in LSZ solutions under crystallization conditions was investigated by DLS. In line with our expectations, the number of seeds was found to be important as it strongly affects the collision frequency in the aggregation term of our PB model.

Finally, the applied model trends of the supersaturation depletion curves and of the measured CSDs correctly orders of magnitude in particle size, ranging from only a few nanometers up to micrometer-sized particles/crystals. Thus, by the combination of PB modeling and experimentally determined crystallization parameters, insights into the crystal formation mechanism were obtained. To the best of our knowledge this is the first attempt to model growth within a crystal population by an aggregation mechanism induced by seeding with foreign particles.


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INTRODUCTION An in-depth understanding of the mechanisms being involved in protein crystallization is still largely missing due to the complex structure of the macromolecules. During the past decades much effort was put into the development of various techniques for the crystallization of specific proteins, mostly because there is a high demand for single crystals which are needed for structure determination.1 Based on the huge variety of different proteins the generalization of experimental results based on unifying principles is difficult. In fact, crystallization techniques still depend on empiric identification of appropriate crystallization parameters as predictive models for crystallization are largely missing. An important aim in industrial downstream processing is to obtain protein crystals with desired properties in a reproducible way, e.g. regarding subsequent filtration steps. For all these applications kinetic information about the particle ensemble is indispensable. In this study we aim to improve product quality and gain insight on the protein crystal formation mechanism by using defined foreign seed material for nucleation control. In the first step, a possible model for crystal formation is established based on seeded crystallization experiments in ml-scale where the supersaturation depletion as well as the evolution of crystal size distribution of hen egg white lysozyme (LSZ) is monitored. In the next step, important parameters for modeling crystal growth and aggregation are determined from dynamic light scattering (DLS) experiments Growth and aggregation parameters are then incorporated in a subordinate population balance model (PBM) in order to simulate the crystallization kinetics and evolution of


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crystal size distribution. Finally, experimental and computational results are compared to validate the proposed crystal formation theory. Within this work the crystallization of LSZ in ml-scale using silica seed particles with a focus on reaction kinetics is reported for the first time. LSZ and silica were chosen as the model material system as many results in literature are accessible for comparison. Moreover, silica particles offer the opportunity for various surface functionalities which might influence the heterogeneous nucleation. Electrostatic interactions were identified to have a significant impact on the adsorption of LSZ on the silica surface.1 Although the strong attractive electrostatic interactions between LSZ and silica are reduced under crystallization conditions due to the enhanced ionic strength in the presence of buffer salt and sodium chloride as a precipitant, we could recently show that LSZ and silica remain oppositely charged. This still leads to adsorption of LSZ at the particle surface.2 In our previous work, seed particle size-dependent adsorption of LSZ was investigated further as it strongly influences the outcome of LSZ crystallization experiments. In particular, an enhanced adsorption of LSZ molecules at the surface of larger silica particles was observed. These findings were explained by an increasing charge density with increasing seed particle diameter and by a decreasing surface curvature.1 Finally, preferred adsorption resulted in enhanced heterogeneous nucleation as it was confirmed by measured shorter induction times in both, µl- and ml-scale experiments. These findings are advantageous regarding the applicability of seeding material in industrial processes for process control. For a final removal of seeding material after the crystallization step the use of magnetic particles with an inert shell is proposed. In this way protein crystals containing these particles could be transferred to fresh buffer solution for dissolution. Then the magnetic seeding material would be removed by applying a magnetic field.


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The crystallization experiments we had conducted using labelled silica seed particles (fluorescent dye) revealed that many of these particles were incorporated in one single LSZ crystal (see Figure 1). Thus, this is clearly not a situation where one seed finally forms one single LSZ crystal but in turn indicates i) that LSZ crystals are composed of larger building blocks and ii) that protein crystal growth proceeds by the attachment of larger protein-particle aggregates. Remarkably, the formed solid in our experiments displays defined crystal faces, although the solid formation is shifted to significantly shorter time scales compared to the unseeded case. One possible explanation of the observed protein crystals containing seed particles could be that only void space is filled with seeding material after crystallization, without the preliminary formation of larger building blocks. However, this is rather unlikely due to strong electrostatic interactions between LSZ and silica seed particles (Weichsel et al., Crystal Growth & Design, 2015) and the subsequent irreversible aggregate formation under crystallization conditions (see Figure S2_1). Moreover, protein crystals in the presence of seed material display more defined facets and larger size compared to the unseeded case, evidencing that the formed solid material from seeded crystallization experiments is different. All this underlines that the seed particles decisively

take

part

in

the

crystal

formation

process.


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Figure 1

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LSZ crystals from µl-scale batch crystallization experiments using negatively

charged and labeled Stöber silica seed particles; fluorescent dye: [Ru(phen)3]Cl2 with λex=460 nm and λem=600 nm; crystallization conditions: T=22 °C, 0.1 M sodium acetate buffer, pH=5, cNaCl=50 g/l, cLSZ=30 g/l. t=24 h. Seed particle size: a) 134.9 nm and b) 1.501 µm.

Herein, the LSZ crystal formation is explained by the aggregation of larger protein-seed particle aggregates and modeled by population balance equations (PBE). The aspect of aggregation is of special importance because our experimental results strongly provide an indication of the formation of protein crystals from aggregating bioconjugates or larger subunits. Instead of classical growth which is described by a stepwise attachment of primary growth units like molecules to a nucleus surface, the obtained results can be rather explained by the so called non-classical crystallization that has been originally established by Cölfen et al.3 mainly for biomineral crystals. Herein, they describe the formation of mesoscopically structured crystals by aggregation of NPs as building blocks. Additionally, they report on amorphous intermediates as building blocks with subsequent reorganization to a crystallographic structure. In the context of protein crystallization it was already shown that alternative crystal formation pathways do exist as well. Vekilov describes the so-called two-step nucleation mechanism by the formation of dense liquid droplets and the subsequent nucleation of crystals within these droplets.4 Although this concept was proven for nucleation at high supersaturations close to the fluid-fluid critical point without the addition of seeds, it underlines the importance of the work of Cölfen et al. also in the context of protein crystallization. For our investigations we used silica seed particles as it is known that protein-mediated aggregation occurs which supports our approach.5 By this, we


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shed light on the formation mechanism of a protein crystal from seeded experiments and apply the approach of Cölfen et al. to protein molecule assemblies. With respect to modeling, the following studies were identified to be relevant for our work. Most authors investigated the kinetics of an unseeded batch crystallization of LSZ. They used population balance models (PBMs) including nucleation and growth terms. Both, nucleation and growth were modeled according to a power-law dependence on supersaturation. By evaluation of experimentally determined nucleation and growth rates, the parameters needed for PB modeling were determined.6–11 Judge et al. measured crystal size distributions (CSDs) with time of a seeded batch crystallization of ovalbumin.12 Seeding was performed by the addition of protein crystals and the obtained growth kinetics of a protein crystal ensemble were used to predict concentration profiles of the solute. In another study, Ataka et al.13 measured concentration profiles while varying initial LSZ concentrations to study nucleation and growth of orthorhombic crystals. For data evaluation a model was successfully applied which was originally developed for protein self-assembly processes. They suggest that protein crystal growth is another example of ordered protein aggregation and thus comparable to phenomena like fibril formation. The latter work is of special importance as it underlines the aspect of oriented aggregation phenomena during protein crystal formation as discussed above. To gain a better understanding of the aggregation of larger building blocks the reader is referred to reviews of de Yoreo from 2015 and Lv et al.14,15 They give an overview of existing studies in literature to investigate growth mechanisms with a focus on statistical kinetic models. Within this review the advances in theoretical simulations are presented. Most strategies to model the aggregation process are based on the size evolution of species driven by collision. Here, the models range from dimer formation models to polymerization models to population


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balance models. Moreover, models exist which are based on DLVO theory with non-covalent interactions like van der Waals, Coulombic or dipolar interactions. They also report on extended DLVO models which consider the anisotropic growth of species by aggregation by further aspects such as H-bonds, steric forces and hydration. Finally, Lv et al. give an overview of simulations at the atomic level using molecular dynamics (MD), Monte Carlo (MC) and density functional theory (DFT). For example Zhang et al. studied the role of van der Waals and Coulombic interactions on the lattice orientations of crystals. They simulated the energy change during the attachment of two 4 nm spheres on different crystal surfaces.15,16 In the present work population balance equations (PBEs) were used to simulate the growth and aggregation of crystal building blocks. More recently, Kwon et al. published a number of articles on the modeling and control of crystal size and shape for tetragonal LSZ crystals in batch crystallization as well as in continuous mode. In general, they developed a kinetic Monte Carlo model which is combined with PB modeling to describe the evolution of crystal volume distributions. In the case of batch crystallization, they include nucleation and growth terms based on experimental findings in literature.7,10,17,18 Most importantly, they further consider shear-induced aggregation of protein crystals since this effect was found to influence the final CSD. Moreover, for a profound investigation of crystal growth and shape evolution, seeded experiments with crystals of the same material in plug flow configuration have been simulated to decouple nucleation and crystal growth.19 The mentioned aspect of aggregation as a possible growth pathway was already described for inorganic colloidal particle systems i.e. by Look and Zukoski. They derived a titania particle growth mechanism based on reduced electrostatic repulsion and further fusion of primary particles by reaction products during precipitation.20


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In our work we followed the approach of Kwon which assumes that homogeneous nucleation is negligible at intermediate supersaturation values due to the presence of seeds.21,22In contrast to the use of LSZ crystals we apply foreign seed particles to achieve well defined initial conditions in terms of the provided foreign surface area. Therefore, an experimental determination of nucleation rates is not necessary. This simplifies the comparison between simulation and experiment as literature data considering protein nucleation rates under comparable conditions vary by 16 orders of magnitude (105-1021 m-3s-1).23,24 For this reason, the created PB model for the seeded batch crystallization of LSZ including crystal growth and aggregation of the seed particles is seen to be highly advantageous since the starting conditions are only defined by the seed PSD and the seed number concentration. By this approach supersaturation depletion curves and CSDs of crystallization experiments are reproduced and a fundamental mechanism for the seeded experiments is derived. We believe that the combination of experiments and modeling is an important step to gain insights into the crystal formation mechanism and kinetics during protein crystallization allowing a future reduction of laborious measurements.

MATERIALS & METHODS Seed particle system In this study, silica NPs with different mean sizes of 10, 30, 50, 100 and 200 nm were used. Table 1 represents characteristic data of the different silica particles obtained from the manufacturer (Micromod) which were confirmed and complemented by own measurements. All particle sizes determined by dynamic light scattering (DLS) are within the specifications of the manufacturer. For transmission electron microscopy (TEM) and scanning electron microscopy (SEM) images of the particles as well as PSDs measured by DLS, the reader is referred to our


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previous publication.2 All analyses confirm the spherical particle shape claimed by the manufacturer as expected from the synthesis process (Stöber silica). In addition, the smallest particles of 10 nm are close to the size of a globular LSZ monomer which has geometric dimensions of L x W x H = 4.5 x 3.5 x 3.5 nm and a hydrodynamic diameter of 3.5 nm.1 The pH values of the delivered dispersions are within a range from pH 8.0 to 8.6.2 The mass specific surface charge density of the manufacturer given in Table 1 is recalculated to a surface specific charge density with the assumption of silanol groups being responsible for surface charges. The result shows an increasing charge density from 0.18, 0.44, 0.61, 0.83 to 1.24 SiOH/nm2 with increasing silica particle size from 10, 30, 50, 100 and 200 nm. In agreement with the literature, the isoelectric point (IEP) of silica was found to be situated between pH = 3-4 and is caused by the high number of silanol groups at the particle surface. In contrast, LSZ is positively charged with a zeta potential of 31.6 ± 4.9 mV at pH = 3. It has an IEP of pH 11. Thus, for pH = 5 that is used in our crystallization experiments, LSZ and all silica NPs have opposite charges and the occurrence of Coulomb interactions is expected.2 Table 1. Properties of the silica seed particles (Micromod) in the initial suspensions; listed are: diameter x, z-average from DLS, concentration of silica cSiO2, surface charge density δ according to the manufacturer, number of particles per ml #SiO2, surface area per ml A, and pH.2 x nm

z-ave DLS nm

cSiO2 mg/ml

10

16.93

25

30

25.37 ± 0.70

50 100

δ µmol/g

SiICP mg/ml

cSiO2 #/ml

Aparticle 103nm2

A nm2/ml

pH -

85

9.57±0.12

2.4·1016

0.3

7.5·1018

8.3

25

70

10.95±0.19

8.9·1014

2.8

2.5·1018

8.0

54.11 ± 1.15

25

60

11.29±0.18

1.9·1014

7.9

1.5·1018

8.5

94.45 ± 2.29

50

40

21.61±0.24

4.8·1013

31.4

1.5·1018

8.5


10

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200

193.6 ± 4.17

50

30

19.61±0.10

6.0·1012

125.6

7.5·1017

8.6

Solution preparation and protein solubility All crystallization experiments of LSZ were conducted in sodium acetate buffer solution (98%, Carl Roth). First, the buffer salt was dissolved in ultra-pure water to reach a 0.1 M concentration. Then, the pH value was adjusted by acetic acid (100%, Carl Roth). Sodium chloride (>99.8%, Carl Roth) was used as precipitating agent and was dissolved in buffer to reach a stock solution concentration of 150 g/l. Hen egg-white LSZ (80%, Carl Roth) was three times crystallized and lyophilized (lot no. 12678054, EG.Nr 2357473) and then used without further purification. LSZ consists of 129 amino acids with a molecular weight of 14.4 kDa. The lyophilized powder was dissolved in buffer to reach a stock solution concentration of 100 g/l. Salt and buffer stock solutions were filtered with syringe filters of 0.2 µm pore diameter (Cellulose acetate, 25 mm, VWR International) whereas the protein stock solution of high concentration was filtered with a sterile syringe filter of 0.2 µm pore diameter (Acrodisc Supor, 13 mm, VWR International). LSZ solubilities were calculated by third order polynomial fits of solubility data determined by Cacioppo and Pusey.25

Crystallization experiments LSZ crystallization experiments were conducted in microcentrifuge tubes (V = 2 ml, VWR International) to monitor both, the decrease in supersaturation with time and the CSDs. By mixing the stock solutions of protein, sodium chloride and seed particle dispersion with buffer


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(with NaCl and particle dispersion being the last additives) the preset supersaturation was achieved. The microcentrifuge tubes were put in a water bath with temperature control and a rotating shaker system. This assures ongoing mixing of the solution and especially prevents sedimentation of the formed solid material. For all seeded crystallization experiments, a constant foreign

particle

surface

area

(ASiO2 = 1.5*1016 nm2/ml,

ASiO2 =

1.5*1015 nm2/ml,

ASiO2 = 1.5*1014 nm2/ml) upon the addition of the differently sized particles was added to the protein solution. This surface area was calculated from the manufacturer´s specifications of the number of particles per volume and from the specified particle size. Normalization to a constant foreign particle surface is mandatory within the framework of a heterogeneous nucleation concept. Depletion of supersaturation The decrease in supersaturation of the batch crystallization was determined by measuring the protein concentration in the mother liquor. This was realized by UV-Vis absorption measurements at a wavelength of 280 nm using a Cary 100 Scan (Varian). For conversion of absorption data to concentrations of LSZ, an extinction coefficient of 2.64 ml·mg-1·cm-1 was used.1 At certain time-steps, samples were taken (50 µl), filtered with a syringe filter of 0.2 µm pore size (Acrodisc Supor, 13 mm, VWR International) and then 10 µl of the filtrate were diluted with buffer (1:100) before the measurements were conducted. Measurement of particle and crystal size distributions The challenge in this work is to cover a very broad range of sizes, concerning both, the crystallization experiments and the simulations. LSZ molecules for instance display a hydrodynamic diameter of about 3.5 nm, whereas protein crystals under the chosen conditions


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reach mass specific mean diameters of x50,3 values up to 50 µm. For this reason, DLS was used to monitor the early stages of crystal formation (covering 0.3 nm to a few µm, manufacturer specification) and a laser diffraction device for the determination of µm-sized crystals (covering 1 µm to 900 µm, manufacturer specification). In a first instance, DLS was used for the experimental determination of crystal growth rates. In situ measurements of the PSD were conducted with a Zetasizer Nano ZS (Malvern Instruments). Based on the Stokes-Einstein equation for the diffusion of spherical particles in a liquid medium, the diffusion coefficient is converted to particle sizes.26 Starting point for the measurement is the addition of sodium chloride which lowers the solubility of LSZ and leads to a continuous increase in particle/aggregate size with time. Initial values of supersaturation were adjusted by variation of the protein concentration and salt concentration in solution. Figure 2a exemplarily shows the evolution of the intensity distribution with time. The peak of the LSZ monomers is shifted to slightly higher particle diameters of 6 nm instead of 3.5 nm for the pure monomer (see Figure S1_1). This is explained by stronger attractive interactions between protein molecules caused by the addition of sodium chloride solution which is necessary to reach a certain supersaturation. At this point it needs to be mentioned that with an increasing salt concentration in solution, the viscosity increases as well which leads to lower diffusion coefficients and larger particle sizes. To separate viscosity effects from interaction effects, a series of measurements with varying salt and protein concentrations was conducted. To account for viscosity effects the obtained data were normalized by extrapolated D0 values (diffusion coefficient at infinite dilution). The results reveal that the above mentioned trends still apply which underlines the importance of attractive interactions between protein molecules under crystallization conditions.


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Finally, during ongoing crystallization, the intensity of the monomer peak is continuously reduced due to consumption of LSZ molecules during crystal growth (see Figure S1_1).

Figure 2

a) Intensity distributions of a LSZ solution at different time steps and b) z-average

value plotted with time for LSZ solutions within a supersaturation range of 4.5 ≤ 18.2 under crystallization conditions: T=22 °C, 0.1 M sodium acetate buffer, pH=5, cNaCl=60 g/l, solubility of LSZ c*=2.2 g/l. Shortly after the addition of NaCl to the LSZ solution and thus after the adjustment of a certain level of supersaturation in the sample, the formation of aggregates exceeding a particle size of 100 nm is monitored. This peak is shifted to larger particle sizes with time until the upper limit of the measuring range of the device is reached. It is important to mention here, that intermediate aggregate sizes should exist in the size range between a monomer and larger aggregates. However, the quantification of dimers, trimers and oligomers is hardly possible with DLS due to the fact that at the initial stage of the reaction the monomer concentration of LSZ is very high


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and thus oligomers are not detected. At later stages, the formation of larger aggregates > 100 nm dominates the overall measurement signal. From these PSDs the mean value of the intensity distribution (z-average) is plotted for four different LSZ concentrations (and thus supersaturations) with time (see Fig. 1b). Especially for the lower and intermediate LSZ concentrations, a linear dependence is observed within the first minutes of crystallization. The slope of the curves represents crystal growth rates which increase with higher initial supersaturation (4.5 ≤ S0 ≤ 18.2). Since the initial supersaturation value is not kept constant during the reaction, the growth rates will decrease with decreasing supersaturation. For the determination of crystal growth rates it is therefore crucial to only evaluate data obtained in the linear range. This was realized by only considering data points of intermediate initial supersaturations within the first 10 min of the reaction and with a corr. R2 > 0.9. In brief, the initial slope of the increasing mean z-average value with time is plotted against the initial supersaturation to determine the growth rate parameters. This will be explained in more detail in section 3.1. It is important to mention here, that within the following paragraphs crystal growth kinetics were primarily determined from DLS measurements in the absence of seed particles. Identical measurements have been conducted in the presence of the differently sized silica particles at various protein concentrations. However, the result was that aggregation rates were rapidly increased in the presence of seed particles and superimposed growth. Since all experiments are conducted at excess concentrations of LSZ, this finding is probably due to the fact that already small amounts of LSZ in contact with silica particles lead to the mentioned destabilization of the colloidal particle system and the formation of a particle-protein network (see Figures S2_1 and S2_2 in the Supporting Information). In fact, the growing small primary particles could not be


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resolved anymore during light scattering due to the presence of larger aggregates. Due to this superposition of growth and aggregation, no dependence on initial protein concentration could be derived. On the basis of the enhanced aggregation rates and the demonstrated decoration of the silica seed particles with LSZ by adsorption2, we believe that the interaction between adsorbed and free LSZ molecules in solution determines the overall growth process rather than the interaction between LSZ and plain silica surface. For this reason we think it is justified to determine growth parameters in the absence of seed particles and assume the obtained growth kinetics to be a lower limit for further discussions as aggregation rates were enhanced in the presence of seed particles. CSDs in the µm-range were determined by laser diffraction measurements using a LS 130 (Beckman Coulter). After a certain crystallization time, depending on the particular conditions of the experiment, a few droplets of the crystal suspension were added to a stirred cell in the laser diffraction device to reach a solid concentration of 8 – 12 wt-%. The cell was filled with 15 ml of a saturated protein solution (filtered 0.2 µm) to prevent both, dissolution and further growth of the formed crystals. The saturated solutions were adjusted by an identical sodium chloride concentration used in the experiments and a LSZ concentration of 5 g/l. The presented results are the average of three measurements (90 s each) per sample. Each measurement of a sample is corrected by offset and background measurements. In addition, the solid material was investigated with respect to the appearance of defined crystal faces by light microscopy using a Zeiss Imager.M1m (Carl Zeiss). Confocal laser scanning microscope images were taken with a Leica TCS SP5 system (Leica). Numerical approach


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Population balance equations (PBEs), commonly applied to model the dynamic evolution of particles populations, are used to gain insights into particle formation processes and to identify the most important influencing parameters on a final product. By means of PBEs temporal and spatial changes of internal variables are traced within a given control volume. Changes are caused by sources and sinks within the system as well as by exchange processes via the surface of the control volume. A basic PB model for a crystallization process includes terms of nucleation, growth and aggregation. With respect to the boundary conditions of experimental analyses, the two latter are comparatively well accessible, whereas the determination of nucleation kinetics remains a challenging task. According to Mersmann, nucleation events can be divided into i) primary homogeneous nucleation including homogeneous nucleation from solution, ii) primary heterogeneous nucleation in the presence of a foreign surface, e.g. seed particles and iii) secondary surface nucleation on solution-own crystals (e.g. attrition).27 For an industrial process it is of major importance to know which mechanism dominates the overall process under certain conditions. For instance, at high supersaturations homogeneous nucleation prevails, whereas at low supersaturations surface nucleation is energetically-favored.27 Due to the presence of seed particles –which reduce the energy barrier for nuclei formation- and the choice of moderate initial supersaturation values, we neglect the homogeneous and surface nucleation term in our PBM. The validity of the former assumption is further supported by the fact that free seed particles are observed in light microscope images after crystallization for the starting condition of a foreign seed particle surface area of ASiO2=1.5*1016 nm2/ml. Heterogeneous nucleation is addressed in our model by using the measured PSD of the seeds and their respective concentration as a starting condition for further growth and aggregation terms.


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Consequently, regarding the seeded batch crystallization, the following simplified onedimensional PBE based on the assumption of a well-mixed system is derived: d(Gn) dn =+Bagg − Dagg dx dt (1) The evolution of the particle number density distribution with time is described by the growth rate G and the birth and death terms for aggregation, Bagg and Dagg. Analytical solutions of this integro-differential equation only exist for simplified problems. Thus, numerical approaches are needed that provide accurate and efficient solutions. An overview of numerical methods is given by Ramkrishna.28 Numerical calculations were performed with the simulation package PARSIVAL (CiT GmbH) using the Galerkin h-p method based on a generalized finite-element scheme with a time discretization of Rothe´s type.29 One-dimensional PBE with the particle size being the internal property coordinate can be conveniently solved by this method providing information on the evolution of the PSD. Phenomena occurring in solid particle systems such as particle breakage, sintering and aggregation have already been investigated in studies of milling,30 gas phase synthesis31 and precipitation.32,33 Regarding our methodology, first crystal growth rates were determined experimentally. For the derivation of crystal growth kinetics different measurement techniques can be applied. Crystal growth data are accessible by methods such as optical microscopy as well as by atomic force microscopy (AFM).34,35 Both are working on a molecular level and thus provide information on the mechanism of crystal growth. References36,37 report on the determination of crystal growth rates using interferometry (Mach-Zehnder, Michelson). Due to the fact that these methods are rather laborious, invasive and working with single crystals only, crystal growth kinetics were investigated experimentally by DLS within this study. Moreover, DLS measurements enable us


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to monitor the initial stages of solid formation within a certain volume. Thus, it is a powerful non-invasive tool for the characterization of crystallization conditions of a protein solution.38,39 Solution properties such as protein and salt concentration were varied systematically to study changes of the diffusion coefficient of contained particle species with time. Especially the aggregation behavior of the silica seed particles with a variation of particle size and number concentration under LSZ crystallization conditions was found to strongly influence the reaction kinetics and product properties. For this reason the aggregation kinetics of the seed particles under crystallization conditions were measured and simulated with PARSIVAL. Finally, seeded crystallization experiments in ml-scale were conducted using silica seed particles of different size and analyzed by supersaturation depletion and by the measurement of CSDs by laser diffraction. These global parameters are then compared to simulation results.

RESULTS & DISCUSSION Regarding the technical crystallization of proteins, it is of major importance to identify the prevailing crystal formation mechanism as it plays a key role for any successful process design. In the following, a mechanism is proposed based on experimental observations and already published results. Then the extension of a “standard” PBM by aggregation will be discussed being identified as an important influencing parameter in the growth of protein crystals. Finally, the proposed mechanism was validated by comparison of simulation and experiments. Proposed mechanism derived from experimental results Based on the already mentioned observation of the multiple inclusion of labelled seed particles within a LSZ crystal we propose the following mechanism for the seeded crystallization of LSZ


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which is illustrated in Scheme 1. After the already mentioned adsorption of protein molecules to the seed particle surface (I) and the subsequent aggregation of protein-particle conjugates (II) an orientation and growth step (III) is assumed to form defined crystalline structures. Within this network of protein molecules and seed particles, a reorientation of protein molecules is expected as they have time to attain the thermodynamically stable form. This rearrangement was described by Patro and Przybycien who simulated the formation of reversible and irreversible protein aggregates based on hydrophobic interactions. From a free energy profile of the aggregating system they identified four phases: Nucleation, growth, relaxation and fluctuation approaching a minimum energy state. Within the relaxation and fluctuation state, organized and unorganized regions of the aggregate structures start to rearrange which is comparable to an aging or ripening step. Noteworthy, reversible aggregates are less dense, energetically more stable and they display a higher order at the end of the relaxation phase compared to their irreversible counterparts.40 Scheme 1 Proposed mechanism based on experimental seeded crystallization results for the formation of LSZ crystals. (Proportions in the drawing are not true to scale).


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This is a strong indication for the facilitated formation of ordered LSZ layers on the seed particles and a rearrangement and orientation of the LSZ molecules (III). Consequently, within the early stages both, unstructured protein-particle aggregates and aggregates with partly or complete long-range order, might exist. Together with single protein molecules and pure protein aggregates these two species might serve as building blocks to reach the observed crystal sizes in the µm range. However, it is barely possible at this point of the investigations to distinguish between the various species regarding the molecular orientation of adsorbed protein molecules on the particle/aggregate surface. Within the following, the proposed mechanism of protein crystal formation is tested by experimental investigation of the aggregation of seed particles during protein crystallization experiments in ml-scale and by PBM.

Modeling of crystal growth In the following paragraphs a PBM including crystal growth and aggregation will be established. These aspects will be discussed separately. Whenever necessary, it will be explained how physico-chemical quantities are deduced from experimental data. As nucleation is seen to be negligible, first, an expression for the crystal growth rate needs to be identified. The investigation of crystal growth kinetics is mostly conducted by the determination of growth rates of single crystals as a function of supersaturation and transport conditions.41 For a description of the dependence of the effective growth rates on supersaturation, a power-law expression was used in a number of investigations.6,10,11,42 Besides the description of the growth rate it additionally allows the differentiation between integration and transport controlled growth mechanisms and enables the experimental determination of all parameters needed for the expression of the growth rate:


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G=kg S-1g (2) kg is an overall growth rate coefficient which depends on temperature, relative velocity between involved species in the solution phase and impurities in the system.43 The exponent g describes the overall order of the crystallization. According to the literature, g = 1 indicates that the incorporation step of growth units into the crystal lattice is fast compared to diffusion of monomers to the surface and the overall growth mechanism is transport controlled. In contrast, an exponent g > 2 would lead to the assumption that the transport of growth units to the crystal surface is fast compared to the integration step indicating an integration controlled growth mechanism.27 Depending on the applied supersaturations and on the specific conditions of the crystallization experiment, either of the mechanisms may be dominant. As described in the experimental part (see section 2.5), initial slopes of evolving intensity distributions of supersaturated LSZ solutions obtained from DLS experiments during the early stages of crystal growth were evaluated. Figure 3a exemplarily shows our approach for the data evaluation for three initial supersaturations of 4.5, 9.1 and 13.6. Within the first 10 min of the measurement, the curves basically follow a linear trend. With an increasing initial supersaturation this linear correlation is reduced as the value of R2 decreases from 0.98 to 0.96 to 0.86. For this reason -and as already described in the experimental part- only the slopes for the experiments below S0=13 with R2 > 0.9 were used for the determination of growth kinetics based on Equation 2. Since the initial supersaturation value is not kept constant during the reaction, the growth rates will decrease with decreasing supersaturation. For the determination of crystal growth rates it is therefore crucial to only evaluate data obtained in the linear range. This was realized by only considering data points of intermediate initial supersaturations within the first


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10 min of the reaction and with a corr. R2 > 0.9. The final results that were used further are indicated in Figure 3b by black squares. It summarizes all initial slopes of the z-average value with time when they are plotted against the relative initial supersaturation (S0-1).

Figure 3 a) z-average value plotted with time for LSZ solutions within a supersaturation range of 4.5 ≤ 13.6 and b) initial slope d(z-average)/dt in dependence on initial relative supersaturation S0-1; crystallization conditions: T=22 °C, 0.1 M sodium acetate buffer, pH=5, cNaCl=60 g/l, c*=2.2 g/l. Analyzing the experimental data by DLS using the growth model described by Equation (2), a mean growth rate coefficient kg = 0.166 nm/s (kg = 1.66*10-10 m/s) is obtained from the slope of the curve. Even more important, the linear dependence of the received data on the initial relative supersaturation reveals an exponent g = 1 (R² = 0.966). Thus, the initial overall growth behavior tends to be transport limited. This finding is, at first glance, unexpected since the size and complexity of a single protein molecule should necessarily lead to integration limitation. This


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transport limitation is supported by additional DLS experiments (see SI S2) and by µlcrystallization experiments for the determination of crystal growth rates without and with the addition of silica seed particles. The latter show decreasing crystal growth rates with increasing seed particle size. Together with the enhanced aggregate formation with increasing seed particle size (SI S2) this can be explained by lower diffusivities for the larger aggregates. Consequently, mass transfer is shifted more to the side of transport limitation. To further investigate this aspect a literature review was performed in which the focus was set on findings regarding reaction vs. transport limitation. At this point it has to be mentioned that such a survey has to be considered with care. Several reasons prevent a direct comparison of results: i) different analytical methods, ii) single crystals vs. crystal populations that were analysed, iii) seeded vs. unseeded experiments, iv) different methods to create a supersaturation, v) use of specific temperature treatment and of temperature profiles, vi) use of flow cell vs. stagnant medium, vii) purity of the feed substances44,45, viii) sample preparation.46 A selection of references is displayed in Table 2 which were chosen because very detailed information was given concerning the aforementioned aspects. Moreover, this selection should be comparable to our experimental boundary conditions for the crystallization of LSZ. Marked cells in blue and green denote either diffusion or integration limitation for the particular system. It becomes clear that both cases are discussed in equal measure and many authors report on at least comparable rates of diffusion and integration. For example for tetragonal LSZ, Durbin and Feher suggest a defect-mediated mechanism at low supersaturations and two-dimensional nucleation at high supersaturations with a strong integration limitation,10 whereas Gorti et al. identify a transition region from integration limitation to diffusion limitation for increasing supersaturation values. However, two important assumptions were made in the work of Durbin


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and Feher: i) LSZ in solution is monomeric and ii) growth of the LSZ crystals proceeds by the attachment of monomers. Several investigations by AFM, interferometry and light scattering techniques show that dimers, tetramers, octamers as well as larger clusters may serve as building blocks.47–49 Nadarajah et al. have shown that the growth rate curve can be divided into different regions. At low supersaturation a nonlinear dependence is followed by a strong increase in growth rate until it reaches a maximum.48 They interpreted characteristic growth curves by taking into consideration underlying aggregation mechanisms and growth by integration of larger growth units. Thus, the fact that diffusion limitation occurs is explained by a crystal growth mechanism which is based on multimeric or cluster-like growth units. Those units have significantly lower diffusion coefficients.50–52 This aspect is of major importance for our work as the use of seed particles additionally initiates the formation of larger conjugates/aggregates. Despite the variations of growth rate coefficients in literature, we believe that our approach is appropriate as it is based on crystal/aggregate ensembles and allows for a fast determination of growth kinetics in our own experiments. The obtained growth coefficients can then directly be used within the PBM. Regarding the crystal growth coefficient kg our value of kg = 1.66*1010

m/s is comparable to the obtained values of Pusey, Snyder and Naumann and of Saikumar,

Glatz and Larson (compare with Table 2). This assures the applicability of our approach. Table 2 Literature findings concerning protein crystal growth with focus on reaction (green) vs. diffusion (blue) limitation. LSZ: Lysozyme and STMV: Satellite tobacco mosaic virus.

Authors & Year

Method

Kam, Shore, Feher DLS, microscopy, 1978 53 absorbance

Protein

Coefficients / Growth limitation

Tetragonal LSZ

Rates of diffusion and attachment comparable, k=5*10-7 m/s


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Fiddis, Longman, Calvert 1979 54

Light microscopy

Tetragonal LSZ

Controlled by surface nucleation, high reaction order of n=6-8.5

Light microscopy

Tetragonal LSZ

Defect-mediated growth at low S, at high S surface nucleation; G=K(c-s)n with n=2.0-3.8, S=c/s=1.2-10

Pusey & Naumann Light microscopy 1986 55

Tetragonal LSZ

Growth is surface kinetics limited, ms=k[(ci-cs/cs)]b with b=2.08 and k=1.11*10-11 m/s

Pusey, Snyder, Naumann 1986 56

Light microscopy

Tetragonal LSZ

σ=(ci-cs)/cs), R=kσr, k=0.146*10-10 m/s and r=2, attachment or surface effects are rate limiting

Ataka & Asai, Bessho, Ataka, Asai, Katsura 1990, 1994 13,57

Depletion of S, theory of selfassembly

Growth via attachment of Orthorhombic monomers, hint on diffusion LSZ controlled growth

DLS

STMV, Apoferritin, Ferritin

Limited by diffusion of STMV clusters, n=0.33-0.54; Apoferritin limited by surface kinetics, n=0.81.0

Optical microscopy, interferometry

Tetragonal LSZ

σ=(c-s)/s, σ10 bulk transport becoming important

Land, Malkin, Kuznetsov, McPherson, DeYoreo 1995 59

AFM

Cubic STMV, Canavalin

STMV growth limited by incorporation kinetics; Canavalin growth limited by solute transport, σ=ln(c/s), σ=1.8

Judge, Johns, White 1995 12

Microscope counting

Ovalbumin

G=kgσa, a=2

Nadarajah, Li, Pusey 1997 52

Model calculations

Tetragonal LSZ

Growth rate model based on aggregation, octamer growth units, transport and attachment kinetics competitive

Saikumar, Glatz, Larson 1998 11

Light microscopy

Tetragonal LSZ

G=kg((c-s)/s)2, kg=3.08*10-10 m/s (3.72*10-10 m/s from fit)

Gorti, Forsythe, Pusey 2005 34

Light microscopy, AFM

Tetragonal LSZ

Beyond a critical S diffusion limitation, σ=ln(c/s), c/s=1-13

Durbin & Feher 1986 10

Malkin & McPherson 1993 50

Monaco & Rosenberger 1993 58

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After having determined the growth kinetics we exemplarily simulate the growth of our largest (200 nm) silica seed particles with the obtained growth rate coefficients within 300 min to compare the results with a standard seeded crystallization experiment. This is important because it gives a first hint on whether the size range of obtained crystal sizes is met considering only growth of the particles or if further phenomena have to be taken into consideration. For the following simulations all relevant parameters are listed in Table 3. Table 3 Simulation parameters: Temperature T, molecular weight of LSZ MLSZ, density of LSZ ρLSZ, molecular weight of the solution Msolution, density of the solution ρsolution, solubility of LSZ c*, growth coefficient kg, growth exponent g, concentration of added silica particles cSiO2, particle size and standard deviation of added particles x (Gauss distribution). T °C

MLSZ kg/mol

ρLSZ kg/m3

MSolutio nkg/mo l

ρSolution kg/m3

c* kg/m3

kg nm/s

g -

cSiO2 kg/m3

x nm

22

14.4

1300

0.018

1000

2.51

0.16

1

1

200±20

The results shown in Figure 4a indicate that the supersaturation is depleted within the first 15 min in the simulation, whereas the experimentally measured depletion is much slower when seeds are used (even after a crystallization time of 150 min the LSZ concentration in the supernatant is not approaching the LSZ equilibrium concentration at S = 1). This cannot be explained by a variation of the growth coefficients as higher values that are reported in literature (see Table 2) would lead to even faster supersaturation depletion. As a next step, the CSD is calculated and compared to the experimental result. As can be seen from Figure 4b, after a crystallization time of t = 300 min the simulation reveals a very narrow CSD and a median


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crystal size that does not exceed a value of 1.0 µm. This is in sharp contrast to the comparably broad CSD and x50,3 value of 40.7 µm obtained from the experiment.

Figure 4

Comparison of simulated growth of 200 nm seed particles with experimental

crystallization results for a) depletion of supersaturation and b) CSDs; crystallization conditions: T=22

° C,

0.1 M

sodium

acetate

buffer,

pH=5,

cNaCl=50 g/l,

xSiO2=200 nm

and

ASiO2=1.5*1016 nm2/ml; simulation parameters: kg=0.16 nm/s, g=1, t=300 min. Consequently, the obtained discrepancy between simulation and results, both concerning supersaturation depletion curves as well as final CSDs, once more suggest that aggregation needs to be included in our model. Aggregation slows down the integration of monomers into the crystal surface because of a continuously reducing number of seed particles and thus shifts the supersaturation depletion curve to longer crystallization times. Moreover, aggregation would result in significantly larger mean crystal sizes due to the collision and adhesion of large seed particle aggregates.


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Modeling of aggregation The aggregation of the (growing) seed particles is decisive for the overall crystallization process. Due to the use of sodium acetate buffer at pH=5 and a high sodium chloride content of about 0.85-1 mol/l (and thus a high ionic strength), the negative zeta potential of the silica particles is reduced. This causes the formation of larger aggregates. Additionally, a proteinmediated aggregation of the silica particles in contact with LSZ was reported by Bharti et al.5 and confirmed by own DLS measurements under crystallization conditions (see SI S2). Bharti et al. investigated the aggregation of 20 nm silica particles depending on the pH value. They concluded that in the pH range of 4-6 partial binding of LSZ occurs at the particle surface which is accompanied by the formation of compact aggregates. This was attributed to strong electrostatic interactions as LSZ has an opposite zeta potential compared to SiO2 in this pH region. In the presence of sodium chloride, a further increase in the packing density around pH=5 was observed by the same authors using analytical centrifugation (AC) and small angle X-ray scattering (SAXS) to characterize the formed aggregates.60 This secondary effect was explained by the screening of repulsive electrostatic interactions between the silica particles together with bridging of the particles by a small number of protein molecules. For higher pH values the adsorbed amount of LSZ was found to increase which then leads to low-coordinated open aggregate structures. Accordingly, aggregation has to be included into the PBM. For a successful aggregation event two prerequisites have to be fulfilled: Collision of the particles followed by their adhesion. Physically, the aggregation rate Bij is usually described by the decrease of the number of primary particles N with time t:


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= −

= −β

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(3)

The aggregation kernel β depends on the particle sizes of the collision partners, hydrodynamics (diffusion, convection and/or sedimentation) and on particle interactions. Since the experimental setup enables ongoing mixing (end-over-end shaker) of the crystallizing solutions, sediment formation at the bottom of the vials can be excluded. Thus, as a first step aggregation due to diffusion is considered for the simulations with seed particle sizes between 10 and 200 nm. For particles smaller than 1 µm collision events take mostly place due to Brownian motion. Smoluchowski defined the corresponding collision kernel for perikinetic aggregation containing the stability factor W:61 βBrown =

1 2kB 1 1 xi +xj + W 3µ xi xj (4)

xi and xj denote the diameter of the interacting particles i and j and µ is the dynamic viscosity. According to these equations aggregation is strong for small particles with high diffusivities at high particle concentrations. As aggregation leads to an increase in particle size, the respective diffusivities decrease and the aggregation rate slows down. W provides information on the interactions between particles being thus a measure for successful collisions.62 It describes the relation between the actual aggregation rate and the perikinetic aggregation rate without considering interparticulate or hydrodynamic interactions:63 W = 0.5·xi + xj

∞

xi + xj ⁄2

φr

e kB T dr Gh r2 (5)


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r denotes the core-to-core particle distance, φr is the total interaction potential and Gh is a

measure of hydrodynamic interactions which is estimated to be unity for large r.63 In general it is assumed that W is unity for hard spheres, smaller than one for attractive interactions and larger than one for repulsive interactions. To sharpen our model and to investigate the impact of fluid flow on the aggregation of seed particles, an expression of the collision kernel in laminar shear flow based on the work of Smoluchowski was used:61 βlaminar =

1 4 xi xj 3 · + ∗ 3 2 2

(6)

Laminar flow conditions were chosen due to the fact that the end over end shaker provides relatively low shear rates (rotational speed: 20 rpm). It is rather used to prevent sedimentation of aggregates/crystals at the bottom of the vials than for the introduction of turbulence and intense mixing. As a next step, the seed particle size-dependent transition between Brownian diffusion and shear-induced aggregation and the prevailing shear rates in our system were estimated. For this purpose both collision kernels, βBrown and βlaminar, were calculated for the differently sized seed particles and for relatively low shear rates of γ = 0.1, 1.0 and 10 s-1 with collision partners in the range of 1 nm to 100 µm. Here the assumption is made that every collision is successful and subsequently leads to aggregate formation. The obtained results are displayed in Figure S4_1 and in Table S4_1 (SI S4). For a detailed discussion the reader is referred to SI S4. In general it can be seen that for higher shear rates shear-induced collisions dominate the process at shorter reaction times. Seed particle size-dependent Brownian diffusion dominates the aggregation kinetics up to particle sizes of 10 µm for low shear rates of γ = 0.1 s-1. Moreover, for low shear


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rates Brownian diffusion dominates collision events over a significant period of the total reaction time. For the largest seed particle size of 200 nm, a critical reaction time (at which the Brownian collision kernel crosses with the shear-induced collision kernel) was estimated at 37 min. With an increasing seed particle size the transition to shear-induced collisions is reached faster (for shear rates of γ = 10 s-1 the transition particle size and reaction time are reduced to 1 µm and 0.17 min for 200 nm seed particles). Within the following section, results will be exemplarily presented for the largest seed particle size of 200 nm. The influence of aggregation on protein crystallization To further verify that aggregation is an influencing factor in the crystallization of LSZ, we simulate the addition of 200 nm silica seed particles and their subsequent aggregation by Brownian diffusion. The simulation results for supersaturation depletion curves and CSDs are compared with measurement data obtained for a variation of the added amount of silica seed particles. Aim is to test if the applied model is – once growth parameters kg, g as well as stability ratio W have been fixed – able to reproduce the observed phenomena and trends. In the following, results are first presented using 200 nm silica particles prior size effects will be discussed. Figure 5a shows the comparison of the calculated and measured supersaturation depletion during the batch crystallization for three different amounts of 200 nm silica seed particles at constant crystallization conditions (T=22 °C, 0.1 M sodium acetate buffer, pH=5, cNaCl=50 g/l, S0=9.9). The highest amount of seed particles (see solid line) results in a fast depletion of supersaturation. For example a 60% depletion of supersaturation is reached within 150 min. With a decreasing amount of seed particles of dilution factors 10 and 100 (broken and dashed lines), the supersaturation depletion is shifted to longer crystallization times (after a 60% depletion) of


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190 and 230 min due to a reduction of foreign surface area. This trend is nicely reproduced by the simulation and is explained by the reduction of crystal growth on a continuously reducing number of seed particles due to aggregation.

Figure 5

a) Simulated and experimental supersaturation curves and b) corresponding CSDs

with a variation of the added amount of seed particles; crystallization conditions: T=22 °C, 0.1 M sodium acetate buffer, pH=5, cNaCl=50 g/l, xSiO2=200 nm (ASiO2=1.5*1016, ASiO2=1.5*1015, ASiO2=1.5*1014 nm2/ml); simulation parameters: kg=0.16 nm/s, g=1, W=0.1, t=200-250 min. Figure 5b depicts the respective CSDs measured after 60% of the initial supersaturation were depleted. Noteworthy, CSD determination at comparable values of supersaturation is crucial to assure that the batches are at similar stages of crystal growth. For the highest amount of seed particles (solid line) a mean crystal size of x50,3=42 µm is obtained. With a decreasing amount of seed particles by dilution factors of 10 and 100 the mean crystal sizes decrease to reach values of 35 and 32 µm, respectively. This trend underlines the importance of aggregation on the overall process. Without aggregation, the opposite trend concerning x50,3 value is expected because


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growth occurs on less seed particles resulting in larger mean crystal sizes (see SI S5). However, in our experiments with a high number of seed particles the probability for protein-mediated aggregation events is strongly increased leading to the advantageous formation of larger crystal units. For the following simulations again a value of W=0.1 was fixed as the experimental results using the differently sized seed particles are comparable to those presented in Figure 5. For a detailed comparison of experimental and simulated data concerning the variation of W the reader is referred to the Supporting Information (SI S6). To confirm the non-classical growth of protein crystals light microscope images of the crystal suspensions shown in Fig. 5b were taken and are presented in Figure 6. As can be seen from the images a, b and c, with an increasing amount of seed particles the formed crystals increase in size. It is important to mention here, that for the highest seed particle content (ASiO2=1.5*1016 nm2/ml) microscope images reveal the presence of free seed particle aggregates (the enlarged Figure 6c is shown in Figure S3_1 in SI S3). This strongly indicates that enough foreign surface was provided and thus mainly energetically favored heterogeneous nucleation events – instead of homogeneous nucleation - led to the formation of protein crystals. Moreover and as mentioned previously, reference experiments conducted with dye-labeled silica particles suggest that one protein crystal contains many seed particles (Figure 1). As a consequence, the growth of the protein crystals occurs by the attachment of larger building blocks (composed of aggregates) instead of the incorporation of monomers only. Obviously, the presence of a large amount of particles with the tendency to cause the formation of protein-particle aggregates results in a faster overall process with desirable solid properties. Astonishingly, the seed particles not only seem to capture free LSZ from solution but also serve as a template for the creation of highly ordered protein crystals.


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Figure 6

Microscope images of LSZ crystals with a variation of the added amount of seed

particles with xSiO2=200 nm: a) ASiO2=1.5*1014 nm2/ml, b) ASiO2=1.5*1015 nm2/ml and c) ASiO2=1.5*1016 nm2/ml; crystallization conditions: T=22 °C, 0.1 M sodium acetate buffer, pH=5, cNaCl=50 g/l, t=200-250 min. In our previous publication we reported an enhanced crystallization of LSZ with an increasing seed particle Microscope images of LSZ crystals with a variation of the added amount of seed particles with xSiO2=200 nm: a) ASiO2=1.5*1014 nm2/ml, b) ASiO2=1.5*1015 nm2/ml and c) ASiO2=1.5*1016 nm2/ml; crystallization conditions: T=22 °C, 0.1 M sodium acetate buffer, pH=5, cNaCl=50 g/l, t=200-250 min. size from 10 nm (in the size range of a LSZ molecule) to 200 nm. It has to be mentioned here, that for all experiments a constant foreign surface area (calculated from manufacturer´s specifications) and thus a decreasing particle number with increasing diameter was provided (5.0*1019 - 10 nm, 5.3*1018 - 30 nm, 1.9*1018 - 50 nm, 1.2*1017 m-3 200 nm). It was also shown before that induction times in ml-scale crystallization experiments were reproducibly shorter for the larger silica particles. This is explained by two effects: First, an enhanced nucleation on the larger seed particles would lead to stronger supersaturation depletion by growth. Second, enhanced aggregation due higher seed particle numbers is assumed to positively influence the crystallization kinetics.


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Based on the above mentioned findings, experimentally determined induction times are displayed in Figure 7a. Here, the induction time was determined by visual inspection of the turbidity of the sample. In the shown experiment the crystallization reactions were performed only once as a significant improvement of reproducibility was observed in all our experiments in the presence of seed particles. Due to the fact that nucleation is a stochastic event, especially without the addition of seed particles a strong fluctuation of induction times was observed in our reference experiments. A clear trend of decreasing induction times with an increasing total foreign particle surface ASiO2 (see squares, circles and triangles with a variation of ASiO2 in Figure 7a) is monitored. For instance, for the 200 nm silica seed particles the induction times shift from 160 min for the lowest amount of seeds to 80 min for the highest amount. This trend is confirmed for all different seed particle sizes and shows that a larger foreign surface area leads to a faster depletion of supersaturation as more protein molecules are consumed by crystal growth. Regarding the influence of foreign surface area on depletion kinetics the reader is referred to Figure 5 and its respective discussion. Data points shown in Figure 7a correspond to the obtained depletion curves in Figure 5a.

Figure 7

a) Experimentally determined induction times; crystallization conditions:

T=22 °C, 0.1 M sodium acetate buffer, pH=5, cNaCl=50 g/l, S0=9.9, xSiO2=10, 30, 50 and 200 nm and ASiO2=1.5*1016, ASiO2=1.5*1015, ASiO2=1.5*1014 nm2/ml; b) experimentally determined


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supersaturation depletion curves; crystallization conditions: T=22 °C, 0.1 M sodium acetate buffer, pH=5, cNaCl=50 g/l, S0=10.8, xSiO2=10, 30, 50 and 200 nm and ASiO2=1.5*1016 nm2/ml; and c) simulated supersaturation depletion; simulation parameters: kg=0.16 nm/s, g=1, W=0.1, t=300 min. In addition to the effects of the provided total surface area, the absolute particle number matters as induction times decrease with an increasing seed particle size. A comparison of the lowest amount of seed particles (see triangles, highlighted by the broken line) shows an induction time of 225 min for the 10 nm seed particles, whereas the induction time is decreased to 175 min and 160 min for the 30, 50 and 200 nm seeds. The black square for the 10 nm seeded experiment is seen as an outlier as the stated correlation was observed in many other experiments (see SI S7). The diagrams in the SI S7 show the error bars as additional information and confirm that the discussed influence of seed particle size was observed in repeated experiments. The shorter induction times for the larger seed particles can on the one hand be explained by an enhanced nucleation (and thus growth) mechanism due to a higher relative amount of adsorbed LSZ on the particle surface.2 On the other hand, simulations confirm that the provided foreign surface area is reduced much faster for smaller seed particles due to aggregation. Consequently, this leads to a slower depletion of supersaturation (see SI S5). In order to understand the influence of seed particle size on the aggregation behavior, we simulated the crystallization using additional seed particle sizes of 10, 30, 50 and 200 nm to compare the obtained results with corresponding experiments. Figure 7b displays the experimental supersaturation depletion curves which were obtained at slightly higher protein concentrations (resulting in S0=10.8; same data as in SI S7) compared to the previously shown data. Figure 7b displays the experimental supersaturation depletion curves which were obtained


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at slightly higher protein concentrations (resulting in S0=10.8; same data as in SI S7) compared to the previously shown data. This slight difference in initial supersaturation value is considered to be uncritical as it is the main intention of the presented data to underline the observed shifts in induction times and depletion curves. These curves illustrate the already mentioned observation of faster crystallization kinetics in the presence of larger silica seed particles. In Figure 7c the presented simulations show the same trend. Noteworthy, this is achieved in the presence of aggregation of the silica seed particles and the therefrom resulting change of the foreign particle surface with time (“only growth” and “only aggregation” simulations as already presented in SI S5). It becomes clear that due to the high number of small seed particles, aggregation is more pronounced and consequently the provided surface area is reduced to a larger extent. This in turn results in a deceleration of the overall reaction kinetics (indicated by an arrow in Fig. 7b and c). However, from the measured CSDs shown in Figure 5b it becomes clear that further phenomena are involved during crystallization to obtain a broader distribution. For this reason we will discuss the aspect of shear-induced aggregation which becomes more dominant with increasing aggregate/crystal size in the next section. Consequently, appropriate values of shear rates present in the end-over-end shaker system need to be defined. Low shear rates are expected within the end-over-end shaker system since the main focus was set on the prevention of sedimentation of larger crystals using a low rotational speed of 20 rpm. Results from Smejkal et al. were used to determine the prevalent shear rates in our system.64 They used stirred tank reactors with a volume of 6 ml to 1 l with 50-300 rpm and determined mean power inputs to be ε = 2.4-61.5 mW/kg. For the laminar flow regime a linear


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correlation between stirrer speed and mean shear rates was proven by Metzner et al. From this a mean shear rate below γ = 5 s-1 was derived for our system.65 Noteworthy, this estimate is based on a comparable material system (LSZ crystals in aqueous medium) using different agitation systems (stirred tank reactor). For this reason it is believed to represent an upper limit of existing shear rates in our system. Significantly lower shear rates are expected in our system as the end-over-end shaking with low rotational speed mainly prevents sedimentation phenomena. For this reason rough estimates of γ = 0.1, 0.5 and 1.0 s-1 were used in the simulations. It has to be emphasized at this point that it is our intention to reproduce the order of magnitude of CSDs and to reproduce the shown trends regarding the use of foreign seed particle. The respective results are depicted in Figure 8 to estimate the influence of shear rate on supersaturation depletion and final CSD. From Figure 8a it becomes clear that the determined regime of shear rates reproduces the experimental data. As expected, with the increase in shear rate values the crystallization kinetics are slowed down due to the occurrence of stronger aggregation of the seed particles. However, it becomes clear from Figure 8b that only comparably low values of γ = 0.1 s-1 lead to final crystal sizes matching our experimental values. For higher shear rates a strong overestimation of final crystal sizes was observed (x50,3 = 150 µm after 200 min for 200 nm silica particles with γ = 1.0 s-1). These results confirm the above assumption of low shear stress in our end-over-end shaker. Moreover, by the implementation of aggregation into our PBM it was possible to cover a broad particle size range from 10 nm of the seed particles to about 50 µm of final crystal size.


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Figure 8

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Comparison of simulations using the shear-induced aggregation model. a)

Depletion of supersaturation and b) CSDs; crystallization conditions: T=22 °C, 0.1 M sodium acetate buffer, pH=5, cNaCl=50 g/l, xSiO2=200 nm and ASiO2=1.5*1016 nm2/ml; simulation parameters: kg=0.16 nm/s, g=1, γ=0.1, 0.5 and 1.0 s-1, t=240 min. Our validated model is an important step towards knowledge-based process control of protein crystallization. Numerous studies exist on the crystallization behavior of single protein crystals but much less is known on the behavior of protein crystal ensembles. With the presented model it is possible to gain a deeper insight into LSZ crystal formation within the framework of seeded crystallization experiments. Additionally, it could be shown that similar mechanisms seem to apply for the seeded protein crystallization as well as for the formation of mesocrystals in biomineralization reactions.


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CONCLUSIONS In this work the LSZ crystal formation mechanism was investigated by means of ml-scale seeded batch crystallization experiments. Experimental data allow suggesting a mechanism for the formation of LSZ crystals based on the oriented aggregation of larger building blocks consisting of LSZ-seed particle (foreign) conjugates. To confirm our hypothesis, simulations based on population balance equations were performed. They contained terms for crystal growth and especially aggregation as the latter was identified to strongly influence the reaction kinetics. For a fast determination of the growth rate coefficient and exponent, dynamic light scattering (DLS) measurements were conducted. The growth coefficient kg and the growth exponent g were determined by fitting experimental values to an empirical growth rate expression with power-law dependence on the relative supersaturation. It was shown that growth is rather limited by diffusion than by the integration of growth units to the crystal surface. Furthermore, aggregation of the seed particles was found to be crucial for the overall process. It was taken into account by implementing the collision kernel due to Brownian motion of the particles and due to shearinduced aggregation in laminar fluid flow. By taking shear-induced aggregation in laminar fluid flow into consideration, a better description of the overall crystal formation was achieved. Here, a low shear rate of γ = 0.1 s-1 was used to reproduce the obtained experimental results. Consequently, experimental and simulation results prove for the first time that Cölfen’s oriented attachment concepts can be applied in the context of bio-macromolecules as well, thus, proving the generality of the approach. The deeper understanding of the overall crystallization process is seen to be an important link from seeded protein crystallization on lab scale towards tailored protein crystals with optimum size and shape for filtration on a technical scale with reduced process times.


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Supporting Information. DLS intensity distributions of LSZ monomers under crystallization conditions, aggregation kinetics of silica particles, free seed particles, collision kernels, simulations of either growth or aggregation of differently sized silica seed particles, variation of W-factor for differently sized silica seed particles, experimental results using differently sized silica particles. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author *Wolfgang Peukert; E-mail: [email protected] List of Symbols Latin Symbols A

overall surface area

[m2]

Aparticle

particle surface area

[m2]

ASiO2

silica particle surface area

[m2 m-3]

Bij

aggregation rate

[m-3 s-1]

c*

solubility

[mol m-3]

cLSZ

concentration of lysozyme

[kg m-3]

cNaCl

concentration of sodium chloride

[kg m-3]

cSiO2

concentration of silica

[kg m-3]

g

crystal growth exponent

[-]

G

growth rate

[m s-1]

kB

Boltzmann constant

[J K-1]

kg

crystal growth coefficient

[m s-1]


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MLSZ

molecular weight of LSZ

[kg mol-1]

MSolution

molecular weight of the solution

[kg mol-1]

N

particle number

[-]

n

particle number per volume

[m-3]

Q3

cumulative volume distribution

[-]

r

particle distance

[m]

S

supersaturation

[-]

S0

initial supersaturation

[-]

t

time

[s]

tind

induction time

[s]

T

temperature

[K]

W,W*

stability factor

[-]

x

particle size

[m]

xSiO2

silica particle size

[m]

x50,3

median particle size

[m]

z-ave

z-average

[m]

βij

collision kernel

[m3 s-1]

βBrown

collision kernel Brown

[m3 s-1]

βlaminar

collision kernel laminar

[m3 s-1]

γ

shear rate

[s-1]

δ

charge density

[mol kg-1]

Greek Symbols


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λ

wave length

[m]

µ

dynamic viscosity

[Pa s]

ρLSZ

LSZ density

[kg m-3]

ρSolution

solution density

[kg m-3]

φ

total interaction potential

[V]

Abbreviations CSD

crystal size distribution

DLS

dynamic light scattering

LSZ

lysozyme

NP

nanoparticle

PBM

population balance model(ing)

PSD

particle size distribution

SAXS

small-angle x-ray scattering

SEM

scanning electron microscopy

STMV

satellite tobacco mosaic virus

TEM

transmission electron microscopy

REFERENCES (1) Vertegel, A. A.; Siegel, R. W.; Dordick, J. S. Silica nanoparticle size influences the structure and enzymatic activity of adsorbed lysozyme. Langmuir 2004, 20, 6800–6807. (2) Weichsel, U.; Segets, D.; Janeke, S.; Peukert, W. Enhanced nucleation of lysozyme using inorganic silica seed particles of different size. Cryst. Growth Des. 2015, 15, pp 3582–3593.


44

Page 45 of 54

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(3) Cölfen, H.; Antonietti, M. Mesocrystals and nonclassical crystallization; John Wiley & Sons, 2008. (4) Vekilov, P. G. Two-step mechanism for the nucleation of crystals from solution. J. Cryst. Growth 2005, 275, 65–76. (5) Bharti, B.; Meissner, J.; Findenegg, G. H. Aggregation of silica nanoparticles directed by adsorption of lysozyme. Langmuir 2011, 27, 9823–9833. (6) Shi, D.; Mhaskar, P.; El-Farra, N. H.; Christofides, P. D. Predictive control of crystal size distribution in protein crystallization. Nanotechnology 2005, 16, S562. (7) Galkin, O.; Vekilov, P. G. Direct determination of the nucleation rates of protein crystals. J. Phys. Chem. B 1999, 103, 10965–10971. (8) Darcy, P. A.; Wiencek, J. M. Estimating lysozyme crystallization growth rates and solubility from isothermal microcalorimetry. Acta Crystallogr., Sect. D: Biol. Crystallogr. 1998, 54, 1387– 1394. (9) Bhamidi, V.; Varanasi, S.; Schall, C. A. Measurement and modeling of protein crystal nucleation kinetics. Cryst. Growth Des. 2002, 2, 395–400. (10) Durbin, S. D.; Feher, G. Crystal growth studies of lysozyme as a model for protein crystallization. J. Cryst. Growth 1986, 76, 583–592. (11) Saikumar, M. V.; Glatz, C. E.; Larson, M. A. Lysozyme crystal growth and nucleation kinetics. J. Cryst. Growth 1998, 187, 277–288.


45


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 54

(12) Judge, R. A.; Johns, M. R.; White, E. T. Protein purification by bulk crystallization: the recovery of ovalbumin. Biotechnol. Bioeng. 1995, 48, 316–323. (13) Ataka, M.; Asai, M. Analysis of the nucleation and crystal growth kinetics of lysozyme by a theory of self-assembly. Biophys. J. 1990, 58, 807. (14) Yoreo, J. J. de; Gilbert, P. U.; Sommerdijk, N. A.; Penn, R. L.; Whitelam, S.; Joester, D.; Zhang, H.; Rimer, J. D.; Navrotsky, A.; Banfield, J. F. Crystallization by particle attachment in synthetic, biogenic, and geologic environments. Science 2015, 349, 6760. (15) Lv, W.; He, W.; Wang, X.; Niu, Y.; Cao, H.; Dickerson, J. H.; Wang, Z. Understanding the oriented-attachment growth of nanocrystals from an energy point of view: a review. Nanoscale 2014, 6, 2531–2547. (16) Zhang, H.; Banfield, J. F. Energy calculations predict nanoparticle attachment orientations and asymmetric crystal formation. J. Phys. Chem. Lett. 2012, 3, 2882–2886. (17) Pusey, M. L.; Nadarajah, A. A model for tetragonal lysozyme crystal nucleation and growth. Cryst. Growth Des. 2002, 2, 475–483. (18) Forsythe, E. L.; Judge, R. A.; Pusey, M. L. Tetragonal chicken egg white lysozyme solubility in sodium chloride solutions. J. Chem. Eng. Data 1999, 44, 637–640. (19) Kwon, J. S.-I.; Nayhouse, M.; Christofides, P. D.; Orkoulas, G. Modeling and control of crystal shape in continuous protein crystallization. Chem. Eng. Sci. 2014, 107, 47–57. (20) Look, J.- L.; Zukoski, C. F. Colloidal stability and titania precipitate morphology: Influence of short-range repulsions. J. Am. Ceram. Soc. 1995, 78, 21-32.


46

Page 47 of 54

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(21) Liu, J. J.; Ma, C. Y.; Hu, Y. D.; Wang, X. Z. Effect of seed loading and cooling rate on crystal size and shape distributions in protein crystallization—a study using morphological population balance simulation. Comput. Chem. Eng. 2010, 34, 1945–1952. (22) Hojjati, H.; Rohani, S. Cooling and seeding effect on supersaturation and final crystal size distribution (CSD) of ammonium sulphate in a batch crystallizer. Chem. Eng. Process. Process Intensif. 2005, 44, 949–957. (23) Galkin, O.; Vekilov, P. G. Nucleation of protein crystals: critical nuclei, phase behavior, and control pathways. J. Cryst. Growth 2001, 232, 63–76. (24) Darcy, P. A.; Wiencek, J. M. Identifying nucleation temperatures for lysozyme via differential scanning calorimetry. J. Cryst. Growth 1999, 196, 243–249. (25) Cacioppo, E.; Pusey, M. L. The solubility of the tetragonal form of hen egg white lysozyme from pH 4.0 to 5.4. J. Cryst. Growth 1991, 114, 286–292. (26) Einstein, A. Investigations on the Theory of the Brownian Movement; Courier Corporation, 1956. (27) Mersmann, A. Crystallization technology handbook. Drying Technol. 1995, 13, 1037–1038. (28) Ramkrishna, D. Population balances: Theory and applications to particulate systems in engineering; Academic Press, 2000. (29) Wulkow, M.; Gerstlauer, A.; Nieken, U. Modeling and simulation of crystallization processes using parsival. Chem. Eng. Sci. 2001, 56, 2575–2588.


47


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 48 of 54

(30) Sommer, M.; Stenger, F.; Peukert, W.; Wagner, N. J. Agglomeration and breakage of nanoparticles in stirred media mills—a comparison of different methods and models. Chem. Eng. Sci. 2006, 61, 135–148. (31) Körmer, R.; Schmid, H.-J.; Peukert, W. Aerosol synthesis of silicon nanoparticles with narrow size distribution—Part 2: Theoretical analysis of the formation mechanism. J. Aerosol Sci. 2010, 41, 1008–1019. (32) Schwarzer, H.-C.; Schwertfirm, F.; Manhart, M.; Schmid, H.-J.; Peukert, W. Predictive simulation of nanoparticle precipitation based on the population balance equation. Chem. Eng. Sci. 2006, 61, 167–181. (33) Haderlein, M.; Segets, D.; Gröschel, M.; Pflug, L.; Leugering, G.; Peukert, W. FIMOR: An efficient simulation for ZnO quantum dot ripening applied to the optimization of nanoparticle synthesis. Chem. Eng. J. 2015, 260, 706–715. (34) Gorti, S.; Forsythe, E. L.; Pusey, M. L. Growth modes and energetics of (101) face lysozyme crystal growth. Cryst. Growth Des. 2005, 5, 473–482. (35) McPherson, A.; Kuznetsov, Y. G.; Malkin, A.; Plomp, M. Macromolecular crystal growth as revealed by atomic force microscopy. J. Struct. Biol. 2003, 142, 32–46. (36) Duan, L.; Kang, Q.; Hu, W. R.; Li, G. P.; Wang, D. C. The mass transfer process and the growth rate of protein crystals. Biophys. Chem. 2002, 97, 189–201.


48

Page 49 of 54

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(37) Vekilov, P. G.; Ataka, M.; Katsura, T. Growth process of protein crystals revealed by laser Michelson interferometry investigation. Acta Crystallogr., Sect. D: Biol. Crystallogr. 1995, 51, 207–219. (38) Wilson, W. W. Monitoring crystallization experiments using dynamic light scattering: Assaying and monitoring protein crystallization in solution. Methods 1990, 1, 110–117. (39) Muschol, M.; Rosenberger, F. Liquid–liquid phase separation in supersaturated lysozyme solutions and associated precipitate formation/crystallization. J. Chem. Phys. 1997, 107, 1953– 1962. (40) Patro, S. Y.; Przybycien, T. M. Simulations of reversible protein aggregate and crystal structure. Biophys. J. 1996, 70, 2888. (41) Rosenberger, F. Protein crystallization. J. Cryst. Growth 1996, 166, 40–54. (42) Li, M.; Nadarajah, A.; Pusey, M. L. Modeling the growth rates of tetragonal lysozyme crystals. J. Cryst. Growth 1995, 156, 121–132. (43) Garside, J.; Mersmann, A.; Nývlt, J. Measurement of crystal growth and nucleation rates; Istitution of Chemical Engineering, 2002. (44) Lorber, B.; Skouri, M.; Munch, J.-P.; Giegé, R. The influence of impurities on protein crystallization; the case of lysozyme. J. Cryst. Growth 1993, 128, 1203–1211. (45) Judge, R. A.; Forsythe, E. L.; Pusey, M. L. The effect of protein impurities on lysozyme crystal growth. Biotechnol. Bioeng. 1998, 59, 776–785.


49


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 50 of 54

(46) Skouri, M.; Lorber, B.; Giegé, R.; Munch, J.-P.; Candau, J. S. Effect of macromolecular impurities on lysozyme solubility and crystallizability: dynamic light scattering, phase diagram, and crystal growth studies. J. Cryst. Growth 1995, 152, 209–220. (47) Wilson, L. J.; Pusey, M. L. Determination of monomer concentrations in crystallizing lysozyme solutions. J. Cryst. Growth 1992, 122, 8–13. (48) Nadarajah, A.; Forsythe, E. L.; Pusey, M. L. The averaged face growth rates of lysozyme crystals: the effect of temperature. J. Cryst. Growth 1995, 151, 163–172. (49) Skouri, M.; Delsanti, M.; Munch, J.-P.; Lorber, B.; Giegé, R. Dynamic light scattering studies of the aggregation of lysozyme under crystallization conditions. FEBS Lett. 1991, 295, 84–88. (50) Forsythe, E. L.; Nadarajah, A.; Pusey, M. L. Growth of (101) faces of tetragonal lysozyme crystals: measured growth-rate trends. Acta Crystallogr., Sect. D: Biol. Crystallogr. 1999, 55, 1005–1011. (51) Malkin, A. J.; McPherson, A. Light scattering investigations of protein and virus crystal growth: ferritin, apoferritin and satellite tobacco mosaic virus. J. Cryst. Growth 1993, 128, 1232–1235. (52) Nadarajah, A.; Li, M.; Pusey, M. L. Growth mechanism of the (110) face of tetragonal lysozyme crystals. Acta Crystallogr., Sect. D: Biol. Crystallogr. 1997, 53, 524–534. (53) Kam, Z.; Shore, H. B.; Feher, G. On the crystallization of proteins. J. Mol. Biol. 1978, 123, 539–555.


50

Page 51 of 54

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(54) Fiddis, R. W.; Longman, R. A.; Calvert, P. D. Crystal growth kinetics of globular proteins. Lysozyme and insulin. J. Chem. Soc., Faraday Trans. 1 F 1979, 75, 2753–2761. (55) Pusey, M.; Naumann, R. Growth kinetics of tetragonal lysozyme crystals. J. Cryst. Growth 1986, 76, 593–599. (56) Pusey, M. L.; Snyder, R. S.; Naumann, R. Protein crystal growth. Growth kinetics for tetragonal lysozyme crystals. J. Biol. Chem 1986, 261, 6524–6529. (57) Bessho, Y.; Ataka, M.; Asai, M.; Katsura, T. Analysis of the crystallization kinetics of lysozyme using a model with polynuclear growth mechanism. Biophys. J. 1994, 66, 310–313. (58) Monaco, L. A.; Rosenberger, F. Growth and etching kinetics of tetragonal lysozyme. J. Cryst. Growth, 129, 465–484. (59) Land, T. A.; Malkin, A. J.; Kuznetsov, Y. G.; McPherson, A.; Yoreo, J. J. de. Mechanisms of protein crystal growth: an atomic force microscopy study of canavalin crystallization. Phys. Rev. Lett. 1995, 75, 2774. (60) Bharti, B.; Meissner, J.; Klapp, S. H. L.; Findenegg, G. H. Bridging interactions of proteins with silica nanoparticles: The influence of pH, ionic strength and protein concentration. Soft Matter 2014, 10, 718–728. (61) Smoluchowski, M. Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen 1917. (62) Fuchs, v. N. Über die stabilität und aufladung der aerosole. Z. Phys. 1934, 89, 736–743.


51


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Page 52 of 54

(63) Hanus, L. H.; Hartzler, R. U.; Wagner, N. J. Electrolyte-induced aggregation of acrylic latex. 1. Dilute particle concentrations. Langmuir 2001, 17, 3136–3147. (64) Smejkal, B.; Helk, B.; Rondeau, J.; Anton, S.; Wilke, A.; Scheyerer, P.; Fries, J.; Hekmat, D.; Weuster‐Botz, D. Protein crystallization in stirred systems—scale‐up via the maximum local energy dissipation. Biotechnol. Bioeng 2013, 110, 1956–1963. (65) Metzner, A. B.; Otto, R. E. Agitation of non‐Newtonian fluids. AlChE J. 1957, 3, 3–10.


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FOR TABLE OF CONTENTS USE ONLY

Enhanced crystallization of lysozyme mediated by the aggregation of inorganic seed particles Ulrike Weichsel1, Doris Segets1,2, Thaseem Thajudeen1,2, Eva-Maria Maier1, Wolfgang Peukert1,2* 1

Institute of Particle Technology (LFG), Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstraße 4, 91058 Erlangen, Germany 2

Interdisciplinary Center for Functional Particle Systems (FPS), Haberstraße 9a, 91058 Erlangen, Germany


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The mechanism of aggregation was derived from seeded lysozyme crystallization experiments and proven by simulations based on population balance equations including terms of crystal growth and aggregation. Experimental and simulation results prove for the first time that Cölfen’s oriented attachment concepts can be applied in the context of bio-macromolecules as well, thus, proving the generality of the approach.


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Enhanced Crystallization of Lysozyme Mediated by the Aggregation of

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